From daf0ea332600262b7210dae6459722664abd0557 Mon Sep 17 00:00:00 2001 From: Collin Boots Date: Mon, 4 Nov 2013 14:13:30 -0500 Subject: [PATCH 01/27] Implemented rolling 2D sine waveform with height blended coloring. --- part1/vert_wave.html | 12 +++++++++--- part1/vert_wave.js | 10 ++++++++-- 2 files changed, 17 insertions(+), 5 deletions(-) diff --git a/part1/vert_wave.html b/part1/vert_wave.html index 57107ca..b3e2e5b 100644 --- a/part1/vert_wave.html +++ b/part1/vert_wave.html @@ -14,10 +14,14 @@ attribute vec2 position; uniform mat4 u_modelViewPerspective; - + uniform float u_time; + varying float height; + void main(void) { - float height = 0.0; + float s_contrib = sin(position.x*2.0*3.14159 + u_time); + float t_contrib = cos(position.y*2.0*3.14159 + u_time); + height = s_contrib*t_contrib; gl_Position = u_modelViewPerspective * vec4(vec3(position, height), 1.0); } @@ -25,9 +29,11 @@ diff --git a/part1/vert_wave.js b/part1/vert_wave.js index b90b9cf..433541e 100644 --- a/part1/vert_wave.js +++ b/part1/vert_wave.js @@ -31,6 +31,8 @@ var positionLocation = 0; var heightLocation = 1; var u_modelViewPerspectiveLocation; + var u_timeLocation; + (function initializeShader() { var program; @@ -39,8 +41,8 @@ var program = createProgram(context, vs, fs, message); context.bindAttribLocation(program, positionLocation, "position"); + u_timeLocation = context.getUniformLocation(program,"u_time"); u_modelViewPerspectiveLocation = context.getUniformLocation(program,"u_modelViewPerspective"); - context.useProgram(program); })(); @@ -126,6 +128,8 @@ numberOfIndices = indices.length; })(); + var time = 0.0; + var delT = 0.01; (function animate(){ /////////////////////////////////////////////////////////////////////////// // Update @@ -137,12 +141,14 @@ mat4.multiply(view, model, mv); var mvp = mat4.create(); mat4.multiply(persp, mv, mvp); - + time = time + delT; + /////////////////////////////////////////////////////////////////////////// // Render context.clear(context.COLOR_BUFFER_BIT | context.DEPTH_BUFFER_BIT); context.uniformMatrix4fv(u_modelViewPerspectiveLocation, false, mvp); + context.uniform1f(u_timeLocation, time); context.drawElements(context.LINES, numberOfIndices, context.UNSIGNED_SHORT,0); window.requestAnimFrame(animate); From 05bd4ade94cc2bc38d9effda5b7ac7983eda2619 Mon Sep 17 00:00:00 2001 From: Collin Boots Date: Mon, 4 Nov 2013 14:24:47 -0500 Subject: [PATCH 02/27] Added simplex wave implementation. --- part1/simplex_wave.html | 86 +++++++++++++++++++++++++++++++++++++++++ part1/vert_wave.js | 2 +- 2 files changed, 87 insertions(+), 1 deletion(-) create mode 100644 part1/simplex_wave.html diff --git a/part1/simplex_wave.html b/part1/simplex_wave.html new file mode 100644 index 0000000..b43bb9f --- /dev/null +++ b/part1/simplex_wave.html @@ -0,0 +1,86 @@ + + + +Vertex Wave + + + + + +
+ + + + + + + + + + + + diff --git a/part1/vert_wave.js b/part1/vert_wave.js index 433541e..883d5d5 100644 --- a/part1/vert_wave.js +++ b/part1/vert_wave.js @@ -129,7 +129,7 @@ })(); var time = 0.0; - var delT = 0.01; + var delT = 0.001; (function animate(){ /////////////////////////////////////////////////////////////////////////// // Update From e2ebb42c3a19931ecc5fe20d346a8a5b3d73f59d Mon Sep 17 00:00:00 2001 From: Collin Boots Date: Mon, 4 Nov 2013 14:35:00 -0500 Subject: [PATCH 03/27] Renamed windows --- part1/simplex_wave.html | 2 +- part1/vert_wave.html | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/part1/simplex_wave.html b/part1/simplex_wave.html index b43bb9f..15b6c76 100644 --- a/part1/simplex_wave.html +++ b/part1/simplex_wave.html @@ -1,7 +1,7 @@ -Vertex Wave +Vertex Simplex Noise Wave diff --git a/part1/vert_wave.html b/part1/vert_wave.html index b3e2e5b..3f6f690 100644 --- a/part1/vert_wave.html +++ b/part1/vert_wave.html @@ -1,7 +1,7 @@ -Vertex Wave +Vertex Sine Wave From 7b0edb56025c665425cf5fe1776ebcb099a542c2 Mon Sep 17 00:00:00 2001 From: Collin Boots Date: Mon, 4 Nov 2013 14:52:03 -0500 Subject: [PATCH 04/27] Implemented simplistic periodic water wave pattern. --- part1/vert_wave.js | 2 +- part1/water_wave.html | 50 +++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 51 insertions(+), 1 deletion(-) create mode 100644 part1/water_wave.html diff --git a/part1/vert_wave.js b/part1/vert_wave.js index 883d5d5..433541e 100644 --- a/part1/vert_wave.js +++ b/part1/vert_wave.js @@ -129,7 +129,7 @@ })(); var time = 0.0; - var delT = 0.001; + var delT = 0.01; (function animate(){ /////////////////////////////////////////////////////////////////////////// // Update diff --git a/part1/water_wave.html b/part1/water_wave.html new file mode 100644 index 0000000..518a8fb --- /dev/null +++ b/part1/water_wave.html @@ -0,0 +1,50 @@ + + + +Water Wave + + + + + +
+ + + + + + + + + + + + From a53e3561b8bac15855630a503095968bafa0b601 Mon Sep 17 00:00:00 2001 From: Collin Boots Date: Mon, 4 Nov 2013 15:27:33 -0500 Subject: [PATCH 05/27] Added some recordings of various waves --- part1/images/simplex.gif | Bin 0 -> 4788318 bytes part1/images/simplex.wmv | Bin 0 -> 5141566 bytes part1/images/sine.gif | Bin 0 -> 3057022 bytes part1/images/sine.wmv | Bin 0 -> 2757530 bytes part1/images/water.gif | Bin 0 -> 1718414 bytes part1/images/water.wmv | Bin 0 -> 1749512 bytes part1/water_wave.html | 6 +++--- 7 files changed, 3 insertions(+), 3 deletions(-) create mode 100644 part1/images/simplex.gif create mode 100644 part1/images/simplex.wmv create mode 100644 part1/images/sine.gif create mode 100644 part1/images/sine.wmv create mode 100644 part1/images/water.gif create mode 100644 part1/images/water.wmv diff --git a/part1/images/simplex.gif b/part1/images/simplex.gif new file mode 100644 index 0000000000000000000000000000000000000000..e2e4af732cf7034a76e8960459da9867f545653c GIT binary patch literal 4788318 zcmV((K;XYeNk%w1Vdw)`0`mX>Iuk&vj;oRvMRHMe`t zFarSq001li0002!16Tq81pbi7Nvpj$>&?6WU?`4cX`X1Ru59bRa4gSsZQppV?|kq7 zz@TtQEE41ejE#0PICJXU$+M@=pFo2O z9ZIyQ(W6L{DqYI7sne%Wqe`7hwW`&tShH%~%C)Q4uVBN99ZR;X*|TWVs$I*rt=qS7 z(BTJr4xw7TUm@{kM%(=7Y z&!9t#9!C>oFt6t5zwd>cgW6PdRySDAyxO3~?&AYen-@tNG7S|l1w(~ z_Q`;vi~9K|q=*#X1`(JFLwO%I= zg>BPf*4#I@2OLU%->cdVsn`fBA`XTUcwhy<$TKb~%ZnDEV+QotG(4hC1W2nCqWl%D z@UgKHMbv;BIhREy4)ADxqyQg5rz|l(5?zp!+MWOqDpQg0kd7!Iy)600MzYL+r);6F zE;z~jiC~CCbN~*Y#i;s$k`TRHqy`LTvZImmeRpKl1qFyjNQxkdajZb?U{*^)-O>-e zYo#QAxl3y9(VFc$7&b8g%h|p1g1YpkvQqad98%3xYkX!Hav4bpNOJ=3bmulZ=(Bl3 zkc=A09t%H(%y4SJV#_q!6xGRw-iZ=%_ME0EFWE~}e!x@sTpu9*+bKjiR+L+s%porc zDu#V_;E3@gKuAM+P$Smxm?wSR(@>hyPb~ldX9SksBF51zbdypbO(;BdD$fn76a)|* zBR^ZJN{4ztgT~|@ta2E#bk@`da*W|ZM>*AxqKv57qNozJsy&t_^{X~J+2?@fEXOtK zsY}?XNmEJHupZ5hJ_RcUwYo&3X7!a8jbmO#incR_g(`4Ds*3`kO3~f#=tRvgn(4!_XiIUAgR9TnT)lQ(UKg24| zMv%P)q;Y|2^{j0ZDA3$0lA=Mqt6PVQte+lLtFF~6;e!6T+_;YRxU_ZER;MN^1~g!= zkt0;f@&v*`CZKPp3Yb6XDOA#$mx!mWWOIuv%zDa}SGDD8x|qAM?mi4)g1uD$z@@o| zoh`gb{U{t^TT0>zm!WfwsO8?9!n~H$h$YM(W&w#z490O!&stQpunQ?e1$P4t$knS# z)hf3YO3cMN>`{>YWS#K-bvz005ZL zS(#dtAzMb#@#ZnHQg-DkuPRp}a#f!b4K#fZR{mkeCU{?(rP{gj%cXR!E?OVvT^?n* zuL(S$0elnMyT}VRiiXtAcuQiCr#xdKKK8*jhVFW^Tw1$YkcbG2)!F{bXe!k!s)hn% z0wzt(n-S_#m-;UF#@6R*LRq3)Bp`BI8`(csmQ~S}aj8FA!b6#HQ6*Mht(SBzP-~CO zoZe}q`C4R3lTf>94plQV>*>UPTB|l(_NuSQUMg4F%2!?=cDbt9BG*pQw#*XJQg>Yo zqmEeXvR2JdW!qo2`P`zzt;q5`M|UR{)mWzBV@K_|7v?+MTILm(qb==X@=9tSgV>cQ z_GQ+&%mPEq^)Cr_uW^qXgUPbg-W*VH{^^Yr&+v9{vhOWbJ`;VX$1I_t{Y-M_Cbd@z zEY(?^2o1&I8S#>X+hZHsR|u-F-`R&nM;)7Ub}IRKYfk|{GWxv! zfr6L!)p8eHu~R65kV>GR{FZRvAFJGw6OjOFZd{M&yd%g%o|}(KT;dv#r^UOf>jqfl z0RrfGOUo|JmL^mJlBaUqQ+C?bQ?}h3Ygyysoz9o#D%^F3T?rG|w0O&?SpzPka$)@R z@PyayU;aNGJ1S?e6jb82pMbFbD^!Ue3^oA1E3yF?!0kmAbfXt#k7as(r#gZ*bnP{L zbTx-o$W@$30XNq&g(d>qH+P3NZ(FuQ-xo#-L^UCkA&1jCTZ4!P zHGGm5c}S#)jOSu)D1{eb0Lk)UoL6=!vvedh0QPq(vc!y1_hrfTfT#CjANNNd_gtSS zV8^sq)F^>>=sP43fp~~$=43X8vTgREFaESOxA$R6b2GZwi9%#aYUpy6*D;%80E2Qf zbTlX*ri=uze5w<8Z?-oLU@8cMfl-!TcL-=k2YvsvR~2T25ZHYV*mwMxI*)>JL?B9Px@EBeE82l*>{qjpX6 zSP&_ZedKy^7yf$DSAEu}IU~S`Teff5^^N;-HgHBi0s>2Pv^B)Giz$hK6A)>L7+krv zGQ|gX%MxH(NCDO2d#A@VwM36mW^Qj8UcM46Y*%K-h&^<8O+rU#NXcS-Nq`BsgGw1? z{AO@=2yNkKPL4x^`9UyW#x^B0lgTJ86Z8Ox_=IlxmCTZY57q$xrnC@oob#pAC420*L{p*H!k}G;_#`popKr zd5xHJYONQ3BE>F=0zTuhFr_qD97f@s)Hh+L3UYs{YA?DCU4bh-`X?D$x=&Aj4hKaZ_rweYsLHMT9g4 zfB>#SN`OjA2gRTl5L_#>bOwV|lLJu;$3DBZtn4ExZmFRcfT?=YG6WD};DT*ahfp$V zY)*G~d}*T(ikrXrd1{)bzL~D-8h}?h0C~wA0F*NdFq9CAblBJcE{L7(6rsghl|^>1 z`nq)cgfEU-j;Yu)kP1M8f>f#*Y6)G z%98Twv0gfkYh;lf!&{1iWE(~tLB^G`lP&=;n!%`0zbZ*O`&uXCfyy+fTBQD(0fsbJ zcvn)IWlc`B_K`x6#rN?^YNRA`B zLK*3R751S|IhBb?m5JCfJ32KQrbN5}KpT~c2wI^LDggzD0I#WVlOnWh2QNY^r5zKY zt=bSRplt$RM~ z`dM%Km*d*5+!(iDvtJz zvtmR(dc;DZyG^Y^K9>e!m-c^ETb|n@s(E5=5cNSZwJ2#9Udt$bq5c?QsycxAG`m~0 zLvmVS{nNI2IJfwVL5_l98a1Y;;YGmfJn4urYq?VoFuY=WkvUe9RtVg#R zslPPJr{l;P93(S_>L@P;pX9QragJLV^5`Phj zpwu&nC!X=t7@u|?*% z1VD_WrdS_|Q%J`?SW_?e_;wCjlk?OwT*|aXrYGsLS}^r(LZ(STDX&JBjqjR5@T
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a/part1/water_wave.html +++ b/part1/water_wave.html @@ -19,14 +19,14 @@ void main(void) { - vec2 waveDir = normalize(vec2(1.0,0.5));//Direction of wave in X Y plane + vec2 waveDir = normalize(vec2(1.0,-1.0));//Direction of wave in X Y plane //Projection of position onto wave direction from origin gives time offset //Constant factor here is cosmetic float wavefrontFactor = 3.0*dot(position, waveDir); //Constants here are cosmetic - vec2 hor_perturb = 0.2*waveDir*(cos(u_time*2.0*3.14159 + wavefrontFactor)); - height = 0.3*sin(u_time*2.0*3.14159 + wavefrontFactor); + vec2 hor_perturb = 0.15*waveDir*(cos(u_time*3.14159 + wavefrontFactor)); + height = 0.25*sin(u_time*3.14159 + wavefrontFactor); gl_Position = u_modelViewPerspective * vec4(vec3(position+hor_perturb, height), 1.0); } </script> From a639497e306be341d9799fbc6aabefa1b9edc0bd Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Mon, 4 Nov 2013 15:31:46 -0500 Subject: [PATCH 06/27] Moved images to resources --- {part1/images => resources}/simplex.gif | Bin {part1/images => resources}/simplex.wmv | Bin {part1/images => resources}/sine.gif | Bin {part1/images => resources}/sine.wmv | Bin {part1/images => resources}/water.gif | Bin {part1/images => resources}/water.wmv | Bin 6 files changed, 0 insertions(+), 0 deletions(-) rename {part1/images => resources}/simplex.gif (100%) rename {part1/images => resources}/simplex.wmv (100%) rename {part1/images => resources}/sine.gif (100%) rename {part1/images => resources}/sine.wmv (100%) rename {part1/images => resources}/water.gif (100%) rename {part1/images => resources}/water.wmv (100%) diff --git a/part1/images/simplex.gif b/resources/simplex.gif similarity index 100% rename from part1/images/simplex.gif rename to resources/simplex.gif diff --git a/part1/images/simplex.wmv b/resources/simplex.wmv similarity index 100% rename from part1/images/simplex.wmv rename to resources/simplex.wmv diff --git a/part1/images/sine.gif b/resources/sine.gif similarity index 100% rename from part1/images/sine.gif rename to resources/sine.gif diff --git a/part1/images/sine.wmv b/resources/sine.wmv similarity index 100% rename from part1/images/sine.wmv rename to resources/sine.wmv diff --git a/part1/images/water.gif b/resources/water.gif similarity index 100% rename from part1/images/water.gif rename to resources/water.gif diff --git a/part1/images/water.wmv b/resources/water.wmv similarity index 100% rename from part1/images/water.wmv rename to resources/water.wmv From 4fab9b74b49fb58f3e65663db7c8b20091fe6f7b Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Mon, 4 Nov 2013 15:35:22 -0500 Subject: [PATCH 07/27] Moved files around. --- {part2 => globe}/earthbump1024.png | Bin {part2 => globe}/earthcloud1024.png | Bin {part2 => globe}/earthlight1024.png | Bin {part2 => globe}/earthmap1024.png | Bin {part2 => globe}/earthspec1024.png | Bin {part2 => globe}/earthtrans1024.png | Bin {part2 => globe}/frag_globe.html | 0 {part2 => globe}/frag_globe.js | 0 {part2 => globe}/gl-matrix.js | 0 {part2 => globe}/webGLUtility.js | 0 waves/gl-matrix.js | 3456 +++++++++++++++++++++++++++ waves/noise3D.js | 316 +++ waves/simplex.vert | 39 + waves/simplex_wave.html | 86 + waves/vert_wave.html | 45 + waves/vert_wave.js | 157 ++ waves/water_wave.html | 50 + waves/webGLUtility.js | 112 + 18 files changed, 4261 insertions(+) rename {part2 => globe}/earthbump1024.png (100%) rename {part2 => globe}/earthcloud1024.png (100%) rename {part2 => globe}/earthlight1024.png (100%) rename {part2 => globe}/earthmap1024.png (100%) rename {part2 => globe}/earthspec1024.png (100%) rename {part2 => globe}/earthtrans1024.png (100%) rename {part2 => globe}/frag_globe.html (100%) rename {part2 => globe}/frag_globe.js (100%) rename {part2 => globe}/gl-matrix.js (100%) rename {part2 => globe}/webGLUtility.js (100%) create mode 100644 waves/gl-matrix.js create mode 100644 waves/noise3D.js create mode 100644 waves/simplex.vert create mode 100644 waves/simplex_wave.html create mode 100644 waves/vert_wave.html create mode 100644 waves/vert_wave.js create mode 100644 waves/water_wave.html create mode 100644 waves/webGLUtility.js diff --git a/part2/earthbump1024.png b/globe/earthbump1024.png similarity index 100% rename from part2/earthbump1024.png rename to globe/earthbump1024.png diff --git a/part2/earthcloud1024.png b/globe/earthcloud1024.png similarity index 100% rename from part2/earthcloud1024.png rename to globe/earthcloud1024.png diff --git a/part2/earthlight1024.png b/globe/earthlight1024.png similarity index 100% rename from part2/earthlight1024.png rename to globe/earthlight1024.png diff --git a/part2/earthmap1024.png b/globe/earthmap1024.png similarity index 100% rename from part2/earthmap1024.png rename to globe/earthmap1024.png diff --git a/part2/earthspec1024.png b/globe/earthspec1024.png similarity index 100% rename from part2/earthspec1024.png rename to globe/earthspec1024.png diff --git a/part2/earthtrans1024.png b/globe/earthtrans1024.png similarity index 100% rename from part2/earthtrans1024.png rename to globe/earthtrans1024.png diff --git a/part2/frag_globe.html b/globe/frag_globe.html similarity index 100% rename from part2/frag_globe.html rename to globe/frag_globe.html diff --git a/part2/frag_globe.js b/globe/frag_globe.js similarity index 100% rename from part2/frag_globe.js rename to globe/frag_globe.js diff --git a/part2/gl-matrix.js b/globe/gl-matrix.js similarity index 100% rename from part2/gl-matrix.js rename to globe/gl-matrix.js diff --git a/part2/webGLUtility.js b/globe/webGLUtility.js similarity index 100% rename from part2/webGLUtility.js rename to globe/webGLUtility.js diff --git a/waves/gl-matrix.js b/waves/gl-matrix.js new file mode 100644 index 0000000..5718055 --- /dev/null +++ b/waves/gl-matrix.js @@ -0,0 +1,3456 @@ +/** + * @fileoverview gl-matrix - High performance matrix and vector operations for WebGL + * @author Brandon Jones + * @author Colin MacKenzie IV + * @version 1.3.7 + */ + +/* + * Copyright (c) 2012 Brandon Jones, Colin MacKenzie IV + * + * This software is provided 'as-is', without any express or implied + * warranty. In no event will the authors be held liable for any damages + * arising from the use of this software. + * + * Permission is granted to anyone to use this software for any purpose, + * including commercial applications, and to alter it and redistribute it + * freely, subject to the following restrictions: + * + * 1. The origin of this software must not be misrepresented; you must not + * claim that you wrote the original software. If you use this software + * in a product, an acknowledgment in the product documentation would be + * appreciated but is not required. + * + * 2. Altered source versions must be plainly marked as such, and must not + * be misrepresented as being the original software. + * + * 3. This notice may not be removed or altered from any source + * distribution. + */ + +// Updated to use a modification of the "returnExportsGlobal" pattern from https://github.com/umdjs/umd + +(function (root, factory) { + if (typeof exports === 'object') { + // Node. Does not work with strict CommonJS, but + // only CommonJS-like enviroments that support module.exports, + // like Node. + module.exports = factory(global); + } else if (typeof define === 'function' && define.amd) { + // AMD. Register as an anonymous module. + define([], function () { + return factory(root); + }); + } else { + // Browser globals + factory(root); + } +}(this, function (root) { + "use strict"; + + // Tweak to your liking + var FLOAT_EPSILON = 0.000001; + + var glMath = {}; + (function() { + if (typeof(Float32Array) != 'undefined') { + var y = new Float32Array(1); + var i = new Int32Array(y.buffer); + + /** + * Fast way to calculate the inverse square root, + * see http://jsperf.com/inverse-square-root/5 + * + * If typed arrays are not available, a slower + * implementation will be used. + * + * @param {Number} number the number + * @returns {Number} Inverse square root + */ + glMath.invsqrt = function(number) { + var x2 = number * 0.5; + y[0] = number; + var threehalfs = 1.5; + + i[0] = 0x5f3759df - (i[0] >> 1); + + var number2 = y[0]; + + return number2 * (threehalfs - (x2 * number2 * number2)); + }; + } else { + glMath.invsqrt = function(number) { return 1.0 / Math.sqrt(number); }; + } + })(); + + /** + * @class System-specific optimal array type + * @name MatrixArray + */ + var MatrixArray = null; + + // explicitly sets and returns the type of array to use within glMatrix + function setMatrixArrayType(type) { + MatrixArray = type; + return MatrixArray; + } + + // auto-detects and returns the best type of array to use within glMatrix, falling + // back to Array if typed arrays are unsupported + function determineMatrixArrayType() { + MatrixArray = (typeof Float32Array !== 'undefined') ? Float32Array : Array; + return MatrixArray; + } + + determineMatrixArrayType(); + + /** + * @class 3 Dimensional Vector + * @name vec3 + */ + var vec3 = {}; + + /** + * Creates a new instance of a vec3 using the default array type + * Any javascript array-like objects containing at least 3 numeric elements can serve as a vec3 + * + * @param {vec3} [vec] vec3 containing values to initialize with + * + * @returns {vec3} New vec3 + */ + vec3.create = function (vec) { + var dest = new MatrixArray(3); + + if (vec) { + dest[0] = vec[0]; + dest[1] = vec[1]; + dest[2] = vec[2]; + } else { + dest[0] = dest[1] = dest[2] = 0; + } + + return dest; + }; + + /** + * Creates a new instance of a vec3, initializing it with the given arguments + * + * @param {number} x X value + * @param {number} y Y value + * @param {number} z Z value + + * @returns {vec3} New vec3 + */ + vec3.createFrom = function (x, y, z) { + var dest = new MatrixArray(3); + + dest[0] = x; + dest[1] = y; + dest[2] = z; + + return dest; + }; + + /** + * Copies the values of one vec3 to another + * + * @param {vec3} vec vec3 containing values to copy + * @param {vec3} dest vec3 receiving copied values + * + * @returns {vec3} dest + */ + vec3.set = function (vec, dest) { + dest[0] = vec[0]; + dest[1] = vec[1]; + dest[2] = vec[2]; + + return dest; + }; + + /** + * Compares two vectors for equality within a certain margin of error + * + * @param {vec3} a First vector + * @param {vec3} b Second vector + * + * @returns {Boolean} True if a is equivalent to b + */ + vec3.equal = function (a, b) { + return a === b || ( + Math.abs(a[0] - b[0]) < FLOAT_EPSILON && + Math.abs(a[1] - b[1]) < FLOAT_EPSILON && + Math.abs(a[2] - b[2]) < FLOAT_EPSILON + ); + }; + + /** + * Performs a vector addition + * + * @param {vec3} vec First operand + * @param {vec3} vec2 Second operand + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + vec3.add = function (vec, vec2, dest) { + if (!dest || vec === dest) { + vec[0] += vec2[0]; + vec[1] += vec2[1]; + vec[2] += vec2[2]; + return vec; + } + + dest[0] = vec[0] + vec2[0]; + dest[1] = vec[1] + vec2[1]; + dest[2] = vec[2] + vec2[2]; + return dest; + }; + + /** + * Performs a vector subtraction + * + * @param {vec3} vec First operand + * @param {vec3} vec2 Second operand + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + vec3.subtract = function (vec, vec2, dest) { + if (!dest || vec === dest) { + vec[0] -= vec2[0]; + vec[1] -= vec2[1]; + vec[2] -= vec2[2]; + return vec; + } + + dest[0] = vec[0] - vec2[0]; + dest[1] = vec[1] - vec2[1]; + dest[2] = vec[2] - vec2[2]; + return dest; + }; + + /** + * Performs a vector multiplication + * + * @param {vec3} vec First operand + * @param {vec3} vec2 Second operand + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + vec3.multiply = function (vec, vec2, dest) { + if (!dest || vec === dest) { + vec[0] *= vec2[0]; + vec[1] *= vec2[1]; + vec[2] *= vec2[2]; + return vec; + } + + dest[0] = vec[0] * vec2[0]; + dest[1] = vec[1] * vec2[1]; + dest[2] = vec[2] * vec2[2]; + return dest; + }; + + /** + * Negates the components of a vec3 + * + * @param {vec3} vec vec3 to negate + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + vec3.negate = function (vec, dest) { + if (!dest) { dest = vec; } + + dest[0] = -vec[0]; + dest[1] = -vec[1]; + dest[2] = -vec[2]; + return dest; + }; + + /** + * Multiplies the components of a vec3 by a scalar value + * + * @param {vec3} vec vec3 to scale + * @param {number} val Value to scale by + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + vec3.scale = function (vec, val, dest) { + if (!dest || vec === dest) { + vec[0] *= val; + vec[1] *= val; + vec[2] *= val; + return vec; + } + + dest[0] = vec[0] * val; + dest[1] = vec[1] * val; + dest[2] = vec[2] * val; + return dest; + }; + + /** + * Generates a unit vector of the same direction as the provided vec3 + * If vector length is 0, returns [0, 0, 0] + * + * @param {vec3} vec vec3 to normalize + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + vec3.normalize = function (vec, dest) { + if (!dest) { dest = vec; } + + var x = vec[0], y = vec[1], z = vec[2], + len = Math.sqrt(x * x + y * y + z * z); + + if (!len) { + dest[0] = 0; + dest[1] = 0; + dest[2] = 0; + return dest; + } else if (len === 1) { + dest[0] = x; + dest[1] = y; + dest[2] = z; + return dest; + } + + len = 1 / len; + dest[0] = x * len; + dest[1] = y * len; + dest[2] = z * len; + return dest; + }; + + /** + * Generates the cross product of two vec3s + * + * @param {vec3} vec First operand + * @param {vec3} vec2 Second operand + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + vec3.cross = function (vec, vec2, dest) { + if (!dest) { dest = vec; } + + var x = vec[0], y = vec[1], z = vec[2], + x2 = vec2[0], y2 = vec2[1], z2 = vec2[2]; + + dest[0] = y * z2 - z * y2; + dest[1] = z * x2 - x * z2; + dest[2] = x * y2 - y * x2; + return dest; + }; + + /** + * Caclulates the length of a vec3 + * + * @param {vec3} vec vec3 to calculate length of + * + * @returns {number} Length of vec + */ + vec3.length = function (vec) { + var x = vec[0], y = vec[1], z = vec[2]; + return Math.sqrt(x * x + y * y + z * z); + }; + + /** + * Caclulates the squared length of a vec3 + * + * @param {vec3} vec vec3 to calculate squared length of + * + * @returns {number} Squared Length of vec + */ + vec3.squaredLength = function (vec) { + var x = vec[0], y = vec[1], z = vec[2]; + return x * x + y * y + z * z; + }; + + /** + * Caclulates the dot product of two vec3s + * + * @param {vec3} vec First operand + * @param {vec3} vec2 Second operand + * + * @returns {number} Dot product of vec and vec2 + */ + vec3.dot = function (vec, vec2) { + return vec[0] * vec2[0] + vec[1] * vec2[1] + vec[2] * vec2[2]; + }; + + /** + * Generates a unit vector pointing from one vector to another + * + * @param {vec3} vec Origin vec3 + * @param {vec3} vec2 vec3 to point to + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + vec3.direction = function (vec, vec2, dest) { + if (!dest) { dest = vec; } + + var x = vec[0] - vec2[0], + y = vec[1] - vec2[1], + z = vec[2] - vec2[2], + len = Math.sqrt(x * x + y * y + z * z); + + if (!len) { + dest[0] = 0; + dest[1] = 0; + dest[2] = 0; + return dest; + } + + len = 1 / len; + dest[0] = x * len; + dest[1] = y * len; + dest[2] = z * len; + return dest; + }; + + /** + * Performs a linear interpolation between two vec3 + * + * @param {vec3} vec First vector + * @param {vec3} vec2 Second vector + * @param {number} lerp Interpolation amount between the two inputs + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + vec3.lerp = function (vec, vec2, lerp, dest) { + if (!dest) { dest = vec; } + + dest[0] = vec[0] + lerp * (vec2[0] - vec[0]); + dest[1] = vec[1] + lerp * (vec2[1] - vec[1]); + dest[2] = vec[2] + lerp * (vec2[2] - vec[2]); + + return dest; + }; + + /** + * Calculates the euclidian distance between two vec3 + * + * Params: + * @param {vec3} vec First vector + * @param {vec3} vec2 Second vector + * + * @returns {number} Distance between vec and vec2 + */ + vec3.dist = function (vec, vec2) { + var x = vec2[0] - vec[0], + y = vec2[1] - vec[1], + z = vec2[2] - vec[2]; + + return Math.sqrt(x*x + y*y + z*z); + }; + + // Pre-allocated to prevent unecessary garbage collection + var unprojectMat = null; + var unprojectVec = new MatrixArray(4); + /** + * Projects the specified vec3 from screen space into object space + * Based on the <a href="http://webcvs.freedesktop.org/mesa/Mesa/src/glu/mesa/project.c?revision=1.4&view=markup">Mesa gluUnProject implementation</a> + * + * @param {vec3} vec Screen-space vector to project + * @param {mat4} view View matrix + * @param {mat4} proj Projection matrix + * @param {vec4} viewport Viewport as given to gl.viewport [x, y, width, height] + * @param {vec3} [dest] vec3 receiving unprojected result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + vec3.unproject = function (vec, view, proj, viewport, dest) { + if (!dest) { dest = vec; } + + if(!unprojectMat) { + unprojectMat = mat4.create(); + } + + var m = unprojectMat; + var v = unprojectVec; + + v[0] = (vec[0] - viewport[0]) * 2.0 / viewport[2] - 1.0; + v[1] = (vec[1] - viewport[1]) * 2.0 / viewport[3] - 1.0; + v[2] = 2.0 * vec[2] - 1.0; + v[3] = 1.0; + + mat4.multiply(proj, view, m); + if(!mat4.inverse(m)) { return null; } + + mat4.multiplyVec4(m, v); + if(v[3] === 0.0) { return null; } + + dest[0] = v[0] / v[3]; + dest[1] = v[1] / v[3]; + dest[2] = v[2] / v[3]; + + return dest; + }; + + var xUnitVec3 = vec3.createFrom(1,0,0); + var yUnitVec3 = vec3.createFrom(0,1,0); + var zUnitVec3 = vec3.createFrom(0,0,1); + + var tmpvec3 = vec3.create(); + /** + * Generates a quaternion of rotation between two given normalized vectors + * + * @param {vec3} a Normalized source vector + * @param {vec3} b Normalized target vector + * @param {quat4} [dest] quat4 receiving operation result. + * + * @returns {quat4} dest if specified, a new quat4 otherwise + */ + vec3.rotationTo = function (a, b, dest) { + if (!dest) { dest = quat4.create(); } + + var d = vec3.dot(a, b); + var axis = tmpvec3; + if (d >= 1.0) { + quat4.set(identityQuat4, dest); + } else if (d < (0.000001 - 1.0)) { + vec3.cross(xUnitVec3, a, axis); + if (vec3.length(axis) < 0.000001) + vec3.cross(yUnitVec3, a, axis); + if (vec3.length(axis) < 0.000001) + vec3.cross(zUnitVec3, a, axis); + vec3.normalize(axis); + quat4.fromAngleAxis(Math.PI, axis, dest); + } else { + var s = Math.sqrt((1.0 + d) * 2.0); + var sInv = 1.0 / s; + vec3.cross(a, b, axis); + dest[0] = axis[0] * sInv; + dest[1] = axis[1] * sInv; + dest[2] = axis[2] * sInv; + dest[3] = s * 0.5; + quat4.normalize(dest); + } + if (dest[3] > 1.0) dest[3] = 1.0; + else if (dest[3] < -1.0) dest[3] = -1.0; + return dest; + }; + + /** + * Returns a string representation of a vector + * + * @param {vec3} vec Vector to represent as a string + * + * @returns {string} String representation of vec + */ + vec3.str = function (vec) { + return '[' + vec[0] + ', ' + vec[1] + ', ' + vec[2] + ']'; + }; + + /** + * @class 3x3 Matrix + * @name mat3 + */ + var mat3 = {}; + + /** + * Creates a new instance of a mat3 using the default array type + * Any javascript array-like object containing at least 9 numeric elements can serve as a mat3 + * + * @param {mat3} [mat] mat3 containing values to initialize with + * + * @returns {mat3} New mat3 + */ + mat3.create = function (mat) { + var dest = new MatrixArray(9); + + if (mat) { + dest[0] = mat[0]; + dest[1] = mat[1]; + dest[2] = mat[2]; + dest[3] = mat[3]; + dest[4] = mat[4]; + dest[5] = mat[5]; + dest[6] = mat[6]; + dest[7] = mat[7]; + dest[8] = mat[8]; + } else { + dest[0] = dest[1] = + dest[2] = dest[3] = + dest[4] = dest[5] = + dest[6] = dest[7] = + dest[8] = 0; + } + + return dest; + }; + + /** + * Creates a new instance of a mat3, initializing it with the given arguments + * + * @param {number} m00 + * @param {number} m01 + * @param {number} m02 + * @param {number} m10 + * @param {number} m11 + * @param {number} m12 + * @param {number} m20 + * @param {number} m21 + * @param {number} m22 + + * @returns {mat3} New mat3 + */ + mat3.createFrom = function (m00, m01, m02, m10, m11, m12, m20, m21, m22) { + var dest = new MatrixArray(9); + + dest[0] = m00; + dest[1] = m01; + dest[2] = m02; + dest[3] = m10; + dest[4] = m11; + dest[5] = m12; + dest[6] = m20; + dest[7] = m21; + dest[8] = m22; + + return dest; + }; + + /** + * Calculates the determinant of a mat3 + * + * @param {mat3} mat mat3 to calculate determinant of + * + * @returns {Number} determinant of mat + */ + mat3.determinant = function (mat) { + var a00 = mat[0], a01 = mat[1], a02 = mat[2], + a10 = mat[3], a11 = mat[4], a12 = mat[5], + a20 = mat[6], a21 = mat[7], a22 = mat[8]; + + return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20); + }; + + /** + * Calculates the inverse matrix of a mat3 + * + * @param {mat3} mat mat3 to calculate inverse of + * @param {mat3} [dest] mat3 receiving inverse matrix. If not specified result is written to mat + * + * @param {mat3} dest is specified, mat otherwise, null if matrix cannot be inverted + */ + mat3.inverse = function (mat, dest) { + var a00 = mat[0], a01 = mat[1], a02 = mat[2], + a10 = mat[3], a11 = mat[4], a12 = mat[5], + a20 = mat[6], a21 = mat[7], a22 = mat[8], + + b01 = a22 * a11 - a12 * a21, + b11 = -a22 * a10 + a12 * a20, + b21 = a21 * a10 - a11 * a20, + + d = a00 * b01 + a01 * b11 + a02 * b21, + id; + + if (!d) { return null; } + id = 1 / d; + + if (!dest) { dest = mat3.create(); } + + dest[0] = b01 * id; + dest[1] = (-a22 * a01 + a02 * a21) * id; + dest[2] = (a12 * a01 - a02 * a11) * id; + dest[3] = b11 * id; + dest[4] = (a22 * a00 - a02 * a20) * id; + dest[5] = (-a12 * a00 + a02 * a10) * id; + dest[6] = b21 * id; + dest[7] = (-a21 * a00 + a01 * a20) * id; + dest[8] = (a11 * a00 - a01 * a10) * id; + return dest; + }; + + /** + * Performs a matrix multiplication + * + * @param {mat3} mat First operand + * @param {mat3} mat2 Second operand + * @param {mat3} [dest] mat3 receiving operation result. If not specified result is written to mat + * + * @returns {mat3} dest if specified, mat otherwise + */ + mat3.multiply = function (mat, mat2, dest) { + if (!dest) { dest = mat; } + + + // Cache the matrix values (makes for huge speed increases!) + var a00 = mat[0], a01 = mat[1], a02 = mat[2], + a10 = mat[3], a11 = mat[4], a12 = mat[5], + a20 = mat[6], a21 = mat[7], a22 = mat[8], + + b00 = mat2[0], b01 = mat2[1], b02 = mat2[2], + b10 = mat2[3], b11 = mat2[4], b12 = mat2[5], + b20 = mat2[6], b21 = mat2[7], b22 = mat2[8]; + + dest[0] = b00 * a00 + b01 * a10 + b02 * a20; + dest[1] = b00 * a01 + b01 * a11 + b02 * a21; + dest[2] = b00 * a02 + b01 * a12 + b02 * a22; + + dest[3] = b10 * a00 + b11 * a10 + b12 * a20; + dest[4] = b10 * a01 + b11 * a11 + b12 * a21; + dest[5] = b10 * a02 + b11 * a12 + b12 * a22; + + dest[6] = b20 * a00 + b21 * a10 + b22 * a20; + dest[7] = b20 * a01 + b21 * a11 + b22 * a21; + dest[8] = b20 * a02 + b21 * a12 + b22 * a22; + + return dest; + }; + + /** + * Transforms the vec2 according to the given mat3. + * + * @param {mat3} matrix mat3 to multiply against + * @param {vec2} vec the vector to multiply + * @param {vec2} [dest] an optional receiving vector. If not given, vec is used. + * + * @returns {vec2} The multiplication result + **/ + mat3.multiplyVec2 = function(matrix, vec, dest) { + if (!dest) dest = vec; + var x = vec[0], y = vec[1]; + dest[0] = x * matrix[0] + y * matrix[3] + matrix[6]; + dest[1] = x * matrix[1] + y * matrix[4] + matrix[7]; + return dest; + }; + + /** + * Transforms the vec3 according to the given mat3 + * + * @param {mat3} matrix mat3 to multiply against + * @param {vec3} vec the vector to multiply + * @param {vec3} [dest] an optional receiving vector. If not given, vec is used. + * + * @returns {vec3} The multiplication result + **/ + mat3.multiplyVec3 = function(matrix, vec, dest) { + if (!dest) dest = vec; + var x = vec[0], y = vec[1], z = vec[2]; + dest[0] = x * matrix[0] + y * matrix[3] + z * matrix[6]; + dest[1] = x * matrix[1] + y * matrix[4] + z * matrix[7]; + dest[2] = x * matrix[2] + y * matrix[5] + z * matrix[8]; + + return dest; + }; + + /** + * Copies the values of one mat3 to another + * + * @param {mat3} mat mat3 containing values to copy + * @param {mat3} dest mat3 receiving copied values + * + * @returns {mat3} dest + */ + mat3.set = function (mat, dest) { + dest[0] = mat[0]; + dest[1] = mat[1]; + dest[2] = mat[2]; + dest[3] = mat[3]; + dest[4] = mat[4]; + dest[5] = mat[5]; + dest[6] = mat[6]; + dest[7] = mat[7]; + dest[8] = mat[8]; + return dest; + }; + + /** + * Compares two matrices for equality within a certain margin of error + * + * @param {mat3} a First matrix + * @param {mat3} b Second matrix + * + * @returns {Boolean} True if a is equivalent to b + */ + mat3.equal = function (a, b) { + return a === b || ( + Math.abs(a[0] - b[0]) < FLOAT_EPSILON && + Math.abs(a[1] - b[1]) < FLOAT_EPSILON && + Math.abs(a[2] - b[2]) < FLOAT_EPSILON && + Math.abs(a[3] - b[3]) < FLOAT_EPSILON && + Math.abs(a[4] - b[4]) < FLOAT_EPSILON && + Math.abs(a[5] - b[5]) < FLOAT_EPSILON && + Math.abs(a[6] - b[6]) < FLOAT_EPSILON && + Math.abs(a[7] - b[7]) < FLOAT_EPSILON && + Math.abs(a[8] - b[8]) < FLOAT_EPSILON + ); + }; + + /** + * Sets a mat3 to an identity matrix + * + * @param {mat3} dest mat3 to set + * + * @returns dest if specified, otherwise a new mat3 + */ + mat3.identity = function (dest) { + if (!dest) { dest = mat3.create(); } + dest[0] = 1; + dest[1] = 0; + dest[2] = 0; + dest[3] = 0; + dest[4] = 1; + dest[5] = 0; + dest[6] = 0; + dest[7] = 0; + dest[8] = 1; + return dest; + }; + + /** + * Transposes a mat3 (flips the values over the diagonal) + * + * Params: + * @param {mat3} mat mat3 to transpose + * @param {mat3} [dest] mat3 receiving transposed values. If not specified result is written to mat + * + * @returns {mat3} dest is specified, mat otherwise + */ + mat3.transpose = function (mat, dest) { + // If we are transposing ourselves we can skip a few steps but have to cache some values + if (!dest || mat === dest) { + var a01 = mat[1], a02 = mat[2], + a12 = mat[5]; + + mat[1] = mat[3]; + mat[2] = mat[6]; + mat[3] = a01; + mat[5] = mat[7]; + mat[6] = a02; + mat[7] = a12; + return mat; + } + + dest[0] = mat[0]; + dest[1] = mat[3]; + dest[2] = mat[6]; + dest[3] = mat[1]; + dest[4] = mat[4]; + dest[5] = mat[7]; + dest[6] = mat[2]; + dest[7] = mat[5]; + dest[8] = mat[8]; + return dest; + }; + + /** + * Copies the elements of a mat3 into the upper 3x3 elements of a mat4 + * + * @param {mat3} mat mat3 containing values to copy + * @param {mat4} [dest] mat4 receiving copied values + * + * @returns {mat4} dest if specified, a new mat4 otherwise + */ + mat3.toMat4 = function (mat, dest) { + if (!dest) { dest = mat4.create(); } + + dest[15] = 1; + dest[14] = 0; + dest[13] = 0; + dest[12] = 0; + + dest[11] = 0; + dest[10] = mat[8]; + dest[9] = mat[7]; + dest[8] = mat[6]; + + dest[7] = 0; + dest[6] = mat[5]; + dest[5] = mat[4]; + dest[4] = mat[3]; + + dest[3] = 0; + dest[2] = mat[2]; + dest[1] = mat[1]; + dest[0] = mat[0]; + + return dest; + }; + + /** + * Returns a string representation of a mat3 + * + * @param {mat3} mat mat3 to represent as a string + * + * @param {string} String representation of mat + */ + mat3.str = function (mat) { + return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] + + ', ' + mat[3] + ', ' + mat[4] + ', ' + mat[5] + + ', ' + mat[6] + ', ' + mat[7] + ', ' + mat[8] + ']'; + }; + + /** + * @class 