Over-constraints detection and resolution in geometric equation systems

Abstract

This paper proposes an original decision-support approach to address over-constrained geometric configurations in Computer-Aided Design. It focuses particularly on the detection and resolution of redundant and conflicting constraints when deforming free-form surfaces made of NURBS patches. Based on a series of structural decompositions coupled with numerical analyses, the proposed approach handles both linear and non-linear constraints. The structural decompositions are particularly efficient because of the local support property of NURBS. Since the result of this detection process is not unique, several criteria are introduced to drive the designer in identifying which constraints should be removed to minimize the impact on his/her original design intent. Thus, even if the kernel of the algorithm works on equations and variables, the decision is taken by considering the user-specified geometric constraints. The method is illustrated on academic and industrial examples realized with our prototype software.