Relaxed parametric design with probabilistic constraints

Yaacov Hel-Or*, Ari Rappoport, Michael Werman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Parametric design is an important modelling paradigm in computer-aided design. Relationships (constraints) are specified between the degrees of freedom (DOFs) of the model, instead of the DOFs themselves, resulting in efficient design modifications and variations. Current parametric modellers require an exact specification of all the constraints involved, which causes overwork for the designer during design iterations. The relaxed-parametric-design modelling paradigm is described, in which decisions which needlessly limit the freedom of design in later stages are avoided. The designer usesb soft constraints, and specifies the level of exactness with which they are to be met. As a specific scheme for implementing relaxed parametric design, probabilistic constraints are presented, where a parametric model is viewed as a stochastic process. The softness of a constraint is represented as the covariance of a suitably distributed random variable. A novel method is described of 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 for the solver to select a particular solution from multiple solutions.

Original languageAmerican English
Pages (from-to)426-434
Number of pages9
JournalCAD Computer Aided Design
Issue number6
StatePublished - Jun 1994


  • Kalman filters
  • design constraints
  • parametric modelling


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