4x4 Matrix + * @name mat4 + */ + var mat4 = {}; + + /** + * Creates a new instance of a mat4 using the default array type + * Any javascript array-like object containing at least 16 numeric elements can serve as a mat4 + * + * @param {mat4} [mat] mat4 containing values to initialize with + * + * @returns {mat4} New mat4 + */ + mat4.create = function (mat) { + var dest = new MatrixArray(16); + + if (mat) { + dest[0] = mat[0]; + dest[1] = mat[1]; + dest[2] = mat[2]; + dest[3] = mat[3]; + dest[4] = mat[4]; + dest[5] = mat[5]; + dest[6] = mat[6]; + dest[7] = mat[7]; + dest[8] = mat[8]; + dest[9] = mat[9]; + dest[10] = mat[10]; + dest[11] = mat[11]; + dest[12] = mat[12]; + dest[13] = mat[13]; + dest[14] = mat[14]; + dest[15] = mat[15]; + } + + return dest; + }; + + /** + * Creates a new instance of a mat4, initializing it with the given arguments + * + * @param {number} m00 + * @param {number} m01 + * @param {number} m02 + * @param {number} m03 + * @param {number} m10 + * @param {number} m11 + * @param {number} m12 + * @param {number} m13 + * @param {number} m20 + * @param {number} m21 + * @param {number} m22 + * @param {number} m23 + * @param {number} m30 + * @param {number} m31 + * @param {number} m32 + * @param {number} m33 + + * @returns {mat4} New mat4 + */ + mat4.createFrom = function (m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) { + var dest = new MatrixArray(16); + + dest[0] = m00; + dest[1] = m01; + dest[2] = m02; + dest[3] = m03; + dest[4] = m10; + dest[5] = m11; + dest[6] = m12; + dest[7] = m13; + dest[8] = m20; + dest[9] = m21; + dest[10] = m22; + dest[11] = m23; + dest[12] = m30; + dest[13] = m31; + dest[14] = m32; + dest[15] = m33; + + return dest; + }; + + /** + * Copies the values of one mat4 to another + * + * @param {mat4} mat mat4 containing values to copy + * @param {mat4} dest mat4 receiving copied values + * + * @returns {mat4} dest + */ + mat4.set = function (mat, dest) { + dest[0] = mat[0]; + dest[1] = mat[1]; + dest[2] = mat[2]; + dest[3] = mat[3]; + dest[4] = mat[4]; + dest[5] = mat[5]; + dest[6] = mat[6]; + dest[7] = mat[7]; + dest[8] = mat[8]; + dest[9] = mat[9]; + dest[10] = mat[10]; + dest[11] = mat[11]; + dest[12] = mat[12]; + dest[13] = mat[13]; + dest[14] = mat[14]; + dest[15] = mat[15]; + return dest; + }; + + /** + * Compares two matrices for equality within a certain margin of error + * + * @param {mat4} a First matrix + * @param {mat4} b Second matrix + * + * @returns {Boolean} True if a is equivalent to b + */ + mat4.equal = function (a, b) { + return a === b || ( + Math.abs(a[0] - b[0]) < FLOAT_EPSILON && + Math.abs(a[1] - b[1]) < FLOAT_EPSILON && + Math.abs(a[2] - b[2]) < FLOAT_EPSILON && + Math.abs(a[3] - b[3]) < FLOAT_EPSILON && + Math.abs(a[4] - b[4]) < FLOAT_EPSILON && + Math.abs(a[5] - b[5]) < FLOAT_EPSILON && + Math.abs(a[6] - b[6]) < FLOAT_EPSILON && + Math.abs(a[7] - b[7]) < FLOAT_EPSILON && + Math.abs(a[8] - b[8]) < FLOAT_EPSILON && + Math.abs(a[9] - b[9]) < FLOAT_EPSILON && + Math.abs(a[10] - b[10]) < FLOAT_EPSILON && + Math.abs(a[11] - b[11]) < FLOAT_EPSILON && + Math.abs(a[12] - b[12]) < FLOAT_EPSILON && + Math.abs(a[13] - b[13]) < FLOAT_EPSILON && + Math.abs(a[14] - b[14]) < FLOAT_EPSILON && + Math.abs(a[15] - b[15]) < FLOAT_EPSILON + ); + }; + + /** + * Sets a mat4 to an identity matrix + * + * @param {mat4} dest mat4 to set + * + * @returns {mat4} dest + */ + mat4.identity = function (dest) { + if (!dest) { dest = mat4.create(); } + dest[0] = 1; + dest[1] = 0; + dest[2] = 0; + dest[3] = 0; + dest[4] = 0; + dest[5] = 1; + dest[6] = 0; + dest[7] = 0; + dest[8] = 0; + dest[9] = 0; + dest[10] = 1; + dest[11] = 0; + dest[12] = 0; + dest[13] = 0; + dest[14] = 0; + dest[15] = 1; + return dest; + }; + + /** + * Transposes a mat4 (flips the values over the diagonal) + * + * @param {mat4} mat mat4 to transpose + * @param {mat4} [dest] mat4 receiving transposed values. If not specified result is written to mat + * + * @param {mat4} dest is specified, mat otherwise + */ + mat4.transpose = function (mat, dest) { + // If we are transposing ourselves we can skip a few steps but have to cache some values + if (!dest || mat === dest) { + var a01 = mat[1], a02 = mat[2], a03 = mat[3], + a12 = mat[6], a13 = mat[7], + a23 = mat[11]; + + mat[1] = mat[4]; + mat[2] = mat[8]; + mat[3] = mat[12]; + mat[4] = a01; + mat[6] = mat[9]; + mat[7] = mat[13]; + mat[8] = a02; + mat[9] = a12; + mat[11] = mat[14]; + mat[12] = a03; + mat[13] = a13; + mat[14] = a23; + return mat; + } + + dest[0] = mat[0]; + dest[1] = mat[4]; + dest[2] = mat[8]; + dest[3] = mat[12]; + dest[4] = mat[1]; + dest[5] = mat[5]; + dest[6] = mat[9]; + dest[7] = mat[13]; + dest[8] = mat[2]; + dest[9] = mat[6]; + dest[10] = mat[10]; + dest[11] = mat[14]; + dest[12] = mat[3]; + dest[13] = mat[7]; + dest[14] = mat[11]; + dest[15] = mat[15]; + return dest; + }; + + /** + * Calculates the determinant of a mat4 + * + * @param {mat4} mat mat4 to calculate determinant of + * + * @returns {number} determinant of mat + */ + mat4.determinant = function (mat) { + // Cache the matrix values (makes for huge speed increases!) + var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3], + a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7], + a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11], + a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15]; + + return (a30 * a21 * a12 * a03 - a20 * a31 * a12 * a03 - a30 * a11 * a22 * a03 + a10 * a31 * a22 * a03 + + a20 * a11 * a32 * a03 - a10 * a21 * a32 * a03 - a30 * a21 * a02 * a13 + a20 * a31 * a02 * a13 + + a30 * a01 * a22 * a13 - a00 * a31 * a22 * a13 - a20 * a01 * a32 * a13 + a00 * a21 * a32 * a13 + + a30 * a11 * a02 * a23 - a10 * a31 * a02 * a23 - a30 * a01 * a12 * a23 + a00 * a31 * a12 * a23 + + a10 * a01 * a32 * a23 - a00 * a11 * a32 * a23 - a20 * a11 * a02 * a33 + a10 * a21 * a02 * a33 + + a20 * a01 * a12 * a33 - a00 * a21 * a12 * a33 - a10 * a01 * a22 * a33 + a00 * a11 * a22 * a33); + }; + + /** + * Calculates the inverse matrix of a mat4 + * + * @param {mat4} mat mat4 to calculate inverse of + * @param {mat4} [dest] mat4 receiving inverse matrix. If not specified result is written to mat + * + * @param {mat4} dest is specified, mat otherwise, null if matrix cannot be inverted + */ + mat4.inverse = function (mat, dest) { + if (!dest) { dest = mat; } + + // Cache the matrix values (makes for huge speed increases!) + var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3], + a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7], + a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11], + a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15], + + b00 = a00 * a11 - a01 * a10, + b01 = a00 * a12 - a02 * a10, + b02 = a00 * a13 - a03 * a10, + b03 = a01 * a12 - a02 * a11, + b04 = a01 * a13 - a03 * a11, + b05 = a02 * a13 - a03 * a12, + b06 = a20 * a31 - a21 * a30, + b07 = a20 * a32 - a22 * a30, + b08 = a20 * a33 - a23 * a30, + b09 = a21 * a32 - a22 * a31, + b10 = a21 * a33 - a23 * a31, + b11 = a22 * a33 - a23 * a32, + + d = (b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06), + invDet; + + // Calculate the determinant + if (!d) { return null; } + invDet = 1 / d; + + dest[0] = (a11 * b11 - a12 * b10 + a13 * b09) * invDet; + dest[1] = (-a01 * b11 + a02 * b10 - a03 * b09) * invDet; + dest[2] = (a31 * b05 - a32 * b04 + a33 * b03) * invDet; + dest[3] = (-a21 * b05 + a22 * b04 - a23 * b03) * invDet; + dest[4] = (-a10 * b11 + a12 * b08 - a13 * b07) * invDet; + dest[5] = (a00 * b11 - a02 * b08 + a03 * b07) * invDet; + dest[6] = (-a30 * b05 + a32 * b02 - a33 * b01) * invDet; + dest[7] = (a20 * b05 - a22 * b02 + a23 * b01) * invDet; + dest[8] = (a10 * b10 - a11 * b08 + a13 * b06) * invDet; + dest[9] = (-a00 * b10 + a01 * b08 - a03 * b06) * invDet; + dest[10] = (a30 * b04 - a31 * b02 + a33 * b00) * invDet; + dest[11] = (-a20 * b04 + a21 * b02 - a23 * b00) * invDet; + dest[12] = (-a10 * b09 + a11 * b07 - a12 * b06) * invDet; + dest[13] = (a00 * b09 - a01 * b07 + a02 * b06) * invDet; + dest[14] = (-a30 * b03 + a31 * b01 - a32 * b00) * invDet; + dest[15] = (a20 * b03 - a21 * b01 + a22 * b00) * invDet; + + return dest; + }; + + /** + * Copies the upper 3x3 elements of a mat4 into another mat4 + * + * @param {mat4} mat mat4 containing values to copy + * @param {mat4} [dest] mat4 receiving copied values + * + * @returns {mat4} dest is specified, a new mat4 otherwise + */ + mat4.toRotationMat = function (mat, dest) { + if (!dest) { dest = mat4.create(); } + + dest[0] = mat[0]; + dest[1] = mat[1]; + dest[2] = mat[2]; + dest[3] = mat[3]; + dest[4] = mat[4]; + dest[5] = mat[5]; + dest[6] = mat[6]; + dest[7] = mat[7]; + dest[8] = mat[8]; + dest[9] = mat[9]; + dest[10] = mat[10]; + dest[11] = mat[11]; + dest[12] = 0; + dest[13] = 0; + dest[14] = 0; + dest[15] = 1; + + return dest; + }; + + /** + * Copies the upper 3x3 elements of a mat4 into a mat3 + * + * @param {mat4} mat mat4 containing values to copy + * @param {mat3} [dest] mat3 receiving copied values + * + * @returns {mat3} dest is specified, a new mat3 otherwise + */ + mat4.toMat3 = function (mat, dest) { + if (!dest) { dest = mat3.create(); } + + dest[0] = mat[0]; + dest[1] = mat[1]; + dest[2] = mat[2]; + dest[3] = mat[4]; + dest[4] = mat[5]; + dest[5] = mat[6]; + dest[6] = mat[8]; + dest[7] = mat[9]; + dest[8] = mat[10]; + + return dest; + }; + + /** + * Calculates the inverse of the upper 3x3 elements of a mat4 and copies the result into a mat3 + * The resulting matrix is useful for calculating transformed normals + * + * Params: + * @param {mat4} mat mat4 containing values to invert and copy + * @param {mat3} [dest] mat3 receiving values + * + * @returns {mat3} dest is specified, a new mat3 otherwise, null if the matrix cannot be inverted + */ + mat4.toInverseMat3 = function (mat, dest) { + // Cache the matrix values (makes for huge speed increases!) + var a00 = mat[0], a01 = mat[1], a02 = mat[2], + a10 = mat[4], a11 = mat[5], a12 = mat[6], + a20 = mat[8], a21 = mat[9], a22 = mat[10], + + b01 = a22 * a11 - a12 * a21, + b11 = -a22 * a10 + a12 * a20, + b21 = a21 * a10 - a11 * a20, + + d = a00 * b01 + a01 * b11 + a02 * b21, + id; + + if (!d) { return null; } + id = 1 / d; + + if (!dest) { dest = mat3.create(); } + + dest[0] = b01 * id; + dest[1] = (-a22 * a01 + a02 * a21) * id; + dest[2] = (a12 * a01 - a02 * a11) * id; + dest[3] = b11 * id; + dest[4] = (a22 * a00 - a02 * a20) * id; + dest[5] = (-a12 * a00 + a02 * a10) * id; + dest[6] = b21 * id; + dest[7] = (-a21 * a00 + a01 * a20) * id; + dest[8] = (a11 * a00 - a01 * a10) * id; + + return dest; + }; + + /** + * Performs a matrix multiplication + * + * @param {mat4} mat First operand + * @param {mat4} mat2 Second operand + * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat + * + * @returns {mat4} dest if specified, mat otherwise + */ + mat4.multiply = function (mat, mat2, dest) { + if (!dest) { dest = mat; } + + // Cache the matrix values (makes for huge speed increases!) + var a00 = mat[ 0], a01 = mat[ 1], a02 = mat[ 2], a03 = mat[3]; + var a10 = mat[ 4], a11 = mat[ 5], a12 = mat[ 6], a13 = mat[7]; + var a20 = mat[ 8], a21 = mat[ 9], a22 = mat[10], a23 = mat[11]; + var a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15]; + + // Cache only the current line of the second matrix + var b0 = mat2[0], b1 = mat2[1], b2 = mat2[2], b3 = mat2[3]; + dest[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30; + dest[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31; + dest[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32; + dest[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33; + + b0 = mat2[4]; + b1 = mat2[5]; + b2 = mat2[6]; + b3 = mat2[7]; + dest[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30; + dest[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31; + dest[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32; + dest[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33; + + b0 = mat2[8]; + b1 = mat2[9]; + b2 = mat2[10]; + b3 = mat2[11]; + dest[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30; + dest[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31; + dest[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32; + dest[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33; + + b0 = mat2[12]; + b1 = mat2[13]; + b2 = mat2[14]; + b3 = mat2[15]; + dest[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30; + dest[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31; + dest[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32; + dest[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33; + + return dest; + }; + + /** + * Transforms a vec3 with the given matrix + * 4th vector component is implicitly '1' + * + * @param {mat4} mat mat4 to transform the vector with + * @param {vec3} vec vec3 to transform + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns {vec3} dest if specified, vec otherwise + */ + mat4.multiplyVec3 = function (mat, vec, dest) { + if (!dest) { dest = vec; } + + var x = vec[0], y = vec[1], z = vec[2]; + + dest[0] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12]; + dest[1] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13]; + dest[2] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14]; + + return dest; + }; + + /** + * Transforms a vec4 with the given matrix + * + * @param {mat4} mat mat4 to transform the vector with + * @param {vec4} vec vec4 to transform + * @param {vec4} [dest] vec4 receiving operation result. If not specified result is written to vec + * + * @returns {vec4} dest if specified, vec otherwise + */ + mat4.multiplyVec4 = function (mat, vec, dest) { + if (!dest) { dest = vec; } + + var x = vec[0], y = vec[1], z = vec[2], w = vec[3]; + + dest[0] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12] * w; + dest[1] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13] * w; + dest[2] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14] * w; + dest[3] = mat[3] * x + mat[7] * y + mat[11] * z + mat[15] * w; + + return dest; + }; + + /** + * Translates a matrix by the given vector + * + * @param {mat4} mat mat4 to translate + * @param {vec3} vec vec3 specifying the translation + * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat + * + * @returns {mat4} dest if specified, mat otherwise + */ + mat4.translate = function (mat, vec, dest) { + var x = vec[0], y = vec[1], z = vec[2], + a00, a01, a02, a03, + a10, a11, a12, a13, + a20, a21, a22, a23; + + if (!dest || mat === dest) { + mat[12] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12]; + mat[13] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13]; + mat[14] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14]; + mat[15] = mat[3] * x + mat[7] * y + mat[11] * z + mat[15]; + return mat; + } + + a00 = mat[0]; a01 = mat[1]; a02 = mat[2]; a03 = mat[3]; + a10 = mat[4]; a11 = mat[5]; a12 = mat[6]; a13 = mat[7]; + a20 = mat[8]; a21 = mat[9]; a22 = mat[10]; a23 = mat[11]; + + dest[0] = a00; dest[1] = a01; dest[2] = a02; dest[3] = a03; + dest[4] = a10; dest[5] = a11; dest[6] = a12; dest[7] = a13; + dest[8] = a20; dest[9] = a21; dest[10] = a22; dest[11] = a23; + + dest[12] = a00 * x + a10 * y + a20 * z + mat[12]; + dest[13] = a01 * x + a11 * y + a21 * z + mat[13]; + dest[14] = a02 * x + a12 * y + a22 * z + mat[14]; + dest[15] = a03 * x + a13 * y + a23 * z + mat[15]; + return dest; + }; + + /** + * Scales a matrix by the given vector + * + * @param {mat4} mat mat4 to scale + * @param {vec3} vec vec3 specifying the scale for each axis + * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat + * + * @param {mat4} dest if specified, mat otherwise + */ + mat4.scale = function (mat, vec, dest) { + var x = vec[0], y = vec[1], z = vec[2]; + + if (!dest || mat === dest) { + mat[0] *= x; + mat[1] *= x; + mat[2] *= x; + mat[3] *= x; + mat[4] *= y; + mat[5] *= y; + mat[6] *= y; + mat[7] *= y; + mat[8] *= z; + mat[9] *= z; + mat[10] *= z; + mat[11] *= z; + return mat; + } + + dest[0] = mat[0] * x; + dest[1] = mat[1] * x; + dest[2] = mat[2] * x; + dest[3] = mat[3] * x; + dest[4] = mat[4] * y; + dest[5] = mat[5] * y; + dest[6] = mat[6] * y; + dest[7] = mat[7] * y; + dest[8] = mat[8] * z; + dest[9] = mat[9] * z; + dest[10] = mat[10] * z; + dest[11] = mat[11] * z; + dest[12] = mat[12]; + dest[13] = mat[13]; + dest[14] = mat[14]; + dest[15] = mat[15]; + return dest; + }; + + /** + * Rotates a matrix by the given angle around the specified axis + * If rotating around a primary axis (X,Y,Z) one of the specialized rotation functions should be used instead for performance + * + * @param {mat4} mat mat4 to rotate + * @param {number} angle Angle (in radians) to rotate + * @param {vec3} axis vec3 representing the axis to rotate around + * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat + * + * @returns {mat4} dest if specified, mat otherwise + */ + mat4.rotate = function (mat, angle, axis, dest) { + var x = axis[0], y = axis[1], z = axis[2], + len = Math.sqrt(x * x + y * y + z * z), + s, c, t, + a00, a01, a02, a03, + a10, a11, a12, a13, + a20, a21, a22, a23, + b00, b01, b02, + b10, b11, b12, + b20, b21, b22; + + if (!len) { return null; } + if (len !== 1) { + len = 1 / len; + x *= len; + y *= len; + z *= len; + } + + s = Math.sin(angle); + c = Math.cos(angle); + t = 1 - c; + + a00 = mat[0]; a01 = mat[1]; a02 = mat[2]; a03 = mat[3]; + a10 = mat[4]; a11 = mat[5]; a12 = mat[6]; a13 = mat[7]; + a20 = mat[8]; a21 = mat[9]; a22 = mat[10]; a23 = mat[11]; + + // Construct the elements of the rotation matrix + b00 = x * x * t + c; b01 = y * x * t + z * s; b02 = z * x * t - y * s; + b10 = x * y * t - z * s; b11 = y * y * t + c; b12 = z * y * t + x * s; + b20 = x * z * t + y * s; b21 = y * z * t - x * s; b22 = z * z * t + c; + + if (!dest) { + dest = mat; + } else if (mat !== dest) { // If the source and destination differ, copy the unchanged last row + dest[12] = mat[12]; + dest[13] = mat[13]; + dest[14] = mat[14]; + dest[15] = mat[15]; + } + + // Perform rotation-specific matrix multiplication + dest[0] = a00 * b00 + a10 * b01 + a20 * b02; + dest[1] = a01 * b00 + a11 * b01 + a21 * b02; + dest[2] = a02 * b00 + a12 * b01 + a22 * b02; + dest[3] = a03 * b00 + a13 * b01 + a23 * b02; + + dest[4] = a00 * b10 + a10 * b11 + a20 * b12; + dest[5] = a01 * b10 + a11 * b11 + a21 * b12; + dest[6] = a02 * b10 + a12 * b11 + a22 * b12; + dest[7] = a03 * b10 + a13 * b11 + a23 * b12; + + dest[8] = a00 * b20 + a10 * b21 + a20 * b22; + dest[9] = a01 * b20 + a11 * b21 + a21 * b22; + dest[10] = a02 * b20 + a12 * b21 + a22 * b22; + dest[11] = a03 * b20 + a13 * b21 + a23 * b22; + return dest; + }; + + /** + * Rotates a matrix by the given angle around the X axis + * + * @param {mat4} mat mat4 to rotate + * @param {number} angle Angle (in radians) to rotate + * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat + * + * @returns {mat4} dest if specified, mat otherwise + */ + mat4.rotateX = function (mat, angle, dest) { + var s = Math.sin(angle), + c = Math.cos(angle), + a10 = mat[4], + a11 = mat[5], + a12 = mat[6], + a13 = mat[7], + a20 = mat[8], + a21 = mat[9], + a22 = mat[10], + a23 = mat[11]; + + if (!dest) { + dest = mat; + } else if (mat !== dest) { // If the source and destination differ, copy the unchanged rows + dest[0] = mat[0]; + dest[1] = mat[1]; + dest[2] = mat[2]; + dest[3] = mat[3]; + + dest[12] = mat[12]; + dest[13] = mat[13]; + dest[14] = mat[14]; + dest[15] = mat[15]; + } + + // Perform axis-specific matrix multiplication + dest[4] = a10 * c + a20 * s; + dest[5] = a11 * c + a21 * s; + dest[6] = a12 * c + a22 * s; + dest[7] = a13 * c + a23 * s; + + dest[8] = a10 * -s + a20 * c; + dest[9] = a11 * -s + a21 * c; + dest[10] = a12 * -s + a22 * c; + dest[11] = a13 * -s + a23 * c; + return dest; + }; + + /** + * Rotates a matrix by the given angle around the Y axis + * + * @param {mat4} mat mat4 to rotate + * @param {number} angle Angle (in radians) to rotate + * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat + * + * @returns {mat4} dest if specified, mat otherwise + */ + mat4.rotateY = function (mat, angle, dest) { + var s = Math.sin(angle), + c = Math.cos(angle), + a00 = mat[0], + a01 = mat[1], + a02 = mat[2], + a03 = mat[3], + a20 = mat[8], + a21 = mat[9], + a22 = mat[10], + a23 = mat[11]; + + if (!dest) { + dest = mat; + } else if (mat !== dest) { // If the source and destination differ, copy the unchanged rows + dest[4] = mat[4]; + dest[5] = mat[5]; + dest[6] = mat[6]; + dest[7] = mat[7]; + + dest[12] = mat[12]; + dest[13] = mat[13]; + dest[14] = mat[14]; + dest[15] = mat[15]; + } + + // Perform axis-specific matrix multiplication + dest[0] = a00 * c + a20 * -s; + dest[1] = a01 * c + a21 * -s; + dest[2] = a02 * c + a22 * -s; + dest[3] = a03 * c + a23 * -s; + + dest[8] = a00 * s + a20 * c; + dest[9] = a01 * s + a21 * c; + dest[10] = a02 * s + a22 * c; + dest[11] = a03 * s + a23 * c; + return dest; + }; + + /** + * Rotates a matrix by the given angle around the Z axis + * + * @param {mat4} mat mat4 to rotate + * @param {number} angle Angle (in radians) to rotate + * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat + * + * @returns {mat4} dest if specified, mat otherwise + */ + mat4.rotateZ = function (mat, angle, dest) { + var s = Math.sin(angle), + c = Math.cos(angle), + a00 = mat[0], + a01 = mat[1], + a02 = mat[2], + a03 = mat[3], + a10 = mat[4], + a11 = mat[5], + a12 = mat[6], + a13 = mat[7]; + + if (!dest) { + dest = mat; + } else if (mat !== dest) { // If the source and destination differ, copy the unchanged last row + dest[8] = mat[8]; + dest[9] = mat[9]; + dest[10] = mat[10]; + dest[11] = mat[11]; + + dest[12] = mat[12]; + dest[13] = mat[13]; + dest[14] = mat[14]; + dest[15] = mat[15]; + } + + // Perform axis-specific matrix multiplication + dest[0] = a00 * c + a10 * s; + dest[1] = a01 * c + a11 * s; + dest[2] = a02 * c + a12 * s; + dest[3] = a03 * c + a13 * s; + + dest[4] = a00 * -s + a10 * c; + dest[5] = a01 * -s + a11 * c; + dest[6] = a02 * -s + a12 * c; + dest[7] = a03 * -s + a13 * c; + + return dest; + }; + + /** + * Generates a frustum matrix with the given bounds + * + * @param {number} left Left bound of the frustum + * @param {number} right Right bound of the frustum + * @param {number} bottom Bottom bound of the frustum + * @param {number} top Top bound of the frustum + * @param {number} near Near bound of the frustum + * @param {number} far Far bound of the frustum + * @param {mat4} [dest] mat4 frustum matrix will be written into + * + * @returns {mat4} dest if specified, a new mat4 otherwise + */ + mat4.frustum = function (left, right, bottom, top, near, far, dest) { + if (!dest) { dest = mat4.create(); } + var rl = (right - left), + tb = (top - bottom), + fn = (far - near); + dest[0] = (near * 2) / rl; + dest[1] = 0; + dest[2] = 0; + dest[3] = 0; + dest[4] = 0; + dest[5] = (near * 2) / tb; + dest[6] = 0; + dest[7] = 0; + dest[8] = (right + left) / rl; + dest[9] = (top + bottom) / tb; + dest[10] = -(far + near) / fn; + dest[11] = -1; + dest[12] = 0; + dest[13] = 0; + dest[14] = -(far * near * 2) / fn; + dest[15] = 0; + return dest; + }; + + /** + * Generates a perspective projection matrix with the given bounds + * + * @param {number} fovy Vertical field of view + * @param {number} aspect Aspect ratio. typically viewport width/height + * @param {number} near Near bound of the frustum + * @param {number} far Far bound of the frustum + * @param {mat4} [dest] mat4 frustum matrix will be written into + * + * @returns {mat4} dest if specified, a new mat4 otherwise + */ + mat4.perspective = function (fovy, aspect, near, far, dest) { + var top = near * Math.tan(fovy * Math.PI / 360.0), + right = top * aspect; + return mat4.frustum(-right, right, -top, top, near, far, dest); + }; + + /** + * Generates a orthogonal projection matrix with the given bounds + * + * @param {number} left Left bound of the frustum + * @param {number} right Right bound of the frustum + * @param {number} bottom Bottom bound of the frustum + * @param {number} top Top bound of the frustum + * @param {number} near Near bound of the frustum + * @param {number} far Far bound of the frustum + * @param {mat4} [dest] mat4 frustum matrix will be written into + * + * @returns {mat4} dest if specified, a new mat4 otherwise + */ + mat4.ortho = function (left, right, bottom, top, near, far, dest) { + if (!dest) { dest = mat4.create(); } + var rl = (right - left), + tb = (top - bottom), + fn = (far - near); + dest[0] = 2 / rl; + dest[1] = 0; + dest[2] = 0; + dest[3] = 0; + dest[4] = 0; + dest[5] = 2 / tb; + dest[6] = 0; + dest[7] = 0; + dest[8] = 0; + dest[9] = 0; + dest[10] = -2 / fn; + dest[11] = 0; + dest[12] = -(left + right) / rl; + dest[13] = -(top + bottom) / tb; + dest[14] = -(far + near) / fn; + dest[15] = 1; + return dest; + }; + + /** + * Generates a look-at matrix with the given eye position, focal point, and up axis + * + * @param {vec3} eye Position of the viewer + * @param {vec3} center Point the viewer is looking at + * @param {vec3} up vec3 pointing "up" + * @param {mat4} [dest] mat4 frustum matrix will be written into + * + * @returns {mat4} dest if specified, a new mat4 otherwise + */ + mat4.lookAt = function (eye, center, up, dest) { + if (!dest) { dest = mat4.create(); } + + var x0, x1, x2, y0, y1, y2, z0, z1, z2, len, + eyex = eye[0], + eyey = eye[1], + eyez = eye[2], + upx = up[0], + upy = up[1], + upz = up[2], + centerx = center[0], + centery = center[1], + centerz = center[2]; + + if (eyex === centerx && eyey === centery && eyez === centerz) { + return mat4.identity(dest); + } + + //vec3.direction(eye, center, z); + z0 = eyex - centerx; + z1 = eyey - centery; + z2 = eyez - centerz; + + // normalize (no check needed for 0 because of early return) + len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2); + z0 *= len; + z1 *= len; + z2 *= len; + + //vec3.normalize(vec3.cross(up, z, x)); + x0 = upy * z2 - upz * z1; + x1 = upz * z0 - upx * z2; + x2 = upx * z1 - upy * z0; + len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2); + if (!len) { + x0 = 0; + x1 = 0; + x2 = 0; + } else { + len = 1 / len; + x0 *= len; + x1 *= len; + x2 *= len; + } + + //vec3.normalize(vec3.cross(z, x, y)); + y0 = z1 * x2 - z2 * x1; + y1 = z2 * x0 - z0 * x2; + y2 = z0 * x1 - z1 * x0; + + len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2); + if (!len) { + y0 = 0; + y1 = 0; + y2 = 0; + } else { + len = 1 / len; + y0 *= len; + y1 *= len; + y2 *= len; + } + + dest[0] = x0; + dest[1] = y0; + dest[2] = z0; + dest[3] = 0; + dest[4] = x1; + dest[5] = y1; + dest[6] = z1; + dest[7] = 0; + dest[8] = x2; + dest[9] = y2; + dest[10] = z2; + dest[11] = 0; + dest[12] = -(x0 * eyex + x1 * eyey + x2 * eyez); + dest[13] = -(y0 * eyex + y1 * eyey + y2 * eyez); + dest[14] = -(z0 * eyex + z1 * eyey + z2 * eyez); + dest[15] = 1; + + return dest; + }; + + /** + * Creates a matrix from a quaternion rotation and vector translation + * This is equivalent to (but much faster than): + * + * mat4.identity(dest); + * mat4.translate(dest, vec); + * var quatMat = mat4.create(); + * quat4.toMat4(quat, quatMat); + * mat4.multiply(dest, quatMat); + * + * @param {quat4} quat Rotation quaternion + * @param {vec3} vec Translation vector + * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to a new mat4 + * + * @returns {mat4} dest if specified, a new mat4 otherwise + */ + mat4.fromRotationTranslation = function (quat, vec, dest) { + if (!dest) { dest = mat4.create(); } + + // Quaternion math + var x = quat[0], y = quat[1], z = quat[2], w = quat[3], + x2 = x + x, + y2 = y + y, + z2 = z + z, + + xx = x * x2, + xy = x * y2, + xz = x * z2, + yy = y * y2, + yz = y * z2, + zz = z * z2, + wx = w * x2, + wy = w * y2, + wz = w * z2; + + dest[0] = 1 - (yy + zz); + dest[1] = xy + wz; + dest[2] = xz - wy; + dest[3] = 0; + dest[4] = xy - wz; + dest[5] = 1 - (xx + zz); + dest[6] = yz + wx; + dest[7] = 0; + dest[8] = xz + wy; + dest[9] = yz - wx; + dest[10] = 1 - (xx + yy); + dest[11] = 0; + dest[12] = vec[0]; + dest[13] = vec[1]; + dest[14] = vec[2]; + dest[15] = 1; + + return dest; + }; + + /** + * Returns a string representation of a mat4 + * + * @param {mat4} mat mat4 to represent as a string + * + * @returns {string} String representation of mat + */ + mat4.str = function (mat) { + return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] + ', ' + mat[3] + + ', ' + mat[4] + ', ' + mat[5] + ', ' + mat[6] + ', ' + mat[7] + + ', ' + mat[8] + ', ' + mat[9] + ', ' + mat[10] + ', ' + mat[11] + + ', ' + mat[12] + ', ' + mat[13] + ', ' + mat[14] + ', ' + mat[15] + ']'; + }; + + /** + * @class Quaternion + * @name quat4 + */ + var quat4 = {}; + + /** + * Creates a new instance of a quat4 using the default array type + * Any javascript array containing at least 4 numeric elements can serve as a quat4 + * + * @param {quat4} [quat] quat4 containing values to initialize with + * + * @returns {quat4} New quat4 + */ + quat4.create = function (quat) { + var dest = new MatrixArray(4); + + if (quat) { + dest[0] = quat[0]; + dest[1] = quat[1]; + dest[2] = quat[2]; + dest[3] = quat[3]; + } else { + dest[0] = dest[1] = dest[2] = dest[3] = 0; + } + + return dest; + }; + + /** + * Creates a new instance of a quat4, initializing it with the given arguments + * + * @param {number} x X value + * @param {number} y Y value + * @param {number} z Z value + * @param {number} w W value + + * @returns {quat4} New quat4 + */ + quat4.createFrom = function (x, y, z, w) { + var dest = new MatrixArray(4); + + dest[0] = x; + dest[1] = y; + dest[2] = z; + dest[3] = w; + + return dest; + }; + + /** + * Copies the values of one quat4 to another + * + * @param {quat4} quat quat4 containing values to copy + * @param {quat4} dest quat4 receiving copied values + * + * @returns {quat4} dest + */ + quat4.set = function (quat, dest) { + dest[0] = quat[0]; + dest[1] = quat[1]; + dest[2] = quat[2]; + dest[3] = quat[3]; + + return dest; + }; + + /** + * Compares two quaternions for equality within a certain margin of error + * + * @param {quat4} a First vector + * @param {quat4} b Second vector + * + * @returns {Boolean} True if a is equivalent to b + */ + quat4.equal = function (a, b) { + return a === b || ( + Math.abs(a[0] - b[0]) < FLOAT_EPSILON && + Math.abs(a[1] - b[1]) < FLOAT_EPSILON && + Math.abs(a[2] - b[2]) < FLOAT_EPSILON && + Math.abs(a[3] - b[3]) < FLOAT_EPSILON + ); + }; + + /** + * Creates a new identity Quat4 + * + * @param {quat4} [dest] quat4 receiving copied values + * + * @returns {quat4} dest is specified, new quat4 otherwise + */ + quat4.identity = function (dest) { + if (!dest) { dest = quat4.create(); } + dest[0] = 0; + dest[1] = 0; + dest[2] = 0; + dest[3] = 1; + return dest; + }; + + var identityQuat4 = quat4.identity(); + + /** + * Calculates the W component of a quat4 from the X, Y, and Z components. + * Assumes that quaternion is 1 unit in length. + * Any existing W component will be ignored. + * + * @param {quat4} quat quat4 to calculate W component of + * @param {quat4} [dest] quat4 receiving calculated values. If not specified result is written to quat + * + * @returns {quat4} dest if specified, quat otherwise + */ + quat4.calculateW = function (quat, dest) { + var x = quat[0], y = quat[1], z = quat[2]; + + if (!dest || quat === dest) { + quat[3] = -Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z)); + return quat; + } + dest[0] = x; + dest[1] = y; + dest[2] = z; + dest[3] = -Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z)); + return dest; + }; + + /** + * Calculates the dot product of two quaternions + * + * @param {quat4} quat First operand + * @param {quat4} quat2 Second operand + * + * @return {number} Dot product of quat and quat2 + */ + quat4.dot = function(quat, quat2){ + return quat[0]*quat2[0] + quat[1]*quat2[1] + quat[2]*quat2[2] + quat[3]*quat2[3]; + }; + + /** + * Calculates the inverse of a quat4 + * + * @param {quat4} quat quat4 to calculate inverse of + * @param {quat4} [dest] quat4 receiving inverse values. If not specified result is written to quat + * + * @returns {quat4} dest if specified, quat otherwise + */ + quat4.inverse = function(quat, dest) { + var q0 = quat[0], q1 = quat[1], q2 = quat[2], q3 = quat[3], + dot = q0*q0 + q1*q1 + q2*q2 + q3*q3, + invDot = dot ? 1.0/dot : 0; + + // TODO: Would be faster to return [0,0,0,0] immediately if dot == 0 + + if(!dest || quat === dest) { + quat[0] *= -invDot; + quat[1] *= -invDot; + quat[2] *= -invDot; + quat[3] *= invDot; + return quat; + } + dest[0] = -quat[0]*invDot; + dest[1] = -quat[1]*invDot; + dest[2] = -quat[2]*invDot; + dest[3] = quat[3]*invDot; + return dest; + }; + + + /** + * Calculates the conjugate of a quat4 + * If the quaternion is normalized, this function is faster than quat4.inverse and produces the same result. + * + * @param {quat4} quat quat4 to calculate conjugate of + * @param {quat4} [dest] quat4 receiving conjugate values. If not specified result is written to quat + * + * @returns {quat4} dest if specified, quat otherwise + */ + quat4.conjugate = function (quat, dest) { + if (!dest || quat === dest) { + quat[0] *= -1; + quat[1] *= -1; + quat[2] *= -1; + return quat; + } + dest[0] = -quat[0]; + dest[1] = -quat[1]; + dest[2] = -quat[2]; + dest[3] = quat[3]; + return dest; + }; + + /** + * Calculates the length of a quat4 + * + * Params: + * @param {quat4} quat quat4 to calculate length of + * + * @returns Length of quat + */ + quat4.length = function (quat) { + var x = quat[0], y = quat[1], z = quat[2], w = quat[3]; + return Math.sqrt(x * x + y * y + z * z + w * w); + }; + + /** + * Generates a unit quaternion of the same direction as the provided quat4 + * If quaternion length is 0, returns [0, 0, 0, 0] + * + * @param {quat4} quat quat4 to normalize + * @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat + * + * @returns {quat4} dest if specified, quat otherwise + */ + quat4.normalize = function (quat, dest) { + if (!dest) { dest = quat; } + + var x = quat[0], y = quat[1], z = quat[2], w = quat[3], + len = Math.sqrt(x * x + y * y + z * z + w * w); + if (len === 0) { + dest[0] = 0; + dest[1] = 0; + dest[2] = 0; + dest[3] = 0; + return dest; + } + len = 1 / len; + dest[0] = x * len; + dest[1] = y * len; + dest[2] = z * len; + dest[3] = w * len; + + return dest; + }; + + /** + * Performs quaternion addition + * + * @param {quat4} quat First operand + * @param {quat4} quat2 Second operand + * @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat + * + * @returns {quat4} dest if specified, quat otherwise + */ + quat4.add = function (quat, quat2, dest) { + if(!dest || quat === dest) { + quat[0] += quat2[0]; + quat[1] += quat2[1]; + quat[2] += quat2[2]; + quat[3] += quat2[3]; + return quat; + } + dest[0] = quat[0]+quat2[0]; + dest[1] = quat[1]+quat2[1]; + dest[2] = quat[2]+quat2[2]; + dest[3] = quat[3]+quat2[3]; + return dest; + }; + + /** + * Performs a quaternion multiplication + * + * @param {quat4} quat First operand + * @param {quat4} quat2 Second operand + * @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat + * + * @returns {quat4} dest if specified, quat otherwise + */ + quat4.multiply = function (quat, quat2, dest) { + if (!dest) { dest = quat; } + + var qax = quat[0], qay = quat[1], qaz = quat[2], qaw = quat[3], + qbx = quat2[0], qby = quat2[1], qbz = quat2[2], qbw = quat2[3]; + + dest[0] = qax * qbw + qaw * qbx + qay * qbz - qaz * qby; + dest[1] = qay * qbw + qaw * qby + qaz * qbx - qax * qbz; + dest[2] = qaz * qbw + qaw * qbz + qax * qby - qay * qbx; + dest[3] = qaw * qbw - qax * qbx - qay * qby - qaz * qbz; + + return dest; + }; + + /** + * Transforms a vec3 with the given quaternion + * + * @param {quat4} quat quat4 to transform the vector with + * @param {vec3} vec vec3 to transform + * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec + * + * @returns dest if specified, vec otherwise + */ + quat4.multiplyVec3 = function (quat, vec, dest) { + if (!dest) { dest = vec; } + + var x = vec[0], y = vec[1], z = vec[2], + qx = quat[0], qy = quat[1], qz = quat[2], qw = quat[3], + + // calculate quat * vec + ix = qw * x + qy * z - qz * y, + iy = qw * y + qz * x - qx * z, + iz = qw * z + qx * y - qy * x, + iw = -qx * x - qy * y - qz * z; + + // calculate result * inverse quat + dest[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy; + dest[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz; + dest[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx; + + return dest; + }; + + /** + * Multiplies the components of a quaternion by a scalar value + * + * @param {quat4} quat to scale + * @param {number} val Value to scale by + * @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat + * + * @returns {quat4} dest if specified, quat otherwise + */ + quat4.scale = function (quat, val, dest) { + if(!dest || quat === dest) { + quat[0] *= val; + quat[1] *= val; + quat[2] *= val; + quat[3] *= val; + return quat; + } + dest[0] = quat[0]*val; + dest[1] = quat[1]*val; + dest[2] = quat[2]*val; + dest[3] = quat[3]*val; + return dest; + }; + + /** + * Calculates a 3x3 matrix from the given quat4 + * + * @param {quat4} quat quat4 to create matrix from + * @param {mat3} [dest] mat3 receiving operation result + * + * @returns {mat3} dest if specified, a new mat3 otherwise + */ + quat4.toMat3 = function (quat, dest) { + if (!dest) { dest = mat3.create(); } + + var x = quat[0], y = quat[1], z = quat[2], w = quat[3], + x2 = x + x, + y2 = y + y, + z2 = z + z, + + xx = x * x2, + xy = x * y2, + xz = x * z2, + yy = y * y2, + yz = y * z2, + zz = z * z2, + wx = w * x2, + wy = w * y2, + wz = w * z2; + + dest[0] = 1 - (yy + zz); + dest[1] = xy + wz; + dest[2] = xz - wy; + + dest[3] = xy - wz; + dest[4] = 1 - (xx + zz); + dest[5] = yz + wx; + + dest[6] = xz + wy; + dest[7] = yz - wx; + dest[8] = 1 - (xx + yy); + + return dest; + }; + + /** + * Calculates a 4x4 matrix from the given quat4 + * + * @param {quat4} quat quat4 to create matrix from + * @param {mat4} [dest] mat4 receiving operation result + * + * @returns {mat4} dest if specified, a new mat4 otherwise + */ + quat4.toMat4 = function (quat, dest) { + if (!dest) { dest = mat4.create(); } + + var x = quat[0], y = quat[1], z = quat[2], w = quat[3], + x2 = x + x, + y2 = y + y, + z2 = z + z, + + xx = x * x2, + xy = x * y2, + xz = x * z2, + yy = y * y2, + yz = y * z2, + zz = z * z2, + wx = w * x2, + wy = w * y2, + wz = w * z2; + + dest[0] = 1 - (yy + zz); + dest[1] = xy + wz; + dest[2] = xz - wy; + dest[3] = 0; + + dest[4] = xy - wz; + dest[5] = 1 - (xx + zz); + dest[6] = yz + wx; + dest[7] = 0; + + dest[8] = xz + wy; + dest[9] = yz - wx; + dest[10] = 1 - (xx + yy); + dest[11] = 0; + + dest[12] = 0; + dest[13] = 0; + dest[14] = 0; + dest[15] = 1; + + return dest; + }; + + /** + * Performs a spherical linear interpolation between two quat4 + * + * @param {quat4} quat First quaternion + * @param {quat4} quat2 Second quaternion + * @param {number} slerp Interpolation amount between the two inputs + * @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat + * + * @returns {quat4} dest if specified, quat otherwise + */ + quat4.slerp = function (quat, quat2, slerp, dest) { + if (!dest) { dest = quat; } + + var cosHalfTheta = quat[0] * quat2[0] + quat[1] * quat2[1] + quat[2] * quat2[2] + quat[3] * quat2[3], + halfTheta, + sinHalfTheta, + ratioA, + ratioB; + + if (Math.abs(cosHalfTheta) >= 1.0) { + if (dest !