Displacement Mapping

Displacement mapping is a powerful technique for adding detail to three dimensional objects and scenes. While bump mapping gives the appearance of increased surface complexity, displacement mapping actually adds surface complexity resulting in correct silhouettes and no parallax errors. This paper presents the background to displacement mapping, current hardware implementations and how to use them, and recent research into algorithms for adaptive displacement mapping. A major benefit of displacement mapping is the ability to use it for both adding surface detail to a model and for creating the model itself. For example the detail added to the surface of a crocodile’s skin could be done with displacement mapping or all the detail required to model a piece of terrain can be stored in a displacement map and a flat plane used for the base surface. Displacement mapping can be applied to different base surfaces for example NPatches as used by DirectX 9 and subdivision surfaces as used by Lee et al [8]. Displacement mapping was first mentioned by Cook [1] as a technique for adding surface detail to objects in a similar manner to texture mapping. A base surface can be defined by a bivariate vector function P(u, v)1 that defines 3D points (x, y, z) on the surface. A corresponding scalar displacement map for that surface can be represented as d(u, v). As an alternative to the one dimensional scalar displacement vector displacements could also be used. The normals on the base surface can be represented as N̂(u, v). Using this representation the points on the new displaced surface P′(u, v) are defined as: