What is a parametric family of solids?
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
Sketch-based pruning of a solution space within a formal geometric constraint solver
Artificial Intelligence
Decomposition plans for geometric constraint systems, part I: performance measures for CAD
Journal of Symbolic Computation
FRONTIER: fully enabling geometric constraints for feature-based modeling and assembly
Proceedings of the sixth ACM symposium on Solid modeling and applications
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Geometric constraints are at the heart of parametric and feature-based CAD systems. Changing values of geometric constraint parameters is one of the most common operations in such systems. However, because allowable parameter values are not known to the user beforehand, this is often a trial-and-error process. We present a solution for automatically determining the allowable range for parameters of geometric constraints. Considered are systems of distance and angle constraints on points in 3D that can be decomposed into triangular and tetrahedral subproblems, by which most practical situations in parametric and feature-based CAD systems can be represented. Our method uses the decomposition to find critical parameter values for which subproblems degenerate. By solving one problem instance for each interval between two subsequent critical values, the exact parameter ranges are determined for which a solution exists.