Algorithms for detecting dependencies and rigid subsystems for CAD [article]

James Farre, Helena Kleinschmidt, Jessica Sidman, Audrey Lee-St.John, Stephanie Stark, Louis Theran, Xilin Yu
2015 arXiv   pre-print
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
more » ... natorial 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.
arXiv:1306.1572v2 fatcat:mwyewcknrzaftnvy7f72rdup7u