An Evolution Equation which describes Random Deformation of a Surface derived by a Variational Principle of Continuum Mechanics

Abstract

The author generalizes the cloth simulation methods about 3DCG animation based on the mathematically rigorous formulation. The motion of the general dimensional surface (manifold) is simulated by the Newtonian equation which is derived for the continuum surface model ( not for the discrete approximation model ) based on the variational principles. This Newtonian equation become a feedback system. If suitable stochastic process is set as the goal trajectory of the feedback system, we can generate virtual interesting 3DCG animations of the surface motions.