Triangles can be generated explicitly or implicitly by their position in the grid. The z coordinate is based on the value in the map at that location.

+-+-+Įach vertex has an x and y coordinate corresponding to the x and y of the pixel in the map. If you think of each pixel as a vertex rather than a face, you can generate a simple triangular mesh. the spacing of the grid in same units as the height map Putting it into code would look like: // sample the height map: Your hightmap is a sampling of some function f on a regular grid. To get a better approximation you need to use at least four points, thus adding a third point (i.e. It can be proven that the best approximation to ∂f/∂x by two samples is archived by: Given a function f : ℝ 2 → ℝ that describes a surface in ℝ 3, a unit normal at (x,y) is given by Each pixel of the image represents a vertex of the grid, so intuitively, from symmetry, its normal is determined by heights of neighboring pixels (i-1,j), (i+1,j), (i,j-1), (i,j+1). or is there a much easier method that I'm missing?

calculate the normals of those two faces.

calculate the normals of those two faces via cross product.

split the four into two triangles: ABC and BCD.

So given the 3D coordinates of A, B, C, and D, would it make sense to: That would mean that the normal at coordinate (i, j) is determined by the heights at (i, j), (i, j + 1), (i + 1, j), and (i + 1, j + 1) (call those A, B, C, and D, respectively). My thinking is that each pixel of the image represents a lattice coordinate in a 256 x 256 grid (hence, why there are 257 x 257 heights). My height texture is currently a 257 x 257 gray-scale image (height values are scaled for visibility purposes):

I have some ideas for how to turn that into a texture of normals, but some feedback would be much appreciated. I've already generated a height map using the midpoint displacement algorithm and saved it to a texture. I'm working on procedurally generating patches of dirt using randomized fractals for a video game.

Bump map generator