View source for Voronoisphere.m

{{DISPLAYTITLE:voronoisphere.m}} __NOTOC__
Voronoi tessellation on a sphere.

==Syntax==

     [vertices,indices,polygons,sangles]=voronoisphere(xyz,res)

==Arguments==

     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)

==Outputs==

     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

==Examples==
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.

[[File:voronoi_example.png]]

==See also==
[[Kernel_utilities#Integration_grids|Integration grids]], [[Appendix I: powder grids]]


''Version 2.6, authors: [[Ilya Kuprov]]''