Dynamic Animation of N-Dimensional Deformable Objects

Abstract

This paper presents a new, accurate, efficient and unified method for dynamic animation of one, two or three-dimensional deformable objects. The objects are modelled as d-dimensional juxtapositions of d- dimensional patches defined as parametric blending of a common d-dimensional mesh of 3D control points. Animation of the object is achieved by dynamic animation of its control points. This ensures that at each time step the object shape conforms to its patches definitions, and, thus, that every property implied by the nature of the blending functions is verified. Dynamic animation of these continuous models implies no “matter discretising” as the control points are not considered as material points but moreover as the degrees of freedom of the continuous object . A generic (both for blending functions nature and object intrinsic dimension d) mechanical model reflecting this idea is proposed. Then, according to this modelling idea, a convenient generic dynamic animation engine is built from Lagrangian Equations. This engine relies upon an accurate and very efficient linear system. Forces and constraints handling as well as numerical resolution process are then briefly discussed in this scheme.