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Voronoi tessellation on a sphere.




    xyz      - (3 x n) array, coordinates of n distinct vectors
                in R^3; these will be normalised

    res      - polygon edges longer than this resolution will
               have extra points added so that spherical plots
               look neat (optional, default is pi/180)


    vertices - (3 x m) array, coordinates of the vertices of the
                Voronoi tessellation

    indices  - (n x 1) cell array, j-th element contains the in-
                dices of the Voronoi cell vertices that corres-
                pond to xyz(:,j). Vertices are oriented counter-
                clockwise when looking from outside.

    polygons - (n x 1) cell array, j-th element contains the dis-
                cretised spherical polygonal coordinates of the
                vertices of the j-th Voronoi cell.

    sangles  - (n x 1) array, solid angles of each Voronoi cell


The output of fundamentals/quadratures/grid_diagrams.m file in the Spinach example set is given below. The solid lines are edges of Voronoi polyhedra computed using this function.

Voronoi example.png

See also

Integration grids, Appendix I: powder grids

Version 2.6, authors: Ilya Kuprov