Inverse Displacement Mapping in the General Case

Inverse Displacement Mapping is a form of displacement mapping which allows the ray tracing of displacement mapped surfaces. The technique performs all calculations in the inverse (parametric) space of the surface thus avoiding the need to explicitly model the complex three dimensional geometry. This produces a compact and general algorithm, Only when the solution, in parametric space, has been determined is it transformed back to 3D space. The algorithm works by projecting the ray into the parametric space of the surface. This ray is then split into a series of segments, each of which can be efficiently handled to calculate the intersection points. The algorithm presented here has been used to ray trace displacement mapped objects from a variety of underlying surface types.