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Relaxed Parametric Design with Probabilistic Constraints

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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.