# 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.