== quat) { + dest[0] = quat[0]; + dest[1] = quat[1]; + dest[2] = quat[2]; + dest[3] = quat[3]; + } + return dest; + } + + halfTheta = Math.acos(cosHalfTheta); + sinHalfTheta = Math.sqrt(1.0 - cosHalfTheta * cosHalfTheta); + + if (Math.abs(sinHalfTheta) < 0.001) { + dest[0] = (quat[0] * 0.5 + quat2[0] * 0.5); + dest[1] = (quat[1] * 0.5 + quat2[1] * 0.5); + dest[2] = (quat[2] * 0.5 + quat2[2] * 0.5); + dest[3] = (quat[3] * 0.5 + quat2[3] * 0.5); + return dest; + } + + ratioA = Math.sin((1 - slerp) * halfTheta) / sinHalfTheta; + ratioB = Math.sin(slerp * halfTheta) / sinHalfTheta; + + dest[0] = (quat[0] * ratioA + quat2[0] * ratioB); + dest[1] = (quat[1] * ratioA + quat2[1] * ratioB); + dest[2] = (quat[2] * ratioA + quat2[2] * ratioB); + dest[3] = (quat[3] * ratioA + quat2[3] * ratioB); + + return dest; + }; + + /** + * Creates a quaternion from the given 3x3 rotation matrix. + * If dest is omitted, a new quaternion will be created. + * + * @param {mat3} mat the rotation matrix + * @param {quat4} [dest] an optional receiving quaternion + * + * @returns {quat4} the quaternion constructed from the rotation matrix + * + */ + quat4.fromRotationMatrix = function(mat, dest) { + if (!dest) dest = quat4.create(); + + // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes + // article "Quaternion Calculus and Fast Animation". + + var fTrace = mat[0] + mat[4] + mat[8]; + var fRoot; + + if ( fTrace > 0.0 ) { + // |w| > 1/2, may as well choose w > 1/2 + fRoot = Math.sqrt(fTrace + 1.0); // 2w + dest[3] = 0.5 * fRoot; + fRoot = 0.5/fRoot; // 1/(4w) + dest[0] = (mat[7]-mat[5])*fRoot; + dest[1] = (mat[2]-mat[6])*fRoot; + dest[2] = (mat[3]-mat[1])*fRoot; + } else { + // |w| <= 1/2 + var s_iNext = quat4.fromRotationMatrix.s_iNext = quat4.fromRotationMatrix.s_iNext || [1,2,0]; + var i = 0; + if ( mat[4] > mat[0] ) + i = 1; + if ( mat[8] > mat[i*3+i] ) + i = 2; + var j = s_iNext[i]; + var k = s_iNext[j]; + + fRoot = Math.sqrt(mat[i*3+i]-mat[j*3+j]-mat[k*3+k] + 1.0); + dest[i] = 0.5 * fRoot; + fRoot = 0.5 / fRoot; + dest[3] = (mat[k*3+j] - mat[j*3+k]) * fRoot; + dest[j] = (mat[j*3+i] + mat[i*3+j]) * fRoot; + dest[k] = (mat[k*3+i] + mat[i*3+k]) * fRoot; + } + + return dest; + }; + + /** + * Alias. See the description for quat4.fromRotationMatrix(). + */ + mat3.toQuat4 = quat4.fromRotationMatrix; + + (function() { + var mat = mat3.create(); + + /** + * Creates a quaternion from the 3 given vectors. They must be perpendicular + * to one another and represent the X, Y and Z axes. + * + * If dest is omitted, a new quat4 will be created. + * + * Example: The default OpenGL orientation has a view vector [0, 0, -1], + * right vector [1, 0, 0], and up vector [0, 1, 0]. A quaternion representing + * this orientation could be constructed with: + * + * quat = quat4.fromAxes([0, 0, -1], [1, 0, 0], [0, 1, 0], quat4.create()); + * + * @param {vec3} view the view vector, or direction the object is pointing in + * @param {vec3} right the right vector, or direction to the "right" of the object + * @param {vec3} up the up vector, or direction towards the object's "up" + * @param {quat4} [dest] an optional receiving quat4 + * + * @returns {quat4} dest + **/ + quat4.fromAxes = function(view, right, up, dest) { + mat[0] = right[0]; + mat[3] = right[1]; + mat[6] = right[2]; + + mat[1] = up[0]; + mat[4] = up[1]; + mat[7] = up[2]; + + mat[2] = view[0]; + mat[5] = view[1]; + mat[8] = view[2]; + + return quat4.fromRotationMatrix(mat, dest); + }; + })(); + + /** + * Sets a quat4 to the Identity and returns it. + * + * @param {quat4} [dest] quat4 to set. If omitted, a + * new quat4 will be created. + * + * @returns {quat4} dest + */ + quat4.identity = function(dest) { + if (!dest) dest = quat4.create(); + dest[0] = 0; + dest[1] = 0; + dest[2] = 0; + dest[3] = 1; + return dest; + }; + + /** + * Sets a quat4 from the given angle and rotation axis, + * then returns it. If dest is not given, a new quat4 is created. + * + * @param {Number} angle the angle in radians + * @param {vec3} axis the axis around which to rotate + * @param {quat4} [dest] the optional quat4 to store the result + * + * @returns {quat4} dest + **/ + quat4.fromAngleAxis = function(angle, axis, dest) { + // The quaternion representing the rotation is + // q = cos(A/2)+sin(A/2)*(x*i+y*j+z*k) + if (!dest) dest = quat4.create(); + + var half = angle * 0.5; + var s = Math.sin(half); + dest[3] = Math.cos(half); + dest[0] = s * axis[0]; + dest[1] = s * axis[1]; + dest[2] = s * axis[2]; + + return dest; + }; + + /** + * Stores the angle and axis in a vec4, where the XYZ components represent + * the axis and the W (4th) component is the angle in radians. + * + * If dest is not given, src will be modified in place and returned, after + * which it should not be considered not a quaternion (just an axis and angle). + * + * @param {quat4} quat the quaternion whose angle and axis to store + * @param {vec4} [dest] the optional vec4 to receive the data + * + * @returns {vec4} dest + */ + quat4.toAngleAxis = function(src, dest) { + if (!dest) dest = src; + // The quaternion representing the rotation is + // q = cos(A/2)+sin(A/2)*(x*i+y*j+z*k) + + var sqrlen = src[0]*src[0]+src[1]*src[1]+src[2]*src[2]; + if (sqrlen > 0) + { + dest[3] = 2 * Math.acos(src[3]); + var invlen = glMath.invsqrt(sqrlen); + dest[0] = src[0]*invlen; + dest[1] = src[1]*invlen; + dest[2] = src[2]*invlen; + } else { + // angle is 0 (mod 2*pi), so any axis will do + dest[3] = 0; + dest[0] = 1; + dest[1] = 0; + dest[2] = 0; + } + + return dest; + }; + + /** + * Returns a string representation of a quaternion + * + * @param {quat4} quat quat4 to represent as a string + * + * @returns {string} String representation of quat + */ + quat4.str = function (quat) { + return '[' + quat[0] + ', ' + quat[1] + ', ' + quat[2] + ', ' + quat[3] + ']'; + }; + + /** + * @class 2 Dimensional Vector + * @name vec2 + */ + var vec2 = {}; + + /** + * Creates a new vec2, initializing it from vec if vec + * is given. + * + * @param {vec2} [vec] the vector's initial contents + * @returns {vec2} a new 2D vector + */ + vec2.create = function(vec) { + var dest = new MatrixArray(2); + + if (vec) { + dest[0] = vec[0]; + dest[1] = vec[1]; + } else { + dest[0] = 0; + dest[1] = 0; + } + return dest; + }; + + /** + * Creates a new instance of a vec2, initializing it with the given arguments + * + * @param {number} x X value + * @param {number} y Y value + + * @returns {vec2} New vec2 + */ + vec2.createFrom = function (x, y) { + var dest = new MatrixArray(2); + + dest[0] = x; + dest[1] = y; + + return dest; + }; + + /** + * Adds the vec2's together. If dest is given, the result + * is stored there. Otherwise, the result is stored in vecB. + * + * @param {vec2} vecA the first operand + * @param {vec2} vecB the second operand + * @param {vec2} [dest] the optional receiving vector + * @returns {vec2} dest + */ + vec2.add = function(vecA, vecB, dest) { + if (!dest) dest = vecB; + dest[0] = vecA[0] + vecB[0]; + dest[1] = vecA[1] + vecB[1]; + return dest; + }; + + /** + * Subtracts vecB from vecA. If dest is given, the result + * is stored there. Otherwise, the result is stored in vecB. + * + * @param {vec2} vecA the first operand + * @param {vec2} vecB the second operand + * @param {vec2} [dest] the optional receiving vector + * @returns {vec2} dest + */ + vec2.subtract = function(vecA, vecB, dest) { + if (!dest) dest = vecB; + dest[0] = vecA[0] - vecB[0]; + dest[1] = vecA[1] - vecB[1]; + return dest; + }; + + /** + * Multiplies vecA with vecB. If dest is given, the result + * is stored there. Otherwise, the result is stored in vecB. + * + * @param {vec2} vecA the first operand + * @param {vec2} vecB the second operand + * @param {vec2} [dest] the optional receiving vector + * @returns {vec2} dest + */ + vec2.multiply = function(vecA, vecB, dest) { + if (!dest) dest = vecB; + dest[0] = vecA[0] * vecB[0]; + dest[1] = vecA[1] * vecB[1]; + return dest; + }; + + /** + * Divides vecA by vecB. If dest is given, the result + * is stored there. Otherwise, the result is stored in vecB. + * + * @param {vec2} vecA the first operand + * @param {vec2} vecB the second operand + * @param {vec2} [dest] the optional receiving vector + * @returns {vec2} dest + */ + vec2.divide = function(vecA, vecB, dest) { + if (!dest) dest = vecB; + dest[0] = vecA[0] / vecB[0]; + dest[1] = vecA[1] / vecB[1]; + return dest; + }; + + /** + * Scales vecA by some scalar number. If dest is given, the result + * is stored there. Otherwise, the result is stored in vecA. + * + * This is the same as multiplying each component of vecA + * by the given scalar. + * + * @param {vec2} vecA the vector to be scaled + * @param {Number} scalar the amount to scale the vector by + * @param {vec2} [dest] the optional receiving vector + * @returns {vec2} dest + */ + vec2.scale = function(vecA, scalar, dest) { + if (!dest) dest = vecA; + dest[0] = vecA[0] * scalar; + dest[1] = vecA[1] * scalar; + return dest; + }; + + /** + * Calculates the euclidian distance between two vec2 + * + * Params: + * @param {vec2} vecA First vector + * @param {vec2} vecB Second vector + * + * @returns {number} Distance between vecA and vecB + */ + vec2.dist = function (vecA, vecB) { + var x = vecB[0] - vecA[0], + y = vecB[1] - vecA[1]; + return Math.sqrt(x*x + y*y); + }; + + /** + * Copies the values of one vec2 to another + * + * @param {vec2} vec vec2 containing values to copy + * @param {vec2} dest vec2 receiving copied values + * + * @returns {vec2} dest + */ + vec2.set = function (vec, dest) { + dest[0] = vec[0]; + dest[1] = vec[1]; + return dest; + }; + + /** + * Compares two vectors for equality within a certain margin of error + * + * @param {vec2} a First vector + * @param {vec2} b Second vector + * + * @returns {Boolean} True if a is equivalent to b + */ + vec2.equal = function (a, b) { + return a === b || ( + Math.abs(a[0] - b[0]) < FLOAT_EPSILON && + Math.abs(a[1] - b[1]) < FLOAT_EPSILON + ); + }; + + /** + * Negates the components of a vec2 + * + * @param {vec2} vec vec2 to negate + * @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vec + * + * @returns {vec2} dest if specified, vec otherwise + */ + vec2.negate = function (vec, dest) { + if (!dest) { dest = vec; } + dest[0] = -vec[0]; + dest[1] = -vec[1]; + return dest; + }; + + /** + * Normlize a vec2 + * + * @param {vec2} vec vec2 to normalize + * @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vec + * + * @returns {vec2} dest if specified, vec otherwise + */ + vec2.normalize = function (vec, dest) { + if (!dest) { dest = vec; } + var mag = vec[0] * vec[0] + vec[1] * vec[1]; + if (mag > 0) { + mag = Math.sqrt(mag); + dest[0] = vec[0] / mag; + dest[1] = vec[1] / mag; + } else { + dest[0] = dest[1] = 0; + } + return dest; + }; + + /** + * Computes the cross product of two vec2's. Note that the cross product must by definition + * produce a 3D vector. If a dest vector is given, it will contain the resultant 3D vector. + * Otherwise, a scalar number will be returned, representing the vector's Z coordinate, since + * its X and Y must always equal 0. + * + * Examples: + * var crossResult = vec3.create(); + * vec2.cross([1, 2], [3, 4], crossResult); + * //=> [0, 0, -2] + * + * vec2.cross([1, 2], [3, 4]); + * //=> -2 + * + * See http://stackoverflow.com/questions/243945/calculating-a-2d-vectors-cross-product + * for some interesting facts. + * + * @param {vec2} vecA left operand + * @param {vec2} vecB right operand + * @param {vec2} [dest] optional vec2 receiving result. If not specified a scalar is returned + * + */ + vec2.cross = function (vecA, vecB, dest) { + var z = vecA[0] * vecB[1] - vecA[1] * vecB[0]; + if (!dest) return z; + dest[0] = dest[1] = 0; + dest[2] = z; + return dest; + }; + + /** + * Caclulates the length of a vec2 + * + * @param {vec2} vec vec2 to calculate length of + * + * @returns {Number} Length of vec + */ + vec2.length = function (vec) { + var x = vec[0], y = vec[1]; + return Math.sqrt(x * x + y * y); + }; + + /** + * Caclulates the squared length of a vec2 + * + * @param {vec2} vec vec2 to calculate squared length of + * + * @returns {Number} Squared Length of vec + */ + vec2.squaredLength = function (vec) { + var x = vec[0], y = vec[1]; + return x * x + y * y; + }; + + /** + * Caclulates the dot product of two vec2s + * + * @param {vec2} vecA First operand + * @param {vec2} vecB Second operand + * + * @returns {Number} Dot product of vecA and vecB + */ + vec2.dot = function (vecA, vecB) { + return vecA[0] * vecB[0] + vecA[1] * vecB[1]; + }; + + /** + * Generates a 2D unit vector pointing from one vector to another + * + * @param {vec2} vecA Origin vec2 + * @param {vec2} vecB vec2 to point to + * @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vecA + * + * @returns {vec2} dest if specified, vecA otherwise + */ + vec2.direction = function (vecA, vecB, dest) { + if (!dest) { dest = vecA; } + + var x = vecA[0] - vecB[0], + y = vecA[1] - vecB[1], + len = x * x + y * y; + + if (!len) { + dest[0] = 0; + dest[1] = 0; + dest[2] = 0; + return dest; + } + + len = 1 / Math.sqrt(len); + dest[0] = x * len; + dest[1] = y * len; + return dest; + }; + + /** + * Performs a linear interpolation between two vec2 + * + * @param {vec2} vecA First vector + * @param {vec2} vecB Second vector + * @param {Number} lerp Interpolation amount between the two inputs + * @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vecA + * + * @returns {vec2} dest if specified, vecA otherwise + */ + vec2.lerp = function (vecA, vecB, lerp, dest) { + if (!dest) { dest = vecA; } + dest[0] = vecA[0] + lerp * (vecB[0] - vecA[0]); + dest[1] = vecA[1] + lerp * (vecB[1] - vecA[1]); + return dest; + }; + + /** + * Returns a string representation of a vector + * + * @param {vec2} vec Vector to represent as a string + * + * @returns {String} String representation of vec + */ + vec2.str = function (vec) { + return '[' + vec[0] + ', ' + vec[1] + ']'; + }; + + /** + * @class 2x2 Matrix + * @name mat2 + */ + var mat2 = {}; + + /** + * Creates a new 2x2 matrix. If src is given, the new matrix + * is initialized to those values. + * + * @param {mat2} [src] the seed values for the new matrix, if any + * @returns {mat2} a new matrix + */ + mat2.create = function(src) { + var dest = new MatrixArray(4); + + if (src) { + dest[0] = src[0]; + dest[1] = src[1]; + dest[2] = src[2]; + dest[3] = src[3]; + } else { + dest[0] = dest[1] = dest[2] = dest[3] = 0; + } + return dest; + }; + + /** + * Creates a new instance of a mat2, initializing it with the given arguments + * + * @param {number} m00 + * @param {number} m01 + * @param {number} m10 + * @param {number} m11 + + * @returns {mat2} New mat2 + */ + mat2.createFrom = function (m00, m01, m10, m11) { + var dest = new MatrixArray(4); + + dest[0] = m00; + dest[1] = m01; + dest[2] = m10; + dest[3] = m11; + + return dest; + }; + + /** + * Copies the values of one mat2 to another + * + * @param {mat2} mat mat2 containing values to copy + * @param {mat2} dest mat2 receiving copied values + * + * @returns {mat2} dest + */ + mat2.set = function (mat, dest) { + dest[0] = mat[0]; + dest[1] = mat[1]; + dest[2] = mat[2]; + dest[3] = mat[3]; + return dest; + }; + + /** + * Compares two matrices for equality within a certain margin of error + * + * @param {mat2} a First matrix + * @param {mat2} b Second matrix + * + * @returns {Boolean} True if a is equivalent to b + */ + mat2.equal = function (a, b) { + return a === b || ( + Math.abs(a[0] - b[0]) < FLOAT_EPSILON && + Math.abs(a[1] - b[1]) < FLOAT_EPSILON && + Math.abs(a[2] - b[2]) < FLOAT_EPSILON && + Math.abs(a[3] - b[3]) < FLOAT_EPSILON + ); + }; + + /** + * Sets a mat2 to an identity matrix + * + * @param {mat2} [dest] mat2 to set. If omitted a new one will be created. + * + * @returns {mat2} dest + */ + mat2.identity = function (dest) { + if (!dest) { dest = mat2.create(); } + dest[0] = 1; + dest[1] = 0; + dest[2] = 0; + dest[3] = 1; + return dest; + }; + + /** + * Transposes a mat2 (flips the values over the diagonal) + * + * @param {mat2} mat mat2 to transpose + * @param {mat2} [dest] mat2 receiving transposed values. If not specified result is written to mat + * + * @param {mat2} dest if specified, mat otherwise + */ + mat2.transpose = function (mat, dest) { + // If we are transposing ourselves we can skip a few steps but have to cache some values + if (!dest || mat === dest) { + var a00 = mat[1]; + mat[1] = mat[2]; + mat[2] = a00; + return mat; + } + + dest[0] = mat[0]; + dest[1] = mat[2]; + dest[2] = mat[1]; + dest[3] = mat[3]; + return dest; + }; + + /** + * Calculates the determinant of a mat2 + * + * @param {mat2} mat mat2 to calculate determinant of + * + * @returns {Number} determinant of mat + */ + mat2.determinant = function (mat) { + return mat[0] * mat[3] - mat[2] * mat[1]; + }; + + /** + * Calculates the inverse matrix of a mat2 + * + * @param {mat2} mat mat2 to calculate inverse of + * @param {mat2} [dest] mat2 receiving inverse matrix. If not specified result is written to mat + * + * @param {mat2} dest is specified, mat otherwise, null if matrix cannot be inverted + */ + mat2.inverse = function (mat, dest) { + if (!dest) { dest = mat; } + var a0 = mat[0], a1 = mat[1], a2 = mat[2], a3 = mat[3]; + var det = a0 * a3 - a2 * a1; + if (!det) return null; + + det = 1.0 / det; + dest[0] = a3 * det; + dest[1] = -a1 * det; + dest[2] = -a2 * det; + dest[3] = a0 * det; + return dest; + }; + + /** + * Performs a matrix multiplication + * + * @param {mat2} matA First operand + * @param {mat2} matB Second operand + * @param {mat2} [dest] mat2 receiving operation result. If not specified result is written to matA + * + * @returns {mat2} dest if specified, matA otherwise + */ + mat2.multiply = function (matA, matB, dest) { + if (!dest) { dest = matA; } + var a11 = matA[0], + a12 = matA[1], + a21 = matA[2], + a22 = matA[3]; + dest[0] = a11 * matB[0] + a12 * matB[2]; + dest[1] = a11 * matB[1] + a12 * matB[3]; + dest[2] = a21 * matB[0] + a22 * matB[2]; + dest[3] = a21 * matB[1] + a22 * matB[3]; + return dest; + }; + + /** + * Rotates a 2x2 matrix by an angle + * + * @param {mat2} mat The matrix to rotate + * @param {Number} angle The angle in radians + * @param {mat2} [dest] Optional mat2 receiving the result. If omitted mat will be used. + * + * @returns {mat2} dest if specified, mat otherwise + */ + mat2.rotate = function (mat, angle, dest) { + if (!dest) { dest = mat; } + var a11 = mat[0], + a12 = mat[1], + a21 = mat[2], + a22 = mat[3], + s = Math.sin(angle), + c = Math.cos(angle); + dest[0] = a11 * c + a12 * s; + dest[1] = a11 * -s + a12 * c; + dest[2] = a21 * c + a22 * s; + dest[3] = a21 * -s + a22 * c; + return dest; + }; + + /** + * Multiplies the vec2 by the given 2x2 matrix + * + * @param {mat2} matrix the 2x2 matrix to multiply against + * @param {vec2} vec the vector to multiply + * @param {vec2} [dest] an optional receiving vector. If not given, vec is used. + * + * @returns {vec2} The multiplication result + **/ + mat2.multiplyVec2 = function(matrix, vec, dest) { + if (!dest) dest = vec; + var x = vec[0], y = vec[1]; + dest[0] = x * matrix[0] + y * matrix[1]; + dest[1] = x * matrix[2] + y * matrix[3]; + return dest; + }; + + /** + * Scales the mat2 by the dimensions in the given vec2 + * + * @param {mat2} matrix the 2x2 matrix to scale + * @param {vec2} vec the vector containing the dimensions to scale by + * @param {vec2} [dest] an optional receiving mat2. If not given, matrix is used. + * + * @returns {mat2} dest if specified, matrix otherwise + **/ + mat2.scale = function(matrix, vec, dest) { + if (!dest) { dest = matrix; } + var a11 = matrix[0], + a12 = matrix[1], + a21 = matrix[2], + a22 = matrix[3], + b11 = vec[0], + b22 = vec[1]; + dest[0] = a11 * b11; + dest[1] = a12 * b22; + dest[2] = a21 * b11; + dest[3] = a22 * b22; + return dest; + }; + + /** + * Returns a string representation of a mat2 + * + * @param {mat2} mat mat2 to represent as a string + * + * @param {String} String representation of mat + */ + mat2.str = function (mat) { + return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] + ', ' + mat[3] + ']'; + }; + + /** + * @class 4 Dimensional Vector + * @name vec4 + */ + var vec4 = {}; + + /** + * Creates a new vec4, initializing it from vec if vec + * is given. + * + * @param {vec4} [vec] the vector's initial contents + * @returns {vec4} a new 2D vector + */ + vec4.create = function(vec) { + var dest = new MatrixArray(4); + + if (vec) { + dest[0] = vec[0]; + dest[1] = vec[1]; + dest[2] = vec[2]; + dest[3] = vec[3]; + } else { + dest[0] = 0; + dest[1] = 0; + dest[2] = 0; + dest[3] = 0; + } + return dest; + }; + + /** + * Creates a new instance of a vec4, initializing it with the given arguments + * + * @param {number} x X value + * @param {number} y Y value + * @param {number} z Z value + * @param {number} w W value + + * @returns {vec4} New vec4 + */ + vec4.createFrom = function (x, y, z, w) { + var dest = new MatrixArray(4); + + dest[0] = x; + dest[1] = y; + dest[2] = z; + dest[3] = w; + + return dest; + }; + + /** + * Adds the vec4's together. If dest is given, the result + * is stored there. Otherwise, the result is stored in vecB. + * + * @param {vec4} vecA the first operand + * @param {vec4} vecB the second operand + * @param {vec4} [dest] the optional receiving vector + * @returns {vec4} dest + */ + vec4.add = function(vecA, vecB, dest) { + if (!dest) dest = vecB; + dest[0] = vecA[0] + vecB[0]; + dest[1] = vecA[1] + vecB[1]; + dest[2] = vecA[2] + vecB[2]; + dest[3] = vecA[3] + vecB[3]; + return dest; + }; + + /** + * Subtracts vecB from vecA. If dest is given, the result + * is stored there. Otherwise, the result is stored in vecB. + * + * @param {vec4} vecA the first operand + * @param {vec4} vecB the second operand + * @param {vec4} [dest] the optional receiving vector + * @returns {vec4} dest + */ + vec4.subtract = function(vecA, vecB, dest) { + if (!dest) dest = vecB; + dest[0] = vecA[0] - vecB[0]; + dest[1] = vecA[1] - vecB[1]; + dest[2] = vecA[2] - vecB[2]; + dest[3] = vecA[3] - vecB[3]; + return dest; + }; + + /** + * Multiplies vecA with vecB. If dest is given, the result + * is stored there. Otherwise, the result is stored in vecB. + * + * @param {vec4} vecA the first operand + * @param {vec4} vecB the second operand + * @param {vec4} [dest] the optional receiving vector + * @returns {vec4} dest + */ + vec4.multiply = function(vecA, vecB, dest) { + if (!dest) dest = vecB; + dest[0] = vecA[0] * vecB[0]; + dest[1] = vecA[1] * vecB[1]; + dest[2] = vecA[2] * vecB[2]; + dest[3] = vecA[3] * vecB[3]; + return dest; + }; + + /** + * Divides vecA by vecB. If dest is given, the result + * is stored there. Otherwise, the result is stored in vecB. + * + * @param {vec4} vecA the first operand + * @param {vec4} vecB the second operand + * @param {vec4} [dest] the optional receiving vector + * @returns {vec4} dest + */ + vec4.divide = function(vecA, vecB, dest) { + if (!dest) dest = vecB; + dest[0] = vecA[0] / vecB[0]; + dest[1] = vecA[1] / vecB[1]; + dest[2] = vecA[2] / vecB[2]; + dest[3] = vecA[3] / vecB[3]; + return dest; + }; + + /** + * Scales vecA by some scalar number. If dest is given, the result + * is stored there. Otherwise, the result is stored in vecA. + * + * This is the same as multiplying each component of vecA + * by the given scalar. + * + * @param {vec4} vecA the vector to be scaled + * @param {Number} scalar the amount to scale the vector by + * @param {vec4} [dest] the optional receiving vector + * @returns {vec4} dest + */ + vec4.scale = function(vecA, scalar, dest) { + if (!dest) dest = vecA; + dest[0] = vecA[0] * scalar; + dest[1] = vecA[1] * scalar; + dest[2] = vecA[2] * scalar; + dest[3] = vecA[3] * scalar; + return dest; + }; + + /** + * Copies the values of one vec4 to another + * + * @param {vec4} vec vec4 containing values to copy + * @param {vec4} dest vec4 receiving copied values + * + * @returns {vec4} dest + */ + vec4.set = function (vec, dest) { + dest[0] = vec[0]; + dest[1] = vec[1]; + dest[2] = vec[2]; + dest[3] = vec[3]; + return dest; + }; + + /** + * Compares two vectors for equality within a certain margin of error + * + * @param {vec4} a First vector + * @param {vec4} b Second vector + * + * @returns {Boolean} True if a is equivalent to b + */ + vec4.equal = function (a, b) { + return a === b || ( + Math.abs(a[0] - b[0]) < FLOAT_EPSILON && + Math.abs(a[1] - b[1]) < FLOAT_EPSILON && + Math.abs(a[2] - b[2]) < FLOAT_EPSILON && + Math.abs(a[3] - b[3]) < FLOAT_EPSILON + ); + }; + + /** + * Negates the components of a vec4 + * + * @param {vec4} vec vec4 to negate + * @param {vec4} [dest] vec4 receiving operation result. If not specified result is written to vec + * + * @returns {vec4} dest if specified, vec otherwise + */ + vec4.negate = function (vec, dest) { + if (!dest) { dest = vec; } + dest[0] = -vec[0]; + dest[1] = -vec[1]; + dest[2] = -vec[2]; + dest[3] = -vec[3]; + return dest; + }; + + /** + * Caclulates the length of a vec2 + * + * @param {vec2} vec vec2 to calculate length of + * + * @returns {Number} Length of vec + */ + vec4.length = function (vec) { + var x = vec[0], y = vec[1], z = vec[2], w = vec[3]; + return Math.sqrt(x * x + y * y + z * z + w * w); + }; + + /** + * Caclulates the squared length of a vec4 + * + * @param {vec4} vec vec4 to calculate squared length of + * + * @returns {Number} Squared Length of vec + */ + vec4.squaredLength = function (vec) { + var x = vec[0], y = vec[1], z = vec[2], w = vec[3]; + return x * x + y * y + z * z + w * w; + }; + + /** + * Performs a linear interpolation between two vec4 + * + * @param {vec4} vecA First vector + * @param {vec4} vecB Second vector + * @param {Number} lerp Interpolation amount between the two inputs + * @param {vec4} [dest] vec4 receiving operation result. If not specified result is written to vecA + * + * @returns {vec4} dest if specified, vecA otherwise + */ + vec4.lerp = function (vecA, vecB, lerp, dest) { + if (!dest) { dest = vecA; } + dest[0] = vecA[0] + lerp * (vecB[0] - vecA[0]); + dest[1] = vecA[1] + lerp * (vecB[1] - vecA[1]); + dest[2] = vecA[2] + lerp * (vecB[2] - vecA[2]); + dest[3] = vecA[3] + lerp * (vecB[3] - vecA[3]); + return dest; + }; + + /** + * Returns a string representation of a vector + * + * @param {vec4} vec Vector to represent as a string + * + * @returns {String} String representation of vec + */ + vec4.str = function (vec) { + return '[' + vec[0] + ', ' + vec[1] + ', ' + vec[2] + ', ' + vec[3] + ']'; + }; + + /* + * Exports + */ + + if(root) { + root.glMatrixArrayType = MatrixArray; + root.MatrixArray = MatrixArray; + root.setMatrixArrayType = setMatrixArrayType; + root.determineMatrixArrayType = determineMatrixArrayType; + root.glMath = glMath; + root.vec2 = vec2; + root.vec3 = vec3; + root.vec4 = vec4; + root.mat2 = mat2; + root.mat3 = mat3; + root.mat4 = mat4; + root.quat4 = quat4; + } + + return { + glMatrixArrayType: MatrixArray, + MatrixArray: MatrixArray, + setMatrixArrayType: setMatrixArrayType, + determineMatrixArrayType: determineMatrixArrayType, + glMath: glMath, + vec2: vec2, + vec3: vec3, + vec4: vec4, + mat2: mat2, + mat3: mat3, + mat4: mat4, + quat4: quat4 + }; +})); diff --git a/waves/noise3D.js b/waves/noise3D.js new file mode 100644 index 0000000..d519f47 --- /dev/null +++ b/waves/noise3D.js @@ -0,0 +1,316 @@ +(function(exports) { + "use strict"; + /*global window,vec3*/ + + exports = exports || window; + + function step(edge, x) { + return [ + (x[0] < edge[0]) ? 0.0 : 1.0, + (x[1] < edge[1]) ? 0.0 : 1.0, + (x[2] < edge[2]) ? 0.0 : 1.0 + ]; + } + + function step_vec4(edge, x) { + return [ + (x[0] < edge[0]) ? 0.0 : 1.0, + (x[1] < edge[1]) ? 0.0 : 1.0, + (x[2] < edge[2]) ? 0.0 : 1.0, + (x[3] < edge[3]) ? 0.0 : 1.0 + ]; + } + + function min(x, y) { + return [ + y[0] < x[0] ? y[0] : x[0], + y[1] < x[1] ? y[1] : x[1], + y[2] < x[2] ? y[2] : x[2] + ]; + } + + function max(x, y) { + return [ + y[0] > x[0] ? y[0] : x[0], + y[1] > x[1] ? y[1] : x[1], + y[2] > x[2] ? y[2] : x[2] + ]; + } + + function max_vec4(x, y) { + return [ + y[0] > x[0] ? y[0] : x[0], + y[1] > x[1] ? y[1] : x[1], + y[2] > x[2] ? y[2] : x[2], + y[3] > x[3] ? y[3] : x[3] + ]; + } + + function vec4_dot(left, right) { + return left[0] * right[0] + + left[1] * right[1] + + left[2] * right[2] + + left[3] * right[3]; + } + + // + // Description : Array and textureless GLSL 2D/3D/4D simplex + // noise functions. + // Author : Ian McEwan, Ashima Arts. + // Maintainer : ijm + // Lastmod : 20110822 (ijm) + // License : Copyright (C) 2011 Ashima Arts. All rights reserved. + // Distributed under the MIT License. See LICENSE file. + // https://github.com/ashima/webgl-noise + // + function mod289_vec3(x) { + var temp = (1.0 / 289.0); + return [ + x[0] - Math.floor(x[0] * temp) * 289.0, + x[1] - Math.floor(x[1] * temp) * 289.0, + x[2] - Math.floor(x[2] * temp) * 289.0 + ]; + } + + function mod289_vec4(x) { + var temp = (1.0 / 289.0); + return [ + x[0] - Math.floor(x[0] * temp) * 289.0, + x[1] - Math.floor(x[1] * temp) * 289.0, + x[2] - Math.floor(x[2] * temp) * 289.0, + x[3] - Math.floor(x[3] * temp) * 289.0 + ]; + } + + function permute_vec4(x) { + return mod289_vec4([ + ((x[0]*34.0)+1.0)*x[0], + ((x[1]*34.0)+1.0)*x[1], + ((x[2]*34.0)+1.0)*x[2], + ((x[3]*34.0)+1.0)*x[3] + ]); + } + + function taylorInvSqrt_vec4(r) { + return [ + 1.79284291400159 - 0.85373472095314 * r[0], + 1.79284291400159 - 0.85373472095314 * r[1], + 1.79284291400159 - 0.85373472095314 * r[2], + 1.79284291400159 - 0.85373472095314 * r[3] + ]; + } + + exports.snoise = function(v) { + // const vec2 C = vec2(1.0f/6.0f, 1.0f/3.0f) ; + // const vec4 D = vec4(0.0f, 0.5f, 1.0f, 2.0f); + var C = [1.0/6.0, 1.0/3.0]; + var D = [0.0, 0.5, 1.0, 2.0]; + + // vec3 i = floor(v + dot(v, vec3(C.y, C.y, C.y)) ); + // vec3 x0 = v - i + dot(i, vec3(C.x, C.x, C.x) ); + var temp0 = vec3.create(); + var temp3 = vec3.dot(v, [C[1], C[1], C[1]]); + vec3.add(v, [temp3, temp3, temp3], temp0); + var i = [Math.floor(temp0[0]), Math.floor(temp0[1]), Math.floor(temp0[2])]; + var temp1 = vec3.create(); + vec3.subtract(v, i, temp1); + var temp2 = vec3.dot(i, [C[0], C[0], C[0]]); + var x0 = vec3.create(); + vec3.add(temp1, [temp2, temp2, temp2], x0); + + // vec3 g = step(vec3(x0.y, x0.z, x0.x), vec3(x0.x, x0.y, x0.z)); + // vec3 l = 1.0f - g; + // vec3 i1 = min( vec3(g.x, g.y, g.z), vec3(l.z, l.x, l.y) ); + // vec3 i2 = max( vec3(g.x, g.y, g.z), vec3(l.z, l.x, l.y) ); + var g = step([x0[1], x0[2], x0[0]], [x0[0], x0[1], x0[2]]); + var l = [1.0 - g[0], 1.0 - g[1], 1.0 - g[2]]; + var i1 = min([g[0], g[1], g[2]], [l[2], l[0], l[1]]); + var i2 = max([g[0], g[1], g[2]], [l[2], l[0], l[1]]); + + // vec3 x1 = x0 - i1 + vec3(C.x, C.x, C.x); + // vec3 x2 = x0 - i2 + vec3(C.y, C.y, C.y); // 2.0*C.x = 1/3 = C.y + // vec3 x3 = x0 - vec3(D.y, D.y, D.y); // -1.0+3.0*C.x = -0.5 = -D.y + var temp4 = vec3.create(); + vec3.subtract(x0, i1, temp4); + var x1 = vec3.create(); + vec3.add(temp4, [C[0], C[0], C[0]], x1); + var temp5 = vec3.create(); + vec3.subtract(x0, i2, temp5); + var x2 = vec3.create(); + vec3.add(temp5, [C[1], C[1], C[1]], x2); + var x3 = vec3.create(); + vec3.subtract(x0, [D[1], D[1], D[1]], x3); + + // i = mod289(i); + // vec4 p = permute( permute( permute( + // i.z + vec4(0.0, i1.z, i2.z, 1.0 )) + // + i.y + vec4(0.0, i1.y, i2.y, 1.0 )) + // + i.x + vec4(0.0, i1.x, i2.x, 1.0 )); + i = mod289_vec3(i); + var p = permute_vec4([i[2] + 0.0, i[2] + i1[2], i[2] + i2[2], i[2] + 1.0]); + p[0] += i[1] + 0.0; + p[1] += i[1] + i1[1]; + p[2] += i[1] + i2[1]; + p[3] += i[1] + 1.0; + p = permute_vec4(p); + p[0] += i[0] + 0.0; + p[1] += i[0] + i1[0]; + p[2] += i[0] + i2[0]; + p[3] += i[0] + 1.0; + p = permute_vec4(p); + + // float n_ = 0.142857142857f; // 1.0/7.0 + // vec3 ns = n_ * vec3(D.w, D.y, D.z) - vec3(D.x, D.z, D.x); +// var n_ = 0.142857142857; // 1.0/7.0 +// var ns = [ +// n_ * D[3] - D[0], +// n_ * D[1] - D[2], +// n_ * D[2] - D[0] +// ]; + var ns = [ + 0.28571430, + -0.92857140, + 0.14285715 + ]; + + // vec4 j = p - 49.0f * floor(p * ns.z * ns.z); // mod(p,7*7) + var j = [ + p[0] - 49.0 * Math.floor(p[0] * ns[2] * ns[2]), + p[1] - 49.0 * Math.floor(p[1] * ns[2] * ns[2]), + p[2] - 49.0 * Math.floor(p[2] * ns[2] * ns[2]), + p[3] - 49.0 * Math.floor(p[3] * ns[2] * ns[2]) + ]; + + // vec4 x_ = floor(j * ns.z); + // vec4 y_ = floor(j - 7.0f * x_ ); // mod(j,N) + var x_ = [ + Math.floor(j[0] * ns[2]), + Math.floor(j[1] * ns[2]), + Math.floor(j[2] * ns[2]), + Math.floor(j[3] * ns[2]) + ]; + var y_ = [ + Math.floor(j[0] - 7.0 * x_[0] ), + Math.floor(j[1] - 7.0 * x_[1] ), + Math.floor(j[2] - 7.0 * x_[2] ), + Math.floor(j[3] - 7.0 * x_[3] ) + ]; + + // vec4 x = x_ *ns.x + vec4(ns.y, ns.y, ns.y, ns.y); + // vec4 y = y_ *ns.x + vec4(ns.y, ns.y, ns.y, ns.y); + // vec4 h = 1.0f - abs(x) - abs(y); + var x = [ + x_[0] *ns[0] + ns[1], + x_[1] *ns[0] + ns[1], + x_[2] *ns[0] + ns[1], + x_[3] *ns[0] + ns[1] + ]; + var y = [ + y_[0] *ns[0] + ns[1], + y_[1] *ns[0] + ns[1], + y_[2] *ns[0] + ns[1], + y_[3] *ns[0] + ns[1] + ]; + var h = [ + 1.0 - Math.abs(x[0]) - Math.abs(y[0]), + 1.0 - Math.abs(x[1]) - Math.abs(y[1]), + 1.0 - Math.abs(x[2]) - Math.abs(y[2]), + 1.0 - Math.abs(x[3]) - Math.abs(y[3]) + ]; + + // vec4 b0 = vec4( vec2(x.x, x.y), vec2(y.x, y.y) ); + // vec4 b1 = vec4( vec2(x.z, x.w), vec2(y.z, y.w) ); + var b0 = [x[0], x[1], y[0], y[1]]; + var b1 = [x[2], x[3], y[2], y[3]]; + + // vec4 s0 = floor(b0)*2.0f + 1.0f; + // vec4 s1 = floor(b1)*2.0f + 1.0f; + // vec4 sh = -step(h, vec4(0.0)); + + var s0 = [ + Math.floor(b0[0])*2.0 + 1.0, + Math.floor(b0[1])*2.0 + 1.0, + Math.floor(b0[2])*2.0 + 1.0, + Math.floor(b0[3])*2.0 + 1.0 + ]; + var s1 = [ + Math.floor(b1[0])*2.0 + 1.0, + Math.floor(b1[1])*2.0 + 1.0, + Math.floor(b1[2])*2.0 + 1.0, + Math.floor(b1[3])*2.0 + 1.0 + ]; + var sh = step_vec4(h, [0.0, 0.0, 0.0, 0.0]); + sh[0] = -sh[0]; + sh[1] = -sh[1]; + sh[2] = -sh[2]; + sh[3] = -sh[3]; + + // vec4 a0 = vec4(b0.x, b0.z, b0.y, b0.w) + vec4(s0.x, s0.z, s0.y, s0.w) * vec4(sh.x, sh.x, sh.y, sh.y) ; + // vec4 a1 = vec4(b1.x, b1.z, b1.y, b1.w) + vec4(s1.x, s1.z, s1.y, s1.w) * vec4(sh.z, sh.z, sh.w, sh.w) ; + var a0 = [ + b0[0] + s0[0] * sh[0], + b0[2] + s0[2] * sh[0], + b0[1] + s0[1] * sh[1], + b0[3] + s0[3] * sh[1] + ]; + var a1 = [ + b1[0] + s1[0] * sh[2], + b1[2] + s1[2] * sh[2], + b1[1] + s1[1] * sh[3], + b1[3] + s1[3] * sh[3] + ]; + + // vec3 p0 = vec3(a0.x, a0.y, h.x); + // vec3 p1 = vec3(a0.z, a0.w, h.y); + // vec3 p2 = vec3(a1.x, a1.y, h.z); + // vec3 p3 = vec3(a1.z, a1.w, h.w); + var p0 = [a0[0], a0[1], h[0]]; + var p1 = [a0[2], a0[3], h[1]]; + var p2 = [a1[0], a1[1], h[2]]; + var p3 = [a1[2], a1[3], h[3]]; + + // vec4 norm = taylorInvSqrt(vec4(dot(p0,p0), dot(p1,p1), dot(p2, p2), dot(p3,p3))); + // p0 *= norm.x; + // p1 *= norm.y; + // p2 *= norm.z; + // p3 *= norm.w; + var norm = taylorInvSqrt_vec4([vec3.dot(p0,p0), vec3.dot(p1,p1), vec3.dot(p2, p2), vec3.dot(p3,p3)]); + p0 = [p0[0]*norm[0], p0[1]*norm[0], p0[2]*norm[0]]; + p1 = [p1[0]*norm[1], p1[1]*norm[1], p1[2]*norm[1]]; + p2 = [p2[0]*norm[2], p2[1]*norm[2], p2[2]*norm[2]]; + p3 = [p3[0]*norm[3], p3[1]*norm[3], p3[2]*norm[3]]; + + // vec4 m = max(0.6f - vec4(dot(x0,x0), dot(x1,x1), dot(x2,x2), dot(x3,x3)), 0.0); + // m = m * m; + var m = max_vec4([ + 0.6 - vec3.dot(x0,x0), + 0.6 - vec3.dot(x1,x1), + 0.6 - vec3.dot(x2,x2), + 0.6 - vec3.dot(x3,x3) + ], [ + 0.0, + 0.0, + 0.0, + 0.0 + ]); + m[0] *= m[0]; + m[1] *= m[1]; + m[2] *= m[2]; + m[3] *= m[3]; + + // return 42.0f * dot( m*m, vec4( dot(p0,x0), dot(p1,x1), + // dot(p2,x2), dot(p3,x3) ) ); + return 42.0 * vec4_dot([ + m[0] * m[0], + m[1] * m[1], + m[2] * m[2], + m[3] * m[3] + ], [ + vec3.dot(p0,x0), + vec3.dot(p1,x1), + vec3.dot(p2,x2), + vec3.dot(p3,x3) + ]); + }; + +}()); diff --git a/waves/simplex.vert b/waves/simplex.vert new file mode 100644 index 0000000..13dd1ca --- /dev/null +++ b/waves/simplex.vert @@ -0,0 +1,39 @@ +vec3 permute(vec3 x) { + x = ((x*34.0)+1.0)*x; + return x - floor(x * (1.0 / 289.0)) * 289.0; +} + +float simplexNoise(vec2 v) + { + const vec4 C = vec4(0.211324865405187, 0.366025403784439, -0.577350269189626, 0.024390243902439); + + vec2 i = floor(v + dot(v, C.yy) ); + vec2 x0 = v - i + dot(i, C.xx); + + vec2 i1; + i1 = (x0.x > x0.y) ? vec2(1.0, 0.0) : vec2(0.0, 1.0); + + vec4 x12 = x0.xyxy + C.xxzz; + x12.xy -= i1; + + i = i - floor(i * (1.0 / 289.0)) * 289.0; + + vec3 p = permute( permute( i.y + vec3(0.0, i1.y, 1.0 )) + + i.x + vec3(0.0, i1.x, 1.0 )); + + vec3 m = max(0.5 - vec3(dot(x0,x0), dot(x12.xy,x12.xy), dot(x12.zw,x12.zw)), 0.0); + m = m*m ; + m = m*m ; + + vec3 x = 2.0 * fract(p * C.www) - 1.0; + vec3 h = abs(x) - 0.5; + vec3 ox = floor(x + 0.5); + vec3 a0 = x - ox; + + m *= inversesqrt( a0*a0 + h*h ); + + vec3 g; + g.x = a0.x * x0.x + h.x * x0.y; + g.yz = a0.yz * x12.xz + h.yz * x12.yw; + return 130.0 * dot(m, g); +} \ No newline at end of file diff --git a/waves/simplex_wave.html b/waves/simplex_wave.html new file mode 100644 index 0000000..15b6c76 --- /dev/null +++ b/waves/simplex_wave.html @@ -0,0 +1,86 @@ +<html> + +<head> +<title>Vertex Simplex Noise Wave</title> +<meta charset ="utf-8"> +<meta http-equiv="X-UA-Compatible" content="chrome=1"> <!