Displacement mapping uses a sinusoidal function to turn a plane into a rippled surface. It adds geometric detail. It is expensive to compute.

This is a torus with a large, noisy displacement map. It becomes a crusty barnicle. Large displacements are generally harder than small displacements.

Sharp creases in the displacement map can cause cracking. This algorithm never cracks and handles extreme displacements across complete discontinuities.

Primitives, like spheres, are broken down into tiny triangles before displacement. If the sphere is tessellated into polygons with 5 pixel long edges, and then displaced, the polygons get stretched out and become visible.

When the polygons are retessellated after displacement, the stretching goes away. Retessellation is tricky to implement.

The last image is retessellated down to 1.5 pixel polygons, which really shows off a lot of detail.

The bugs are by far the best thing about displacement.