d-Dimensional parametric models for dynamic animation of deformable objects

This paper introduces an accurate, efficient, and unified engine dedicated to dynamic animation of d-dimensional deformable objects. The objects are modelled as d-dimensional manifolds defined as functional combinations of a mesh of 3D control points, weighted by parametric blending functions. This model ensures that, at each time step, the object shape conforms to its manifold definitions. The object motion is deduced from the control points dynamic animation. In fact, control points should be viewed as the degrees of freedom of the continuous object. The chosen dynamic equations (Lagrangian formalism) reflect this generic modelling scheme and yield an exact and computationally efficient linear system.