Subject 6.06: How do I evenly distribute N points on (tesselate) a sphere?
“Evenly distributed” doesn’t have a single definition. There is a sense in which only the five Platonic solids achieve regular tesselations, as they are the only ones whose faces are regular and equal, with each vertex incident to the same number of faces. But generally “even distribution” focusses not so much on the induced tesselation, as it does on the distances and arrangement of the points/vertices. For example, eight points can be placed on the sphere further away from one another than is achieved by the vertices of an inscribed cube: start with an inscribed cube, twist the top face 45 degrees about the north pole, and then move the top and bottom points along the surface towards the equator a bit. The various definitions of “evenly distributed” lead into moderately complex mathematics. This topic happens to be a FAQ on sci.math as well as on comp.graphics.algorithms; a much more extensive and rigorous discussion written by Dave Rusin can be found at: http://www.math.niu.edu/~rus
“Evenly distributed” doesn’t have a single definition. There is a sense in which only the five Platonic solids achieve regular tesselations, as they are the only ones whose faces are regular and equal, with each vertex incident to the same number of faces. But generally “even distribution” focusses not so much on the induced tesselation, as it does on the distances and arrangement of the points/vertices. For example, eight points can be placed on the sphere further away from one another than is achieved by the vertices of an inscribed cube: start with an inscribed cube, twist the top face 45 degrees about the north pole, and then move the top and bottom points along the surface towards the equator a bit. The various definitions of “evenly distributed” lead into moderately complex mathematics. This topic happens to be a FAQ on sci.math as well as on comp.graphics.algorithms; a much more extensive and rigorous discussion written by Dave Rusin can be found at: http://www.math.niu.edu/~rus