-- Use Chrome Frame in IE --> +</head> + +<body> +<div id="message" style="position:absolute;top:100px"></div> <!-- Pixel offset to avoid FPS counter --> +<canvas id="canvas" style="border: none;" width="1024" height="768" tabindex="1"></canvas> + +<script id="vs" type="x-shader/x-vertex"> + attribute vec2 position; + + uniform mat4 u_modelViewPerspective; + uniform float u_time; + varying float height; + + vec3 permute(vec3 x) { + x = ((x*34.0)+1.0)*x; + return x - floor(x * (1.0 / 289.0)) * 289.0; + } + + float simplexNoise(vec2 v) + { + const vec4 C = vec4(0.211324865405187, 0.366025403784439, -0.577350269189626, 0.024390243902439); + + vec2 i = floor(v + dot(v, C.yy) ); + vec2 x0 = v - i + dot(i, C.xx); + + vec2 i1; + i1 = (x0.x > x0.y) ? vec2(1.0, 0.0) : vec2(0.0, 1.0); + + vec4 x12 = x0.xyxy + C.xxzz; + x12.xy -= i1; + + i = i - floor(i * (1.0 / 289.0)) * 289.0; + + vec3 p = permute( permute( i.y + vec3(0.0, i1.y, 1.0 )) + + i.x + vec3(0.0, i1.x, 1.0 )); + + vec3 m = max(0.5 - vec3(dot(x0,x0), dot(x12.xy,x12.xy), dot(x12.zw,x12.zw)), 0.0); + m = m*m ; + m = m*m ; + + vec3 x = 2.0 * fract(p * C.www) - 1.0; + vec3 h = abs(x) - 0.5; + vec3 ox = floor(x + 0.5); + vec3 a0 = x - ox; + + m *= inversesqrt( a0*a0 + h*h ); + + vec3 g; + g.x = a0.x * x0.x + h.x * x0.y; + g.yz = a0.yz * x12.xz + h.yz * x12.yw; + return 130.0 * dot(m, g); + } + + void main(void) + { + vec2 simplexVec = vec2(u_time, position); + float s_contrib = simplexNoise(simplexVec); + float t_contrib = simplexNoise(vec2(s_contrib,u_time)); + height = s_contrib*t_contrib; + gl_Position = u_modelViewPerspective * vec4(vec3(position, height), 1.0); + } +</script> + +<script id="fs" type="x-shader/x-fragment"> + precision mediump float; + + varying float height; + void main(void) + { + //Height ranges from -1 to 1. Scale appropriately + gl_FragColor = vec4(mix(vec3(1.0, 0.0,0.0), vec3(0.0,0.0,1.0), (height*0.5+0.5)),1.0); + } +</script> + +<script src ="gl-matrix.js" type ="text/javascript"></script> +<script src ="webGLUtility.js" type ="text/javascript"></script> +<script src ="vert_wave.js" type ="text/javascript"></script> +</body> + +</html> diff --git a/waves/vert_wave.html b/waves/vert_wave.html new file mode 100644 index 0000000..3f6f690 --- /dev/null +++ b/waves/vert_wave.html @@ -0,0 +1,45 @@ +<html> + +<head> +<title>Vertex Sine Wave</title> +<meta charset ="utf-8"> +<meta http-equiv="X-UA-Compatible" content="chrome=1"> <!-- Use Chrome Frame in IE --> +</head> + +<body> +<div id="message" style="position:absolute;top:100px"></div> <!-- Pixel offset to avoid FPS counter --> +<canvas id="canvas" style="border: none;" width="1024" height="768" tabindex="1"></canvas> + +<script id="vs" type="x-shader/x-vertex"> + attribute vec2 position; + + uniform mat4 u_modelViewPerspective; + uniform float u_time; + varying float height; + + void main(void) + { + float s_contrib = sin(position.x*2.0*3.14159 + u_time); + float t_contrib = cos(position.y*2.0*3.14159 + u_time); + height = s_contrib*t_contrib; + gl_Position = u_modelViewPerspective * vec4(vec3(position, height), 1.0); + } +</script> + +<script id="fs" type="x-shader/x-fragment"> + precision mediump float; + + varying float height; + void main(void) + { + //Height ranges from -1 to 1. Scale appropriately + gl_FragColor = vec4(mix(vec3(1.0, 0.0,0.0), vec3(0.0,0.0,1.0), (height*0.5+0.5)),1.0); + } +</script> + +<script src ="gl-matrix.js" type ="text/javascript"></script> +<script src ="webGLUtility.js" type ="text/javascript"></script> +<script src ="vert_wave.js" type ="text/javascript"></script> +</body> + +</html> diff --git a/waves/vert_wave.js b/waves/vert_wave.js new file mode 100644 index 0000000..433541e --- /dev/null +++ b/waves/vert_wave.js @@ -0,0 +1,157 @@ +(function() { + "use strict"; + /*global window,document,Float32Array,Uint16Array,mat4,vec3,snoise*/ + /*global getShaderSource,createWebGLContext,createProgram*/ + + var NUM_WIDTH_PTS = 32; + var NUM_HEIGHT_PTS = 32; + + var message = document.getElementById("message"); + var canvas = document.getElementById("canvas"); + var context = createWebGLContext(canvas, message); + if (!context) { + return; + } + + /////////////////////////////////////////////////////////////////////////// + + context.viewport(0, 0, canvas.width, canvas.height); + context.clearColor(1.0, 1.0, 1.0, 1.0); + context.enable(context.DEPTH_TEST); + + var persp = mat4.create(); + mat4.perspective(45.0, 0.5, 0.1, 100.0, persp); + + var eye = [2.0, 1.0, 3.0]; + var center = [0.0, 0.0, 0.0]; + var up = [0.0, 0.0, 1.0]; + var view = mat4.create(); + mat4.lookAt(eye, center, up, view); + + var positionLocation = 0; + var heightLocation = 1; + var u_modelViewPerspectiveLocation; + var u_timeLocation; + + + (function initializeShader() { + var program; + var vs = getShaderSource(document.getElementById("vs")); + var fs = getShaderSource(document.getElementById("fs")); + + var program = createProgram(context, vs, fs, message); + context.bindAttribLocation(program, positionLocation, "position"); + u_timeLocation = context.getUniformLocation(program,"u_time"); + u_modelViewPerspectiveLocation = context.getUniformLocation(program,"u_modelViewPerspective"); + context.useProgram(program); + })(); + + var heights; + var numberOfIndices; + + (function initializeGrid() { + function uploadMesh(positions, heights, indices) { + // Positions + var positionsName = context.createBuffer(); + context.bindBuffer(context.ARRAY_BUFFER, positionsName); + context.bufferData(context.ARRAY_BUFFER, positions, context.STATIC_DRAW); + context.vertexAttribPointer(positionLocation, 2, context.FLOAT, false, 0, 0); + context.enableVertexAttribArray(positionLocation); + + if (heights) + { + // Heights + var heightsName = context.createBuffer(); + context.bindBuffer(context.ARRAY_BUFFER, heightsName); + context.bufferData(context.ARRAY_BUFFER, heights.length * heights.BYTES_PER_ELEMENT, context.STREAM_DRAW); + context.vertexAttribPointer(heightLocation, 1, context.FLOAT, false, 0, 0); + context.enableVertexAttribArray(heightLocation); + } + + // Indices + var indicesName = context.createBuffer(); + context.bindBuffer(context.ELEMENT_ARRAY_BUFFER, indicesName); + context.bufferData(context.ELEMENT_ARRAY_BUFFER, indices, context.STATIC_DRAW); + } + + var WIDTH_DIVISIONS = NUM_WIDTH_PTS - 1; + var HEIGHT_DIVISIONS = NUM_HEIGHT_PTS - 1; + + var numberOfPositions = NUM_WIDTH_PTS * NUM_HEIGHT_PTS; + + var positions = new Float32Array(2 * numberOfPositions); + var indices = new Uint16Array(2 * ((NUM_HEIGHT_PTS * (NUM_WIDTH_PTS - 1)) + (NUM_WIDTH_PTS * (NUM_HEIGHT_PTS - 1)))); + + var positionsIndex = 0; + var indicesIndex = 0; + var length; + + for (var j = 0; j < NUM_WIDTH_PTS; ++j) + { + positions[positionsIndex++] = j /(NUM_WIDTH_PTS - 1); + positions[positionsIndex++] = 0.0; + + if (j>=1) + { + length = positionsIndex / 2; + indices[indicesIndex++] = length - 2; + indices[indicesIndex++] = length - 1; + } + } + + for (var i = 0; i < HEIGHT_DIVISIONS; ++i) + { + var v = (i + 1) / (NUM_HEIGHT_PTS - 1); + positions[positionsIndex++] = 0.0; + positions[positionsIndex++] = v; + + length = (positionsIndex / 2); + indices[indicesIndex++] = length - 1; + indices[indicesIndex++] = length - 1 - NUM_WIDTH_PTS; + + for (var k = 0; k < WIDTH_DIVISIONS; ++k) + { + positions[positionsIndex++] = (k + 1) / (NUM_WIDTH_PTS - 1); + positions[positionsIndex++] = v; + + length = positionsIndex / 2; + var new_pt = length - 1; + indices[indicesIndex++] = new_pt - 1; // Previous side + indices[indicesIndex++] = new_pt; + + indices[indicesIndex++] = new_pt - NUM_WIDTH_PTS; // Previous bottom + indices[indicesIndex++] = new_pt; + } + } + + uploadMesh(positions, heights, indices); + numberOfIndices = indices.length; + })(); + + var time = 0.0; + var delT = 0.01; + (function animate(){ + /////////////////////////////////////////////////////////////////////////// + // Update + + var model = mat4.create(); + mat4.identity(model); + mat4.translate(model, [-0.5, -0.5, 0.0]); + var mv = mat4.create(); + mat4.multiply(view, model, mv); + var mvp = mat4.create(); + mat4.multiply(persp, mv, mvp); + time = time + delT; + + /////////////////////////////////////////////////////////////////////////// + // Render + context.clear(context.COLOR_BUFFER_BIT | context.DEPTH_BUFFER_BIT); + + context.uniformMatrix4fv(u_modelViewPerspectiveLocation, false, mvp); + context.uniform1f(u_timeLocation, time); + context.drawElements(context.LINES, numberOfIndices, context.UNSIGNED_SHORT,0); + + window.requestAnimFrame(animate); + })(); + +}()); diff --git a/waves/water_wave.html b/waves/water_wave.html new file mode 100644 index 0000000..1f22a26 --- /dev/null +++ b/waves/water_wave.html @@ -0,0 +1,50 @@ +<html> + +<head> +<title>Water Wave</title> +<meta charset ="utf-8"> +<meta http-equiv="X-UA-Compatible" content="chrome=1"> <!-- Use Chrome Frame in IE --> +</head> + +<body> +<div id="message" style="position:absolute;top:100px"></div> <!-- Pixel offset to avoid FPS counter --> +<canvas id="canvas" style="border: none;" width="1024" height="768" tabindex="1"></canvas> + +<script id="vs" type="x-shader/x-vertex"> + attribute vec2 position; + + uniform mat4 u_modelViewPerspective; + uniform float u_time; + varying float height; + + void main(void) + { + vec2 waveDir = normalize(vec2(1.0,-1.0));//Direction of wave in X Y plane + //Projection of position onto wave direction from origin gives time offset + //Constant factor here is cosmetic + float wavefrontFactor = 3.0*dot(position, waveDir); + + //Constants here are cosmetic + vec2 hor_perturb = 0.15*waveDir*(cos(u_time*3.14159 + wavefrontFactor)); + height = 0.25*sin(u_time*3.14159 + wavefrontFactor); + gl_Position = u_modelViewPerspective * vec4(vec3(position+hor_perturb, height), 1.0); + } +</script> + +<script id="fs" type="x-shader/x-fragment"> + precision mediump float; + + varying float height; + void main(void) + { + //Height ranges from -1 to 1. Scale appropriately + gl_FragColor = vec4(mix(vec3(1.0, 0.0,0.0), vec3(0.0,0.0,1.0), (height*0.5+0.5)),1.0); + } +</script> + +<script src ="gl-matrix.js" type ="text/javascript"></script> +<script src ="webGLUtility.js" type ="text/javascript"></script> +<script src ="vert_wave.js" type ="text/javascript"></script> +</body> + +</html> diff --git a/waves/webGLUtility.js b/waves/webGLUtility.js new file mode 100644 index 0000000..ae19646 --- /dev/null +++ b/waves/webGLUtility.js @@ -0,0 +1,112 @@ +(function(exports) { + "use strict"; + /*global window*/ + + exports = exports || window; + + /////////////////////////////////////////////////////////////////////////// + // Shim from http://paulirish.com/2011/requestanimationframe-for-smart-animating/ + + exports.requestAnimFrame = + window.requestAnimationFrame || + window.webkitRequestAnimationFrame || + window.mozRequestAnimationFrame || + window.oRequestAnimationFrame || + window.msRequestAnimationFrame || + function( callback ){ + window.setTimeout(callback, 1000 / 60); + }; + + /////////////////////////////////////////////////////////////////////////// + // getShader based on http://learningwebgl.com/cookbook/index.php/Loading_shaders_from_HTML_script_tags + + exports.getShaderSource = function(script) { + var str = ""; + var k = script.firstChild; + while (k) { + if (k.nodeType == 3) { + str += k.textContent; + } + k = k.nextSibling; + } + + return str; + }; + + /////////////////////////////////////////////////////////////////////////// + + exports.createWebGLContext = function(canvas, message) { + if (!window.WebGLRenderingContext) { + message.innerText = "The browser does not support WebGL. Visit http://get.webgl.org."; + return undefined; + } + var options = { alpha: false }; + var context = canvas.getContext("experimental-webgl", options); + + if (!context && message) { + message.innerText = "The browser supports WebGL, but initialization failed."; + } + + return context; + }; + + exports.createProgram = function(context, vertexShaderSource, fragmentShaderSource, message) { + var program = context.createProgram(); + var vs = context.createShader(context.VERTEX_SHADER); + var fs = context.createShader(context.FRAGMENT_SHADER); + + context.attachShader(program, vs); + context.attachShader(program, fs); + + // Mark shader for deletion when the program is deleted + context.deleteShader(vs); + context.deleteShader(fs); + + context.shaderSource(vs, vertexShaderSource); + context.compileShader(vs); + if (!context.getShaderParameter(vs, context.COMPILE_STATUS)) { + if (message) { + message.innerText += context.getShaderInfoLog(vs) + "\n"; + alert(context.getShaderInfoLog(vs)); + } + else + { + alert(context.getShaderInfoLog(vs)); + } + context.deleteProgram(program); + return; + } + + context.shaderSource(fs, fragmentShaderSource); + context.compileShader(fs); + if (!context.getShaderParameter(fs, context.COMPILE_STATUS)) { + if (message) { + message.innerText += context.getShaderInfoLog(fs) + "\n"; + alert(context.getShaderInfoLog(fs)); + } + else + { + alert(context.getShaderInfoLog(fs)); + } + context.deleteProgram(program); + return; + } + + context.linkProgram(program); + if (!context.getProgramParameter(program, context.LINK_STATUS)) { + if (message) { + message.innerText += context.getProgramInfoLog(program) + "\n"; + alert(context.getShaderInfoLog(program)); + } + else + { + alert(context.getShaderInfoLog(program)); + } + context.deleteProgram(program); + return; + } + + return program; + }; + +}()); From 7af23f67c06e43bbd447360de5284b482b35b0a5 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Mon, 4 Nov 2013 15:41:06 -0500 Subject: [PATCH 08/27] Deleted old directory. --- part1/gl-matrix.js | 3456 --------------------------------------- part1/noise3D.js | 316 ---- part1/simplex.vert | 39 - part1/simplex_wave.html | 86 - part1/vert_wave.html | 45 - part1/vert_wave.js | 157 -- part1/water_wave.html | 50 - part1/webGLUtility.js | 112 -- 8 files changed, 4261 deletions(-) delete mode 100644 part1/gl-matrix.js delete mode 100644 part1/noise3D.js delete mode 100644 part1/simplex.vert delete mode 100644 part1/simplex_wave.html delete mode 100644 part1/vert_wave.html delete mode 100644 part1/vert_wave.js delete mode 100644 part1/water_wave.html delete mode 100644 part1/webGLUtility.js diff --git a/part1/gl-matrix.js b/part1/gl-matrix.js deleted file mode 100644 index 5718055..0000000 --- a/part1/gl-matrix.js +++ /dev/null @@ -1,3456 +0,0 @@ -/** - * @fileoverview gl-matrix - High performance matrix and vector operations for WebGL - * @author Brandon Jones - * @author Colin MacKenzie IV - * @version 1.3.7 - */ - -/* - * Copyright (c) 2012 Brandon Jones, Colin MacKenzie IV - * - * This software is provided 'as-is', without any express or implied - * warranty. In no event will the authors be held liable for any damages - * arising from the use of this software. - * - * Permission is granted to anyone to use this software for any purpose, - * including commercial applications, and to alter it and redistribute it - * freely, subject to the following restrictions: - * - * 1. The origin of this software must not be misrepresented; you must not - * claim that you wrote the original software. If you use this software - * in a product, an acknowledgment in the product documentation would be - * appreciated but is not required. - * - * 2. Altered source versions must be plainly marked as such, and must not - * be misrepresented as being the original software. - * - * 3. This notice may not be removed or altered from any source - * distribution. - */ - -// Updated to use a modification of the "returnExportsGlobal" pattern from https://github.com/umdjs/umd - -(function (root, factory) { - if (typeof exports === 'object') { - // Node. Does not work with strict CommonJS, but - // only CommonJS-like enviroments that support module.exports, - // like Node. - module.exports = factory(global); - } else if (typeof define === 'function' && define.amd) { - // AMD. Register as an anonymous module. - define([], function () { - return factory(root); - }); - } else { - // Browser globals - factory(root); - } -}(this, function (root) { - "use strict"; - - // Tweak to your liking - var FLOAT_EPSILON = 0.000001; - - var glMath = {}; - (function() { - if (typeof(Float32Array) != 'undefined') { - var y = new Float32Array(1); - var i = new Int32Array(y.buffer); - - /** - * Fast way to calculate the inverse square root, - * see http://jsperf.com/inverse-square-root/5 - * - * If typed arrays are not available, a slower - * implementation will be used. - * - * @param {Number} number the number - * @returns {Number} Inverse square root - */ - glMath.invsqrt = function(number) { - var x2 = number * 0.5; - y[0] = number; - var threehalfs = 1.5; - - i[0] = 0x5f3759df - (i[0] >> 1); - - var number2 = y[0]; - - return number2 * (threehalfs - (x2 * number2 * number2)); - }; - } else { - glMath.invsqrt = function(number) { return 1.0 / Math.sqrt(number); }; - } - })(); - - /** - * @class System-specific optimal array type - * @name MatrixArray - */ - var MatrixArray = null; - - // explicitly sets and returns the type of array to use within glMatrix - function setMatrixArrayType(type) { - MatrixArray = type; - return MatrixArray; - } - - // auto-detects and returns the best type of array to use within glMatrix, falling - // back to Array if typed arrays are unsupported - function determineMatrixArrayType() { - MatrixArray = (typeof Float32Array !== 'undefined') ? Float32Array : Array; - return MatrixArray; - } - - determineMatrixArrayType(); - - /** - * @class 3 Dimensional Vector - * @name vec3 - */ - var vec3 = {}; - - /** - * Creates a new instance of a vec3 using the default array type - * Any javascript array-like objects containing at least 3 numeric elements can serve as a vec3 - * - * @param {vec3} [vec] vec3 containing values to initialize with - * - * @returns {vec3} New vec3 - */ - vec3.create = function (vec) { - var dest = new MatrixArray(3); - - if (vec) { - dest[0] = vec[0]; - dest[1] = vec[1]; - dest[2] = vec[2]; - } else { - dest[0] = dest[1] = dest[2] = 0; - } - - return dest; - }; - - /** - * Creates a new instance of a vec3, initializing it with the given arguments - * - * @param {number} x X value - * @param {number} y Y value - * @param {number} z Z value - - * @returns {vec3} New vec3 - */ - vec3.createFrom = function (x, y, z) { - var dest = new MatrixArray(3); - - dest[0] = x; - dest[1] = y; - dest[2] = z; - - return dest; - }; - - /** - * Copies the values of one vec3 to another - * - * @param {vec3} vec vec3 containing values to copy - * @param {vec3} dest vec3 receiving copied values - * - * @returns {vec3} dest - */ - vec3.set = function (vec, dest) { - dest[0] = vec[0]; - dest[1] = vec[1]; - dest[2] = vec[2]; - - return dest; - }; - - /** - * Compares two vectors for equality within a certain margin of error - * - * @param {vec3} a First vector - * @param {vec3} b Second vector - * - * @returns {Boolean} True if a is equivalent to b - */ - vec3.equal = function (a, b) { - return a === b || ( - Math.abs(a[0] - b[0]) < FLOAT_EPSILON && - Math.abs(a[1] - b[1]) < FLOAT_EPSILON && - Math.abs(a[2] - b[2]) < FLOAT_EPSILON - ); - }; - - /** - * Performs a vector addition - * - * @param {vec3} vec First operand - * @param {vec3} vec2 Second operand - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - vec3.add = function (vec, vec2, dest) { - if (!dest || vec === dest) { - vec[0] += vec2[0]; - vec[1] += vec2[1]; - vec[2] += vec2[2]; - return vec; - } - - dest[0] = vec[0] + vec2[0]; - dest[1] = vec[1] + vec2[1]; - dest[2] = vec[2] + vec2[2]; - return dest; - }; - - /** - * Performs a vector subtraction - * - * @param {vec3} vec First operand - * @param {vec3} vec2 Second operand - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - vec3.subtract = function (vec, vec2, dest) { - if (!dest || vec === dest) { - vec[0] -= vec2[0]; - vec[1] -= vec2[1]; - vec[2] -= vec2[2]; - return vec; - } - - dest[0] = vec[0] - vec2[0]; - dest[1] = vec[1] - vec2[1]; - dest[2] = vec[2] - vec2[2]; - return dest; - }; - - /** - * Performs a vector multiplication - * - * @param {vec3} vec First operand - * @param {vec3} vec2 Second operand - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - vec3.multiply = function (vec, vec2, dest) { - if (!dest || vec === dest) { - vec[0] *= vec2[0]; - vec[1] *= vec2[1]; - vec[2] *= vec2[2]; - return vec; - } - - dest[0] = vec[0] * vec2[0]; - dest[1] = vec[1] * vec2[1]; - dest[2] = vec[2] * vec2[2]; - return dest; - }; - - /** - * Negates the components of a vec3 - * - * @param {vec3} vec vec3 to negate - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - vec3.negate = function (vec, dest) { - if (!dest) { dest = vec; } - - dest[0] = -vec[0]; - dest[1] = -vec[1]; - dest[2] = -vec[2]; - return dest; - }; - - /** - * Multiplies the components of a vec3 by a scalar value - * - * @param {vec3} vec vec3 to scale - * @param {number} val Value to scale by - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - vec3.scale = function (vec, val, dest) { - if (!dest || vec === dest) { - vec[0] *= val; - vec[1] *= val; - vec[2] *= val; - return vec; - } - - dest[0] = vec[0] * val; - dest[1] = vec[1] * val; - dest[2] = vec[2] * val; - return dest; - }; - - /** - * Generates a unit vector of the same direction as the provided vec3 - * If vector length is 0, returns [0, 0, 0] - * - * @param {vec3} vec vec3 to normalize - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - vec3.normalize = function (vec, dest) { - if (!dest) { dest = vec; } - - var x = vec[0], y = vec[1], z = vec[2], - len = Math.sqrt(x * x + y * y + z * z); - - if (!len) { - dest[0] = 0; - dest[1] = 0; - dest[2] = 0; - return dest; - } else if (len === 1) { - dest[0] = x; - dest[1] = y; - dest[2] = z; - return dest; - } - - len = 1 / len; - dest[0] = x * len; - dest[1] = y * len; - dest[2] = z * len; - return dest; - }; - - /** - * Generates the cross product of two vec3s - * - * @param {vec3} vec First operand - * @param {vec3} vec2 Second operand - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - vec3.cross = function (vec, vec2, dest) { - if (!dest) { dest = vec; } - - var x = vec[0], y = vec[1], z = vec[2], - x2 = vec2[0], y2 = vec2[1], z2 = vec2[2]; - - dest[0] = y * z2 - z * y2; - dest[1] = z * x2 - x * z2; - dest[2] = x * y2 - y * x2; - return dest; - }; - - /** - * Caclulates the length of a vec3 - * - * @param {vec3} vec vec3 to calculate length of - * - * @returns {number} Length of vec - */ - vec3.length = function (vec) { - var x = vec[0], y = vec[1], z = vec[2]; - return Math.sqrt(x * x + y * y + z * z); - }; - - /** - * Caclulates the squared length of a vec3 - * - * @param {vec3} vec vec3 to calculate squared length of - * - * @returns {number} Squared Length of vec - */ - vec3.squaredLength = function (vec) { - var x = vec[0], y = vec[1], z = vec[2]; - return x * x + y * y + z * z; - }; - - /** - * Caclulates the dot product of two vec3s - * - * @param {vec3} vec First operand - * @param {vec3} vec2 Second operand - * - * @returns {number} Dot product of vec and vec2 - */ - vec3.dot = function (vec, vec2) { - return vec[0] * vec2[0] + vec[1] * vec2[1] + vec[2] * vec2[2]; - }; - - /** - * Generates a unit vector pointing from one vector to another - * - * @param {vec3} vec Origin vec3 - * @param {vec3} vec2 vec3 to point to - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - vec3.direction = function (vec, vec2, dest) { - if (!dest) { dest = vec; } - - var x = vec[0] - vec2[0], - y = vec[1] - vec2[1], - z = vec[2] - vec2[2], - len = Math.sqrt(x * x + y * y + z * z); - - if (!len) { - dest[0] = 0; - dest[1] = 0; - dest[2] = 0; - return dest; - } - - len = 1 / len; - dest[0] = x * len; - dest[1] = y * len; - dest[2] = z * len; - return dest; - }; - - /** - * Performs a linear interpolation between two vec3 - * - * @param {vec3} vec First vector - * @param {vec3} vec2 Second vector - * @param {number} lerp Interpolation amount between the two inputs - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - vec3.lerp = function (vec, vec2, lerp, dest) { - if (!dest) { dest = vec; } - - dest[0] = vec[0] + lerp * (vec2[0] - vec[0]); - dest[1] = vec[1] + lerp * (vec2[1] - vec[1]); - dest[2] = vec[2] + lerp * (vec2[2] - vec[2]); - - return dest; - }; - - /** - * Calculates the euclidian distance between two vec3 - * - * Params: - * @param {vec3} vec First vector - * @param {vec3} vec2 Second vector - * - * @returns {number} Distance between vec and vec2 - */ - vec3.dist = function (vec, vec2) { - var x = vec2[0] - vec[0], - y = vec2[1] - vec[1], - z = vec2[2] - vec[2]; - - return Math.sqrt(x*x + y*y + z*z); - }; - - // Pre-allocated to prevent unecessary garbage collection - var unprojectMat = null; - var unprojectVec = new MatrixArray(4); - /** - * Projects the specified vec3 from screen space into object space - * Based on the <a href="http://webcvs.freedesktop.org/mesa/Mesa/src/glu/mesa/project.c?revision=1.4&view=markup">Mesa gluUnProject implementation</a> - * - * @param {vec3} vec Screen-space vector to project - * @param {mat4} view View matrix - * @param {mat4} proj Projection matrix - * @param {vec4} viewport Viewport as given to gl.viewport [x, y, width, height] - * @param {vec3} [dest] vec3 receiving unprojected result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - vec3.unproject = function (vec, view, proj, viewport, dest) { - if (!dest) { dest = vec; } - - if(!unprojectMat) { - unprojectMat = mat4.create(); - } - - var m = unprojectMat; - var v = unprojectVec; - - v[0] = (vec[0] - viewport[0]) * 2.0 / viewport[2] - 1.0; - v[1] = (vec[1] - viewport[1]) * 2.0 / viewport[3] - 1.0; - v[2] = 2.0 * vec[2] - 1.0; - v[3] = 1.0; - - mat4.multiply(proj, view, m); - if(!mat4.inverse(m)) { return null; } - - mat4.multiplyVec4(m, v); - if(v[3] === 0.0) { return null; } - - dest[0] = v[0] / v[3]; - dest[1] = v[1] / v[3]; - dest[2] = v[2] / v[3]; - - return dest; - }; - - var xUnitVec3 = vec3.createFrom(1,0,0); - var yUnitVec3 = vec3.createFrom(0,1,0); - var zUnitVec3 = vec3.createFrom(0,0,1); - - var tmpvec3 = vec3.create(); - /** - * Generates a quaternion of rotation between two given normalized vectors - * - * @param {vec3} a Normalized source vector - * @param {vec3} b Normalized target vector - * @param {quat4} [dest] quat4 receiving operation result. - * - * @returns {quat4} dest if specified, a new quat4 otherwise - */ - vec3.rotationTo = function (a, b, dest) { - if (!dest) { dest = quat4.create(); } - - var d = vec3.dot(a, b); - var axis = tmpvec3; - if (d >= 1.0) { - quat4.set(identityQuat4, dest); - } else if (d < (0.000001 - 1.0)) { - vec3.cross(xUnitVec3, a, axis); - if (vec3.length(axis) < 0.000001) - vec3.cross(yUnitVec3, a, axis); - if (vec3.length(axis) < 0.000001) - vec3.cross(zUnitVec3, a, axis); - vec3.normalize(axis); - quat4.fromAngleAxis(Math.PI, axis, dest); - } else { - var s = Math.sqrt((1.0 + d) * 2.0); - var sInv = 1.0 / s; - vec3.cross(a, b, axis); - dest[0] = axis[0] * sInv; - dest[1] = axis[1] * sInv; - dest[2] = axis[2] * sInv; - dest[3] = s * 0.5; - quat4.normalize(dest); - } - if (dest[3] > 1.0) dest[3] = 1.0; - else if (dest[3] < -1.0) dest[3] = -1.0; - return dest; - }; - - /** - * Returns a string representation of a vector - * - * @param {vec3} vec Vector to represent as a string - * - * @returns {string} String representation of vec - */ - vec3.str = function (vec) { - return '[' + vec[0] + ', ' + vec[1] + ', ' + vec[2] + ']'; - }; - - /** - * @class 3x3 Matrix - * @name mat3 - */ - var mat3 = {}; - - /** - * Creates a new instance of a mat3 using the default array type - * Any javascript array-like object containing at least 9 numeric elements can serve as a mat3 - * - * @param {mat3} [mat] mat3 containing values to initialize with - * - * @returns {mat3} New mat3 - */ - mat3.create = function (mat) { - var dest = new MatrixArray(9); - - if (mat) { - dest[0] = mat[0]; - dest[1] = mat[1]; - dest[2] = mat[2]; - dest[3] = mat[3]; - dest[4] = mat[4]; - dest[5] = mat[5]; - dest[6] = mat[6]; - dest[7] = mat[7]; - dest[8] = mat[8]; - } else { - dest[0] = dest[1] = - dest[2] = dest[3] = - dest[4] = dest[5] = - dest[6] = dest[7] = - dest[8] = 0; - } - - return dest; - }; - - /** - * Creates a new instance of a mat3, initializing it with the given arguments - * - * @param {number} m00 - * @param {number} m01 - * @param {number} m02 - * @param {number} m10 - * @param {number} m11 - * @param {number} m12 - * @param {number} m20 - * @param {number} m21 - * @param {number} m22 - - * @returns {mat3} New mat3 - */ - mat3.createFrom = function (m00, m01, m02, m10, m11, m12, m20, m21, m22) { - var dest = new MatrixArray(9); - - dest[0] = m00; - dest[1] = m01; - dest[2] = m02; - dest[3] = m10; - dest[4] = m11; - dest[5] = m12; - dest[6] = m20; - dest[7] = m21; - dest[8] = m22; - - return dest; - }; - - /** - * Calculates the determinant of a mat3 - * - * @param {mat3} mat mat3 to calculate determinant of - * - * @returns {Number} determinant of mat - */ - mat3.determinant = function (mat) { - var a00 = mat[0], a01 = mat[1], a02 = mat[2], - a10 = mat[3], a11 = mat[4], a12 = mat[5], - a20 = mat[6], a21 = mat[7], a22 = mat[8]; - - return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20); - }; - - /** - * Calculates the inverse matrix of a mat3 - * - * @param {mat3} mat mat3 to calculate inverse of - * @param {mat3} [dest] mat3 receiving inverse matrix. If not specified result is written to mat - * - * @param {mat3} dest is specified, mat otherwise, null if matrix cannot be inverted - */ - mat3.inverse = function (mat, dest) { - var a00 = mat[0], a01 = mat[1], a02 = mat[2], - a10 = mat[3], a11 = mat[4], a12 = mat[5], - a20 = mat[6], a21 = mat[7], a22 = mat[8], - - b01 = a22 * a11 - a12 * a21, - b11 = -a22 * a10 + a12 * a20, - b21 = a21 * a10 - a11 * a20, - - d = a00 * b01 + a01 * b11 + a02 * b21, - id; - - if (!d) { return null; } - id = 1 / d; - - if (!dest) { dest = mat3.create(); } - - dest[0] = b01 * id; - dest[1] = (-a22 * a01 + a02 * a21) * id; - dest[2] = (a12 * a01 - a02 * a11) * id; - dest[3] = b11 * id; - dest[4] = (a22 * a00 - a02 * a20) * id; - dest[5] = (-a12 * a00 + a02 * a10) * id; - dest[6] = b21 * id; - dest[7] = (-a21 * a00 + a01 * a20) * id; - dest[8] = (a11 * a00 - a01 * a10) * id; - return dest; - }; - - /** - * Performs a matrix multiplication - * - * @param {mat3} mat First operand - * @param {mat3} mat2 Second operand - * @param {mat3} [dest] mat3 receiving operation result. If not specified result is written to mat - * - * @returns {mat3} dest if specified, mat otherwise - */ - mat3.multiply = function (mat, mat2, dest) { - if (!dest) { dest = mat; } - - - // Cache the matrix values (makes for huge speed increases!) - var a00 = mat[0], a01 = mat[1], a02 = mat[2], - a10 = mat[3], a11 = mat[4], a12 = mat[5], - a20 = mat[6], a21 = mat[7], a22 = mat[8], - - b00 = mat2[0], b01 = mat2[1], b02 = mat2[2], - b10 = mat2[3], b11 = mat2[4], b12 = mat2[5], - b20 = mat2[6], b21 = mat2[7], b22 = mat2[8]; - - dest[0] = b00 * a00 + b01 * a10 + b02 * a20; - dest[1] = b00 * a01 + b01 * a11 + b02 * a21; - dest[2] = b00 * a02 + b01 * a12 + b02 * a22; - - dest[3] = b10 * a00 + b11 * a10 + b12 * a20; - dest[4] = b10 * a01 + b11 * a11 + b12 * a21; - dest[5] = b10 * a02 + b11 * a12 + b12 * a22; - - dest[6] = b20 * a00 + b21 * a10 + b22 * a20; - dest[7] = b20 * a01 + b21 * a11 + b22 * a21; - dest[8] = b20 * a02 + b21 * a12 + b22 * a22; - - return dest; - }; - - /** - * Transforms the vec2 according to the given mat3. - * - * @param {mat3} matrix mat3 to multiply against - * @param {vec2} vec the vector to multiply - * @param {vec2} [dest] an