All You Need Is Force: a constraint-based approach for rigid body dynamics in computer animation

Abstract

Over the last few years, simulating themotion of linked articulated rigid bodies based on classical rigid body dynamics has become a valuable paradigmfor making realistic 3-D computer animations. Although several operational methods for dynamical simulation have been developed, in general these are both concep- tually and computationally complex. To inspire further research in devising alter- native and possibly simpler schemes for dealing with articulated rigid bodies, this paper discusses an alternative approach to rigid body dynamics which is based on (conceptually much simpler) point mechanics. Geometric constraints, e.g. the re- quirement that the distance between two points should be conserved, take the form of additional algebraic equations. We propose to solve these algebraic constraints in concert with the numerical integration. First, we give a general formulation of such a scheme. Next, we describe a preliminar implementation on the basis of a very naive numerical solver for ODE’s (ordinary differential equations).