John C. Platt

Elastically deformable models

The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible metals. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces, constraints, ambient media, and impenetrable obstacles. The models are fundamentally dynamic and realistic animation is created by numerically solving their underlying differential equations. Thus, the description of shape and the description of motion are unified.

Constraints methods for flexible models

Simulating flexible models can create aesthetic motion for computer animation. Animators can control these motions through the use of constraints on the physical behavior of the models. This paper shows how to use mathematical constraint methods based on physics and on optimization theory to create controlled, realistic animation of physically-based flexible models. Two types of constraints are presented in this paper: reaction constraints (RCs) and augrmented Lagrangian constraints (ALCs). RCs allow the fast computation of collisions of flexible models with polygonal models. In addition, RCs allow flexible models to be pushed and pulled under the control of an animator. ALCs create animation effects such as volume-preserving squashing and the molding of taffy-like substances. ALCs are compatible with RCs. In this paper, we describe how to apply these constraint methods to a flexible model that uses finite elements.

Heating and melting deformable models

We develop physically-based graphics models of non-rigid objects capable of heat conduction, thermoelasticity, melting and fluid-like behaviour in the molten state. These deformable models feature non-rigid dynamics governed by Lagrangian equations of motion and conductive heat transfer governed by the heat equation for non-homogeneous, non-isotropic media. In its solid state, the discretized model is an assembly of hexahedral finite elements in which thermoelastic units interconnect particles situated in a lattice. The stiffness of a thermoelastic unit decreases as its temperature increases, and the unit fuses when its temperature exceeds the melting point. The molten state of the model involves a molecular dynamics simulation in which ‘fluid’ particles that have broken free from the lattice interact through long-range attraction forces and short-range repulsion forces. We present a physically-based animation of a thermoelastic model in a simulated physical world populated by hot constraint surfaces.

A generalization of dynamic constraints

Abstract This paper presents a constraint method for physically based computer graphics models, based on the constraint stabilization method of Baumgarte and on the dynamic constraints of Barzel and Barr. These new constraints are called generalized dynamic constraints (GDCs). GDCs extend dynamic constraints to obey the principle of virtual work and to fulfill time-varying and inequality constraints. The constraint forces of GDCs are computed by a sparse linear system and are proportional to the Lagrange multipliers of the constraints. GDCs are used to assemble deformable computer graphics models and to simulate collisions between the models.

An approach for solving the parameters setting problem

A fundamental problem in modeling biological phenomena is choosing the parameter values which give the model its best predictive capability. A general approach is presented that automatically determines locally optimal parameter values to most closely match the models behavior with the experimentally observed behavior. As a proof of the concept, the method is applied to the Hodgkin-Huxley model of the membrane action potential.<<ETX>>