optional receiving vector. If not given, vec is used. - * - * @returns {vec2} The multiplication result - **/ - mat3.multiplyVec2 = function(matrix, vec, dest) { - if (!dest) dest = vec; - var x = vec[0], y = vec[1]; - dest[0] = x * matrix[0] + y * matrix[3] + matrix[6]; - dest[1] = x * matrix[1] + y * matrix[4] + matrix[7]; - return dest; - }; - - /** - * Transforms the vec3 according to the given mat3 - * - * @param {mat3} matrix mat3 to multiply against - * @param {vec3} vec the vector to multiply - * @param {vec3} [dest] an optional receiving vector. If not given, vec is used. - * - * @returns {vec3} The multiplication result - **/ - mat3.multiplyVec3 = function(matrix, vec, dest) { - if (!dest) dest = vec; - var x = vec[0], y = vec[1], z = vec[2]; - dest[0] = x * matrix[0] + y * matrix[3] + z * matrix[6]; - dest[1] = x * matrix[1] + y * matrix[4] + z * matrix[7]; - dest[2] = x * matrix[2] + y * matrix[5] + z * matrix[8]; - - return dest; - }; - - /** - * Copies the values of one mat3 to another - * - * @param {mat3} mat mat3 containing values to copy - * @param {mat3} dest mat3 receiving copied values - * - * @returns {mat3} dest - */ - mat3.set = function (mat, dest) { - dest[0] = mat[0]; - dest[1] = mat[1]; - dest[2] = mat[2]; - dest[3] = mat[3]; - dest[4] = mat[4]; - dest[5] = mat[5]; - dest[6] = mat[6]; - dest[7] = mat[7]; - dest[8] = mat[8]; - return dest; - }; - - /** - * Compares two matrices for equality within a certain margin of error - * - * @param {mat3} a First matrix - * @param {mat3} b Second matrix - * - * @returns {Boolean} True if a is equivalent to b - */ - mat3.equal = function (a, b) { - return a === b || ( - Math.abs(a[0] - b[0]) < FLOAT_EPSILON && - Math.abs(a[1] - b[1]) < FLOAT_EPSILON && - Math.abs(a[2] - b[2]) < FLOAT_EPSILON && - Math.abs(a[3] - b[3]) < FLOAT_EPSILON && - Math.abs(a[4] - b[4]) < FLOAT_EPSILON && - Math.abs(a[5] - b[5]) < FLOAT_EPSILON && - Math.abs(a[6] - b[6]) < FLOAT_EPSILON && - Math.abs(a[7] - b[7]) < FLOAT_EPSILON && - Math.abs(a[8] - b[8]) < FLOAT_EPSILON - ); - }; - - /** - * Sets a mat3 to an identity matrix - * - * @param {mat3} dest mat3 to set - * - * @returns dest if specified, otherwise a new mat3 - */ - mat3.identity = function (dest) { - if (!dest) { dest = mat3.create(); } - dest[0] = 1; - dest[1] = 0; - dest[2] = 0; - dest[3] = 0; - dest[4] = 1; - dest[5] = 0; - dest[6] = 0; - dest[7] = 0; - dest[8] = 1; - return dest; - }; - - /** - * Transposes a mat3 (flips the values over the diagonal) - * - * Params: - * @param {mat3} mat mat3 to transpose - * @param {mat3} [dest] mat3 receiving transposed values. If not specified result is written to mat - * - * @returns {mat3} dest is specified, mat otherwise - */ - mat3.transpose = function (mat, dest) { - // If we are transposing ourselves we can skip a few steps but have to cache some values - if (!dest || mat === dest) { - var a01 = mat[1], a02 = mat[2], - a12 = mat[5]; - - mat[1] = mat[3]; - mat[2] = mat[6]; - mat[3] = a01; - mat[5] = mat[7]; - mat[6] = a02; - mat[7] = a12; - return mat; - } - - dest[0] = mat[0]; - dest[1] = mat[3]; - dest[2] = mat[6]; - dest[3] = mat[1]; - dest[4] = mat[4]; - dest[5] = mat[7]; - dest[6] = mat[2]; - dest[7] = mat[5]; - dest[8] = mat[8]; - return dest; - }; - - /** - * Copies the elements of a mat3 into the upper 3x3 elements of a mat4 - * - * @param {mat3} mat mat3 containing values to copy - * @param {mat4} [dest] mat4 receiving copied values - * - * @returns {mat4} dest if specified, a new mat4 otherwise - */ - mat3.toMat4 = function (mat, dest) { - if (!dest) { dest = mat4.create(); } - - dest[15] = 1; - dest[14] = 0; - dest[13] = 0; - dest[12] = 0; - - dest[11] = 0; - dest[10] = mat[8]; - dest[9] = mat[7]; - dest[8] = mat[6]; - - dest[7] = 0; - dest[6] = mat[5]; - dest[5] = mat[4]; - dest[4] = mat[3]; - - dest[3] = 0; - dest[2] = mat[2]; - dest[1] = mat[1]; - dest[0] = mat[0]; - - return dest; - }; - - /** - * Returns a string representation of a mat3 - * - * @param {mat3} mat mat3 to represent as a string - * - * @param {string} String representation of mat - */ - mat3.str = function (mat) { - return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] + - ', ' + mat[3] + ', ' + mat[4] + ', ' + mat[5] + - ', ' + mat[6] + ', ' + mat[7] + ', ' + mat[8] + ']'; - }; - - /** - * @class 4x4 Matrix - * @name mat4 - */ - var mat4 = {}; - - /** - * Creates a new instance of a mat4 using the default array type - * Any javascript array-like object containing at least 16 numeric elements can serve as a mat4 - * - * @param {mat4} [mat] mat4 containing values to initialize with - * - * @returns {mat4} New mat4 - */ - mat4.create = function (mat) { - var dest = new MatrixArray(16); - - if (mat) { - dest[0] = mat[0]; - dest[1] = mat[1]; - dest[2] = mat[2]; - dest[3] = mat[3]; - dest[4] = mat[4]; - dest[5] = mat[5]; - dest[6] = mat[6]; - dest[7] = mat[7]; - dest[8] = mat[8]; - dest[9] = mat[9]; - dest[10] = mat[10]; - dest[11] = mat[11]; - dest[12] = mat[12]; - dest[13] = mat[13]; - dest[14] = mat[14]; - dest[15] = mat[15]; - } - - return dest; - }; - - /** - * Creates a new instance of a mat4, initializing it with the given arguments - * - * @param {number} m00 - * @param {number} m01 - * @param {number} m02 - * @param {number} m03 - * @param {number} m10 - * @param {number} m11 - * @param {number} m12 - * @param {number} m13 - * @param {number} m20 - * @param {number} m21 - * @param {number} m22 - * @param {number} m23 - * @param {number} m30 - * @param {number} m31 - * @param {number} m32 - * @param {number} m33 - - * @returns {mat4} New mat4 - */ - mat4.createFrom = function (m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) { - var dest = new MatrixArray(16); - - dest[0] = m00; - dest[1] = m01; - dest[2] = m02; - dest[3] = m03; - dest[4] = m10; - dest[5] = m11; - dest[6] = m12; - dest[7] = m13; - dest[8] = m20; - dest[9] = m21; - dest[10] = m22; - dest[11] = m23; - dest[12] = m30; - dest[13] = m31; - dest[14] = m32; - dest[15] = m33; - - return dest; - }; - - /** - * Copies the values of one mat4 to another - * - * @param {mat4} mat mat4 containing values to copy - * @param {mat4} dest mat4 receiving copied values - * - * @returns {mat4} dest - */ - mat4.set = function (mat, dest) { - dest[0] = mat[0]; - dest[1] = mat[1]; - dest[2] = mat[2]; - dest[3] = mat[3]; - dest[4] = mat[4]; - dest[5] = mat[5]; - dest[6] = mat[6]; - dest[7] = mat[7]; - dest[8] = mat[8]; - dest[9] = mat[9]; - dest[10] = mat[10]; - dest[11] = mat[11]; - dest[12] = mat[12]; - dest[13] = mat[13]; - dest[14] = mat[14]; - dest[15] = mat[15]; - return dest; - }; - - /** - * Compares two matrices for equality within a certain margin of error - * - * @param {mat4} a First matrix - * @param {mat4} b Second matrix - * - * @returns {Boolean} True if a is equivalent to b - */ - mat4.equal = function (a, b) { - return a === b || ( - Math.abs(a[0] - b[0]) < FLOAT_EPSILON && - Math.abs(a[1] - b[1]) < FLOAT_EPSILON && - Math.abs(a[2] - b[2]) < FLOAT_EPSILON && - Math.abs(a[3] - b[3]) < FLOAT_EPSILON && - Math.abs(a[4] - b[4]) < FLOAT_EPSILON && - Math.abs(a[5] - b[5]) < FLOAT_EPSILON && - Math.abs(a[6] - b[6]) < FLOAT_EPSILON && - Math.abs(a[7] - b[7]) < FLOAT_EPSILON && - Math.abs(a[8] - b[8]) < FLOAT_EPSILON && - Math.abs(a[9] - b[9]) < FLOAT_EPSILON && - Math.abs(a[10] - b[10]) < FLOAT_EPSILON && - Math.abs(a[11] - b[11]) < FLOAT_EPSILON && - Math.abs(a[12] - b[12]) < FLOAT_EPSILON && - Math.abs(a[13] - b[13]) < FLOAT_EPSILON && - Math.abs(a[14] - b[14]) < FLOAT_EPSILON && - Math.abs(a[15] - b[15]) < FLOAT_EPSILON - ); - }; - - /** - * Sets a mat4 to an identity matrix - * - * @param {mat4} dest mat4 to set - * - * @returns {mat4} dest - */ - mat4.identity = function (dest) { - if (!dest) { dest = mat4.create(); } - dest[0] = 1; - dest[1] = 0; - dest[2] = 0; - dest[3] = 0; - dest[4] = 0; - dest[5] = 1; - dest[6] = 0; - dest[7] = 0; - dest[8] = 0; - dest[9] = 0; - dest[10] = 1; - dest[11] = 0; - dest[12] = 0; - dest[13] = 0; - dest[14] = 0; - dest[15] = 1; - return dest; - }; - - /** - * Transposes a mat4 (flips the values over the diagonal) - * - * @param {mat4} mat mat4 to transpose - * @param {mat4} [dest] mat4 receiving transposed values. If not specified result is written to mat - * - * @param {mat4} dest is specified, mat otherwise - */ - mat4.transpose = function (mat, dest) { - // If we are transposing ourselves we can skip a few steps but have to cache some values - if (!dest || mat === dest) { - var a01 = mat[1], a02 = mat[2], a03 = mat[3], - a12 = mat[6], a13 = mat[7], - a23 = mat[11]; - - mat[1] = mat[4]; - mat[2] = mat[8]; - mat[3] = mat[12]; - mat[4] = a01; - mat[6] = mat[9]; - mat[7] = mat[13]; - mat[8] = a02; - mat[9] = a12; - mat[11] = mat[14]; - mat[12] = a03; - mat[13] = a13; - mat[14] = a23; - return mat; - } - - dest[0] = mat[0]; - dest[1] = mat[4]; - dest[2] = mat[8]; - dest[3] = mat[12]; - dest[4] = mat[1]; - dest[5] = mat[5]; - dest[6] = mat[9]; - dest[7] = mat[13]; - dest[8] = mat[2]; - dest[9] = mat[6]; - dest[10] = mat[10]; - dest[11] = mat[14]; - dest[12] = mat[3]; - dest[13] = mat[7]; - dest[14] = mat[11]; - dest[15] = mat[15]; - return dest; - }; - - /** - * Calculates the determinant of a mat4 - * - * @param {mat4} mat mat4 to calculate determinant of - * - * @returns {number} determinant of mat - */ - mat4.determinant = function (mat) { - // Cache the matrix values (makes for huge speed increases!) - var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3], - a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7], - a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11], - a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15]; - - return (a30 * a21 * a12 * a03 - a20 * a31 * a12 * a03 - a30 * a11 * a22 * a03 + a10 * a31 * a22 * a03 + - a20 * a11 * a32 * a03 - a10 * a21 * a32 * a03 - a30 * a21 * a02 * a13 + a20 * a31 * a02 * a13 + - a30 * a01 * a22 * a13 - a00 * a31 * a22 * a13 - a20 * a01 * a32 * a13 + a00 * a21 * a32 * a13 + - a30 * a11 * a02 * a23 - a10 * a31 * a02 * a23 - a30 * a01 * a12 * a23 + a00 * a31 * a12 * a23 + - a10 * a01 * a32 * a23 - a00 * a11 * a32 * a23 - a20 * a11 * a02 * a33 + a10 * a21 * a02 * a33 + - a20 * a01 * a12 * a33 - a00 * a21 * a12 * a33 - a10 * a01 * a22 * a33 + a00 * a11 * a22 * a33); - }; - - /** - * Calculates the inverse matrix of a mat4 - * - * @param {mat4} mat mat4 to calculate inverse of - * @param {mat4} [dest] mat4 receiving inverse matrix. If not specified result is written to mat - * - * @param {mat4} dest is specified, mat otherwise, null if matrix cannot be inverted - */ - mat4.inverse = function (mat, dest) { - if (!dest) { dest = mat; } - - // Cache the matrix values (makes for huge speed increases!) - var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3], - a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7], - a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11], - a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15], - - b00 = a00 * a11 - a01 * a10, - b01 = a00 * a12 - a02 * a10, - b02 = a00 * a13 - a03 * a10, - b03 = a01 * a12 - a02 * a11, - b04 = a01 * a13 - a03 * a11, - b05 = a02 * a13 - a03 * a12, - b06 = a20 * a31 - a21 * a30, - b07 = a20 * a32 - a22 * a30, - b08 = a20 * a33 - a23 * a30, - b09 = a21 * a32 - a22 * a31, - b10 = a21 * a33 - a23 * a31, - b11 = a22 * a33 - a23 * a32, - - d = (b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06), - invDet; - - // Calculate the determinant - if (!d) { return null; } - invDet = 1 / d; - - dest[0] = (a11 * b11 - a12 * b10 + a13 * b09) * invDet; - dest[1] = (-a01 * b11 + a02 * b10 - a03 * b09) * invDet; - dest[2] = (a31 * b05 - a32 * b04 + a33 * b03) * invDet; - dest[3] = (-a21 * b05 + a22 * b04 - a23 * b03) * invDet; - dest[4] = (-a10 * b11 + a12 * b08 - a13 * b07) * invDet; - dest[5] = (a00 * b11 - a02 * b08 + a03 * b07) * invDet; - dest[6] = (-a30 * b05 + a32 * b02 - a33 * b01) * invDet; - dest[7] = (a20 * b05 - a22 * b02 + a23 * b01) * invDet; - dest[8] = (a10 * b10 - a11 * b08 + a13 * b06) * invDet; - dest[9] = (-a00 * b10 + a01 * b08 - a03 * b06) * invDet; - dest[10] = (a30 * b04 - a31 * b02 + a33 * b00) * invDet; - dest[11] = (-a20 * b04 + a21 * b02 - a23 * b00) * invDet; - dest[12] = (-a10 * b09 + a11 * b07 - a12 * b06) * invDet; - dest[13] = (a00 * b09 - a01 * b07 + a02 * b06) * invDet; - dest[14] = (-a30 * b03 + a31 * b01 - a32 * b00) * invDet; - dest[15] = (a20 * b03 - a21 * b01 + a22 * b00) * invDet; - - return dest; - }; - - /** - * Copies the upper 3x3 elements of a mat4 into another mat4 - * - * @param {mat4} mat mat4 containing values to copy - * @param {mat4} [dest] mat4 receiving copied values - * - * @returns {mat4} dest is specified, a new mat4 otherwise - */ - mat4.toRotationMat = function (mat, dest) { - if (!dest) { dest = mat4.create(); } - - dest[0] = mat[0]; - dest[1] = mat[1]; - dest[2] = mat[2]; - dest[3] = mat[3]; - dest[4] = mat[4]; - dest[5] = mat[5]; - dest[6] = mat[6]; - dest[7] = mat[7]; - dest[8] = mat[8]; - dest[9] = mat[9]; - dest[10] = mat[10]; - dest[11] = mat[11]; - dest[12] = 0; - dest[13] = 0; - dest[14] = 0; - dest[15] = 1; - - return dest; - }; - - /** - * Copies the upper 3x3 elements of a mat4 into a mat3 - * - * @param {mat4} mat mat4 containing values to copy - * @param {mat3} [dest] mat3 receiving copied values - * - * @returns {mat3} dest is specified, a new mat3 otherwise - */ - mat4.toMat3 = function (mat, dest) { - if (!dest) { dest = mat3.create(); } - - dest[0] = mat[0]; - dest[1] = mat[1]; - dest[2] = mat[2]; - dest[3] = mat[4]; - dest[4] = mat[5]; - dest[5] = mat[6]; - dest[6] = mat[8]; - dest[7] = mat[9]; - dest[8] = mat[10]; - - return dest; - }; - - /** - * Calculates the inverse of the upper 3x3 elements of a mat4 and copies the result into a mat3 - * The resulting matrix is useful for calculating transformed normals - * - * Params: - * @param {mat4} mat mat4 containing values to invert and copy - * @param {mat3} [dest] mat3 receiving values - * - * @returns {mat3} dest is specified, a new mat3 otherwise, null if the matrix cannot be inverted - */ - mat4.toInverseMat3 = function (mat, dest) { - // Cache the matrix values (makes for huge speed increases!) - var a00 = mat[0], a01 = mat[1], a02 = mat[2], - a10 = mat[4], a11 = mat[5], a12 = mat[6], - a20 = mat[8], a21 = mat[9], a22 = mat[10], - - b01 = a22 * a11 - a12 * a21, - b11 = -a22 * a10 + a12 * a20, - b21 = a21 * a10 - a11 * a20, - - d = a00 * b01 + a01 * b11 + a02 * b21, - id; - - if (!d) { return null; } - id = 1 / d; - - if (!dest) { dest = mat3.create(); } - - dest[0] = b01 * id; - dest[1] = (-a22 * a01 + a02 * a21) * id; - dest[2] = (a12 * a01 - a02 * a11) * id; - dest[3] = b11 * id; - dest[4] = (a22 * a00 - a02 * a20) * id; - dest[5] = (-a12 * a00 + a02 * a10) * id; - dest[6] = b21 * id; - dest[7] = (-a21 * a00 + a01 * a20) * id; - dest[8] = (a11 * a00 - a01 * a10) * id; - - return dest; - }; - - /** - * Performs a matrix multiplication - * - * @param {mat4} mat First operand - * @param {mat4} mat2 Second operand - * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat - * - * @returns {mat4} dest if specified, mat otherwise - */ - mat4.multiply = function (mat, mat2, dest) { - if (!dest) { dest = mat; } - - // Cache the matrix values (makes for huge speed increases!) - var a00 = mat[ 0], a01 = mat[ 1], a02 = mat[ 2], a03 = mat[3]; - var a10 = mat[ 4], a11 = mat[ 5], a12 = mat[ 6], a13 = mat[7]; - var a20 = mat[ 8], a21 = mat[ 9], a22 = mat[10], a23 = mat[11]; - var a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15]; - - // Cache only the current line of the second matrix - var b0 = mat2[0], b1 = mat2[1], b2 = mat2[2], b3 = mat2[3]; - dest[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30; - dest[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31; - dest[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32; - dest[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33; - - b0 = mat2[4]; - b1 = mat2[5]; - b2 = mat2[6]; - b3 = mat2[7]; - dest[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30; - dest[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31; - dest[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32; - dest[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33; - - b0 = mat2[8]; - b1 = mat2[9]; - b2 = mat2[10]; - b3 = mat2[11]; - dest[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30; - dest[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31; - dest[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32; - dest[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33; - - b0 = mat2[12]; - b1 = mat2[13]; - b2 = mat2[14]; - b3 = mat2[15]; - dest[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30; - dest[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31; - dest[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32; - dest[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33; - - return dest; - }; - - /** - * Transforms a vec3 with the given matrix - * 4th vector component is implicitly '1' - * - * @param {mat4} mat mat4 to transform the vector with - * @param {vec3} vec vec3 to transform - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns {vec3} dest if specified, vec otherwise - */ - mat4.multiplyVec3 = function (mat, vec, dest) { - if (!dest) { dest = vec; } - - var x = vec[0], y = vec[1], z = vec[2]; - - dest[0] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12]; - dest[1] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13]; - dest[2] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14]; - - return dest; - }; - - /** - * Transforms a vec4 with the given matrix - * - * @param {mat4} mat mat4 to transform the vector with - * @param {vec4} vec vec4 to transform - * @param {vec4} [dest] vec4 receiving operation result. If not specified result is written to vec - * - * @returns {vec4} dest if specified, vec otherwise - */ - mat4.multiplyVec4 = function (mat, vec, dest) { - if (!dest) { dest = vec; } - - var x = vec[0], y = vec[1], z = vec[2], w = vec[3]; - - dest[0] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12] * w; - dest[1] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13] * w; - dest[2] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14] * w; - dest[3] = mat[3] * x + mat[7] * y + mat[11] * z + mat[15] * w; - - return dest; - }; - - /** - * Translates a matrix by the given vector - * - * @param {mat4} mat mat4 to translate - * @param {vec3} vec vec3 specifying the translation - * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat - * - * @returns {mat4} dest if specified, mat otherwise - */ - mat4.translate = function (mat, vec, dest) { - var x = vec[0], y = vec[1], z = vec[2], - a00, a01, a02, a03, - a10, a11, a12, a13, - a20, a21, a22, a23; - - if (!dest || mat === dest) { - mat[12] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12]; - mat[13] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13]; - mat[14] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14]; - mat[15] = mat[3] * x + mat[7] * y + mat[11] * z + mat[15]; - return mat; - } - - a00 = mat[0]; a01 = mat[1]; a02 = mat[2]; a03 = mat[3]; - a10 = mat[4]; a11 = mat[5]; a12 = mat[6]; a13 = mat[7]; - a20 = mat[8]; a21 = mat[9]; a22 = mat[10]; a23 = mat[11]; - - dest[0] = a00; dest[1] = a01; dest[2] = a02; dest[3] = a03; - dest[4] = a10; dest[5] = a11; dest[6] = a12; dest[7] = a13; - dest[8] = a20; dest[9] = a21; dest[10] = a22; dest[11] = a23; - - dest[12] = a00 * x + a10 * y + a20 * z + mat[12]; - dest[13] = a01 * x + a11 * y + a21 * z + mat[13]; - dest[14] = a02 * x + a12 * y + a22 * z + mat[14]; - dest[15] = a03 * x + a13 * y + a23 * z + mat[15]; - return dest; - }; - - /** - * Scales a matrix by the given vector - * - * @param {mat4} mat mat4 to scale - * @param {vec3} vec vec3 specifying the scale for each axis - * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat - * - * @param {mat4} dest if specified, mat otherwise - */ - mat4.scale = function (mat, vec, dest) { - var x = vec[0], y = vec[1], z = vec[2]; - - if (!dest || mat === dest) { - mat[0] *= x; - mat[1] *= x; - mat[2] *= x; - mat[3] *= x; - mat[4] *= y; - mat[5] *= y; - mat[6] *= y; - mat[7] *= y; - mat[8] *= z; - mat[9] *= z; - mat[10] *= z; - mat[11] *= z; - return mat; - } - - dest[0] = mat[0] * x; - dest[1] = mat[1] * x; - dest[2] = mat[2] * x; - dest[3] = mat[3] * x; - dest[4] = mat[4] * y; - dest[5] = mat[5] * y; - dest[6] = mat[6] * y; - dest[7] = mat[7] * y; - dest[8] = mat[8] * z; - dest[9] = mat[9] * z; - dest[10] = mat[10] * z; - dest[11] = mat[11] * z; - dest[12] = mat[12]; - dest[13] = mat[13]; - dest[14] = mat[14]; - dest[15] = mat[15]; - return dest; - }; - - /** - * Rotates a matrix by the given angle around the specified axis - * If rotating around a primary axis (X,Y,Z) one of the specialized rotation functions should be used instead for performance - * - * @param {mat4} mat mat4 to rotate - * @param {number} angle Angle (in radians) to rotate - * @param {vec3} axis vec3 representing the axis to rotate around - * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat - * - * @returns {mat4} dest if specified, mat otherwise - */ - mat4.rotate = function (mat, angle, axis, dest) { - var x = axis[0], y = axis[1], z = axis[2], - len = Math.sqrt(x * x + y * y + z * z), - s, c, t, - a00, a01, a02, a03, - a10, a11, a12, a13, - a20, a21, a22, a23, - b00, b01, b02, - b10, b11, b12, - b20, b21, b22; - - if (!len) { return null; } - if (len !== 1) { - len = 1 / len; - x *= len; - y *= len; - z *= len; - } - - s = Math.sin(angle); - c = Math.cos(angle); - t = 1 - c; - - a00 = mat[0]; a01 = mat[1]; a02 = mat[2]; a03 = mat[3]; - a10 = mat[4]; a11 = mat[5]; a12 = mat[6]; a13 = mat[7]; - a20 = mat[8]; a21 = mat[9]; a22 = mat[10]; a23 = mat[11]; - - // Construct the elements of the rotation matrix - b00 = x * x * t + c; b01 = y * x * t + z * s; b02 = z * x * t - y * s; - b10 = x * y * t - z * s; b11 = y * y * t + c; b12 = z * y * t + x * s; - b20 = x * z * t + y * s; b21 = y * z * t - x * s; b22 = z * z * t + c; - - if (!dest) { - dest = mat; - } else if (mat !== dest) { // If the source and destination differ, copy the unchanged last row - dest[12] = mat[12]; - dest[13] = mat[13]; - dest[14] = mat[14]; - dest[15] = mat[15]; - } - - // Perform rotation-specific matrix multiplication - dest[0] = a00 * b00 + a10 * b01 + a20 * b02; - dest[1] = a01 * b00 + a11 * b01 + a21 * b02; - dest[2] = a02 * b00 + a12 * b01 + a22 * b02; - dest[3] = a03 * b00 + a13 * b01 + a23 * b02; - - dest[4] = a00 * b10 + a10 * b11 + a20 * b12; - dest[5] = a01 * b10 + a11 * b11 + a21 * b12; - dest[6] = a02 * b10 + a12 * b11 + a22 * b12; - dest[7] = a03 * b10 + a13 * b11 + a23 * b12; - - dest[8] = a00 * b20 + a10 * b21 + a20 * b22; - dest[9] = a01 * b20 + a11 * b21 + a21 * b22; - dest[10] = a02 * b20 + a12 * b21 + a22 * b22; - dest[11] = a03 * b20 + a13 * b21 + a23 * b22; - return dest; - }; - - /** - * Rotates a matrix by the given angle around the X axis - * - * @param {mat4} mat mat4 to rotate - * @param {number} angle Angle (in radians) to rotate - * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat - * - * @returns {mat4} dest if specified, mat otherwise - */ - mat4.rotateX = function (mat, angle, dest) { - var s = Math.sin(angle), - c = Math.cos(angle), - a10 = mat[4], - a11 = mat[5], - a12 = mat[6], - a13 = mat[7], - a20 = mat[8], - a21 = mat[9], - a22 = mat[10], - a23 = mat[11]; - - if (!dest) { - dest = mat; - } else if (mat !== dest) { // If the source and destination differ, copy the unchanged rows - dest[0] = mat[0]; - dest[1] = mat[1]; - dest[2] = mat[2]; - dest[3] = mat[3]; - - dest[12] = mat[12]; - dest[13] = mat[13]; - dest[14] = mat[14]; - dest[15] = mat[15]; - } - - // Perform axis-specific matrix multiplication - dest[4] = a10 * c + a20 * s; - dest[5] = a11 * c + a21 * s; - dest[6] = a12 * c + a22 * s; - dest[7] = a13 * c + a23 * s; - - dest[8] = a10 * -s + a20 * c; - dest[9] = a11 * -s + a21 * c; - dest[10] = a12 * -s + a22 * c; - dest[11] = a13 * -s + a23 * c; - return dest; - }; - - /** - * Rotates a matrix by the given angle around the Y axis - * - * @param {mat4} mat mat4 to rotate - * @param {number} angle Angle (in radians) to rotate - * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat - * - * @returns {mat4} dest if specified, mat otherwise - */ - mat4.rotateY = function (mat, angle, dest) { - var s = Math.sin(angle), - c = Math.cos(angle), - a00 = mat[0], - a01 = mat[1], - a02 = mat[2], - a03 = mat[3], - a20 = mat[8], - a21 = mat[9], - a22 = mat[10], - a23 = mat[11]; - - if (!dest) { - dest = mat; - } else if (mat !== dest) { // If the source and destination differ, copy the unchanged rows - dest[4] = mat[4]; - dest[5] = mat[5]; - dest[6] = mat[6]; - dest[7] = mat[7]; - - dest[12] = mat[12]; - dest[13] = mat[13]; - dest[14] = mat[14]; - dest[15] = mat[15]; - } - - // Perform axis-specific matrix multiplication - dest[0] = a00 * c + a20 * -s; - dest[1] = a01 * c + a21 * -s; - dest[2] = a02 * c + a22 * -s; - dest[3] = a03 * c + a23 * -s; - - dest[8] = a00 * s + a20 * c; - dest[9] = a01 * s + a21 * c; - dest[10] = a02 * s + a22 * c; - dest[11] = a03 * s + a23 * c; - return dest; - }; - - /** - * Rotates a matrix by the given angle around the Z axis - * - * @param {mat4} mat mat4 to rotate - * @param {number} angle Angle (in radians) to rotate - * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to mat - * - * @returns {mat4} dest if specified, mat otherwise - */ - mat4.rotateZ = function (mat, angle, dest) { - var s = Math.sin(angle), - c = Math.cos(angle), - a00 = mat[0], - a01 = mat[1], - a02 = mat[2], - a03 = mat[3], - a10 = mat[4], - a11 = mat[5], - a12 = mat[6], - a13 = mat[7]; - - if (!dest) { - dest = mat; - } else if (mat !== dest) { // If the source and destination differ, copy the unchanged last row - dest[8] = mat[8]; - dest[9] = mat[9]; - dest[10] = mat[10]; - dest[11] = mat[11]; - - dest[12] = mat[12]; - dest[13] = mat[13]; - dest[14] = mat[14]; - dest[15] = mat[15]; - } - - // Perform axis-specific matrix multiplication - dest[0] = a00 * c + a10 * s; - dest[1] = a01 * c + a11 * s; - dest[2] = a02 * c + a12 * s; - dest[3] = a03 * c + a13 * s; - - dest[4] = a00 * -s + a10 * c; - dest[5] = a01 * -s + a11 * c; - dest[6] = a02 * -s + a12 * c; - dest[7] = a03 * -s + a13 * c; - - return dest; - }; - - /** - * Generates a frustum matrix with the given bounds - * - * @param {number} left Left bound of the frustum - * @param {number} right Right bound of the frustum - * @param {number} bottom Bottom bound of the frustum - * @param {number} top Top bound of the frustum - * @param {number} near Near bound of the frustum - * @param {number} far Far bound of the frustum - * @param {mat4} [dest] mat4 frustum matrix will be written into - * - * @returns {mat4} dest if specified, a new mat4 otherwise - */ - mat4.frustum = function (left, right, bottom, top, near, far, dest) { - if (!dest) { dest = mat4.create(); } - var rl = (right - left), - tb = (top - bottom), - fn = (far - near); - dest[0] = (near * 2) / rl; - dest[1] = 0; - dest[2] = 0; - dest[3] = 0; - dest[4] = 0; - dest[5] = (near * 2) / tb; - dest[6] = 0; - dest[7] = 0; - dest[8] = (right + left) / rl; - dest[9] = (top + bottom) / tb; - dest[10] = -(far + near) / fn; - dest[11] = -1; - dest[12] = 0; - dest[13] = 0; - dest[14] = -(far * near * 2) / fn; - dest[15] = 0; - return dest; - }; - - /** - * Generates a perspective projection matrix with the given bounds - * - * @param {number} fovy Vertical field of view - * @param {number} aspect Aspect ratio. typically viewport width/height - * @param {number} near Near bound of the frustum - * @param {number} far Far bound of the frustum - * @param {mat4} [dest] mat4 frustum matrix will be written into - * - * @returns {mat4} dest if specified, a new mat4 otherwise - */ - mat4.perspective = function (fovy, aspect, near, far, dest) { - var top = near * Math.tan(fovy * Math.PI / 360.0), - right = top * aspect; - return mat4.frustum(-right, right, -top, top, near, far, dest); - }; - - /** - * Generates a orthogonal projection matrix with the given bounds - * - * @param {number} left Left bound of the frustum - * @param {number} right Right bound of the frustum - * @param {number} bottom Bottom bound of the frustum - * @param {number} top Top bound of the frustum - * @param {number} near Near bound of the frustum - * @param {number} far Far bound of the frustum - * @param {mat4} [dest] mat4 frustum matrix will be written into - * - * @returns {mat4} dest if specified, a new mat4 otherwise - */ - mat4.ortho = function (left, right, bottom, top, near, far, dest) { - if (!dest) { dest = mat4.create(); } - var rl = (right - left), - tb = (top - bottom), - fn = (far - near); - dest[0] = 2 / rl; - dest[1] = 0; - dest[2] = 0; - dest[3] = 0; - dest[4] = 0; - dest[5] = 2 / tb; - dest[6] = 0; - dest[7] = 0; - dest[8] = 0; - dest[9] = 0; - dest[10] = -2 / fn; - dest[11] = 0; - dest[12] = -(left + right) / rl; - dest[13] = -(top + bottom) / tb; - dest[14] = -(far + near) / fn; - dest[15] = 1; - return dest; - }; - - /** - * Generates a look-at matrix with the given eye position, focal point, and up axis - * - * @param {vec3} eye Position of the viewer - * @param {vec3} center Point the viewer is looking at - * @param {vec3} up vec3 pointing "up" - * @param {mat4} [dest] mat4 frustum matrix will be written into - * - * @returns {mat4} dest if specified, a new mat4 otherwise - */ - mat4.lookAt = function (eye, center, up, dest) { - if (!dest) { dest = mat4.create(); } - - var x0, x1, x2, y0, y1, y2, z0, z1, z2, len, - eyex = eye[0], - eyey = eye[1], - eyez = eye[2], - upx = up[0], - upy = up[1], - upz = up[2], - centerx = center[0], - centery = center[1], - centerz = center[2]; - - if (eyex === centerx && eyey === centery && eyez === centerz) { - return mat4.identity(dest); - } - - //vec3.direction(eye, center, z); - z0 = eyex - centerx; - z1 = eyey - centery; - z2 = eyez - centerz; - - // normalize (no check needed for 0 because of early return) - len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2); - z0 *= len; - z1 *= len; - z2 *= len; - - //vec3.normalize(vec3.cross(up, z, x)); - x0 = upy * z2 - upz * z1; - x1 = upz * z0 - upx * z2; - x2 = upx * z1 - upy * z0; - len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2); - if (!len) { - x0 = 0; - x1 = 0; - x2 = 0; - } else { - len = 1 / len; - x0 *= len; - x1 *= len; - x2 *= len; - } - - //vec3.normalize(vec3.cross(z, x, y)); - y0 = z1 * x2 - z2 * x1; - y1 = z2 * x0 - z0 * x2; - y2 = z0 * x1 - z1 * x0; - - len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2); - if (!len) { - y0 = 0; - y1 = 0; - y2 = 0; - } else { - len = 1 / len; - y0 *= len; - y1 *= len; - y2 *= len; - } - - dest[0] = x0; - dest[1] = y0; - dest[2] = z0; - dest[3] = 0; - dest[4] = x1; - dest[5] = y1; - dest[6] = z1; - dest[7] = 0; - dest[8] = x2; - dest[9] = y2; - dest[10] = z2; - dest[11] = 0; - dest[12] = -(x0 * eyex + x1 * eyey + x2 * eyez); - dest[13] = -(y0 * eyex + y1 * eyey + y2 * eyez); - dest[14] = -(z0 * eyex + z1 * eyey + z2 * eyez); - dest[15] = 1; - - return dest; - }; - - /** - * Creates a matrix from a quaternion rotation and vector translation - * This is equivalent to (but much faster than): - * - * mat4.identity(dest); - * mat4.translate(dest, vec); - * var quatMat = mat4.create(); - * quat4.toMat4(quat, quatMat); - * mat4.multiply(dest, quatMat); - * - * @param {quat4} quat Rotation quaternion - * @param {vec3} vec Translation vector - * @param {mat4} [dest] mat4 receiving operation result. If not specified result is written to a new mat4 - * - * @returns {mat4} dest if specified, a new mat4 otherwise - */ - mat4.fromRotationTranslation = function (quat, vec, dest) { - if (!dest) { dest = mat4.create(); } - - // Quaternion math - var x = quat[0], y = quat[1], z = quat[2], w = quat[3], - x2 = x + x, - y2 = y + y, - z2 = z + z, - - xx = x * x2, - xy = x * y2, - xz = x * z2, - yy = y * y2, - yz = y * z2, - zz = z * z2, - wx = w * x2, - wy = w * y2, - wz = w * z2; - - dest[0] = 1 - (yy + zz); - dest[1] = xy + wz; - dest[2] = xz - wy; - dest[3] = 0; - dest[4] = xy - wz; - dest[5] = 1 - (xx + zz); - dest[6] = yz + wx; - dest[7] = 0; - dest[8] = xz + wy; - dest[9] = yz - wx; - dest[10] = 1 - (xx + yy); - dest[11] = 0; - dest[12] = vec[0]; - dest[13] = vec[1]; - dest[14] = vec[2]; - dest[15] = 1; - - return dest; - }; - - /** - * Returns a string representation of a mat4 - * - * @param {mat4} mat mat4 to represent as a string - * - * @returns {string} String representation of mat - */ - mat4.str = function (mat) { - return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] + ', ' + mat[3] + - ', ' + mat[4] + ', ' + mat[5] + ', ' + mat[6] + ', ' + mat[7] + - ', ' + mat[8] + ', ' + mat[9] + ', ' + mat[10] + ', ' + mat[11] + - ', ' + mat[12] + ', ' + mat[13] + ', ' + mat[14] + ', ' + mat[15] + ']'; - }; - - /** - * @class Quaternion - * @name quat4 - */ - var quat4 = {}; - - /** - * Creates a new instance of a quat4 using the default array type - * Any javascript array containing at least 4 numeric elements can serve as a quat4 - * - * @param {quat4} [quat] quat4 containing values to initialize with - * - * @returns {quat4} New quat4 - */ - quat4.create = function (quat) { - var dest = new MatrixArray(4); - - if (quat) { - dest[0] = quat[0]; - dest[1] = quat[1]; - dest[2] = quat[2]; - dest[3] = quat[3]; - } else { - dest[0] = dest[1] = dest[2] = dest[3] = 0; - } - - return dest; - }; - - /** - * Creates a new instance of a quat4, initializing it with the given arguments - * - * @param {number} x X value - * @param {number} y Y value - * @param {number} z Z value - * @param {number} w W value - - * @returns {quat4} New quat4 - */ - quat4.createFrom = function (x, y, z, w) { - var dest = new MatrixArray(4); - - dest[0] = x; - dest[1] = y; - dest[2] = z; - dest[3] = w; - - return dest; - }; - - /** - * Copies the values of one quat4 to another - * - * @param {quat4} quat quat4 containing values to copy - * @param {quat4} dest quat4 receiving copied values - * - * @returns {quat4} dest - */ - quat4.set = function (quat, dest) { - dest[0] = quat[0]; - dest[1] = quat[1]; - dest[2] = quat[2]; - dest[3] = quat[3]; - - return dest; - }; - - /** - * Compares two quaternions for equality within a certain margin of error - * - * @param {quat4} a First vector - * @param {quat4} b Second vector - * - * @returns {Boolean} True if a is equivalent to b - */ - quat4.equal = function (a, b) { - return a === b || ( - Math.abs(a[0] - b[0]) < FLOAT_EPSILON && - Math.abs(a[1] - b[1]) < FLOAT_EPSILON && - Math.abs(a[2] - b[2]) < FLOAT_EPSILON && - Math.abs(a[3] - b[3]) < FLOAT_EPSILON - ); - }; - - /** - * Creates a new identity Quat4 - * - * @param {quat4} [dest] quat4 receiving copied values - * - * @returns {quat4} dest is specified, new quat4 otherwise - */ - quat4.identity = function (dest) { - if (!dest) { dest = quat4.create(); } - dest[0] = 0; - dest[1] = 0; - dest[2] = 0; - dest[3] = 1; - return dest; - }; - - var identityQuat4 = quat4.identity(); - - /** - * Calculates the W component of a quat4 from the X, Y, and Z components. - * Assumes that quaternion is 1 unit in length. - * Any existing W component will be ignored. - * - * @param {quat4} quat quat4 to calculate W component of - * @param {quat4} [dest] quat4 receiving calculated values. If not specified result is written to quat - * - * @returns {quat4} dest if specified, quat otherwise - */ - quat4.calculateW = function (quat, dest) { - var x = quat[0], y = quat[1], z = quat[2]; - - if (!dest || quat === dest) { - quat[3] = -Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z)); - return quat; - } - dest[0] = x; - dest[1] = y; - dest[2] = z; - dest[3] = -Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z)); - return dest; - }; - - /** - * Calculates the dot product of two quaternions - * - * @param {quat4} quat First operand - * @param {quat4} quat2 Second operand - * - * @return {number} Dot product of quat and quat2 - */ - quat4.dot = function(quat, quat2){ - return quat[0]*quat2[0] + quat[1]*quat2[1] + quat[2]*quat2[2] + quat[3]*quat2[3]; - }; - - /** - * Calculates the inverse of a quat4 - * - * @param {quat4} quat quat4 to calculate inverse of - * @param {quat4} [dest] quat4 receiving inverse values. If not specified result is written to quat - * - * @returns {quat4} dest if specified, quat otherwise - */ - quat4.inverse = function(quat, dest) { - var q0 = quat[0], q1 = quat[1], q2 = quat[2], q3 = quat[3], - dot = q0*q0 + q1*q1 + q2*q2 + q3*q3, - invDot = dot ? 