# Spherical object with n vertices and no coordinate singularities

I'm programming a tool where I want to track the directions of a unit vector. I want to store the position to which the vector is pointing on a unit ball. Each time the vector points to a position $x$ it's (float)value is increased

I'm using a radial gradient around the stored position to produce a small falloff, so I also need to access the "neighbour" elements. It is also possible that I use less tracking-positions(vertices) and round my tracked position to the next possible one .

Up until now I was simply using a 360x360-float-array, but since there are coordinate singularities I'm looking for an alternative

The optimal shape should provide:

• No coordinate singularities
• An arbitrary number of vertices, since I want to be able to alter memory usage