add Cone primitive

Author: ffreyer

src/GeometryBasics.jl

@@ -17,6 +17,7 @@ include("primitives/spheres.jl")
 include("primitives/cylinders.jl")
 include("primitives/pyramids.jl")
 include("primitives/particles.jl")
+include("primitives/Cone.jl")
 
 include("interfaces.jl")
 include("viewtypes.jl")
@@ -56,7 +57,7 @@ export triangle_mesh, triangle_mesh, uv_mesh
 export uv_mesh, normal_mesh, uv_normal_mesh
 
 export height, origin, radius, width, widths
-export HyperSphere, Circle, Sphere
+export HyperSphere, Circle, Sphere, Cone
 export Cylinder, Pyramid, extremity
 export HyperRectangle, Rect, Rect2, Rect3, Recti, Rect2i, Rect3i, Rectf, Rect2f, Rect3f, Rectd, Rect2d, Rect3d, RectT
 export before, during, meets, overlaps, intersects, finishes

src/primitives/Cone.jl

@@ -0,0 +1,102 @@
+"""
+    Cone{T}(origin::Point3, tip::Point3, radius)
+
+A Cone is a cylinder where one end has a radius of 0. It is defined by an
+`origin` with a finite `radius` which linearly decreases to 0 at the `tip`.
+"""
+struct Cone{T} <: GeometryPrimitive{3, T}
+    origin::Point3{T}
+    tip::Point3{T}
+    radius::T
+end
+
+function Cone(origin::Point3{T1}, tip::Point3{T2}, radius::T3) where {T1, T2, T3}
+    T = promote_type(T1, T2, T3)
+    return Cone{T}(origin, tip, radius)
+end
+
+origin(c::Cone) = c.origin
+extremity(c::Cone) = c.tip
+radius(c::Cone) = c.radius
+height(c::Cone) = norm(c.tip - c.origin)
+direction(c::Cone) = (c.tip .- c.origin) ./ height(c)
+
+function rotation(c::Cone{T}) where {T}
+    d3 = direction(c)
+    u = Vec{3, T}(d3[1], d3[2], d3[3])
+    if abs(u[1]) > 0 || abs(u[2]) > 0
+        v = Vec{3, T}(u[2], -u[1], T(0))
+    else
+        v = Vec{3, T}(T(0), -u[3], u[2])
+    end
+    v = normalize(v)
+    w = Vec{3, T}(u[2] * v[3] - u[3] * v[2], -u[1] * v[3] + u[3] * v[1],
+                  u[1] * v[2] - u[2] * v[1])
+    return Mat{3, 3, T}(v..., w..., u...)
+end
+
+function coordinates(c::Cone{T}, nvertices=30) where {T}
+    nvertices += isodd(nvertices)
+    nhalf = div(nvertices, 2)
+
+    R = rotation(c)
+    step = 2pi / nhalf
+
+    ps = Vector{Point3{T}}(undef, nhalf + 2)
+    for i in 1:nhalf
+        phi = (i-1) * step
+        ps[i] = R * Point3{T}(c.radius * cos(phi), c.radius * sin(phi), 0) + c.origin
+    end
+    ps[end-1] = c.tip
+    ps[end] = c.origin
+
+    return ps
+end
+
+function normals(c::Cone, nvertices = 30)
+    nvertices += isodd(nvertices)
+    nhalf = div(nvertices, 2)
+
+    R = rotation(c)
+    step = 2pi / nhalf
+
+    ns = Vector{Vec3f}(undef, nhalf + 2)
+    # shell at origin
+    # normals are angled in z direction due to change in radius (from radius to 0)
+    # This can be calculated from triangles
+    z = radius(c) / height(c)
+    norm = 1.0 / sqrt(1 + z*z)
+    for i in 1:nhalf
+        phi = (i-1) * step
+        ns[i] = R * (norm * Vec3f(cos(phi), sin(phi), z))
+    end
+
+    # tip - this is undefined / should be all ring angles at once
+    # for rendering it is useful to define this as Vec3f(0), because tip normal
+    # has no useful value to contribute to the interpolated fragment normal
+    ns[end-1] = Vec3f(0)
+
+    # cap
+    ns[end] = Vec3f(normalize(c.origin - c.tip))
+
+    return ns
+end
+
+function faces(::Cone, facets=30)
+    nvertices = facets + isodd(facets)
+    nhalf = div(nvertices, 2)
+
+    faces = Vector{GLTriangleFace}(undef, nvertices)
+
+    # shell
+    for i in 1:nhalf
+        faces[i] = GLTriangleFace(i, mod1(i+1, nhalf), nhalf+1)
+    end
+
+    # cap
+    for i in 1:nhalf
+        faces[i+nhalf] = GLTriangleFace(i, mod1(i+1, nhalf), nhalf+2)
+    end
+
+    return faces
+end