1.0/dot : 0; - - // TODO: Would be faster to return [0,0,0,0] immediately if dot == 0 - - if(!dest || quat === dest) { - quat[0] *= -invDot; - quat[1] *= -invDot; - quat[2] *= -invDot; - quat[3] *= invDot; - return quat; - } - dest[0] = -quat[0]*invDot; - dest[1] = -quat[1]*invDot; - dest[2] = -quat[2]*invDot; - dest[3] = quat[3]*invDot; - return dest; - }; - - - /** - * Calculates the conjugate of a quat4 - * If the quaternion is normalized, this function is faster than quat4.inverse and produces the same result. - * - * @param {quat4} quat quat4 to calculate conjugate of - * @param {quat4} [dest] quat4 receiving conjugate values. If not specified result is written to quat - * - * @returns {quat4} dest if specified, quat otherwise - */ - quat4.conjugate = function (quat, dest) { - if (!dest || quat === dest) { - quat[0] *= -1; - quat[1] *= -1; - quat[2] *= -1; - return quat; - } - dest[0] = -quat[0]; - dest[1] = -quat[1]; - dest[2] = -quat[2]; - dest[3] = quat[3]; - return dest; - }; - - /** - * Calculates the length of a quat4 - * - * Params: - * @param {quat4} quat quat4 to calculate length of - * - * @returns Length of quat - */ - quat4.length = function (quat) { - var x = quat[0], y = quat[1], z = quat[2], w = quat[3]; - return Math.sqrt(x * x + y * y + z * z + w * w); - }; - - /** - * Generates a unit quaternion of the same direction as the provided quat4 - * If quaternion length is 0, returns [0, 0, 0, 0] - * - * @param {quat4} quat quat4 to normalize - * @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat - * - * @returns {quat4} dest if specified, quat otherwise - */ - quat4.normalize = function (quat, dest) { - if (!dest) { dest = quat; } - - var x = quat[0], y = quat[1], z = quat[2], w = quat[3], - len = Math.sqrt(x * x + y * y + z * z + w * w); - if (len === 0) { - dest[0] = 0; - dest[1] = 0; - dest[2] = 0; - dest[3] = 0; - return dest; - } - len = 1 / len; - dest[0] = x * len; - dest[1] = y * len; - dest[2] = z * len; - dest[3] = w * len; - - return dest; - }; - - /** - * Performs quaternion addition - * - * @param {quat4} quat First operand - * @param {quat4} quat2 Second operand - * @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat - * - * @returns {quat4} dest if specified, quat otherwise - */ - quat4.add = function (quat, quat2, dest) { - if(!dest || quat === dest) { - quat[0] += quat2[0]; - quat[1] += quat2[1]; - quat[2] += quat2[2]; - quat[3] += quat2[3]; - return quat; - } - dest[0] = quat[0]+quat2[0]; - dest[1] = quat[1]+quat2[1]; - dest[2] = quat[2]+quat2[2]; - dest[3] = quat[3]+quat2[3]; - return dest; - }; - - /** - * Performs a quaternion multiplication - * - * @param {quat4} quat First operand - * @param {quat4} quat2 Second operand - * @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat - * - * @returns {quat4} dest if specified, quat otherwise - */ - quat4.multiply = function (quat, quat2, dest) { - if (!dest) { dest = quat; } - - var qax = quat[0], qay = quat[1], qaz = quat[2], qaw = quat[3], - qbx = quat2[0], qby = quat2[1], qbz = quat2[2], qbw = quat2[3]; - - dest[0] = qax * qbw + qaw * qbx + qay * qbz - qaz * qby; - dest[1] = qay * qbw + qaw * qby + qaz * qbx - qax * qbz; - dest[2] = qaz * qbw + qaw * qbz + qax * qby - qay * qbx; - dest[3] = qaw * qbw - qax * qbx - qay * qby - qaz * qbz; - - return dest; - }; - - /** - * Transforms a vec3 with the given quaternion - * - * @param {quat4} quat quat4 to transform the vector with - * @param {vec3} vec vec3 to transform - * @param {vec3} [dest] vec3 receiving operation result. If not specified result is written to vec - * - * @returns dest if specified, vec otherwise - */ - quat4.multiplyVec3 = function (quat, vec, dest) { - if (!dest) { dest = vec; } - - var x = vec[0], y = vec[1], z = vec[2], - qx = quat[0], qy = quat[1], qz = quat[2], qw = quat[3], - - // calculate quat * vec - ix = qw * x + qy * z - qz * y, - iy = qw * y + qz * x - qx * z, - iz = qw * z + qx * y - qy * x, - iw = -qx * x - qy * y - qz * z; - - // calculate result * inverse quat - dest[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy; - dest[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz; - dest[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx; - - return dest; - }; - - /** - * Multiplies the components of a quaternion by a scalar value - * - * @param {quat4} quat to scale - * @param {number} val Value to scale by - * @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat - * - * @returns {quat4} dest if specified, quat otherwise - */ - quat4.scale = function (quat, val, dest) { - if(!dest || quat === dest) { - quat[0] *= val; - quat[1] *= val; - quat[2] *= val; - quat[3] *= val; - return quat; - } - dest[0] = quat[0]*val; - dest[1] = quat[1]*val; - dest[2] = quat[2]*val; - dest[3] = quat[3]*val; - return dest; - }; - - /** - * Calculates a 3x3 matrix from the given quat4 - * - * @param {quat4} quat quat4 to create matrix from - * @param {mat3} [dest] mat3 receiving operation result - * - * @returns {mat3} dest if specified, a new mat3 otherwise - */ - quat4.toMat3 = function (quat, dest) { - if (!dest) { dest = mat3.create(); } - - var x = quat[0], y = quat[1], z = quat[2], w = quat[3], - x2 = x + x, - y2 = y + y, - z2 = z + z, - - xx = x * x2, - xy = x * y2, - xz = x * z2, - yy = y * y2, - yz = y * z2, - zz = z * z2, - wx = w * x2, - wy = w * y2, - wz = w * z2; - - dest[0] = 1 - (yy + zz); - dest[1] = xy + wz; - dest[2] = xz - wy; - - dest[3] = xy - wz; - dest[4] = 1 - (xx + zz); - dest[5] = yz + wx; - - dest[6] = xz + wy; - dest[7] = yz - wx; - dest[8] = 1 - (xx + yy); - - return dest; - }; - - /** - * Calculates a 4x4 matrix from the given quat4 - * - * @param {quat4} quat quat4 to create matrix from - * @param {mat4} [dest] mat4 receiving operation result - * - * @returns {mat4} dest if specified, a new mat4 otherwise - */ - quat4.toMat4 = function (quat, dest) { - if (!dest) { dest = mat4.create(); } - - var x = quat[0], y = quat[1], z = quat[2], w = quat[3], - x2 = x + x, - y2 = y + y, - z2 = z + z, - - xx = x * x2, - xy = x * y2, - xz = x * z2, - yy = y * y2, - yz = y * z2, - zz = z * z2, - wx = w * x2, - wy = w * y2, - wz = w * z2; - - dest[0] = 1 - (yy + zz); - dest[1] = xy + wz; - dest[2] = xz - wy; - dest[3] = 0; - - dest[4] = xy - wz; - dest[5] = 1 - (xx + zz); - dest[6] = yz + wx; - dest[7] = 0; - - dest[8] = xz + wy; - dest[9] = yz - wx; - dest[10] = 1 - (xx + yy); - dest[11] = 0; - - dest[12] = 0; - dest[13] = 0; - dest[14] = 0; - dest[15] = 1; - - return dest; - }; - - /** - * Performs a spherical linear interpolation between two quat4 - * - * @param {quat4} quat First quaternion - * @param {quat4} quat2 Second quaternion - * @param {number} slerp Interpolation amount between the two inputs - * @param {quat4} [dest] quat4 receiving operation result. If not specified result is written to quat - * - * @returns {quat4} dest if specified, quat otherwise - */ - quat4.slerp = function (quat, quat2, slerp, dest) { - if (!dest) { dest = quat; } - - var cosHalfTheta = quat[0] * quat2[0] + quat[1] * quat2[1] + quat[2] * quat2[2] + quat[3] * quat2[3], - halfTheta, - sinHalfTheta, - ratioA, - ratioB; - - if (Math.abs(cosHalfTheta) >= 1.0) { - if (dest !== quat) { - dest[0] = quat[0]; - dest[1] = quat[1]; - dest[2] = quat[2]; - dest[3] = quat[3]; - } - return dest; - } - - halfTheta = Math.acos(cosHalfTheta); - sinHalfTheta = Math.sqrt(1.0 - cosHalfTheta * cosHalfTheta); - - if (Math.abs(sinHalfTheta) < 0.001) { - dest[0] = (quat[0] * 0.5 + quat2[0] * 0.5); - dest[1] = (quat[1] * 0.5 + quat2[1] * 0.5); - dest[2] = (quat[2] * 0.5 + quat2[2] * 0.5); - dest[3] = (quat[3] * 0.5 + quat2[3] * 0.5); - return dest; - } - - ratioA = Math.sin((1 - slerp) * halfTheta) / sinHalfTheta; - ratioB = Math.sin(slerp * halfTheta) / sinHalfTheta; - - dest[0] = (quat[0] * ratioA + quat2[0] * ratioB); - dest[1] = (quat[1] * ratioA + quat2[1] * ratioB); - dest[2] = (quat[2] * ratioA + quat2[2] * ratioB); - dest[3] = (quat[3] * ratioA + quat2[3] * ratioB); - - return dest; - }; - - /** - * Creates a quaternion from the given 3x3 rotation matrix. - * If dest is omitted, a new quaternion will be created. - * - * @param {mat3} mat the rotation matrix - * @param {quat4} [dest] an optional receiving quaternion - * - * @returns {quat4} the quaternion constructed from the rotation matrix - * - */ - quat4.fromRotationMatrix = function(mat, dest) { - if (!dest) dest = quat4.create(); - - // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes - // article "Quaternion Calculus and Fast Animation". - - var fTrace = mat[0] + mat[4] + mat[8]; - var fRoot; - - if ( fTrace > 0.0 ) { - // |w| > 1/2, may as well choose w > 1/2 - fRoot = Math.sqrt(fTrace + 1.0); // 2w - dest[3] = 0.5 * fRoot; - fRoot = 0.5/fRoot; // 1/(4w) - dest[0] = (mat[7]-mat[5])*fRoot; - dest[1] = (mat[2]-mat[6])*fRoot; - dest[2] = (mat[3]-mat[1])*fRoot; - } else { - // |w| <= 1/2 - var s_iNext = quat4.fromRotationMatrix.s_iNext = quat4.fromRotationMatrix.s_iNext || [1,2,0]; - var i = 0; - if ( mat[4] > mat[0] ) - i = 1; - if ( mat[8] > mat[i*3+i] ) - i = 2; - var j = s_iNext[i]; - var k = s_iNext[j]; - - fRoot = Math.sqrt(mat[i*3+i]-mat[j*3+j]-mat[k*3+k] + 1.0); - dest[i] = 0.5 * fRoot; - fRoot = 0.5 / fRoot; - dest[3] = (mat[k*3+j] - mat[j*3+k]) * fRoot; - dest[j] = (mat[j*3+i] + mat[i*3+j]) * fRoot; - dest[k] = (mat[k*3+i] + mat[i*3+k]) * fRoot; - } - - return dest; - }; - - /** - * Alias. See the description for quat4.fromRotationMatrix(). - */ - mat3.toQuat4 = quat4.fromRotationMatrix; - - (function() { - var mat = mat3.create(); - - /** - * Creates a quaternion from the 3 given vectors. They must be perpendicular - * to one another and represent the X, Y and Z axes. - * - * If dest is omitted, a new quat4 will be created. - * - * Example: The default OpenGL orientation has a view vector [0, 0, -1], - * right vector [1, 0, 0], and up vector [0, 1, 0]. A quaternion representing - * this orientation could be constructed with: - * - * quat = quat4.fromAxes([0, 0, -1], [1, 0, 0], [0, 1, 0], quat4.create()); - * - * @param {vec3} view the view vector, or direction the object is pointing in - * @param {vec3} right the right vector, or direction to the "right" of the object - * @param {vec3} up the up vector, or direction towards the object's "up" - * @param {quat4} [dest] an optional receiving quat4 - * - * @returns {quat4} dest - **/ - quat4.fromAxes = function(view, right, up, dest) { - mat[0] = right[0]; - mat[3] = right[1]; - mat[6] = right[2]; - - mat[1] = up[0]; - mat[4] = up[1]; - mat[7] = up[2]; - - mat[2] = view[0]; - mat[5] = view[1]; - mat[8] = view[2]; - - return quat4.fromRotationMatrix(mat, dest); - }; - })(); - - /** - * Sets a quat4 to the Identity and returns it. - * - * @param {quat4} [dest] quat4 to set. If omitted, a - * new quat4 will be created. - * - * @returns {quat4} dest - */ - quat4.identity = function(dest) { - if (!dest) dest = quat4.create(); - dest[0] = 0; - dest[1] = 0; - dest[2] = 0; - dest[3] = 1; - return dest; - }; - - /** - * Sets a quat4 from the given angle and rotation axis, - * then returns it. If dest is not given, a new quat4 is created. - * - * @param {Number} angle the angle in radians - * @param {vec3} axis the axis around which to rotate - * @param {quat4} [dest] the optional quat4 to store the result - * - * @returns {quat4} dest - **/ - quat4.fromAngleAxis = function(angle, axis, dest) { - // The quaternion representing the rotation is - // q = cos(A/2)+sin(A/2)*(x*i+y*j+z*k) - if (!dest) dest = quat4.create(); - - var half = angle * 0.5; - var s = Math.sin(half); - dest[3] = Math.cos(half); - dest[0] = s * axis[0]; - dest[1] = s * axis[1]; - dest[2] = s * axis[2]; - - return dest; - }; - - /** - * Stores the angle and axis in a vec4, where the XYZ components represent - * the axis and the W (4th) component is the angle in radians. - * - * If dest is not given, src will be modified in place and returned, after - * which it should not be considered not a quaternion (just an axis and angle). - * - * @param {quat4} quat the quaternion whose angle and axis to store - * @param {vec4} [dest] the optional vec4 to receive the data - * - * @returns {vec4} dest - */ - quat4.toAngleAxis = function(src, dest) { - if (!dest) dest = src; - // The quaternion representing the rotation is - // q = cos(A/2)+sin(A/2)*(x*i+y*j+z*k) - - var sqrlen = src[0]*src[0]+src[1]*src[1]+src[2]*src[2]; - if (sqrlen > 0) - { - dest[3] = 2 * Math.acos(src[3]); - var invlen = glMath.invsqrt(sqrlen); - dest[0] = src[0]*invlen; - dest[1] = src[1]*invlen; - dest[2] = src[2]*invlen; - } else { - // angle is 0 (mod 2*pi), so any axis will do - dest[3] = 0; - dest[0] = 1; - dest[1] = 0; - dest[2] = 0; - } - - return dest; - }; - - /** - * Returns a string representation of a quaternion - * - * @param {quat4} quat quat4 to represent as a string - * - * @returns {string} String representation of quat - */ - quat4.str = function (quat) { - return '[' + quat[0] + ', ' + quat[1] + ', ' + quat[2] + ', ' + quat[3] + ']'; - }; - - /** - * @class 2 Dimensional Vector - * @name vec2 - */ - var vec2 = {}; - - /** - * Creates a new vec2, initializing it from vec if vec - * is given. - * - * @param {vec2} [vec] the vector's initial contents - * @returns {vec2} a new 2D vector - */ - vec2.create = function(vec) { - var dest = new MatrixArray(2); - - if (vec) { - dest[0] = vec[0]; - dest[1] = vec[1]; - } else { - dest[0] = 0; - dest[1] = 0; - } - return dest; - }; - - /** - * Creates a new instance of a vec2, initializing it with the given arguments - * - * @param {number} x X value - * @param {number} y Y value - - * @returns {vec2} New vec2 - */ - vec2.createFrom = function (x, y) { - var dest = new MatrixArray(2); - - dest[0] = x; - dest[1] = y; - - return dest; - }; - - /** - * Adds the vec2's together. If dest is given, the result - * is stored there. Otherwise, the result is stored in vecB. - * - * @param {vec2} vecA the first operand - * @param {vec2} vecB the second operand - * @param {vec2} [dest] the optional receiving vector - * @returns {vec2} dest - */ - vec2.add = function(vecA, vecB, dest) { - if (!dest) dest = vecB; - dest[0] = vecA[0] + vecB[0]; - dest[1] = vecA[1] + vecB[1]; - return dest; - }; - - /** - * Subtracts vecB from vecA. If dest is given, the result - * is stored there. Otherwise, the result is stored in vecB. - * - * @param {vec2} vecA the first operand - * @param {vec2} vecB the second operand - * @param {vec2} [dest] the optional receiving vector - * @returns {vec2} dest - */ - vec2.subtract = function(vecA, vecB, dest) { - if (!dest) dest = vecB; - dest[0] = vecA[0] - vecB[0]; - dest[1] = vecA[1] - vecB[1]; - return dest; - }; - - /** - * Multiplies vecA with vecB. If dest is given, the result - * is stored there. Otherwise, the result is stored in vecB. - * - * @param {vec2} vecA the first operand - * @param {vec2} vecB the second operand - * @param {vec2} [dest] the optional receiving vector - * @returns {vec2} dest - */ - vec2.multiply = function(vecA, vecB, dest) { - if (!dest) dest = vecB; - dest[0] = vecA[0] * vecB[0]; - dest[1] = vecA[1] * vecB[1]; - return dest; - }; - - /** - * Divides vecA by vecB. If dest is given, the result - * is stored there. Otherwise, the result is stored in vecB. - * - * @param {vec2} vecA the first operand - * @param {vec2} vecB the second operand - * @param {vec2} [dest] the optional receiving vector - * @returns {vec2} dest - */ - vec2.divide = function(vecA, vecB, dest) { - if (!dest) dest = vecB; - dest[0] = vecA[0] / vecB[0]; - dest[1] = vecA[1] / vecB[1]; - return dest; - }; - - /** - * Scales vecA by some scalar number. If dest is given, the result - * is stored there. Otherwise, the result is stored in vecA. - * - * This is the same as multiplying each component of vecA - * by the given scalar. - * - * @param {vec2} vecA the vector to be scaled - * @param {Number} scalar the amount to scale the vector by - * @param {vec2} [dest] the optional receiving vector - * @returns {vec2} dest - */ - vec2.scale = function(vecA, scalar, dest) { - if (!dest) dest = vecA; - dest[0] = vecA[0] * scalar; - dest[1] = vecA[1] * scalar; - return dest; - }; - - /** - * Calculates the euclidian distance between two vec2 - * - * Params: - * @param {vec2} vecA First vector - * @param {vec2} vecB Second vector - * - * @returns {number} Distance between vecA and vecB - */ - vec2.dist = function (vecA, vecB) { - var x = vecB[0] - vecA[0], - y = vecB[1] - vecA[1]; - return Math.sqrt(x*x + y*y); - }; - - /** - * Copies the values of one vec2 to another - * - * @param {vec2} vec vec2 containing values to copy - * @param {vec2} dest vec2 receiving copied values - * - * @returns {vec2} dest - */ - vec2.set = function (vec, dest) { - dest[0] = vec[0]; - dest[1] = vec[1]; - return dest; - }; - - /** - * Compares two vectors for equality within a certain margin of error - * - * @param {vec2} a First vector - * @param {vec2} b Second vector - * - * @returns {Boolean} True if a is equivalent to b - */ - vec2.equal = function (a, b) { - return a === b || ( - Math.abs(a[0] - b[0]) < FLOAT_EPSILON && - Math.abs(a[1] - b[1]) < FLOAT_EPSILON - ); - }; - - /** - * Negates the components of a vec2 - * - * @param {vec2} vec vec2 to negate - * @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vec - * - * @returns {vec2} dest if specified, vec otherwise - */ - vec2.negate = function (vec, dest) { - if (!dest) { dest = vec; } - dest[0] = -vec[0]; - dest[1] = -vec[1]; - return dest; - }; - - /** - * Normlize a vec2 - * - * @param {vec2} vec vec2 to normalize - * @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vec - * - * @returns {vec2} dest if specified, vec otherwise - */ - vec2.normalize = function (vec, dest) { - if (!dest) { dest = vec; } - var mag = vec[0] * vec[0] + vec[1] * vec[1]; - if (mag > 0) { - mag = Math.sqrt(mag); - dest[0] = vec[0] / mag; - dest[1] = vec[1] / mag; - } else { - dest[0] = dest[1] = 0; - } - return dest; - }; - - /** - * Computes the cross product of two vec2's. Note that the cross product must by definition - * produce a 3D vector. If a dest vector is given, it will contain the resultant 3D vector. - * Otherwise, a scalar number will be returned, representing the vector's Z coordinate, since - * its X and Y must always equal 0. - * - * Examples: - * var crossResult = vec3.create(); - * vec2.cross([1, 2], [3, 4], crossResult); - * //=> [0, 0, -2] - * - * vec2.cross([1, 2], [3, 4]); - * //=> -2 - * - * See http://stackoverflow.com/questions/243945/calculating-a-2d-vectors-cross-product - * for some interesting facts. - * - * @param {vec2} vecA left operand - * @param {vec2} vecB right operand - * @param {vec2} [dest] optional vec2 receiving result. If not specified a scalar is returned - * - */ - vec2.cross = function (vecA, vecB, dest) { - var z = vecA[0] * vecB[1] - vecA[1] * vecB[0]; - if (!dest) return z; - dest[0] = dest[1] = 0; - dest[2] = z; - return dest; - }; - - /** - * Caclulates the length of a vec2 - * - * @param {vec2} vec vec2 to calculate length of - * - * @returns {Number} Length of vec - */ - vec2.length = function (vec) { - var x = vec[0], y = vec[1]; - return Math.sqrt(x * x + y * y); - }; - - /** - * Caclulates the squared length of a vec2 - * - * @param {vec2} vec vec2 to calculate squared length of - * - * @returns {Number} Squared Length of vec - */ - vec2.squaredLength = function (vec) { - var x = vec[0], y = vec[1]; - return x * x + y * y; - }; - - /** - * Caclulates the dot product of two vec2s - * - * @param {vec2} vecA First operand - * @param {vec2} vecB Second operand - * - * @returns {Number} Dot product of vecA and vecB - */ - vec2.dot = function (vecA, vecB) { - return vecA[0] * vecB[0] + vecA[1] * vecB[1]; - }; - - /** - * Generates a 2D unit vector pointing from one vector to another - * - * @param {vec2} vecA Origin vec2 - * @param {vec2} vecB vec2 to point to - * @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vecA - * - * @returns {vec2} dest if specified, vecA otherwise - */ - vec2.direction = function (vecA, vecB, dest) { - if (!dest) { dest = vecA; } - - var x = vecA[0] - vecB[0], - y = vecA[1] - vecB[1], - len = x * x + y * y; - - if (!len) { - dest[0] = 0; - dest[1] = 0; - dest[2] = 0; - return dest; - } - - len = 1 / Math.sqrt(len); - dest[0] = x * len; - dest[1] = y * len; - return dest; - }; - - /** - * Performs a linear interpolation between two vec2 - * - * @param {vec2} vecA First vector - * @param {vec2} vecB Second vector - * @param {Number} lerp Interpolation amount between the two inputs - * @param {vec2} [dest] vec2 receiving operation result. If not specified result is written to vecA - * - * @returns {vec2} dest if specified, vecA otherwise - */ - vec2.lerp = function (vecA, vecB, lerp, dest) { - if (!dest) { dest = vecA; } - dest[0] = vecA[0] + lerp * (vecB[0] - vecA[0]); - dest[1] = vecA[1] + lerp * (vecB[1] - vecA[1]); - return dest; - }; - - /** - * Returns a string representation of a vector - * - * @param {vec2} vec Vector to represent as a string - * - * @returns {String} String representation of vec - */ - vec2.str = function (vec) { - return '[' + vec[0] + ', ' + vec[1] + ']'; - }; - - /** - * @class 2x2 Matrix - * @name mat2 - */ - var mat2 = {}; - - /** - * Creates a new 2x2 matrix. If src is given, the new matrix - * is initialized to those values. - * - * @param {mat2} [src] the seed values for the new matrix, if any - * @returns {mat2} a new matrix - */ - mat2.create = function(src) { - var dest = new MatrixArray(4); - - if (src) { - dest[0] = src[0]; - dest[1] = src[1]; - dest[2] = src[2]; - dest[3] = src[3]; - } else { - dest[0] = dest[1] = dest[2] = dest[3] = 0; - } - return dest; - }; - - /** - * Creates a new instance of a mat2, initializing it with the given arguments - * - * @param {number} m00 - * @param {number} m01 - * @param {number} m10 - * @param {number} m11 - - * @returns {mat2} New mat2 - */ - mat2.createFrom = function (m00, m01, m10, m11) { - var dest = new MatrixArray(4); - - dest[0] = m00; - dest[1] = m01; - dest[2] = m10; - dest[3] = m11; - - return dest; - }; - - /** - * Copies the values of one mat2 to another - * - * @param {mat2} mat mat2 containing values to copy - * @param {mat2} dest mat2 receiving copied values - * - * @returns {mat2} dest - */ - mat2.set = function (mat, dest) { - dest[0] = mat[0]; - dest[1] = mat[1]; - dest[2] = mat[2]; - dest[3] = mat[3]; - return dest; - }; - - /** - * Compares two matrices for equality within a certain margin of error - * - * @param {mat2} a First matrix - * @param {mat2} b Second matrix - * - * @returns {Boolean} True if a is equivalent to b - */ - mat2.equal = function (a, b) { - return a === b || ( - Math.abs(a[0] - b[0]) < FLOAT_EPSILON && - Math.abs(a[1] - b[1]) < FLOAT_EPSILON && - Math.abs(a[2] - b[2]) < FLOAT_EPSILON && - Math.abs(a[3] - b[3]) < FLOAT_EPSILON - ); - }; - - /** - * Sets a mat2 to an identity matrix - * - * @param {mat2} [dest] mat2 to set. If omitted a new one will be created. - * - * @returns {mat2} dest - */ - mat2.identity = function (dest) { - if (!dest) { dest = mat2.create(); } - dest[0] = 1; - dest[1] = 0; - dest[2] = 0; - dest[3] = 1; - return dest; - }; - - /** - * Transposes a mat2 (flips the values over the diagonal) - * - * @param {mat2} mat mat2 to transpose - * @param {mat2} [dest] mat2 receiving transposed values. If not specified result is written to mat - * - * @param {mat2} dest if specified, mat otherwise - */ - mat2.transpose = function (mat, dest) { - // If we are transposing ourselves we can skip a few steps but have to cache some values - if (!dest || mat === dest) { - var a00 = mat[1]; - mat[1] = mat[2]; - mat[2] = a00; - return mat; - } - - dest[0] = mat[0]; - dest[1] = mat[2]; - dest[2] = mat[1]; - dest[3] = mat[3]; - return dest; - }; - - /** - * Calculates the determinant of a mat2 - * - * @param {mat2} mat mat2 to calculate determinant of - * - * @returns {Number} determinant of mat - */ - mat2.determinant = function (mat) { - return mat[0] * mat[3] - mat[2] * mat[1]; - }; - - /** - * Calculates the inverse matrix of a mat2 - * - * @param {mat2} mat mat2 to calculate inverse of - * @param {mat2} [dest] mat2 receiving inverse matrix. If not specified result is written to mat - * - * @param {mat2} dest is specified, mat otherwise, null if matrix cannot be inverted - */ - mat2.inverse = function (mat, dest) { - if (!dest) { dest = mat; } - var a0 = mat[0], a1 = mat[1], a2 = mat[2], a3 = mat[3]; - var det = a0 * a3 - a2 * a1; - if (!det) return null; - - det = 1.0 / det; - dest[0] = a3 * det; - dest[1] = -a1 * det; - dest[2] = -a2 * det; - dest[3] = a0 * det; - return dest; - }; - - /** - * Performs a matrix multiplication - * - * @param {mat2} matA First operand - * @param {mat2} matB Second operand - * @param {mat2} [dest] mat2 receiving operation result. If not specified result is written to matA - * - * @returns {mat2} dest if specified, matA otherwise - */ - mat2.multiply = function (matA, matB, dest) { - if (!dest) { dest = matA; } - var a11 = matA[0], - a12 = matA[1], - a21 = matA[2], - a22 = matA[3]; - dest[0] = a11 * matB[0] + a12 * matB[2]; - dest[1] = a11 * matB[1] + a12 * matB[3]; - dest[2] = a21 * matB[0] + a22 * matB[2]; - dest[3] = a21 * matB[1] + a22 * matB[3]; - return dest; - }; - - /** - * Rotates a 2x2 matrix by an angle - * - * @param {mat2} mat The matrix to rotate - * @param {Number} angle The angle in radians - * @param {mat2} [dest] Optional mat2 receiving the result. If omitted mat will be used. - * - * @returns {mat2} dest if specified, mat otherwise - */ - mat2.rotate = function (mat, angle, dest) { - if (!dest) { dest = mat; } - var a11 = mat[0], - a12 = mat[1], - a21 = mat[2], - a22 = mat[3], - s = Math.sin(angle), - c = Math.cos(angle); - dest[0] = a11 * c + a12 * s; - dest[1] = a11 * -s + a12 * c; - dest[2] = a21 * c + a22 * s; - dest[3] = a21 * -s + a22 * c; - return dest; - }; - - /** - * Multiplies the vec2 by the given 2x2 matrix - * - * @param {mat2} matrix the 2x2 matrix to multiply against - * @param {vec2} vec the vector to multiply - * @param {vec2} [dest] an optional receiving vector. If not given, vec is used. - * - * @returns {vec2} The multiplication result - **/ - mat2.multiplyVec2 = function(matrix, vec, dest) { - if (!dest) dest = vec; - var x = vec[0], y = vec[1]; - dest[0] = x * matrix[0] + y * matrix[1]; - dest[1] = x * matrix[2] + y * matrix[3]; - return dest; - }; - - /** - * Scales the mat2 by the dimensions in the given vec2 - * - * @param {mat2} matrix the 2x2 matrix to scale - * @param {vec2} vec the vector containing the dimensions to scale by - * @param {vec2} [dest] an optional receiving mat2. If not given, matrix is used. - * - * @returns {mat2} dest if specified, matrix otherwise - **/ - mat2.scale = function(matrix, vec, dest) { - if (!dest) { dest = matrix; } - var a11 = matrix[0], - a12 = matrix[1], - a21 = matrix[2], - a22 = matrix[3], - b11 = vec[0], - b22 = vec[1]; - dest[0] = a11 * b11; - dest[1] = a12 * b22; - dest[2] = a21 * b11; - dest[3] = a22 * b22; - return dest; - }; - - /** - * Returns a string representation of a mat2 - * - * @param {mat2} mat mat2 to represent as a string - * - * @param {String} String representation of mat - */ - mat2.str = function (mat) { - return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] + ', ' + mat[3] + ']'; - }; - - /** - * @class 4 Dimensional Vector - * @name vec4 - */ - var vec4 = {}; - - /** - * Creates a new vec4, initializing it from vec if vec - * is given. - * - * @param {vec4} [vec] the vector's initial contents - * @returns {vec4} a new 2D vector - */ - vec4.create = function(vec) { - var dest = new MatrixArray(4); - - if (vec) { - dest[0] = vec[0]; - dest[1] = vec[1]; - dest[2] = vec[2]; - dest[3] = vec[3]; - } else { - dest[0] = 0; - dest[1] = 0; - dest[2] = 0; - dest[3] = 0; - } - return dest; - }; - - /** - * Creates a new instance of a vec4, initializing it with the given arguments - * - * @param {number} x X value - * @param {number} y Y value - * @param {number} z Z value - * @param {number} w W value - - * @returns {vec4} New vec4 - */ - vec4.createFrom = function (x, y, z, w) { - var dest = new MatrixArray(4); - - dest[0] = x; - dest[1] = y; - dest[2] = z; - dest[3] = w; - - return dest; - }; - - /** - * Adds the vec4's together. If dest is given, the result - * is stored there. Otherwise, the result is stored in vecB. - * - * @param {vec4} vecA the first operand - * @param {vec4} vecB the second operand - * @param {vec4} [dest] the optional receiving vector - * @returns {vec4} dest - */ - vec4.add = function(vecA, vecB, dest) { - if (!dest) dest = vecB; - dest[0] = vecA[0] + vecB[0]; - dest[1] = vecA[1] + vecB[1]; - dest[2] = vecA[2] + vecB[2]; - dest[3] = vecA[3] + vecB[3]; - return dest; - }; - - /** - * Subtracts vecB from vecA. If dest is given, the result - * is stored there. Otherwise, the result is stored in vecB. - * - * @param {vec4} vecA the first operand - * @param {vec4} vecB the second operand - * @param {vec4} [dest] the optional receiving vector - * @returns {vec4} dest - */ - vec4.subtract = function(vecA, vecB, dest) { - if (!dest) dest = vecB; - dest[0] = vecA[0] - vecB[0]; - dest[1] = vecA[1] - vecB[1]; - dest[2] = vecA[2] - vecB[2]; - dest[3] = vecA[3] - vecB[3]; - return dest; - }; - - /** - * Multiplies vecA with vecB. If dest is given, the result - * is stored there. Otherwise, the result is stored in vecB. - * - * @param {vec4} vecA the first operand - * @param {vec4} vecB the second operand - * @param {vec4} [dest] the optional receiving vector - * @returns {vec4} dest - */ - vec4.multiply = function(vecA, vecB, dest) { - if (!dest) dest = vecB; - dest[0] = vecA[0] * vecB[0]; - dest[1] = vecA[1] * vecB[1]; - dest[2] = vecA[2] * vecB[2]; - dest[3] = vecA[3] * vecB[3]; - return dest; - }; - - /** - * Divides vecA by vecB. If dest is given, the result - * is stored there. Otherwise, the result is stored in vecB. - * - * @param {vec4} vecA the first operand - * @param {vec4} vecB the second operand - * @param {vec4} [dest] the optional receiving vector - * @returns {vec4} dest - */ - vec4.divide = function(vecA, vecB, dest) { - if (!dest) dest = vecB; - dest[0] = vecA[0] / vecB[0]; - dest[1] = vecA[1] / vecB[1]; - dest[2] = vecA[2] / vecB[2]; - dest[3] = vecA[3] / vecB[3]; - return dest; - }; - - /** - * Scales vecA by some scalar number. If dest is given, the result - * is stored there. Otherwise, the result is stored in vecA. - * - * This is the same as multiplying each component of vecA - * by the given scalar. - * - * @param {vec4} vecA the vector to be scaled - * @param {Number} scalar the amount to scale the vector by - * @param {vec4} [dest] the optional receiving vector - * @returns {vec4} dest - */ - vec4.scale = function(vecA, scalar, dest) { - if (!dest) dest = vecA; - dest[0] = vecA[0] * scalar; - dest[1] = vecA[1] * scalar; - dest[2] = vecA[2] * scalar; - dest[3] = vecA[3] * scalar; - return dest; - }; - - /** - * Copies the values of one vec4 to another - * - * @param {vec4} vec vec4 containing values to copy - * @param {vec4} dest vec4 receiving copied values - * - * @returns {vec4} dest - */ - vec4.set = function (vec, dest) { - dest[0] = vec[0]; - dest[1] = vec[1]; - dest[2] = vec[2]; - dest[3] = vec[3]; - return dest; - }; - - /** - * Compares two vectors for equality within a certain margin of error - * - * @param {vec4} a First vector - * @param {vec4} b Second vector - * - * @returns {Boolean} True if a is equivalent to b - */ - vec4.equal = function (a, b) { - return a === b || ( - Math.abs(a[0] - b[0]) < FLOAT_EPSILON && - Math.abs(a[1] - b[1]) < FLOAT_EPSILON && - Math.abs(a[2] - b[2]) < FLOAT_EPSILON && - Math.abs(a[3] - b[3]) < FLOAT_EPSILON - ); - }; - - /** - * Negates the components of a vec4 - * - * @param {vec4} vec vec4 to negate - * @param {vec4} [dest] vec4 receiving operation result. If not specified result is written to vec - * - * @returns {vec4} dest if specified, vec otherwise - */ - vec4.negate = function (vec, dest) { - if (!dest) { dest = vec; } - dest[0] = -vec[0]; - dest[1] = -vec[1]; - dest[2] = -vec[2]; - dest[3] = -vec[3]; - return dest; - }; - - /** - * Caclulates the length of a vec2 - * - * @param {vec2} vec vec2 to calculate length of - * - * @returns {Number} Length of vec - */ - vec4.length = function (vec) { - var x = vec[0], y = vec[1], z = vec[2], w = vec[3]; - return Math.sqrt(x * x + y * y + z * z + w * w); - }; - - /** - * Caclulates the squared length of a vec4 - * - * @param {vec4} vec vec4 to calculate squared length of - * - * @returns {Number} Squared Length of vec - */ - vec4.squaredLength = function (vec) { - var x = vec[0], y = vec[1], z = vec[2], w = vec[3]; - return x * x + y * y + z * z + w * w; - }; - - /** - * Performs a linear interpolation between two vec4 - * - * @param {vec4} vecA First vector - * @param {vec4} vecB Second vector - * @param {Number} lerp Interpolation amount between the two inputs - * @param {vec4} [dest] vec4 receiving operation result. If not specified result is written to vecA - * - * @returns {vec4} dest if specified, vecA otherwise - */ - vec4.lerp = function (vecA, vecB, lerp, dest) { - if (!dest) { dest = vecA; } - dest[0] = vecA[0] + lerp * (vecB[0] - vecA[0]); - dest[1] = vecA[1] + lerp * (vecB[1] - vecA[1]); - dest[2] = vecA[2] + lerp * (vecB[2] - vecA[2]); - dest[3] = vecA[3] + lerp * (vecB[3] - vecA[3]); - return dest; - }; - - /** - * Returns a string representation of a vector - * - * @param {vec4} vec Vector to represent as a string - * - * @returns {String} String representation of vec - */ - vec4.str = function (vec) { - return '[' + vec[0] + ', ' + vec[1] + ', ' + vec[2] + ', ' + vec[3] + ']'; - }; - - /* - * Exports - */ - - if(root) { - root.glMatrixArrayType = MatrixArray; - root.MatrixArray = MatrixArray; - root.setMatrixArrayType = setMatrixArrayType; - root.determineMatrixArrayType = determineMatrixArrayType; - root.glMath = glMath; - root.vec2 = vec2; - root.vec3 = vec3; - root.vec4 = vec4; - root.mat2 = mat2; - root.mat3 = mat3; - root.mat4 = mat4; - root.quat4 = quat4; - } - - return { - glMatrixArrayType: MatrixArray, - MatrixArray: MatrixArray, - setMatrixArrayType: setMatrixArrayType, - determineMatrixArrayType: determineMatrixArrayType, - glMath: glMath, - vec2: vec2, - vec3: vec3, - vec4: vec4, - mat2: mat2, - mat3: mat3, - mat4: mat4, - quat4: quat4 - }; -})); diff --git a/part1/noise3D.js b/part1/noise3D.js deleted file mode 100644 index d519f47..0000000 --- a/part1/noise3D.js +++ /dev/null @@ -1,316 +0,0 @@ -(function(exports) { - "use strict"; - /*global window,vec3*/ - - exports = exports || window; - - function step(edge, x) { - return [ - (x[0] < edge[0]) ? 0.0 : 1.0, - (x[1] < edge[1]) ? 0.0 : 1.0, - (x[2] < edge[2]) ? 0.0 : 1.0 - ]; - } - - function step_vec4(edge, x) { - return [ - (x[0] < edge[0]) ? 0.0 : 1.0, - (x[1] < edge[1]) ? 0.0 : 1.0, - (x[2] < edge[2]) ? 0.0 : 1.0, - (x[3] < edge[3]) ? 