An approximation for normal vectors of deformable models

A physically-based deformable model proposed by Terzopoulous et al. is governed by the Lagrange's form, that establishes the relation between the dynamics of deformable models under the influence of applied forces. The net instantaneous potential energy of deformation is derived on the basis of the geometric properties, namely the first and second fundamental forms. For simplicity, the normal vector at each sample point is approximated by the second derivative. We present another approximation for the normal vector which offers better visual simulation. Some comparisons are given.