The algebraic geometry of motions of bar-and-body frameworks
SIAM Journal on Algebraic and Discrete Methods
Constraining Plane Configurations in Computer-Aided Design: Combinatorics of Directions and Lengths
SIAM Journal on Discrete Mathematics
Solving spatial basic geometric constraint configurations with locus intersection
Proceedings of the seventh ACM symposium on Solid modeling and applications
Constraining Plane Configurations in CAD: Circles, Lines, and Angles in the Plane
SIAM Journal on Discrete Mathematics
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
Detecting all dependences in systems of geometric constraints using the witness method
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Body-and-cad geometric constraint systems
Computational Geometry: Theory and Applications
Computation of components' interfaces in highly complex assemblies
Computer-Aided Design
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We study the rigidity of body-and-cad frameworks which capture the majority of the geometric constraints used in 3D mechanical engineering CAD software. We present a combinatorial characterization of the generic minimal rigidity of a subset of body-and-cad frameworks in which we treat 20 of the 21 body-and-cad constraints, omitting only point-point coincidences. While the handful of classical combinatorial characterizations of rigidity focus on distance constraints between points, this is the first result simultaneously addressing coincidence, angular, and distance constraints. Our result is stated in terms of the partitioning of a graph into edge-disjoint spanning trees. This combinatorial approach provides the theoretical basis for the development of deterministic algorithms (that will not depend on numerical methods) for analyzing the rigidity of body-and-cad frameworks.