Call it SphereScaper or an equally creative name. But what can we actually do with it? I decided to go for a very minimalistic Townscaper вЂњcloneвЂќ which uses the sphere mesh for tile placement. Using my approach, the final result looks like this:Д«onus: Tiles and Marching Squares Deforming the Tiles all quads should have approximately the same area.each quad should be as square as possible.There are probably many good ways too relax the mesh but some good guidelines should be: In the end I needed to augment this by adding forces which try to prevent too small/large and thin quads as well. However, I approached the problem from a slightly different angle and started with (a restricted version of) Laplacian smoothing which is generally used to smooth meshes. I see no reason why an approach like this shouldnвЂ™t work on a spherical mesh as well. In the simpler case of a grid in a plane, there are some ressources available which outline possible relaxation methods, like this article from v, but most of them seem to involve letting each quad force its vertices into a square shape. For me, this was the trickiest step since it involved some experimentation to get it to look just right. This is where the mesh relaxation comes in. We are now almost where we want to be but the mesh does not look very organic yet. The mesh with all faces subdivided into quads. It is, of course, not the only triangulation but it has some nice properties including the fact that all triangles have the same size. In the tweet above this is the triangulation of a hexagon but we can triangulate any surface, really.ДЄ popular triangulation of the surface of a sphere is the so-called icosphere. Simply put, we split our initial shape into many smaller triangles. What is a triangulation, you ask? Well, there are many definitions ( including but not limited to tracking bad guys in police crime dramas) but in our case we will define it as surface triangulation which, with the words of Wikipedia, is вЂњa net of triangles, which covers a given surface partly or totallyвЂќ. The first step of the algorithm requires a triangulation. Relax the grid to make it look more natural.Subdivide all quads and triangles into new quads.Remove random edges triangles to create quads (we will now have a grid consisting of mostly quads but also some triangles).Start with a triangulation (in the tweeet above triangles in a hexagon).The surprisingly simple answer is: nothing.ДЇor the slightly more complicated answer, keep reading. What do we need to do to adapt it for a sphere (or even crazier shapes)? This was, however, only presented for a grid in a plane so far. Tile these babies to infinity /o0kU68uovZ- Oskar StГҐlberg July 7, 2019 Heuristic to reduce (or eliminate) 6 quad vertsДў.

Fairly even irregular quads grid in a hexДЎ.

Simple grids on spheres