0.0 : 1.0 - ]; - } - - function min(x, y) { - return [ - y[0] < x[0] ? y[0] : x[0], - y[1] < x[1] ? y[1] : x[1], - y[2] < x[2] ? y[2] : x[2] - ]; - } - - function max(x, y) { - return [ - y[0] > x[0] ? y[0] : x[0], - y[1] > x[1] ? y[1] : x[1], - y[2] > x[2] ? y[2] : x[2] - ]; - } - - function max_vec4(x, y) { - return [ - y[0] > x[0] ? y[0] : x[0], - y[1] > x[1] ? y[1] : x[1], - y[2] > x[2] ? y[2] : x[2], - y[3] > x[3] ? y[3] : x[3] - ]; - } - - function vec4_dot(left, right) { - return left[0] * right[0] + - left[1] * right[1] + - left[2] * right[2] + - left[3] * right[3]; - } - - // - // Description : Array and textureless GLSL 2D/3D/4D simplex - // noise functions. - // Author : Ian McEwan, Ashima Arts. - // Maintainer : ijm - // Lastmod : 20110822 (ijm) - // License : Copyright (C) 2011 Ashima Arts. All rights reserved. - // Distributed under the MIT License. See LICENSE file. - // https://github.com/ashima/webgl-noise - // - function mod289_vec3(x) { - var temp = (1.0 / 289.0); - return [ - x[0] - Math.floor(x[0] * temp) * 289.0, - x[1] - Math.floor(x[1] * temp) * 289.0, - x[2] - Math.floor(x[2] * temp) * 289.0 - ]; - } - - function mod289_vec4(x) { - var temp = (1.0 / 289.0); - return [ - x[0] - Math.floor(x[0] * temp) * 289.0, - x[1] - Math.floor(x[1] * temp) * 289.0, - x[2] - Math.floor(x[2] * temp) * 289.0, - x[3] - Math.floor(x[3] * temp) * 289.0 - ]; - } - - function permute_vec4(x) { - return mod289_vec4([ - ((x[0]*34.0)+1.0)*x[0], - ((x[1]*34.0)+1.0)*x[1], - ((x[2]*34.0)+1.0)*x[2], - ((x[3]*34.0)+1.0)*x[3] - ]); - } - - function taylorInvSqrt_vec4(r) { - return [ - 1.79284291400159 - 0.85373472095314 * r[0], - 1.79284291400159 - 0.85373472095314 * r[1], - 1.79284291400159 - 0.85373472095314 * r[2], - 1.79284291400159 - 0.85373472095314 * r[3] - ]; - } - - exports.snoise = function(v) { - // const vec2 C = vec2(1.0f/6.0f, 1.0f/3.0f) ; - // const vec4 D = vec4(0.0f, 0.5f, 1.0f, 2.0f); - var C = [1.0/6.0, 1.0/3.0]; - var D = [0.0, 0.5, 1.0, 2.0]; - - // vec3 i = floor(v + dot(v, vec3(C.y, C.y, C.y)) ); - // vec3 x0 = v - i + dot(i, vec3(C.x, C.x, C.x) ); - var temp0 = vec3.create(); - var temp3 = vec3.dot(v, [C[1], C[1], C[1]]); - vec3.add(v, [temp3, temp3, temp3], temp0); - var i = [Math.floor(temp0[0]), Math.floor(temp0[1]), Math.floor(temp0[2])]; - var temp1 = vec3.create(); - vec3.subtract(v, i, temp1); - var temp2 = vec3.dot(i, [C[0], C[0], C[0]]); - var x0 = vec3.create(); - vec3.add(temp1, [temp2, temp2, temp2], x0); - - // vec3 g = step(vec3(x0.y, x0.z, x0.x), vec3(x0.x, x0.y, x0.z)); - // vec3 l = 1.0f - g; - // vec3 i1 = min( vec3(g.x, g.y, g.z), vec3(l.z, l.x, l.y) ); - // vec3 i2 = max( vec3(g.x, g.y, g.z), vec3(l.z, l.x, l.y) ); - var g = step([x0[1], x0[2], x0[0]], [x0[0], x0[1], x0[2]]); - var l = [1.0 - g[0], 1.0 - g[1], 1.0 - g[2]]; - var i1 = min([g[0], g[1], g[2]], [l[2], l[0], l[1]]); - var i2 = max([g[0], g[1], g[2]], [l[2], l[0], l[1]]); - - // vec3 x1 = x0 - i1 + vec3(C.x, C.x, C.x); - // vec3 x2 = x0 - i2 + vec3(C.y, C.y, C.y); // 2.0*C.x = 1/3 = C.y - // vec3 x3 = x0 - vec3(D.y, D.y, D.y); // -1.0+3.0*C.x = -0.5 = -D.y - var temp4 = vec3.create(); - vec3.subtract(x0, i1, temp4); - var x1 = vec3.create(); - vec3.add(temp4, [C[0], C[0], C[0]], x1); - var temp5 = vec3.create(); - vec3.subtract(x0, i2, temp5); - var x2 = vec3.create(); - vec3.add(temp5, [C[1], C[1], C[1]], x2); - var x3 = vec3.create(); - vec3.subtract(x0, [D[1], D[1], D[1]], x3); - - // i = mod289(i); - // vec4 p = permute( permute( permute( - // i.z + vec4(0.0, i1.z, i2.z, 1.0 )) - // + i.y + vec4(0.0, i1.y, i2.y, 1.0 )) - // + i.x + vec4(0.0, i1.x, i2.x, 1.0 )); - i = mod289_vec3(i); - var p = permute_vec4([i[2] + 0.0, i[2] + i1[2], i[2] + i2[2], i[2] + 1.0]); - p[0] += i[1] + 0.0; - p[1] += i[1] + i1[1]; - p[2] += i[1] + i2[1]; - p[3] += i[1] + 1.0; - p = permute_vec4(p); - p[0] += i[0] + 0.0; - p[1] += i[0] + i1[0]; - p[2] += i[0] + i2[0]; - p[3] += i[0] + 1.0; - p = permute_vec4(p); - - // float n_ = 0.142857142857f; // 1.0/7.0 - // vec3 ns = n_ * vec3(D.w, D.y, D.z) - vec3(D.x, D.z, D.x); -// var n_ = 0.142857142857; // 1.0/7.0 -// var ns = [ -// n_ * D[3] - D[0], -// n_ * D[1] - D[2], -// n_ * D[2] - D[0] -// ]; - var ns = [ - 0.28571430, - -0.92857140, - 0.14285715 - ]; - - // vec4 j = p - 49.0f * floor(p * ns.z * ns.z); // mod(p,7*7) - var j = [ - p[0] - 49.0 * Math.floor(p[0] * ns[2] * ns[2]), - p[1] - 49.0 * Math.floor(p[1] * ns[2] * ns[2]), - p[2] - 49.0 * Math.floor(p[2] * ns[2] * ns[2]), - p[3] - 49.0 * Math.floor(p[3] * ns[2] * ns[2]) - ]; - - // vec4 x_ = floor(j * ns.z); - // vec4 y_ = floor(j - 7.0f * x_ ); // mod(j,N) - var x_ = [ - Math.floor(j[0] * ns[2]), - Math.floor(j[1] * ns[2]), - Math.floor(j[2] * ns[2]), - Math.floor(j[3] * ns[2]) - ]; - var y_ = [ - Math.floor(j[0] - 7.0 * x_[0] ), - Math.floor(j[1] - 7.0 * x_[1] ), - Math.floor(j[2] - 7.0 * x_[2] ), - Math.floor(j[3] - 7.0 * x_[3] ) - ]; - - // vec4 x = x_ *ns.x + vec4(ns.y, ns.y, ns.y, ns.y); - // vec4 y = y_ *ns.x + vec4(ns.y, ns.y, ns.y, ns.y); - // vec4 h = 1.0f - abs(x) - abs(y); - var x = [ - x_[0] *ns[0] + ns[1], - x_[1] *ns[0] + ns[1], - x_[2] *ns[0] + ns[1], - x_[3] *ns[0] + ns[1] - ]; - var y = [ - y_[0] *ns[0] + ns[1], - y_[1] *ns[0] + ns[1], - y_[2] *ns[0] + ns[1], - y_[3] *ns[0] + ns[1] - ]; - var h = [ - 1.0 - Math.abs(x[0]) - Math.abs(y[0]), - 1.0 - Math.abs(x[1]) - Math.abs(y[1]), - 1.0 - Math.abs(x[2]) - Math.abs(y[2]), - 1.0 - Math.abs(x[3]) - Math.abs(y[3]) - ]; - - // vec4 b0 = vec4( vec2(x.x, x.y), vec2(y.x, y.y) ); - // vec4 b1 = vec4( vec2(x.z, x.w), vec2(y.z, y.w) ); - var b0 = [x[0], x[1], y[0], y[1]]; - var b1 = [x[2], x[3], y[2], y[3]]; - - // vec4 s0 = floor(b0)*2.0f + 1.0f; - // vec4 s1 = floor(b1)*2.0f + 1.0f; - // vec4 sh = -step(h, vec4(0.0)); - - var s0 = [ - Math.floor(b0[0])*2.0 + 1.0, - Math.floor(b0[1])*2.0 + 1.0, - Math.floor(b0[2])*2.0 + 1.0, - Math.floor(b0[3])*2.0 + 1.0 - ]; - var s1 = [ - Math.floor(b1[0])*2.0 + 1.0, - Math.floor(b1[1])*2.0 + 1.0, - Math.floor(b1[2])*2.0 + 1.0, - Math.floor(b1[3])*2.0 + 1.0 - ]; - var sh = step_vec4(h, [0.0, 0.0, 0.0, 0.0]); - sh[0] = -sh[0]; - sh[1] = -sh[1]; - sh[2] = -sh[2]; - sh[3] = -sh[3]; - - // vec4 a0 = vec4(b0.x, b0.z, b0.y, b0.w) + vec4(s0.x, s0.z, s0.y, s0.w) * vec4(sh.x, sh.x, sh.y, sh.y) ; - // vec4 a1 = vec4(b1.x, b1.z, b1.y, b1.w) + vec4(s1.x, s1.z, s1.y, s1.w) * vec4(sh.z, sh.z, sh.w, sh.w) ; - var a0 = [ - b0[0] + s0[0] * sh[0], - b0[2] + s0[2] * sh[0], - b0[1] + s0[1] * sh[1], - b0[3] + s0[3] * sh[1] - ]; - var a1 = [ - b1[0] + s1[0] * sh[2], - b1[2] + s1[2] * sh[2], - b1[1] + s1[1] * sh[3], - b1[3] + s1[3] * sh[3] - ]; - - // vec3 p0 = vec3(a0.x, a0.y, h.x); - // vec3 p1 = vec3(a0.z, a0.w, h.y); - // vec3 p2 = vec3(a1.x, a1.y, h.z); - // vec3 p3 = vec3(a1.z, a1.w, h.w); - var p0 = [a0[0], a0[1], h[0]]; - var p1 = [a0[2], a0[3], h[1]]; - var p2 = [a1[0], a1[1], h[2]]; - var p3 = [a1[2], a1[3], h[3]]; - - // vec4 norm = taylorInvSqrt(vec4(dot(p0,p0), dot(p1,p1), dot(p2, p2), dot(p3,p3))); - // p0 *= norm.x; - // p1 *= norm.y; - // p2 *= norm.z; - // p3 *= norm.w; - var norm = taylorInvSqrt_vec4([vec3.dot(p0,p0), vec3.dot(p1,p1), vec3.dot(p2, p2), vec3.dot(p3,p3)]); - p0 = [p0[0]*norm[0], p0[1]*norm[0], p0[2]*norm[0]]; - p1 = [p1[0]*norm[1], p1[1]*norm[1], p1[2]*norm[1]]; - p2 = [p2[0]*norm[2], p2[1]*norm[2], p2[2]*norm[2]]; - p3 = [p3[0]*norm[3], p3[1]*norm[3], p3[2]*norm[3]]; - - // vec4 m = max(0.6f - vec4(dot(x0,x0), dot(x1,x1), dot(x2,x2), dot(x3,x3)), 0.0); - // m = m * m; - var m = max_vec4([ - 0.6 - vec3.dot(x0,x0), - 0.6 - vec3.dot(x1,x1), - 0.6 - vec3.dot(x2,x2), - 0.6 - vec3.dot(x3,x3) - ], [ - 0.0, - 0.0, - 0.0, - 0.0 - ]); - m[0] *= m[0]; - m[1] *= m[1]; - m[2] *= m[2]; - m[3] *= m[3]; - - // return 42.0f * dot( m*m, vec4( dot(p0,x0), dot(p1,x1), - // dot(p2,x2), dot(p3,x3) ) ); - return 42.0 * vec4_dot([ - m[0] * m[0], - m[1] * m[1], - m[2] * m[2], - m[3] * m[3] - ], [ - vec3.dot(p0,x0), - vec3.dot(p1,x1), - vec3.dot(p2,x2), - vec3.dot(p3,x3) - ]); - }; - -}()); diff --git a/part1/simplex.vert b/part1/simplex.vert deleted file mode 100644 index 13dd1ca..0000000 --- a/part1/simplex.vert +++ /dev/null @@ -1,39 +0,0 @@ -vec3 permute(vec3 x) { - x = ((x*34.0)+1.0)*x; - return x - floor(x * (1.0 / 289.0)) * 289.0; -} - -float simplexNoise(vec2 v) - { - const vec4 C = vec4(0.211324865405187, 0.366025403784439, -0.577350269189626, 0.024390243902439); - - vec2 i = floor(v + dot(v, C.yy) ); - vec2 x0 = v - i + dot(i, C.xx); - - vec2 i1; - i1 = (x0.x > x0.y) ? vec2(1.0, 0.0) : vec2(0.0, 1.0); - - vec4 x12 = x0.xyxy + C.xxzz; - x12.xy -= i1; - - i = i - floor(i * (1.0 / 289.0)) * 289.0; - - vec3 p = permute( permute( i.y + vec3(0.0, i1.y, 1.0 )) - + i.x + vec3(0.0, i1.x, 1.0 )); - - vec3 m = max(0.5 - vec3(dot(x0,x0), dot(x12.xy,x12.xy), dot(x12.zw,x12.zw)), 0.0); - m = m*m ; - m = m*m ; - - vec3 x = 2.0 * fract(p * C.www) - 1.0; - vec3 h = abs(x) - 0.5; - vec3 ox = floor(x + 0.5); - vec3 a0 = x - ox; - - m *= inversesqrt( a0*a0 + h*h ); - - vec3 g; - g.x = a0.x * x0.x + h.x * x0.y; - g.yz = a0.yz * x12.xz + h.yz * x12.yw; - return 130.0 * dot(m, g); -} \ No newline at end of file diff --git a/part1/simplex_wave.html b/part1/simplex_wave.html deleted file mode 100644 index 15b6c76..0000000 --- a/part1/simplex_wave.html +++ /dev/null @@ -1,86 +0,0 @@ -<html> - -<head> -<title>Vertex Simplex Noise Wave</title> -<meta charset ="utf-8"> -<meta http-equiv="X-UA-Compatible" content="chrome=1"> <!-- Use Chrome Frame in IE --> -</head> - -<body> -<div id="message" style="position:absolute;top:100px"></div> <!-- Pixel offset to avoid FPS counter --> -<canvas id="canvas" style="border: none;" width="1024" height="768" tabindex="1"></canvas> - -<script id="vs" type="x-shader/x-vertex"> - attribute vec2 position; - - uniform mat4 u_modelViewPerspective; - uniform float u_time; - varying float height; - - vec3 permute(vec3 x) { - x = ((x*34.0)+1.0)*x; - return x - floor(x * (1.0 / 289.0)) * 289.0; - } - - float simplexNoise(vec2 v) - { - const vec4 C = vec4(0.211324865405187, 0.366025403784439, -0.577350269189626, 0.024390243902439); - - vec2 i = floor(v + dot(v, C.yy) ); - vec2 x0 = v - i + dot(i, C.xx); - - vec2 i1; - i1 = (x0.x > x0.y) ? vec2(1.0, 0.0) : vec2(0.0, 1.0); - - vec4 x12 = x0.xyxy + C.xxzz; - x12.xy -= i1; - - i = i - floor(i * (1.0 / 289.0)) * 289.0; - - vec3 p = permute( permute( i.y + vec3(0.0, i1.y, 1.0 )) - + i.x + vec3(0.0, i1.x, 1.0 )); - - vec3 m = max(0.5 - vec3(dot(x0,x0), dot(x12.xy,x12.xy), dot(x12.zw,x12.zw)), 0.0); - m = m*m ; - m = m*m ; - - vec3 x = 2.0 * fract(p * C.www) - 1.0; - vec3 h = abs(x) - 0.5; - vec3 ox = floor(x + 0.5); - vec3 a0 = x - ox; - - m *= inversesqrt( a0*a0 + h*h ); - - vec3 g; - g.x = a0.x * x0.x + h.x * x0.y; - g.yz = a0.yz * x12.xz + h.yz * x12.yw; - return 130.0 * dot(m, g); - } - - void main(void) - { - vec2 simplexVec = vec2(u_time, position); - float s_contrib = simplexNoise(simplexVec); - float t_contrib = simplexNoise(vec2(s_contrib,u_time)); - height = s_contrib*t_contrib; - gl_Position = u_modelViewPerspective * vec4(vec3(position, height), 1.0); - } -</script> - -<script id="fs" type="x-shader/x-fragment"> - precision mediump float; - - varying float height; - void main(void) - { - //Height ranges from -1 to 1. Scale appropriately - gl_FragColor = vec4(mix(vec3(1.0, 0.0,0.0), vec3(0.0,0.0,1.0), (height*0.5+0.5)),1.0); - } -</script> - -<script src ="gl-matrix.js" type ="text/javascript"></script> -<script src ="webGLUtility.js" type ="text/javascript"></script> -<script src ="vert_wave.js" type ="text/javascript"></script> -</body> - -</html> diff --git a/part1/vert_wave.html b/part1/vert_wave.html deleted file mode 100644 index 3f6f690..0000000 --- a/part1/vert_wave.html +++ /dev/null @@ -1,45 +0,0 @@ -<html> - -<head> -<title>Vertex Sine Wave</title> -<meta charset ="utf-8"> -<meta http-equiv="X-UA-Compatible" content="chrome=1"> <!-- Use Chrome Frame in IE --> -</head> - -<body> -<div id="message" style="position:absolute;top:100px"></div> <!-- Pixel offset to avoid FPS counter --> -<canvas id="canvas" style="border: none;" width="1024" height="768" tabindex="1"></canvas> - -<script id="vs" type="x-shader/x-vertex"> - attribute vec2 position; - - uniform mat4 u_modelViewPerspective; - uniform float u_time; - varying float height; - - void main(void) - { - float s_contrib = sin(position.x*2.0*3.14159 + u_time); - float t_contrib = cos(position.y*2.0*3.14159 + u_time); - height = s_contrib*t_contrib; - gl_Position = u_modelViewPerspective * vec4(vec3(position, height), 1.0); - } -</script> - -<script id="fs" type="x-shader/x-fragment"> - precision mediump float; - - varying float height; - void main(void) - { - //Height ranges from -1 to 1. Scale appropriately - gl_FragColor = vec4(mix(vec3(1.0, 0.0,0.0), vec3(0.0,0.0,1.0), (height*0.5+0.5)),1.0); - } -</script> - -<script src ="gl-matrix.js" type ="text/javascript"></script> -<script src ="webGLUtility.js" type ="text/javascript"></script> -<script src ="vert_wave.js" type ="text/javascript"></script> -</body> - -</html> diff --git a/part1/vert_wave.js b/part1/vert_wave.js deleted file mode 100644 index 433541e..0000000 --- a/part1/vert_wave.js +++ /dev/null @@ -1,157 +0,0 @@ -(function() { - "use strict"; - /*global window,document,Float32Array,Uint16Array,mat4,vec3,snoise*/ - /*global getShaderSource,createWebGLContext,createProgram*/ - - var NUM_WIDTH_PTS = 32; - var NUM_HEIGHT_PTS = 32; - - var message = document.getElementById("message"); - var canvas = document.getElementById("canvas"); - var context = createWebGLContext(canvas, message); - if (!context) { - return; - } - - /////////////////////////////////////////////////////////////////////////// - - context.viewport(0, 0, canvas.width, canvas.height); - context.clearColor(1.0, 1.0, 1.0, 1.0); - context.enable(context.DEPTH_TEST); - - var persp = mat4.create(); - mat4.perspective(45.0, 0.5, 0.1, 100.0, persp); - - var eye = [2.0, 1.0, 3.0]; - var center = [0.0, 0.0, 0.0]; - var up = [0.0, 0.0, 1.0]; - var view = mat4.create(); - mat4.lookAt(eye, center, up, view); - - var positionLocation = 0; - var heightLocation = 1; - var u_modelViewPerspectiveLocation; - var u_timeLocation; - - - (function initializeShader() { - var program; - var vs = getShaderSource(document.getElementById("vs")); - var fs = getShaderSource(document.getElementById("fs")); - - var program = createProgram(context, vs, fs, message); - context.bindAttribLocation(program, positionLocation, "position"); - u_timeLocation = context.getUniformLocation(program,"u_time"); - u_modelViewPerspectiveLocation = context.getUniformLocation(program,"u_modelViewPerspective"); - context.useProgram(program); - })(); - - var heights; - var numberOfIndices; - - (function initializeGrid() { - function uploadMesh(positions, heights, indices) { - // Positions - var positionsName = context.createBuffer(); - context.bindBuffer(context.ARRAY_BUFFER, positionsName); - context.bufferData(context.ARRAY_BUFFER, positions, context.STATIC_DRAW); - context.vertexAttribPointer(positionLocation, 2, context.FLOAT, false, 0, 0); - context.enableVertexAttribArray(positionLocation); - - if (heights) - { - // Heights - var heightsName = context.createBuffer(); - context.bindBuffer(context.ARRAY_BUFFER, heightsName); - context.bufferData(context.ARRAY_BUFFER, heights.length * heights.BYTES_PER_ELEMENT, context.STREAM_DRAW); - context.vertexAttribPointer(heightLocation, 1, context.FLOAT, false, 0, 0); - context.enableVertexAttribArray(heightLocation); - } - - // Indices - var indicesName = context.createBuffer(); - context.bindBuffer(context.ELEMENT_ARRAY_BUFFER, indicesName); - context.bufferData(context.ELEMENT_ARRAY_BUFFER, indices, context.STATIC_DRAW); - } - - var WIDTH_DIVISIONS = NUM_WIDTH_PTS - 1; - var HEIGHT_DIVISIONS = NUM_HEIGHT_PTS - 1; - - var numberOfPositions = NUM_WIDTH_PTS * NUM_HEIGHT_PTS; - - var positions = new Float32Array(2 * numberOfPositions); - var indices = new Uint16Array(2 * ((NUM_HEIGHT_PTS * (NUM_WIDTH_PTS - 1)) + (NUM_WIDTH_PTS * (NUM_HEIGHT_PTS - 1)))); - - var positionsIndex = 0; - var indicesIndex = 0; - var length; - - for (var j = 0; j < NUM_WIDTH_PTS; ++j) - { - positions[positionsIndex++] = j /(NUM_WIDTH_PTS - 1); - positions[positionsIndex++] = 0.0; - - if (j>=1) - { - length = positionsIndex / 2; - indices[indicesIndex++] = length - 2; - indices[indicesIndex++] = length - 1; - } - } - - for (var i = 0; i < HEIGHT_DIVISIONS; ++i) - { - var v = (i + 1) / (NUM_HEIGHT_PTS - 1); - positions[positionsIndex++] = 0.0; - positions[positionsIndex++] = v; - - length = (positionsIndex / 2); - indices[indicesIndex++] = length - 1; - indices[indicesIndex++] = length - 1 - NUM_WIDTH_PTS; - - for (var k = 0; k < WIDTH_DIVISIONS; ++k) - { - positions[positionsIndex++] = (k + 1) / (NUM_WIDTH_PTS - 1); - positions[positionsIndex++] = v; - - length = positionsIndex / 2; - var new_pt = length - 1; - indices[indicesIndex++] = new_pt - 1; // Previous side - indices[indicesIndex++] = new_pt; - - indices[indicesIndex++] = new_pt - NUM_WIDTH_PTS; // Previous bottom - indices[indicesIndex++] = new_pt; - } - } - - uploadMesh(positions, heights, indices); - numberOfIndices = indices.length; - })(); - - var time = 0.0; - var delT = 0.01; - (function animate(){ - /////////////////////////////////////////////////////////////////////////// - // Update - - var model = mat4.create(); - mat4.identity(model); - mat4.translate(model, [-0.5, -0.5, 0.0]); - var mv = mat4.create(); - mat4.multiply(view, model, mv); - var mvp = mat4.create(); - mat4.multiply(persp, mv, mvp); - time = time + delT; - - /////////////////////////////////////////////////////////////////////////// - // Render - context.clear(context.COLOR_BUFFER_BIT | context.DEPTH_BUFFER_BIT); - - context.uniformMatrix4fv(u_modelViewPerspectiveLocation, false, mvp); - context.uniform1f(u_timeLocation, time); - context.drawElements(context.LINES, numberOfIndices, context.UNSIGNED_SHORT,0); - - window.requestAnimFrame(animate); - })(); - -}()); diff --git a/part1/water_wave.html b/part1/water_wave.html deleted file mode 100644 index 1f22a26..0000000 --- a/part1/water_wave.html +++ /dev/null @@ -1,50 +0,0 @@ -<html> - -<head> -<title>Water Wave</title> -<meta charset ="utf-8"> -<meta http-equiv="X-UA-Compatible" content="chrome=1"> <!-- Use Chrome Frame in IE --> -</head> - -<body> -<div id="message" style="position:absolute;top:100px"></div> <!-- Pixel offset to avoid FPS counter --> -<canvas id="canvas" style="border: none;" width="1024" height="768" tabindex="1"></canvas> - -<script id="vs" type="x-shader/x-vertex"> - attribute vec2 position; - - uniform mat4 u_modelViewPerspective; - uniform float u_time; - varying float height; - - void main(void) - { - vec2 waveDir = normalize(vec2(1.0,-1.0));//Direction of wave in X Y plane - //Projection of position onto wave direction from origin gives time offset - //Constant factor here is cosmetic - float wavefrontFactor = 3.0*dot(position, waveDir); - - //Constants here are cosmetic - vec2 hor_perturb = 0.15*waveDir*(cos(u_time*3.14159 + wavefrontFactor)); - height = 0.25*sin(u_time*3.14159 + wavefrontFactor); - gl_Position = u_modelViewPerspective * vec4(vec3(position+hor_perturb, height), 1.0); - } -</script> - -<script id="fs" type="x-shader/x-fragment"> - precision mediump float; - - varying float height; - void main(void) - { - //Height ranges from -1 to 1. Scale appropriately - gl_FragColor = vec4(mix(vec3(1.0, 0.0,0.0), vec3(0.0,0.0,1.0), (height*0.5+0.5)),1.0); - } -</script> - -<script src ="gl-matrix.js" type ="text/javascript"></script> -<script src ="webGLUtility.js" type ="text/javascript"></script> -<script src ="vert_wave.js" type ="text/javascript"></script> -</body> - -</html> diff --git a/part1/webGLUtility.js b/part1/webGLUtility.js deleted file mode 100644 index ae19646..0000000 --- a/part1/webGLUtility.js +++ /dev/null @@ -1,112 +0,0 @@ -(function(exports) { - "use strict"; - /*global window*/ - - exports = exports || window; - - /////////////////////////////////////////////////////////////////////////// - // Shim from http://paulirish.com/2011/requestanimationframe-for-smart-animating/ - - exports.requestAnimFrame = - window.requestAnimationFrame || - window.webkitRequestAnimationFrame || - window.mozRequestAnimationFrame || - window.oRequestAnimationFrame || - window.msRequestAnimationFrame || - function( callback ){ - window.setTimeout(callback, 1000 / 60); - }; - - /////////////////////////////////////////////////////////////////////////// - // getShader based on http://learningwebgl.com/cookbook/index.php/Loading_shaders_from_HTML_script_tags - - exports.getShaderSource = function(script) { - var str = ""; - var k = script.firstChild; - while (k) { - if (k.nodeType == 3) { - str += k.textContent; - } - k = k.nextSibling; - } - - return str; - }; - - /////////////////////////////////////////////////////////////////////////// - - exports.createWebGLContext = function(canvas, message) { - if (!window.WebGLRenderingContext) { - message.innerText = "The browser does not support WebGL. Visit http://get.webgl.org."; - return undefined; - } - var options = { alpha: false }; - var context = canvas.getContext("experimental-webgl", options); - - if (!context && message) { - message.innerText = "The browser supports WebGL, but initialization failed."; - } - - return context; - }; - - exports.createProgram = function(context, vertexShaderSource, fragmentShaderSource, message) { - var program = context.createProgram(); - var vs = context.createShader(context.VERTEX_SHADER); - var fs = context.createShader(context.FRAGMENT_SHADER); - - context.attachShader(program, vs); - context.attachShader(program, fs); - - // Mark shader for deletion when the program is deleted - context.deleteShader(vs); - context.deleteShader(fs); - - context.shaderSource(vs, vertexShaderSource); - context.compileShader(vs); - if (!context.getShaderParameter(vs, context.COMPILE_STATUS)) { - if (message) { - message.innerText += context.getShaderInfoLog(vs) + "\n"; - alert(context.getShaderInfoLog(vs)); - } - else - { - alert(context.getShaderInfoLog(vs)); - } - context.deleteProgram(program); - return; - } - - context.shaderSource(fs, fragmentShaderSource); - context.compileShader(fs); - if (!context.getShaderParameter(fs, context.COMPILE_STATUS)) { - if (message) { - message.innerText += context.getShaderInfoLog(fs) + "\n"; - alert(context.getShaderInfoLog(fs)); - } - else - { - alert(context.getShaderInfoLog(fs)); - } - context.deleteProgram(program); - return; - } - - context.linkProgram(program); - if (!context.getProgramParameter(program, context.LINK_STATUS)) { - if (message) { - message.innerText += context.getProgramInfoLog(program) + "\n"; - alert(context.getShaderInfoLog(program)); - } - else - { - alert(context.getShaderInfoLog(program)); - } - context.deleteProgram(program); - return; - } - - return program; - }; - -}()); From 98621f5424b1d5d420c6cfc3b3fc9e8205c2da40 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Mon, 4 Nov 2013 15:49:07 -0500 Subject: [PATCH 09/27] Update README.md --- README.md | 9 ++++++--- 1 file changed, 6 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index 06fcfd4..90650d9 100644 --- a/README.md +++ b/README.md @@ -1,10 +1,13 @@ ------------------------------------------------------------------------------- -CIS565: Project 5: WebGL +CIS565: Basic WebGL Shaders (VBO based Waves and Globe Shading) ------------------------------------------------------------------------------- Fall 2013 ------------------------------------------------------------------------------- -Due Friday 11/08/2013 -------------------------------------------------------------------------------- + +![Water Wave](/resources/water.gif "Water") +![Sine Wave](/resources/sine.gif "Sine Wave") +![Simplex Noise](/resources/simplex.gif "Simplex Noise") + ------------------------------------------------------------------------------- NOTE: From 1132069bcb3d5c85b3569546dbcc94679855df4e Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Mon, 4 Nov 2013 17:47:44 -0500 Subject: [PATCH 10/27] Update README.md --- README.md | 125 +++++++++--------------------------------------------- 1 file changed, 19 insertions(+), 106 deletions(-) diff --git a/README.md b/README.md index 90650d9..28bcedd 100644 --- a/README.md +++ b/README.md @@ -1,12 +1,11 @@ ------------------------------------------------------------------------------- -CIS565: Basic WebGL Shaders (VBO based Waves and Globe Shading) +WebGL Shaders +(Simple Waves and Globe Rendering) ------------------------------------------------------------------------------- Fall 2013 ------------------------------------------------------------------------------- ![Water Wave](/resources/water.gif "Water") -![Sine Wave](/resources/sine.gif "Sine Wave") -![Simplex Noise](/resources/simplex.gif "Simplex Noise") ------------------------------------------------------------------------------- @@ -21,115 +20,29 @@ This project also requires a WebGL capable browser. The project is known to have issues with Chrome on windows, but Firefox seems to run it fine. ------------------------------------------------------------------------------- -INTRODUCTION: +Wave Rendering ------------------------------------------------------------------------------- -In this project, you will get introduced to the world of GLSL in two parts: -vertex shading and fragment shading. The first part of this project is the -Image Processor, and the second part of this project is a Wave Vertex Shader. - -In the first part of this project, you will implement a GLSL vertex shader as -part of a WebGL demo. You will create a dynamic wave animation using code that -runs entirely on the GPU. - -In the second part of this project, you will implement a GLSL fragment shader -to render an interactive globe in WebGL. This will include texture blending, -bump mapping, specular masking, and adding a cloud layer to give your globe a -uniquie feel. - -------------------------------------------------------------------------------- -CONTENTS: -------------------------------------------------------------------------------- -The Project4 root directory contains the following subdirectories: - -* part1/ contains the base code for the Wave Vertex Shader. -* part2/ contains the base code for the Globe Fragment Shader. -* resources/ contains the screenshots found in this readme file. - -------------------------------------------------------------------------------- -PART 1 REQUIREMENTS: -------------------------------------------------------------------------------- - -In Part 1, you are given code for: - -* Drawing a VBO through WebGL -* Javascript code for interfacing with WebGL -* Functions for generating simplex noise - -You are required to implement the following: - -* A sin-wave based vertex shader: +This section is just a simple demo of JS/WebGL Interaction and shader implementation. +Three different waveforms can be animated: -![Example sin wave grid](resources/sinWaveGrid.png) - -* A simplex noise based vertex shader: - -![Example simplex noise wave grid](resources/oceanWave.png) - -* One interesting vertex shader of your choice +**Sine Wave** +![Sine Wave](/resources/sine.gif "Sine Wave") +* Open vert_wave.html to see this animation. +* The 2D sine wave is generated by varying only the height of each vertex in the grid. -------------------------------------------------------------------------------- -PART 1 WALKTHROUGH: -------------------------------------------------------------------------------- -**Sin Wave** - -* For this assignment, you will need the latest version of Firefox. -* Begin by opening index.html. You should see a flat grid of black and white - lines on the xy plane: - -![Example boring grid](resources/emptyGrid.png) - -* In this assignment, you will animate the grid in a wave-like pattern using a - vertex shader, and determine each vertex’s color based on its height, as seen - in the example in the requirements. -* The vertex and fragment shader are located in script tags in `index.html`. -* The JavaScript code that needs to be modified is located in `index.js`. -* Required shader code modifications: - * Add a float uniform named u_time. - * Modify the vertex’s height using the following code: - - ```glsl - float s_contrib = sin(position.x*2.0*3.14159 + u_time); - float t_contrib = cos(position.y*2.0*3.14159 + u_time); - float height = s_contrib*t_contrib; - ``` - - * Use the GLSL mix function to blend together two colors of your choice based - on the vertex’s height. The lowest possible height should be assigned one - color (for example, `vec3(1.0, 0.2, 0.0)`) and the maximum height should be - another (`vec3(0.0, 0.8, 1.0)`). Use a varying variable to pass the color to - the fragment shader, where you will assign it `gl_FragColor`. - -* Required JavaScript code modifications: - * A floating-point time value should be increased every animation step. - Hint: the delta should be less than one. - * To pass the time to the vertex shader as a uniform, first query the location - of `u_time` using `context.getUniformLocation` in `initializeShader()`. - Then, the uniform’s value can be set by calling `context.uniform1f` in - `animate()`. **Simplex Wave** +![Simplex Noise Wave](/resources/simplex.gif "Simplex Noise Wave") +* Open simplex_wave.html to see this animation. -* Now that you have the sin wave working, create a new copy of `index.html`. - Call it `index_simplex.html`, or something similar. -* Open up `simplex.vert`, which contains a compact GLSL simplex noise - implementation, in a text editor. Copy and paste the functions included - inside into your `index_simplex.html`'s vertex shader. -* Try changing s_contrib and t_contrib to use simplex noise instead of sin/cos - functions with the following code: - -```glsl -vec2 simplexVec = vec2(u_time, position); -float s_contrib = snoise(simplexVec); -float t_contrib = snoise(vec2(s_contrib,u_time)); -``` - -**Wave Of Your Choice** - -* Create another copy of `index.html`. Call it `index_custom.html`, or - something similar. -* Implement your own interesting vertex shader! In your README.md with your - submission, describe your custom vertex shader, what it does, and how it - works. +**Water Surface Wave** +![Water Wave](/resources/water.gif "Water") +* Open water_wave.html to see this animation. +* Unlike the previous waves, this wave moves verticies in all directions. +* Each vertex is moved uniformly about a circle in some vertical plane + * This plane can be set in the VS by changing waveDir +* The phase of each point is determined by their distance from the origin in the waveDir direction, resulting in linear wavefronts. +* This simulates in a very simple way how particles move in the surface of ocean waves. ------------------------------------------------------------------------------- PART 2 REQUIREMENTS: From 143c97a9488304ac86d9400c043fabc6b437290f Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Mon, 4 Nov 2013 17:48:26 -0500 Subject: [PATCH 11/27] Update README.md --- README.md | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/README.md b/README.md index 28bcedd..4c436c1 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,5 @@ ------------------------------------------------------------------------------- -WebGL Shaders -(Simple Waves and Globe Rendering) +WebGL Shaders (Simple Waves and Globe Rendering) ------------------------------------------------------------------------------- Fall 2013 ------------------------------------------------------------------------------- From b7ca11a3582e018530b1faa5e34ac4e2d2c3ce28 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Mon, 4 Nov 2013 18:06:10 -0500 Subject: [PATCH 12/27] Increased grid resolution. --- waves/vert_wave.js | 4 ++-- waves/water_wave.html | 9 +++++---- 2 files changed, 7 insertions(+), 6 deletions(-) diff --git a/waves/vert_wave.js b/waves/vert_wave.js index 433541e..a43f0a3 100644 --- a/waves/vert_wave.js +++ b/waves/vert_wave.js @@ -3,8 +3,8 @@ /*global window,document,Float32Array,Uint16Array,mat4,vec3,snoise*/ /*global getShaderSource,createWebGLContext,createProgram*/ - var NUM_WIDTH_PTS = 32; - var NUM_HEIGHT_PTS = 32; + var NUM_WIDTH_PTS = 200; + var NUM_HEIGHT_PTS = 200; var message = document.getElementById("message"); var canvas = document.getElementById("canvas"); diff --git a/waves/water_wave.html b/waves/water_wave.html index 1f22a26..7623151 100644 --- a/waves/water_wave.html +++ b/waves/water_wave.html @@ -19,14 +19,15 @@ void main(void) { - vec2 waveDir = normalize(vec2(1.0,-1.0));//Direction of wave in X Y plane + vec2 waveDir = normalize(vec2(1.0,0.0));//Direction of wave in X Y plane //Projection of position onto wave direction from origin gives time offset //Constant factor here is cosmetic - float wavefrontFactor = 3.0*dot(position, waveDir); + float wavefrontFactor = 1.0*dot(position, waveDir); //Constants here are cosmetic - vec2 hor_perturb = 0.15*waveDir*(cos(u_time*3.14159 + wavefrontFactor)); - height = 0.25*sin(u_time*3.14159 + wavefrontFactor); + vec2 hor_perturb = 0.30*waveDir*(cos(u_time*3.14159 + wavefrontFactor)); + height = 0.5*sin(u_time*3.14159 + wavefrontFactor); + gl_Position = u_modelViewPerspective * vec4(vec3(position+hor_perturb, height), 1.0); } </script> From ae2d6c055685f593abce793084d709653547defd Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Mon, 4 Nov 2013 19:14:01 -0500 Subject: [PATCH 13/27] Update README.md --- README.