A discrete field of vectors denoting offset or displacement.
Displacement maps are currently most visible in three dimensional graphics as a means to add geometric detail without actually modelling it. For transformation, many of the methods used in traditional texture maps may be applied to displacement maps. Early implementations of displacement maps allow an offset along a given axis (either in world or object coordinates) to be discretely represented by a greyscale image. Pixels in the image represent sample points, and intermediate offsets are interpolated to keep the surface of a rendered object relatively smooth.
Later implementations allow for displacement to occur on three axes (defined in RGB-space), but this makes work no less difficult than earlier methods.
The most recent methods allow for displacement along the normal of the mapped object. This is ideal for surfaces like dinosaur skin and tree bark, and allows for a relatively natural appearance with traditional character animation.
Displacement maps also exist in two-dimensional graphics. Most implementations use a discrete image to represent destination pixels for a current location, which is to say that a pixel's value is copied to a pixel in the destination image of an offset (in both x and y) represented in the displacement map. The advantage of such a system is that the displacement map may be pre-rendered and used iteratively to produce a sense of motion without costly per-frame calculations. Cross-fades and transitions may be used during iterative displacement at a fairly low cost with visually impressive results. Displacement maps in two-dimensions are most commonly found in audio-visualization software, but are also found in proffesional graphics packages like Adobe's Photoshop. A less generalized version of this is often called a plasma effect.