sphere_grid/sphere_grid.html

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      SPHERE_GRID - Grids on a Sphere
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      SPHERE_GRID <br> Grids on a Sphere
    </h1>

    <hr>

    <p>
      <b>SPHERE_GRID</b> 
      is a FORTRAN90 library which 
      constructs a variety of sets of points on the surface of the unit sphere.
    </p>

    <p>
      A grid on a sphere may mean a set of points, or a set of points and
      lines that connect them, or a set of points, lines that connect them,
      and the faces that are bounded by those lines.
    </p>

    <p>
      A grid may be desired which simply organizes areas.  In that case,
      something like the latitude and longitude lines on a globe may be
      sufficient, even though "evenly spaced" latitude and longitude
      lines result in grid cells that are close to rectangular near
      the equator, but become more asymmetric near the poles.
    </p>

    <p>
      A grid may also be desired for sampling, that is, for choosing
      a set of points that are well spread across the sphere.  A simple
      Monte Carlo approach can be used, although this means that the
      data is only well spread out in the long view; there may be local 
      clusters and gaps.
    </p>

    <p>
      Other grids are generated by drawing a spiral on the surface of the
      sphere, and choosing points at regular spacings along that line, or
      by projecting an icosahedron onto the surface of the sphere, which
      divides the surface into 20 congruent spherical triangles, and then
      dealing with the simpler issue of choosing points from the triangles.
    </p>

    <h3 align = "center">
      Licensing:
    </h3>

    <p>
      The computer code and data files described and made available on this web page 
      are distributed under
      <a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
    </p>

    <h3 align = "center">
      Languages:
    </h3>

    <p>
      <b>SPHERE_GRID</b> is available in
      <a href = "../../c_src/sphere_grid/sphere_grid.html">a C version</a> and
      <a href = "../../cpp_src/sphere_grid/sphere_grid.html">a C++ version</a> and
      <a href = "../../f77_src/sphere_grid/sphere_grid.html">a FORTRAN77 version</a> and
      <a href = "../../f_src/sphere_grid/sphere_grid.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/sphere_grid/sphere_grid.html">a MATLAB version</a>.
    </p>

    <h3 align = "center">
      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../m_src/distance_to_position_sphere/distance_to_position_sphere.html">
      DISTANCE_TO_POSITION_SPHERE</a>,
      a MATLAB program which
      estimates the positions of cities on a sphere (such as the earth) 
      based on a city-to-city distance table.
    </p>

    <p>
      <a href = "../../f_src/geometry/geometry.html">
      GEOMETRY</a>,
      a FORTRAN90 library which
      performs geometric calculations in 2, 3 and N dimensional space.
    </p>

    <p>
      <a href = "../../f_src/sphere_cvt/sphere_cvt.html">
      SPHERE_CVT</a>, 
      a FORTRAN90 library which 
      creates a mesh of well-separated points on a unit sphere using Centroidal Voronoi
      Tessellations.
    </p>

    <p>
      <a href = "../../f_src/sphere_delaunay/sphere_delaunay.html">
      SPHERE_DELAUNAY</a>,
      a FORTRAN90 program which 
      computes and plots the Delaunay triangulation of points on the unit sphere.
    </p>

    <p>
      <a href = "../../f_src/sphere_design_rule/sphere_design_rule.html">
      SPHERE_DESIGN_RULE</a>,
      a FORTRAN90 library which 
      returns point sets on the surface of the unit sphere, known as "designs",
      which can be useful for estimating integrals on the surface, among other uses.
    </p>

    <p>
      <a href = "../../datasets/sphere_grid/sphere_grid.html">
      SPHERE_GRID</a>, 
      a dataset directory which 
      contains grids of points, lines, triangles or quadrilaterals on a sphere;
    </p>

    <p>
      <a href = "../../f_src/sphere_lebedev_rule/sphere_lebedev_rule.html">
      SPHERE_LEBEDEV_RULE</a>, 
      a FORTRAN90 library which 
      computes Lebedev quadrature rules for the unit sphere;
    </p>