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/README.md b/README.md index 4c436c1..0f63bde 100644 --- a/README.md +++ b/README.md @@ -6,6 +6,8 @@ Fall 2013 ![Water Wave](/resources/water.gif "Water") +<iframe src="http://cboots.github.io/WebGL-Waves-and-Globe/waves/vert_wave.html" width="200" height="200"></iframe> + ------------------------------------------------------------------------------- NOTE: From 71026dab47a2ba5ef05d73ce4af4e5998019298c Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Tue, 5 Nov 2013 10:24:41 -0500 Subject: [PATCH 14/27] Update README.md Improved links to live demos --- README.md | 24 +++++++++++++++++++----- 1 file changed, 19 insertions(+), 5 deletions(-) diff --git a/README.md b/README.md index 0f63bde..de6aa03 100644 --- a/README.md +++ b/README.md @@ -4,9 +4,11 @@ WebGL Shaders (Simple Waves and Globe Rendering) Fall 2013 ------------------------------------------------------------------------------- -![Water Wave](/resources/water.gif "Water") +Click any image to see a live demo. -<iframe src="http://cboots.github.io/WebGL-Waves-and-Globe/waves/vert_wave.html" width="200" height="200"></iframe> +<a href="http://cboots.github.io/WebGL-Waves-and-Globe/waves/water_wave.html"> +<img src="/resources/water.gif" alt="Click to See Live Demo" width="400" height="400"> +</a> ------------------------------------------------------------------------------- @@ -27,17 +29,29 @@ This section is just a simple demo of JS/WebGL Interaction and shader implementa Three different waveforms can be animated: **Sine Wave** -![Sine Wave](/resources/sine.gif "Sine Wave") + +<a href="http://cboots.github.io/WebGL-Waves-and-Globe/waves/vert_wave.html"> +<img src="/resources/sine.gif" alt="Click to See Live Demo" width="400" height="400"> +</a> + * Open vert_wave.html to see this animation. * The 2D sine wave is generated by varying only the height of each vertex in the grid. **Simplex Wave** -![Simplex Noise Wave](/resources/simplex.gif "Simplex Noise Wave") + +<a href="http://cboots.github.io/WebGL-Waves-and-Globe/waves/simplex_wave.html"> +<img src="/resources/simplex.gif" alt="Click to See Live Demo" width="400" height="400"> +</a> + * Open simplex_wave.html to see this animation. **Water Surface Wave** -![Water Wave](/resources/water.gif "Water") + +<a href="http://cboots.github.io/WebGL-Waves-and-Globe/waves/water_wave.html"> +<img src="/resources/water.gif" alt="Click to See Live Demo" width="400" height="400"> +</a> + * Open water_wave.html to see this animation. * Unlike the previous waves, this wave moves verticies in all directions. * Each vertex is moved uniformly about a circle in some vertical plane From 96e80581827e25c916560946ea5d16a2edbdc310 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Fri, 8 Nov 2013 15:25:24 -0500 Subject: [PATCH 15/27] Added night lights and twilight border. --- globe/frag_globe.html | 10 +++++++--- globe/frag_globe.js | 2 +- 2 files changed, 8 insertions(+), 4 deletions(-) diff --git a/globe/frag_globe.html b/globe/frag_globe.html index 6aa5609..f1a627c 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -80,18 +80,22 @@ float diffuse = clamp(dot(u_CameraSpaceDirLight, normal), 0.0, 1.0); + //determine twilight shading mix alpha + float dayalpha = pow(1.0-diffuse,5.0); + + vec3 toReflectedLight = reflect(-u_CameraSpaceDirLight, normal); float specular = max(dot(toReflectedLight, -eyeToPosition), 0.0); specular = pow(specular, 20.0); - float gammaCorrect = 1.0/1.2; //gamma correct by 1/1.2 + float gammaCorrect = 1.6/1.2; //gamma correct by 1/1.2 - vec3 dayColor = texture2D(u_DayDiffuse, v_Texcoord).rgb; + vec3 dayColor = ((0.6 * diffuse) + (0.4 * specular))*texture2D(u_DayDiffuse, v_Texcoord).rgb; vec3 nightColor = texture2D(u_Night, v_Texcoord).rgb; //apply gamma correction to nighttime texture nightColor = pow(nightColor,vec3(gammaCorrect)); - vec3 color = ((0.6 * diffuse) + (0.4 * specular)) * dayColor; + vec3 color = mix(dayColor, nightColor, dayalpha); gl_FragColor = vec4(color, 1.0); } diff --git a/globe/frag_globe.js b/globe/frag_globe.js index 1d8a877..6f8dadc 100644 --- a/globe/frag_globe.js +++ b/globe/frag_globe.js @@ -313,4 +313,4 @@ initializeTexture(transTex, "earthtrans1024.png"); initializeTexture(lightTex, "earthlight1024.png"); initializeTexture(specTex, "earthspec1024.png"); -}()); +}()); \ No newline at end of file From 5586da395baf41da28d7915d92d6a398cc32d1c0 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Fri, 8 Nov 2013 15:28:32 -0500 Subject: [PATCH 16/27] Added specular map into consideration. --- globe/frag_globe.html | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/globe/frag_globe.html b/globe/frag_globe.html index f1a627c..5495308 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -86,10 +86,10 @@ vec3 toReflectedLight = reflect(-u_CameraSpaceDirLight, normal); float specular = max(dot(toReflectedLight, -eyeToPosition), 0.0); - specular = pow(specular, 20.0); + specular = pow(specular, 20.0)*texture2D(u_EarthSpec, v_Texcoord).x;//Choice is arbitrary, map is white/black float gammaCorrect = 1.6/1.2; //gamma correct by 1/1.2 - + vec3 dayColor = ((0.6 * diffuse) + (0.4 * specular))*texture2D(u_DayDiffuse, v_Texcoord).rgb; vec3 nightColor = texture2D(u_Night, v_Texcoord).rgb; //apply gamma correction to nighttime texture From 3501d0ad0d1f2709a39ba39ec05c05cf48600605 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Fri, 8 Nov 2013 15:47:28 -0500 Subject: [PATCH 17/27] Implemented moving clouds --- globe/frag_globe.html | 13 ++++++++++++- globe/frag_globe.js | 3 ++- 2 files changed, 14 insertions(+), 2 deletions(-) diff --git a/globe/frag_globe.html b/globe/frag_globe.html index 5495308..c1202b8 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -92,8 +92,19 @@ vec3 dayColor = ((0.6 * diffuse) + (0.4 * specular))*texture2D(u_DayDiffuse, v_Texcoord).rgb; vec3 nightColor = texture2D(u_Night, v_Texcoord).rgb; - //apply gamma correction to nighttime texture + + //apply gamma correction to nighttime texture (before mixing clouds) nightColor = pow(nightColor,vec3(gammaCorrect)); + + //Mix in cloud data + vec2 cloudTexCoords = v_Texcoord + vec2(u_time, 0.0); + float cloudTrans = texture2D(u_CloudTrans, cloudTexCoords).x; + vec3 cloudColor = texture2D(u_Cloud, cloudTexCoords).rgb; + + dayColor = mix(diffuse*cloudColor, dayColor, cloudTrans); + nightColor = mix(vec3(0.0,0.0,0.0), nightColor, cloudTrans); + + vec3 color = mix(dayColor, nightColor, dayalpha); gl_FragColor = vec4(color, 1.0); diff --git a/globe/frag_globe.js b/globe/frag_globe.js index 6f8dadc..55e029f 100644 --- a/globe/frag_globe.js +++ b/globe/frag_globe.js @@ -265,7 +265,8 @@ gl.uniformMatrix4fv(u_ViewLocation, false, view); gl.uniformMatrix4fv(u_PerspLocation, false, persp); gl.uniformMatrix4fv(u_InvTransLocation, false, invTrans); - + gl.uniform1f(u_timeLocation, -time*0.1); + gl.uniform3fv(u_CameraSpaceDirLightLocation, lightdir); gl.activeTexture(gl.TEXTURE0); From de3fac4ae605e32d6a9a65db4be04fa9cb042f8a Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Fri, 8 Nov 2013 15:57:55 -0500 Subject: [PATCH 18/27] Implemented bump mapping. --- globe/frag_globe.html | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/globe/frag_globe.html b/globe/frag_globe.html index c1202b8..84bac4c 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -75,6 +75,17 @@ { // surface normal - normalized after rasterization vec3 normal = normalize(v_Normal); + + //Bump Mapping + float bumpCenter = texture2D(u_Bump, v_Texcoord).x; + float bumpRight = texture2D(u_Bump, v_Texcoord+vec2(1.0/1024.0, 0.0)).x; + float bumpTop = texture2D(u_Bump, v_Texcoord+vec2(0.0, 1.0/512.0)).x; + + vec3 bump = normalize(vec3(bumpCenter - bumpRight, bumpCenter - bumpTop, 0.3)); + + normal = eastNorthUpToEyeCoordinates(v_positionMC, v_Normal)*bump; + + // normalized eye-to-position vector in camera coordinates vec3 eyeToPosition = normalize(v_Position); From 527bd1e6f813c22d7605b59865226e3f2eaa8fad Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Fri, 8 Nov 2013 16:08:36 -0500 Subject: [PATCH 19/27] Implemented rim lighting, but there are artifacts. --- globe/frag_globe.html | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/globe/frag_globe.html b/globe/frag_globe.html index 84bac4c..f777278 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -115,9 +115,10 @@ dayColor = mix(diffuse*cloudColor, dayColor, cloudTrans); nightColor = mix(vec3(0.0,0.0,0.0), nightColor, cloudTrans); - + float rimFactor = clamp(1.0 + dot(v_Normal, v_Position), 0.0, 1.0); + vec3 rimColor = rimFactor*vec3(0.25, 0.5, 0.5); - vec3 color = mix(dayColor, nightColor, dayalpha); + vec3 color = rimColor + mix(dayColor, nightColor, dayalpha); gl_FragColor = vec4(color, 1.0); } From 20de56002f59962954090c0b9b2bc104161acc00 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Fri, 8 Nov 2013 16:25:32 -0500 Subject: [PATCH 20/27] Added rim lighting. --- globe/frag_globe.html | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/globe/frag_globe.html b/globe/frag_globe.html index f777278..ed2cae3 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -115,7 +115,10 @@ dayColor = mix(diffuse*cloudColor, dayColor, cloudTrans); nightColor = mix(vec3(0.0,0.0,0.0), nightColor, cloudTrans); - float rimFactor = clamp(1.0 + dot(v_Normal, v_Position), 0.0, 1.0); + float rimFactor = pow(clamp(1.0 + dot(v_Normal, v_Position), 0.0, 1.0),2.0); + if(v_Normal.z < 0.0) + rimFactor = 0.0;//Minimize visibility of rasterization artifacts. + vec3 rimColor = rimFactor*vec3(0.25, 0.5, 0.5); vec3 color = rimColor + mix(dayColor, nightColor, dayalpha); From 52447936de91ee7e2a0ce8ffe6e9802e0d1229de Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Fri, 8 Nov 2013 16:41:21 -0500 Subject: [PATCH 21/27] Flat shaded clouds. --- globe/frag_globe.html | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/globe/frag_globe.html b/globe/frag_globe.html index ed2cae3..4872a1b 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -76,6 +76,8 @@ // surface normal - normalized after rasterization vec3 normal = normalize(v_Normal); + float flatdiffuse = clamp(dot(u_CameraSpaceDirLight, normal), 0.0, 1.0); + //Bump Mapping float bumpCenter = texture2D(u_Bump, v_Texcoord).x; float bumpRight = texture2D(u_Bump, v_Texcoord+vec2(1.0/1024.0, 0.0)).x; @@ -89,10 +91,10 @@ // normalized eye-to-position vector in camera coordinates vec3 eyeToPosition = normalize(v_Position); - float diffuse = clamp(dot(u_CameraSpaceDirLight, normal), 0.0, 1.0); + float bumpdiffuse = clamp(dot(u_CameraSpaceDirLight, normal), 0.0, 1.0); //determine twilight shading mix alpha - float dayalpha = pow(1.0-diffuse,5.0); + float dayalpha = pow(1.0-flatdiffuse,5.0); vec3 toReflectedLight = reflect(-u_CameraSpaceDirLight, normal); @@ -101,7 +103,7 @@ float gammaCorrect = 1.6/1.2; //gamma correct by 1/1.2 - vec3 dayColor = ((0.6 * diffuse) + (0.4 * specular))*texture2D(u_DayDiffuse, v_Texcoord).rgb; + vec3 dayColor = ((0.6 * bumpdiffuse) + (0.4 * specular))*texture2D(u_DayDiffuse, v_Texcoord).rgb; vec3 nightColor = texture2D(u_Night, v_Texcoord).rgb; //apply gamma correction to nighttime texture (before mixing clouds) @@ -112,7 +114,7 @@ float cloudTrans = texture2D(u_CloudTrans, cloudTexCoords).x; vec3 cloudColor = texture2D(u_Cloud, cloudTexCoords).rgb; - dayColor = mix(diffuse*cloudColor, dayColor, cloudTrans); + dayColor = mix(flatdiffuse*cloudColor, dayColor, cloudTrans); nightColor = mix(vec3(0.0,0.0,0.0), nightColor, cloudTrans); float rimFactor = pow(clamp(1.0 + dot(v_Normal, v_Position), 0.0, 1.0),2.0); From 1a42f987359154677767115cd6a5793fdd339957 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Fri, 8 Nov 2013 22:32:26 -0500 Subject: [PATCH 22/27] Implemented non-uniform rim lighting. Included field for shadow coordinates in frag shader --- globe/frag_globe.html | 13 ++++++++++--- 1 file changed, 10 insertions(+), 3 deletions(-) diff --git a/globe/frag_globe.html b/globe/frag_globe.html index 4872a1b..07fa8e9 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -24,6 +24,7 @@ varying vec3 v_Normal; varying vec2 v_Texcoord; + varying vec2 v_CloudShadowTexcoord; varying vec3 v_Position; varying vec3 v_positionMC; @@ -31,6 +32,7 @@ { v_Normal = (u_InvTrans*vec4(Normal,0.0)).xyz; v_Texcoord = Texcoord; + v_CloudShadowTexcoord = Texcoord; vec4 world = u_Model * vec4(Position, 1.0); vec4 camera = u_View * world; v_Position = camera.xyz; @@ -66,6 +68,7 @@ varying vec3 v_Normal; // surface normal in camera coordinates varying vec2 v_Texcoord; + varying vec2 v_CloudShadowTexcoord; varying vec3 v_Position; // position in camera coordinates varying vec3 v_positionMC; // position in model coordinates @@ -103,7 +106,9 @@ float gammaCorrect = 1.6/1.2; //gamma correct by 1/1.2 - vec3 dayColor = ((0.6 * bumpdiffuse) + (0.4 * specular))*texture2D(u_DayDiffuse, v_Texcoord).rgb; + float cloudShadowRayTrans = texture2D(u_CloudTrans, v_CloudShadowTexcoord+vec2(u_time, 0.0)).x; + + vec3 dayColor = cloudShadowRayTrans*((0.6 * bumpdiffuse) + (0.4 * specular))*texture2D(u_DayDiffuse, v_Texcoord).rgb; vec3 nightColor = texture2D(u_Night, v_Texcoord).rgb; //apply gamma correction to nighttime texture (before mixing clouds) @@ -117,13 +122,14 @@ dayColor = mix(flatdiffuse*cloudColor, dayColor, cloudTrans); nightColor = mix(vec3(0.0,0.0,0.0), nightColor, cloudTrans); - float rimFactor = pow(clamp(1.0 + dot(v_Normal, v_Position), 0.0, 1.0),2.0); + float rimFactor = pow(clamp(1.0 + dot(v_Normal, v_Position), 0.0, 1.0),1.0); if(v_Normal.z < 0.0) rimFactor = 0.0;//Minimize visibility of rasterization artifacts. vec3 rimColor = rimFactor*vec3(0.25, 0.5, 0.5); - vec3 color = rimColor + mix(dayColor, nightColor, dayalpha); + //Only show rim in daylight + vec3 color = rimColor*(1.0-dayalpha) + mix(dayColor, nightColor, dayalpha); gl_FragColor = vec4(color, 1.0); } @@ -141,6 +147,7 @@ bitangentEC.x, bitangentEC.y, bitangentEC.z, normalEC.x, normalEC.y, normalEC.z); } + </script> <script src ="gl-matrix.js" type ="text/javascript"></script> From c6c6614aea016e3bb5ea28d4b1d1a7b9833c4267 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Fri, 8 Nov 2013 22:34:24 -0500 Subject: [PATCH 23/27] Modified rim lighting parameters. --- globe/frag_globe.html | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/globe/frag_globe.html b/globe/frag_globe.html index 07fa8e9..d64fcf8 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -86,7 +86,7 @@ float bumpRight = texture2D(u_Bump, v_Texcoord+vec2(1.0/1024.0, 0.0)).x; float bumpTop = texture2D(u_Bump, v_Texcoord+vec2(0.0, 1.0/512.0)).x; - vec3 bump = normalize(vec3(bumpCenter - bumpRight, bumpCenter - bumpTop, 0.3)); + vec3 bump = normalize(vec3(bumpCenter - bumpRight, bumpCenter - bumpTop, 0.2)); normal = eastNorthUpToEyeCoordinates(v_positionMC, v_Normal)*bump; @@ -122,7 +122,7 @@ dayColor = mix(flatdiffuse*cloudColor, dayColor, cloudTrans); nightColor = mix(vec3(0.0,0.0,0.0), nightColor, cloudTrans); - float rimFactor = pow(clamp(1.0 + dot(v_Normal, v_Position), 0.0, 1.0),1.0); + float rimFactor = pow(clamp(1.0 + dot(v_Normal, v_Position), 0.0, 1.0),1.5); if(v_Normal.z < 0.0) rimFactor = 0.0;//Minimize visibility of rasterization artifacts. From 0c87009679db39448480ae71192ebfd9d7ae2a7a Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Sat, 9 Nov 2013 00:48:09 -0500 Subject: [PATCH 24/27] Implemented raycasted shadows correctly now. --- globe/frag_globe.html | 65 ++++++++++++++++++++++++++++++++++++++----- globe/frag_globe.js | 19 +++++++++---- 2 files changed, 72 insertions(+), 12 deletions(-) diff --git a/globe/frag_globe.html b/globe/frag_globe.html index d64fcf8..9d4ed7d 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -24,7 +24,6 @@ varying vec3 v_Normal; varying vec2 v_Texcoord; - varying vec2 v_CloudShadowTexcoord; varying vec3 v_Position; varying vec3 v_positionMC; @@ -32,7 +31,6 @@ { v_Normal = (u_InvTrans*vec4(Normal,0.0)).xyz; v_Texcoord = Texcoord; - v_CloudShadowTexcoord = Texcoord; vec4 world = u_Model * vec4(Position, 1.0); vec4 camera = u_View * world; v_Position = camera.xyz; @@ -47,7 +45,9 @@ //View-Space directional light //A unit vector uniform vec3 u_CameraSpaceDirLight; - + uniform vec3 u_ModelSpaceDirLight;//Model space version for ray cast convenience + + //Diffuse texture map for the day uniform sampler2D u_DayDiffuse; //Ambient texture map for the night side @@ -68,12 +68,12 @@ varying vec3 v_Normal; // surface normal in camera coordinates varying vec2 v_Texcoord; - varying vec2 v_CloudShadowTexcoord; varying vec3 v_Position; // position in camera coordinates varying vec3 v_positionMC; // position in model coordinates mat3 eastNorthUpToEyeCoordinates(vec3 positionMC, vec3 normalEC); - + vec3 raySphereIntersect(vec3 ro, vec3 rd, float r); + vec2 dirInSphereToTexcoords(vec3 dir); void main(void) { // surface normal - normalized after rasterization @@ -91,6 +91,7 @@ normal = eastNorthUpToEyeCoordinates(v_positionMC, v_Normal)*bump; + // normalized eye-to-position vector in camera coordinates vec3 eyeToPosition = normalize(v_Position); @@ -104,9 +105,19 @@ float specular = max(dot(toReflectedLight, -eyeToPosition), 0.0); specular = pow(specular, 20.0)*texture2D(u_EarthSpec, v_Texcoord).x;//Choice is arbitrary, map is white/black - float gammaCorrect = 1.6/1.2; //gamma correct by 1/1.2 + float gammaCorrect = 1.6/1.2; //gamma correct by 1.6/1.2 - float cloudShadowRayTrans = texture2D(u_CloudTrans, v_CloudShadowTexcoord+vec2(u_time, 0.0)).x; + + //======Calculate cloud shadows====== + float cloudAltitude = 0.075;//Term is relative to globe radius == 1.0 + vec3 rayOrigin = v_positionMC*(1.0+bumpCenter*cloudAltitude);//Mountains could be as tall as clouds but no taller + vec3 rayDir = normalize(u_ModelSpaceDirLight); + + + vec3 shadowRayIntersectDir = raySphereIntersect(rayOrigin, rayDir, 1.0+cloudAltitude); + + vec2 v_CloudShadowTexcoord = dirInSphereToTexcoords(shadowRayIntersectDir) + vec2(u_time, 0.0); + float cloudShadowRayTrans = texture2D(u_CloudTrans, v_CloudShadowTexcoord).x; vec3 dayColor = cloudShadowRayTrans*((0.6 * bumpdiffuse) + (0.4 * specular))*texture2D(u_DayDiffuse, v_Texcoord).rgb; vec3 nightColor = texture2D(u_Night, v_Texcoord).rgb; @@ -148,6 +159,46 @@ normalEC.x, normalEC.y, normalEC.z); } + + vec3 raySphereIntersect(vec3 ro, vec3 rd, float r) + { + //Solver parameters + float b = dot(rd, ro); + + float radicand = b * b - (dot(ro,ro) - r*r); + + if(radicand < 0.0){ + return normalize(ro);//If no intersection (should never happen) Assume no deviation from vert + } + + float root = sqrt(radicand); + float s1 = (-b + root); + float s2 = (-b - root); + + + float s = 0.0; + if (s1 < 0.0 && s2 < 0.0) { + return normalize(ro);//If no intersection (should never happen) Assume no deviation from vert + } else if (s1 > 0.0 && s2 > 0.0) { + s = min(s1, s2); + } else { + s = max(s1, s2); + } + + return normalize(ro+s*rd); + + } + + vec2 dirInSphereToTexcoords(vec3 dir) + { + float th = atan(dir.z, dir.x); + float phi = acos(dir.y); + float u = (th) / (2.0 * 3.14159265); + float v = phi/3.14159265; + + return vec2(u,v); + } + </script> <script src ="gl-matrix.js" type ="text/javascript"></script> diff --git a/globe/frag_globe.js b/globe/frag_globe.js index 55e029f..edb33ba 100644 --- a/globe/frag_globe.js +++ b/globe/frag_globe.js @@ -31,7 +31,7 @@ mat4.perspective(45.0, canvas.width/canvas.height, 0.1, 100.0, persp); var radius = 5.0; - var azimuth = Math.PI; + var azimuth = 0; var elevation = 0.0001; var eye = sphericalToCartesian(radius, azimuth, elevation); @@ -48,6 +48,7 @@ var u_ViewLocation; var u_PerspLocation; var u_CameraSpaceDirLightLocation; + var u_ModelSpaceDirLightLocation; var u_DayDiffuseLocation; var u_NightLocation; var u_CloudLocation; @@ -76,6 +77,7 @@ u_BumpLocation = gl.getUniformLocation(program,"u_Bump"); u_timeLocation = gl.getUniformLocation(program,"u_time"); u_CameraSpaceDirLightLocation = gl.getUniformLocation(program,"u_CameraSpaceDirLight"); + u_ModelSpaceDirLightLocation = gl.getUniformLocation(program, "u_ModelSpaceDirLight"); gl.useProgram(program); })(); @@ -250,13 +252,18 @@ mat4.inverse(mv, invTrans); mat4.transpose(invTrans); - var lightdir = vec3.create([1.0, 0.0, 1.0]); + var lightdir = vec3.create([1.0, 0.0, 1.0]);//Direction of the light in world space var lightdest = vec4.create(); vec3.normalize(lightdir); mat4.multiplyVec4(view, [lightdir[0], lightdir[1], lightdir[2], 0.0], lightdest); - lightdir = vec3.createFrom(lightdest[0],lightdest[1],lightdest[2]); - vec3.normalize(lightdir); + var lightdirCam = vec3.createFrom(lightdest[0],lightdest[1],lightdest[2]);//View Space + vec3.normalize(lightdirCam); + + var modelInv = mat4.create(); + mat4.inverse(model, modelInv); + mat4.multiplyVec4(modelInv, [lightdir[0], lightdir[1], lightdir[2], 0.0], lightdir); + /////////////////////////////////////////////////////////////////////////// // Render gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT); @@ -267,7 +274,9 @@ gl.uniformMatrix4fv(u_InvTransLocation, false, invTrans); gl.uniform1f(u_timeLocation, -time*0.1); - gl.uniform3fv(u_CameraSpaceDirLightLocation, lightdir); + + gl.uniform3fv(u_ModelSpaceDirLightLocation, lightdir); + gl.uniform3fv(u_CameraSpaceDirLightLocation, lightdirCam); gl.activeTexture(gl.TEXTURE0); gl.bindTexture(gl.TEXTURE_2D, dayTex); From 29f02b8d7870d4297023240285c9b61a1e3e12e1 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Sat, 9 Nov 2013 01:22:47 -0500 Subject: [PATCH 25/27] Added screenshots. --- globe/frag_globe.html | 2 +- globe/frag_globe.js | 2 +- resources/emptyGrid.png | Bin 43211 -> 0 bytes resources/globe_bumpmap.png | Bin 379860 -> 282124 bytes resources/globe_day.png | Bin 380600 -> 0 bytes resources/globe_daycloud.png | Bin 384901 -> 0 bytes resources/globe_initial.png | Bin 225176 -> 0 bytes resources/globe_night.png | Bin 300165 -> 0 bytes resources/globe_nightcloud.png | Bin 251952 -> 0 bytes resources/globe_nobumpmap.PNG | Bin 0 -> 271431 bytes resources/globe_noshadow.PNG | Bin 0 -> 280337 bytes resources/globe_nospecmap.png | Bin 249688 -> 0 bytes resources/globe_se_asia.PNG | Bin 0 -> 228893 bytes resources/globe_shadows.PNG | Bin 0 -> 270450 bytes resources/globe_specmap.png | Bin 257152 -> 0 bytes resources/globe_sunrise.PNG | Bin 0 -> 120666 bytes resources/globe_twilight.png | Bin 386934 -> 179288 bytes 17 files changed, 2 insertions(+), 2 deletions(-) delete mode 100644 resources/emptyGrid.png delete mode 100644 resources/globe_day.png delete mode 100644 resources/globe_daycloud.png delete mode 100644 resources/globe_initial.png delete mode 100644 resources/globe_night.png delete mode 100644 resources/globe_nightcloud.png create mode 100644 resources/globe_nobumpmap.PNG create mode 100644 resources/globe_noshadow.PNG delete mode 100644 resources/globe_nospecmap.png create mode 100644 resources/globe_se_asia.PNG create mode 100644 resources/globe_shadows.PNG delete mode 100644 resources/globe_specmap.png create mode 100644 resources/globe_sunrise.PNG diff --git a/globe/frag_globe.html b/globe/frag_globe.html index 9d4ed7d..c660ff6 100644 --- a/globe/frag_globe.html +++ b/globe/frag_globe.html @@ -117,7 +117,7 @@ vec3 shadowRayIntersectDir = raySphereIntersect(rayOrigin, rayDir, 1.0+cloudAltitude); vec2 v_CloudShadowTexcoord = dirInSphereToTexcoords(shadowRayIntersectDir) + vec2(u_time, 0.0); - float cloudShadowRayTrans = texture2D(u_CloudTrans, v_CloudShadowTexcoord).x; + float cloudShadowRayTrans = 1.0;//texture2D(u_CloudTrans, v_CloudShadowTexcoord).x; vec3 dayColor = cloudShadowRayTrans*((0.6 * bumpdiffuse) + (0.4 * specular))*texture2D(u_DayDiffuse, v_Texcoord).rgb; vec3 nightColor = texture2D(u_Night, v_Texcoord).rgb; diff --git a/globe/frag_globe.js b/globe/frag_globe.js index edb33ba..1c18966 100644 --- a/globe/frag_globe.js +++ b/globe/frag_globe.js @@ -31,7 +31,7 @@ mat4.perspective(45.0, canvas.width/canvas.height, 0.1, 100.0, persp); var radius = 5.0; - var azimuth = 0; + var azimuth = 0.0; var elevation = 0.0001; var eye = sphericalToCartesian(radius, azimuth, elevation); diff --git a/resources/emptyGrid.png 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zkpP;W0(5~~Iy-?)VtO9QaCo=Z+eOVZg)=E%CwNCxSzX`A6stRYjT0Ko36;y)*;C@j z4r{(9#uNgGv}t7q(=-wiI}|ow+kY$a1bE+nHB*G_(xZ-v>QS}EY0DRB<1-v>s*{VM zOB<SL9T$or2Lz2Sx~}7fvjbBEfA?l*^i#EVy&)-j5hXl^ygs7u-SuUg(4aatNRV%r z8`w0GBY6j_CHW5*lk7s&uBUtUj0npANM(Q(_vU{IR8lKQ_>BEMDX2J|nkqapBG{~8 z>}SkIvJ37g<QZlooqq~1nAXtSmdtENE)$(y;5>OeeH@&-W2^76obgp*@p(*Bc}%S~ zjyL8nOD<5F`URbVIFIeaXs0liSxvgZw8z8qbzkpAcK!Ee5b@lbQAhdD;B0Mhe?nR* z(RMv0{_vIW{_;6?N$N8Aw`a`6DMd<Glj41pxAPU+Roy|Uq-^IM=1Do!5pj?%Xm{j1 zoKky!X1p;4G;qmFl%W+oa(36s1BT8kTv-vx6Z!rVX_LL7^m79jUxkbJ+%Xu|w1h;8 zs$ZH#T-2YPxl$-L**T8cj!|}z2kwgpIq_lh*4?M1<25-?-}U*aqaD8EBaWUa^X1=n zgDAy&D9uBA#z>$49-p84b>8uB*Qj8>O}=04G$;GEg^n*I9XTOg1BH$rjHa@Q<!^gY z`<u60Ra4WCmPm7-!j;;Z99kkLC>P(G>SBl|Yjtuqbr@ChCpVUS9_lcrEA7aCx9@(y z(VC=x#G-y*c!yug%WKjNnZ{yC-+J`-_uKXlhNH@^#l-yagtMnFZ5u9--Fn0h@#v## wb=)sBY5&~+zu*6@!2ic9@cc63?2`I_-PRgTq2}}wf8Io2$3(kU%PIE%0eEjQ=>Px# From a1c6ecff129e9f475862957fd7224606ccc18253 Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Sat, 9 Nov 2013 01:24:01 -0500 Subject: [PATCH 26/27] Update README.md --- README.md | 54 ++++++++++++++++-------------------------------------- 1 file changed, 16 insertions(+), 38 deletions(-) diff --git a/README.md b/README.md index de6aa03..7152d95 100644 --- a/README.md +++ b/README.md @@ -10,6 +10,12 @@ Click any image to see a live demo. <img src="/resources/water.gif" alt="Click to See Live Demo" width="400" height="400"> </a> +<dl> +<a href="http://youtu.be/ZDPF2lz9Sww" target="_blank"><img src="http://img.youtube.com/vi/ZDPF2lz9Sww/0.jpg" +alt="Youtube Video of Globe Rendering" width="640" height="480" border="10" /></a> +</dl> + + ------------------------------------------------------------------------------- NOTE: @@ -60,52 +66,24 @@ Three different waveforms can be animated: * This simulates in a very simple way how particles move in the surface of ocean waves. ------------------------------------------------------------------------------- -PART 2 REQUIREMENTS: +Globe Rendering ------------------------------------------------------------------------------- -In Part 2, you are given code for: - -* Reading and loading textures -* Rendering a sphere with textures mapped on -* Basic passthrough fragment and vertex shaders -* A basic globe with Earth terrain color mapping -* Gamma correcting textures -* javascript to interact with the mouse +Globe Renderer * left-click and drag moves the camera around * right-click and drag moves the camera in and out -You are required to implement: - +Features: * Bump mapped terrain -* Rim lighting to simulate atmosphere -* Night-time lights on the dark side of the globe -* Specular mapping -* Moving clouds - -You are also required to pick one open-ended effect to implement: - -* Procedural water rendering and animation using noise -* Shade based on altitude using the height map -* Cloud shadows via ray-tracing through the cloud map in the fragment shader -* Orbiting Moon with texture mapping and shadow casting onto Earth -* Draw a skybox around the entire scene for the stars. -* Your choice! Email Liam and Patrick to get approval first +![No Bump Map](resources/globe_nobumpmap.PNG) ![With Bump Map](resources/globe_bumpmap.PNG) -Finally in addition to your readme, you must also set up a gh-pages branch -(explained below) to expose your beautiful WebGL globe to the world. - -Some examples of what your completed globe renderer will look like: - -![Completed globe, day side](resources/globe_day.png) - -Figure 0. Completed globe renderer, daylight side. - -![Completed globe, twilight](resources/globe_twilight.png) - -Figure 1. Completed globe renderer, twilight border. +* Sunrise-based rim lighting to simulate atmosphere + * Rather than drawing uniform rim lighting, I only shade the sunward side. This leads to cool sunrise effects: +![Sunrise](resources/globe_sunrise.PNG) +* Night-time lights on the dark side of the globe -![Completed globe, night side](resources/globe_night.png) +* Specular mapping (only water is specularly reflective) +* Moving clouds with procedurally generated shadows. -Figure 2. Completed globe renderer, night side. ------------------------------------------------------------------------------- PART 2 WALKTHROUGH: From c9794ac176dde23415347a1ee09e592594006edb Mon Sep 17 00:00:00 2001 From: Collin Boots <cboots@seas.upenn.edu> Date: Sat, 9 Nov 2013 01:33:25 -0500 Subject: [PATCH 27/27] Update README.md --- README.md | 217 +++++------------------------------------------------- 1 file changed, 19 insertions(+), 198 deletions(-) diff --git a/README.md b/README.md index 7152d95..dcaebbe 100644 --- a/README.md +++ b/README.md @@ -73,210 +73,31 @@ Globe Renderer * right-click and drag moves the camera in and out Features: -* Bump mapped terrain -![No Bump Map](resources/globe_nobumpmap.PNG) ![With Bump Map](resources/globe_bumpmap.PNG) +*Soft twilight border -* Sunrise-based rim lighting to simulate atmosphere - * Rather than drawing uniform rim lighting, I only shade the sunward side. This leads to cool sunrise effects: -![Sunrise](resources/globe_sunrise.PNG) -* Night-time lights on the dark side of the globe - -* Specular mapping (only water is specularly reflective) -* Moving clouds with procedurally generated shadows. - - -------------------------------------------------------------------------------- -PART 2 WALKTHROUGH: -------------------------------------------------------------------------------- - -Open part2/frag_globe.html in Firefox to run it. You’ll see a globe -with Phong lighting like the one in Figure 3. All changes you need to make -will be in the fragment shader portion of this file. - -![Initial globe](resources/globe_initial.png) - -Figure 3. Initial globe with diffuse and specular lighting. - -**Night Lights** - -The backside of the globe not facing the sun is completely black in the -initial globe. Use the `diffuse` lighting component to detect if a fragment -is on this side of the globe, and, if so, shade it with the color from the -night light texture, `u_Night`. Do not abruptly switch from day to night; -instead use the `GLSL mix` function to smoothly transition from day to night -over a reasonable period. The resulting globe will look like Figure 4. -Consider brightening the night lights by multiplying the value by two. - -The base code shows an example of how to gamma correct the nighttime texture: - -```glsl -float gammaCorrect = 1/1.2; -vec4 nightColor = pow(texture2D(u_Night, v_Texcoord), vec4(gammaCorrect)); -``` - -Feel free to play with gamma correcting the night and day textures if you -wish. Find values that you think look nice! - -![Day/Night without specular mapping](resources/globe_nospecmap.png) - -Figure 4. Globe with night lights and day/night blending at dusk/dawn. - -**Specular Map** - -Our day/night color still shows specular highlights on landmasses, which -should only be diffuse lit. Only the ocean should receive specular highlights. -Use `u_EarthSpec` to determine if a fragment is on ocean or land, and only -include the specular component if it is in ocean. - -![Day/Night with specular mapping](resources/globe_specmap.png) - -Figure 5. Globe with specular map. Compare to Figure 4. Here, the specular -component is not used when shading the land. - -**Clouds** - -In day time, clouds should be diffuse lit. Use `u_Cloud` to determine the -cloud color, and `u_CloudTrans` and `mix` to determine how much a daytime -fragment is affected by the day diffuse map or cloud color. See Figure 6. - -In night time, clouds should obscure city lights. Use `u_CloudTrans` and `mix` -to blend between the city lights and solid black. See Figure 7. - -Animate the clouds by offseting the `s` component of `v_Texcoord` by `u_time` -when reading `u_Cloud` and `u_CloudTrans`. - -![Day with clouds](resources/globe_daycloud.png) - -Figure 6. Clouds with day time shading. - -![Night with clouds](resources/globe_nightcloud.png) - -Figure 7. Clouds observing city nights on the dark side of the globe. - -**Bump Mapping** - -Add the appearance of mountains by perturbing the normal used for diffuse -lighting the ground (not the clouds) by using the bump map texture, `u_Bump`. -This texture is 1024x512, and is zero when the fragment is at sea-level, and -one when the fragment is on the highest mountain. Read three texels from this -texture: once using `v_Texcoord`; once one texel to the right; and once one -texel above. Create a perturbed normal in tangent space: - -`normalize(vec3(center - right, center - top, 0.2))` - -Use `eastNorthUpToEyeCoordinates` to transform this normal to eye coordinates, -normalize it, then use it for diffuse lighting the ground instead of the -original normal. - -![Globe with bump mapping](resources/globe_bumpmap.png) - -Figure 8. Bump mapping brings attention to mountains. - -**Rim Lighting** - -Rim lighting is a simple post-processed lighting effect we can apply to make -the globe look as if it has an atmospheric layer catching light from the sun. -Implementing rim lighting is simple; we being by finding the dot product of -`v_Normal` and `v_Position`, and add 1 to the dot product. We call this value -our rim factor. If the rim factor is greater than 0, then we add a blue color -based on the rim factor to the current fragment color. You might use a color -something like `vec4(rim/4, rim/2, rim/2, 1)`. If our rim factor is not greater -than 0, then we leave the fragment color as is. Figures 0,1 and 2 show our -finished globe with rim lighting. - -For more information on rim lighting, -read http://www.fundza.com/rman_shaders/surface/fake_rim/fake_rim1.html. - -------------------------------------------------------------------------------- -GH-PAGES -------------------------------------------------------------------------------- -Since this assignment is in WebGL you will make your project easily viewable by -taking advantage of GitHub's project pages feature. - -Once you are done you will need to create a new branch named gh-pages: - -`git branch gh-pages` - -Switch to your new branch: - -`git checkout gh-pages` - -Create an index.html file that is either your renamed frag_globe.html or -contains a link to it, commit, and then push as usual. Now you can go to - -`<user_name>.github.io/<project_name>` - -to see your beautiful globe from anywhere. - -------------------------------------------------------------------------------- -README -------------------------------------------------------------------------------- -All students must replace or augment the contents of this Readme.md in a clear -manner with the following: - -* A brief description of the project and the specific features you implemented. -* At least one screenshot of your project running. -* A 30 second or longer video of your project running. To create the video you - can use http://www.microsoft.com/expression/products/Encoder4_Overview.aspx -* A performance evaluation (described in detail below). +<a href="http://cboots.github.io/WebGL-Waves-and-Globe/globe/frag_globe.html"> +![Twilight](resources/globe_twilight.png) +</a> -------------------------------------------------------------------------------- -PERFORMANCE EVALUATION -------------------------------------------------------------------------------- -The performance evaluation is where you will investigate how to make your -program more efficient using the skills you've learned in class. You must have -performed at least one experiment on your code to investigate the positive or -negative effects on performance. +* Bump mapped terrain -We encourage you to get creative with your tweaks. Consider places in your code -that could be considered bottlenecks and try to improve them. +<a href="http://cboots.github.io/WebGL-Waves-and-Globe/globe/frag_globe.html"> +![No Bump Map](resources/globe_nobumpmap.PNG) ![With Bump Map](resources/globe_bumpmap.png) +</a> -Each student should provide no more than a one page summary of their -optimizations along with tables and or graphs to visually explain any -performance differences. +* Night-time lights on the dark side of the globe +* Sunrise-based rim lighting to simulate atmosphere + * Rather than drawing uniform rim lighting, I only shade the sunward side. This leads to cool sunrise effects: -------------------------------------------------------------------------------- -THIRD PARTY CODE POLICY -------------------------------------------------------------------------------- -* Use of any third-party code must be approved by asking on the Google groups. - If it is approved, all students are welcome to use it. Generally, we approve - use of third-party code that is not a core part of the project. For example, - for the ray tracer, we would approve using a third-party library for loading - models, but would not approve copying and pasting a CUDA function for doing - refraction. -* Third-party code must be credited in README.md. -* Using third-party code without its approval, including using another - student's code, is an academic integrity violation, and will result in you - receiving an F for the semester. -------------------------------------------------------------------------------- -SELF-GRADING -------------------------------------------------------------------------------- -* On the submission date, email your grade, on a scale of 0 to 100, to Liam, - liamboone@gmail.com, with a one paragraph explanation. Be concise and - realistic. Recall that we reserve 30 points as a sanity check to adjust your - grade. Your actual grade will be (0.7 * your grade) + (0.3 * our grade). We - hope to only use this in extreme cases when your grade does not realistically - reflect your work - it is either too high or too low. In most cases, we plan - to give you the exact grade you suggest. -* Projects are not weighted evenly, e.g., Project 0 doesn't count as much as - the path tracer. We will determine the weighting at the end of the semester - based on the size of each project. +<a href="http://cboots.github.io/WebGL-Waves-and-Globe/globe/frag_globe.html"> +![Sunrise](resources/globe_sunrise.PNG) +</a> +* Specular mapping (only water is specularly reflective) +* Moving clouds with procedurally generated shadows. ---- -SUBMISSION ---- -As with the previous project, you should fork this project and work inside of -your fork. Upon completion, commit your finished project back to your fork, and -make a pull request to the master repository. You should include a README.md -file in the root directory detailing the following +<a href="http://cboots.github.io/WebGL-Waves-and-Globe/globe/frag_globe.html"> +![No Shadows](resources/globe_noshadow.PNG) ![With Shadows](resources/globe_shadows.PNG) +</a> -* A brief description of the project and specific features you implemented -* At least one screenshot of your project running. -* A link to a video of your project running. -* Instructions for building and running your project if they differ from the - base code. -* A performance writeup as detailed above. -* A list of all third-party code used. -* This Readme file edited as described above in the README section.

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