siddharth-maddali/SphereMesh

Delaunay surface meshes on spheres

SphereMesh: Delaunay mesh on the surface of a sphere

This Matlab/Octave code base provides routines to create Delaunay meshes on the surface of a unit sphere, by recursively bisecting the edges of chosen regular polyhedrons (in particular, Platonic solids).

Usage:

% For Matlab/Octave
[ P, tri ] = generateSphereMesh( generation, type );

Input parameters:

1. generation is the number of recursive bisections desired. The more this value, the finer the mesh, but also the larger the output arrays. If generation is set to zero, then the surface meshes of the original platonic solids are returned. A value of 3 or 4 for an icosahedral mesh results in approximately equal-sized triangular mesh elements. The node positions in these high-density cases can be used as an approximation for uniform sampling of a sphere.
2. type can currently take three string values: tet, oct and ico for tetrahedral, octahedral and icosahedral starting shapes respectively.

Outputs:

1. P is a 3XN array of 3D points on the unit sphere (norm of each column is 1) which denote the mesh nodes.
2. tri is a Mx3 integer array whose rows denote the vertices of each triangular mesh element.

The spherical mesh can ve visualized in Matlab/Octave with the command:

figure; 
trisurf( tri, P(1,:), P(2,:), P(3,:), 'EdgeColor', 'k' );
axis image; 

Examples