Deformations expressed as displacement maps an easy way to combine deformations

Abstract

Upto now, assuming a geometric object as being a set of points, a deformation was defined as a mathematical function which mapped the original object set of points into a new one. In short, a new point was linked with each object point in the zone of influence of the deformation. With such a statement, it was not possible to apply several deformations simultaneously as soon as their zones of influence overlapped each other. A new formal definition of a deformation is brought out in this paper. Instead of a new point, this definition links a displacement with each object point in the zone of influence of the deformation. Thus, applying several deformations simultaneously is made feasible by blending, for each point of the original object, the displacement due to each deformation. © Springer-Verlag Berlin Heidelberg 2002.