Physically-Based Deformations Constrained in Displacements and Volume

Abstract

This paper presents a method of constraining physically-based deformable objects. In this method, an object can be defined locally in terms of kinetic and dynamic (mass, position, speed), and physical parameters (compressibility, elasticity, motor functioning). Several problems are solved: constant volume deformation, displacement constraints (fixed or moving required positions), and real object modelling. An object is described by a set of mass points on its contour. The evolution algorithm runs in two phases dealing successively with forces and constraints (which are presented as reaction forces).The main contribution of the method is the control of object volumes during evolution. We define a function that explicitly gives the inside volume of an object in order to use it as a constraint. Thus, the volume can be kept exactly constant during deformation without using an iterative process, in opposition to lagrangian approaches. Some results are illustrated by examples at the end of the paper.