Algorithms for detecting dependencies and rigid subsystems for CAD
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.
Cite
@article{arxiv.1306.1572,
title = {Algorithms for detecting dependencies and rigid subsystems for CAD},
author = {James Farre and Helena Kleinschmidt and Jessica Sidman and Audrey Lee-St. John and Stephanie Stark and Louis Theran and Xilin Yu},
journal= {arXiv preprint arXiv:1306.1572},
year = {2015}
}
Comments
37 pages, 14 figures (v2 is an expanded version of an AGD'14 abstract based on v1)