Deformable object simulation with Poisson equation

This paper presents a new methodology for the deformation of soft objects by drawing an analogy between Poisson equation and elastic deformation. The potential energy stored in an elastic body as a result of a deformation caused by an external force is propagated among mass points by the Poisson equation. An improved Poisson model is developed for propagating the energy generated by the external force in a natural manner. A method is presented to derive the internal forces from the potential energy distribution. This proposed methodology not only deals with large-range deformations, but also accommodates both isotropic and anisotropic materials by simply changing the constitutive coefficients. Examples are presented to demonstrate the efficiency of the proposed methodology.