Is there a formula or algorithm with which one can interpolate the points of a triangle that lies on the unit sphere in a spherical manner?
Let me elaborate:
If you want to interpolate two points on a unit sphere spherical, you use slerp.
If you want to interpolate between points of a planar triangle, you probably want to use barycentric coordinates.
My overall goal is to create points within the triangle of the sphere which are evenly positioned, in regards to their angle, if possible.
In particular, I want to do create a geodesic polyhedron (based on an icosahedron) in which the triangles on the surface of the approximated sphere are as evenly spread as possible, without the points closer to an original corner of the icosahedron having smaller distances to each other than those in the middle.
My approach do to so so far was to interpolate spherical on two of the edges using slerp, and then between the points created in this manner, but a more direct approach over something like barycentric coordinates would be appreciated.