Angular Rigidity in 3D: Combinatorial Characterizations and Algorithms

Audrey Lee-St.john, Mount Holyoke College
Ileana Streinu, Smith College

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Constraint-based CAD software, used by engineers to design sophisticated mechanical systems, relies on a wide range of geometrical constraints. In this paper we focus on one special case: angular constraints in 3D. We give a complete combinatorial characterization for generic minimal rigidity in two new models: line- plane-and-angle and body-and-angle structures. As an immediate consequence, we obtain efficient algorithms for analyzing angular rigidity.