Texture mapping, bump mapping, and displacement maps are central instruments in computer graphics aiming to achieve photo-realistic renderings. In all these techniques, the mapping is typically one-to-one and a single surface location is assigned a single texture color, normal, or displacement. Other specialized techniques have also been developed for the rendering of supplementary surface details such as fur, hair, or scales.

This work presents an extended view of these procedures and allows one to precisely assign a single surface location with few continuously deformed displacements, each with possibly different texture color or normal, employing trivariate functions in a similar way to FFDs. As a consequence, arbitrary regular geometry could be employed as part of the presented scheme as supplementary surface texture details. This work also augments recent results on texturing and parameterization of surfaces of arbitrary topologies by providing more flexible control over the phase of texture modeling.

By completely and continuously parameterizing the space above the surface of the object as a trivariate vector function, we are able, in this work, to not only control the mapping of the texture on the surface but also to control this mapping in the volume surrounding the surface.