Dynamic deformation of solid primitives with constraints

This paper develops a systematic approach to deriving dynamic models from parametrically defined solid primitives, global geometric deformations and local finite- element deformations. Even though their kinematics is styl- ized by the particular solid primitive used, the models be- have in a physically correct way with prescribed mass dis- tributions and elasticities. We also propose efficient con- straint methods for connecting these new dynamic primitives together to make articulated models. Our techniques make it possible to build and animate constrained, nonrigid, unibody or multibody objects in simulated physical environments at interactive rates. 1 Introduction The graphics literature is replete with solid object representa- tions. Unfortunately, it is not particularly easy to synthesize realistic animation through direct application of the geomet- ric representations of solid modeling (5), and the problems are exacerbated when animate objects can deform. Physics- based animation has begun to overcome some of the difficul- ties. We propose a systematic approach for creating dynamic solid models capable of realistic physical behaviors starting from common solid primitives such as spheres, cylinders, cones, or superquadrics. Such primitives can "deform" kine- matically in simple ways; for example, a cylinder deforms as its radius or length is changed. To gain additional model- ing power we allow the primitives to undergo parameterized global deformations (bends, tapers, twists, shears, etc.) of the sort proposed in (2). To further enhance the geometric flexibility, we permit local free-form deformations. Our lo- cal deformations are similar in spirit to the FFDs of (12), but rather than being ambient space warps (12, 10), they are in- corporated directly into the solid primitive as finite element shape functions. Through the application of Lagrangian mechanics and the finite element method our models inherit generalized coor- dinates that comprise the geometric parameters of the solid primitive, the global and local deformation parameters, and the six degrees of freedom of rigid-body motion. Lagrange equations govern the dynamics, dictating the evolution of the