Relaxed Parametric Design with Probabilistic Constraints

Yacov Hel-Or, Ari Rappoport and Michael Werman

Parametric design is an important modeling paradigm in computer aided design. Relationships (constraints) between the degrees of freedom (DOFs) of the model, instead of the DOFs themselves, are specified, resulting in efficient design modifications and variations. Current parametric modelers require an exact specification of all the constraints involved, which causes over-work on the part of the designer during design iterations.

We describe the relaxed parametric design modeling paradigm, in which decisions which needlessly limit the freedom of design in later stages are avoided. The designer uses soft constraints and specifies the exactness by which they are to be met. As a specific scheme for implementing relaxed parametric design, we present probabilistic constraints, where a parametric model is viewed as a stochastic process. Softness of a constraint is represented as the covariance of a suitably distributed random variable. We describe a novel method for expressing the DOFs and the model as a system of probabilistic equations, which is then solved using the Kalman filter, a powerful estimation tool for stochastic systems. An a priori covariance matrix associated with a DOF can be used as a guideline to the solver to select a particular solution among multiple solutions.

Computer-Aided Design, 26(6):426-434, 1994. Also: proceedings, Second ACM/Siggraph Symposium on Solid Modeling and Applications (Solid Modeling '93), May 1993, Montreal, ACM Press, pp. 261-270.