Body-and-cad Geometric Constraint Systems

Details Body-and-cad Geometric Constraint Systems Body-and-cad Geometric Constraint Systems

2010-06-06

arxiv.org/abs/1006.1126v1

Computer Science

Computational Geometry

33 pages, to appear in Computational Geometry: Theory and Applications (an abbreviated version appeared in: 24th Annual ACM Sy

Scientific paper

Motivated by constraint-based CAD software, we develop the foundation for the rigidity theory of a very general model: the body-and-cad structure, composed of rigid bodies in 3D constrained by pairwise coincidence, angular and distance constraints. We identify 21 relevant geometric constraints and develop the corresponding infinitesimal rigidity theory for these structures. The classical body-and-bar rigidity model can be viewed as a body-and-cad structure that uses only one constraint from this new class. As a consequence, we identify a new, necessary, but not sufficient, counting condition for minimal rigidity of body-and-cad structures: nested sparsity. This is a slight generalization of the well-known sparsity condition of Maxwell.

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