If you have played with Bryce or Terragen you know that Terrain Generation is fun and useless. The Midpoint Displacement Algorithm is one of the simplest methods to build a triangle mesh that resembles the terrain found in nature. You can see its output on the right.

While this looks like a mountain of some sorts, the algorithm does not produce good mountains every time you invoke it. Instead, the result is quite random and almost always bad. Have a look at the algorithm:

- Make one triangle.
- Subdivide all your triangles into four new ones (use the edge midpoints as new vertices).
- Move your new midpoints along the y-axis by a random offset.
- Repeat 2 and 3 with half the offset.

The algorithm refines its terrain model recursively with every step, producing self-similar (in other words fractal) patches of terrain. It is short and easy to understand. Too bad real mountains are only superficially self-similar. One of the most visible shortcomings of the algorithm can be seen when the random displacement is replaced by its expected value. The “expected value” for the algorithm looks like this:

These furrows can be seen in most randomly displaced terrains, too, when viewed from specific angles or directly from above. (The yellow cube is the light source)

A better approach might be to use Perlin noise as a heightmap since it does not introduce visible artifacts. I’ll probably test this later.

Concerning the implementation, i spent most of the time implementing the fundamental mesh operations like splitting lines and triangles. Since this will not be last time i’ll handle triangle meshes and i might save other Lispers the pain i am thinking about expanding this and publishing it as a general mesh handling and drawing library for Common Lisp.

Those who have played with World Machine ( http://www.world-machine.com ) know that Terrain Generation is serious and usefull ;)