    <p>
      <a href = "../../f_src/sphere_stereograph/sphere_stereograph.html">
      SPHERE_STEREOGRAPH</a>,
      a FORTRAN90 library which
      computes the stereographic mapping between points on the unit sphere
      and points on the plane Z = 1; a generalized mapping is also available.
    </p>

    <p>
      <a href = "../../f_src/sphere_triangle_quad/sphere_triangle_quad.html">
      SPHERE_TRIANGLE_QUAD</a>,
      a FORTRAN90 library which 
      estimates the integral of a function over a spherical triangle.
    </p>

    <p>
      <a href = "../../f_src/sphere_voronoi/sphere_voronoi.html">
      SPHERE_VORONOI</a>,
      a FORTRAN90 program which 
      computes and plots the Voronoi diagram of points on the unit sphere.
    </p>

    <p> 
      <a href = "../../m_src/sphere_xyz_display/sphere_xyz_display.html">
      SPHERE_XYZ_DISPLAY</a>, 
      a MATLAB program which
      reads XYZ information defining points in 3D, 
      and displays a unit sphere and the points in the MATLAB graphics window.
    </p>

    <p> 
      <a href = "../../cpp_src/sphere_xyz_display_opengl/sphere_xyz_display_opengl.html">
      SPHERE_XYZ_DISPLAY_OPENGL</a>,
      a C++ program which
      reads XYZ information defining points in 3D, 
      and displays a unit sphere and the points, using OpenGL.
    </p>

    <p>
      <a href = "../../f_src/stripack/stripack.html">
      STRIPACK</a>,
      a FORTRAN90 library which 
      computes the Delaunay triangulation or Voronoi diagram of points on a unit sphere.
    </p>

    <p>
      <a href = "../../f_src/stripack_interactive/stripack_interactive.html">
      STRIPACK_INTERACTIVE</a>,
      a FORTRAN90 program which 
      reads a set of points on the unit sphere, computes the Delaunay triangulation, 
      and writes it to a file.
    </p>

    <p>
      <a href = "../../f_src/stroud/stroud.html">
      STROUD</a>,
      a FORTRAN90 library which
      defines quadrature rules for a variety of multidimensional regions.
    </p>

    <p> 
      <a href = "../../m_src/xyz_display/xyz_display.html">
      XYZ_DISPLAY</a>, 
      a MATLAB program which
      reads XYZ information defining points in 3D, 
      and displays an image in the MATLAB graphics window.
    </p>

    <p> 
      <a href = "../../cpp_src/xyz_display_opengl/xyz_display_opengl.html">
      XYZ_DISPLAY_OPENGL</a>,
      a C++ program which
      reads XYZ information defining points in 3D, 
      and displays an image using OpenGL.
    </p>

    <h3 align = "center">
      Reference:
    </h3>

    <p>
      <ol>
        <li>
          Edward Saff, Arno Kuijlaars,<br>
          Distributing Many Points on a Sphere,<br>
          The Mathematical Intelligencer,<br>
          Volume 19, Number 1, 1997, pages 5-11.
        </li>
      </ol>
    </p>

    <h3 align = "center">
      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "sphere_grid.f90">sphere_grid.f90</a>, the source code.
        </li>
        <li>
          <a href = "sphere_grid.sh">sphere_grid.sh</a>,
          BASH commands to compile the source code.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "sphere_grid_prb.f90">sphere_grid_prb.f90</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sphere_grid_prb.sh">sphere_grid_prb.sh</a>,
          BASH commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sphere_grid_prb_output.txt">sphere_grid_prb_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      To see data files and images of the sphere grids created by this
      example program, go to 
      <a href = "../../datasets/sphere_grid/sphere_grid.html">
      the SPHERE_GRID dataset directory</a>.
    </p>

