Not only is x + y + z = 0, but the absolute values of x, y and z are equal to twice the radius of the ring. This should be sufficient to identify every hexagon on each successive ring: var radius = 4; for(var i = 0; i < radius; i++) { for(var j … Read more
The shape you have is one of so called “Goldberg polyhedra”, is also a geodesic polyhedra. The (rather elegant) algorithm to generate this (and many many more) can be succinctly encoded in something called a Conway Polyhedron Notation. The construction is easy to follow step by step, you can click the images below to get … Read more
(UPDATED: Refactored code to make more understandable and more efficient) (UPDATED: Reduced answer length, fixed bugs in code, improved quality of images) This image shows the top left corner of a hexagonal grid and overlaid is a blue square grid. It is easy to find which of the squares a point is inside and this … Read more
For clarity, let the “hexagonal” coordinates be (r,g,b) where r, g, and b are the red, green, and blue coordinates, respectively. The coordinates (r,g,b) and (x,y) are related by the following: y = 3/2 * s * b b = 2/3 * y / s x = sqrt(3) * s * ( b/2 + r) … Read more
Take a look at vraid/earthgen; it uses hexagons (plus a few pentagons) and includes source code (see planet/grid/create_grid.cpp). As of 2018 a new version is available based on racket.