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arXiv · 1306.1572

Algorithms for detecting dependencies and rigid subsystems for CAD

James Farre·Helena Kleinschmidt·Jessica Sidman·Audrey Lee-St. John·Stephanie Stark·Louis Theran·Xilin Yu
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Abstract

Geometric constraint systems underly popular Computer Aided Design soft- ware. Automated approaches for detecting dependencies in a design are critical for developing robust solvers and providing informative user feedback, and we provide algorithms for two types of dependencies. First, we give a pebble game algorithm for detecting generic dependencies. Then, we focus on identifying the "special positions" of a design in which generically independent constraints become dependent. We present combinatorial algorithms for identifying subgraphs associated to factors of a particular polynomial, whose vanishing indicates a special position and resulting dependency. Further factoring in the Grassmann- Cayley algebra may allow a geometric interpretation giving conditions (e.g., "these two lines being parallel cause a dependency") determining the special position.

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James Farre, Helena Kleinschmidt, Jessica Sidman, Audrey Lee-St. John, Stephanie Stark, Louis Theran, Xilin Yu. 2013-06-06. Algorithms for detecting dependencies and rigid subsystems for CAD. https://arxiv.org/abs/1306.1572

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