    <h3 align = "center">
      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>ARC_COSINE</b> computes the arc cosine function, with argument truncation.
        </li>
        <li>
          <b>ARC_SINE</b> computes the arc sine function, with argument truncation.
        </li>
        <li>
          <b>ATAN4</b> computes the inverse tangent of the ratio Y / X.
        </li>
        <li>
          <b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
        </li>
        <li>
          <b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
        </li>
        <li>
          <b>ICOS_SHAPE</b> describes an icosahedron.
        </li>
        <li>
          <b>ICOS_NUM</b> gives "sizes" for an icosahedron in 3D.
        </li>
        <li>
          <b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
        </li>
        <li>
          <b>R8MAT_TRANSPOSE_PRINT</b> prints a R8MAT, transposed.
        </li>
        <li>
          <b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
        </li>
        <li>
          <b>R8VEC_DIFF_NORM</b> returns the L2 norm of the difference of R8VEC's.
        </li>
        <li>
          <b>R8VEC_NORM</b> returns the L2 norm of an R8VEC.
        </li>
        <li>
          <b>R8VEC_POLARIZE</b> decomposes an R8VEC into normal and parallel components.
        </li>
        <li>
          <b>R8VEC_PRINT</b> prints an R8VEC.
        </li>
        <li>
          <b>SPHERE_CUBED_IJK_TO_XYZ:</b> cubed sphere IJK to XYZ coordinates.
        </li>
        <li>
          <b>SPHERE_CUBED_LINE_NUM</b> counts lines on a cubed sphere grid.
        </li>
        <li>
          <b>SPHERE_CUBED_POINTS</b> computes the points on a cubed sphere grid.
        </li>
        <li>
          <b>SPHERE_CUBED_POINTS_FACE:</b> points on one face of a cubed sphere grid.
        </li>
        <li>
          <b>SPHERE_CUBED_POINT_NUM</b> counts the points on a cubed sphere grid.
        </li>
        <li>
          <b>SPHERE_DISTANCE_XYZ</b> computes great circle distances on a sphere.
        </li>
        <li>
          <b>SPHERE_GRID_Q4:</b> rectangular grid on a sphere.
        </li>
        <li>
          <b>SPHERE_GRID_T3</b> produces a triangle grid on a sphere.
        </li>
        <li>
          <b>SPHERE_ICOS_EDGE_NUM</b> sizes an icosahedral grid on a sphere.
        </li>
        <li>
          <b>SPHERE_ICOS_FACE_NUM</b> sizes an icosahedral grid on a sphere.
        </li>
        <li>
          <b>SPHERE_ICOS_POINT_NUM</b> sizes an icosahedral grid on a sphere.
        </li>
        <li>
          <b>SPHERE_ICOS1_POINTS</b> returns icosahedral grid points on a sphere.
        </li>
        <li>
          <b>SPHERE_ICOS2_POINTS</b> returns icosahedral grid points on a sphere.
        </li>
        <li>
          <b>SPHERE_LINE_PROJECT</b> projects a line onto a sphere.
        </li>
        <li>
          <b>SPHERE_LL_LINES</b> produces lines for a latitude/longitude grid.
        </li>
        <li>
          <b>SPHERE_LL_LINE_NUM</b> counts lines for a latitude/longitude grid.
        </li>
        <li>
          <b>SPHERE_LL_POINTS</b> produces points for a latitude/longitude grid.
        </li>
        <li>
          <b>SPHERE_LL_POINT_NUM</b> counts points for a latitude/longitude grid.
        </li>
        <li>
          <b>SPHERE_LLQ_LINES:</b> latitude/longitude quadrilateral grid lines.
        </li>
        <li>
          <b>SPHERE_LLQ_LINE_NUM</b> counts lines for a latitude/longitude quadrilateral grid.
        </li>
        <li>
          <b>SPHERE_SPIRALPOINTS:</b> spiral points on a sphere.
        </li>
        <li>
          <b>SPHERE_UNIT_SAMPLE</b> picks a random point on the unit sphere.
        </li>
        <li>
          <b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f_src.html">
      the FORTRAN90 source codes</a>.
    </p>

    <hr>

    <i>
      Last revised on 11 October 2012.
    </i>

    <!-- John Burkardt -->
 
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