Showing papers by "John Platt published in 1988"

Constraints methods for flexible models

Abstract: 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.

Constrained Differential Optimization for Neural Networks

Abstract: Many optimization models of neural networks need constraints to restrict the space of outputs to subspace which satisfies external criteria. Optimizations using energy methods yield "forces" which act upon the state of the neural network. The penalty method, in which quadratic energy constraints are added to an existing optimization energy, has become popular recently, but is not guaranteed to satisfy the constraint conditions when there are other forces on the neural model or when there are multiple constraints. In this paper, we present the basic differential multiplier method (BDMM), which satisfies constraints exactly; we create forces which gradually apply the constraints over time, using "neurons" that estimate Lagrange multipliers. The basic differential multiplier method is a system of differential equations first proposed by [ARROW] as an economic model. These differential equations locally converge to a constrained minimum. Examples of applications of the differential method of multipliers include enforcing permutation codewords in the analog decoding problem and enforcing valid tours in the traveling salesman problem.