Thickening: an operation for animation

In this paper, we present a modelling operation dedicated to animation. This operation, called thickening, is a generalization of the extrusion operation. It allows to build from a graph 3-D objects with circular section and 4-D objects with spherical or toric section. Moreover, the date and the number of mergings and splittings in the associated animation are perfectly controlled, and the trajectory of each of the animated objects is completely established. Several types of thickening are presented in this paper, to build a surface or a volume, starting from a graph drawn in a surface or in a volume. Copyright # 2000 John Wiley & Sons, Ltd.