# voronoisphere.m

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.

## See also

Integration grids, Appendix I: powder grids

*Version 2.6, authors: Ilya Kuprov*