Body-and-cad geometric constraint systems

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• 作者：Kirk Haller^a ; ^{khaller@solidworks.com} ; Audrey Lee-St.John^b ; ¹ ; ² ; ^{astjohn@mtholyoke.edu} ; Meera Sitharam^c ; ³ ; ^{sitharam@cise.ufl.edu} ; Ileana Streinu^d ; ¹ ; ⁴ ; ^{istreinu@smith.edu} ; Neil White^c ; ^{white@math.ufl.edu}
• 关键词：Rigidity theory ; Computer aided design ; Geometric constraint system
• 刊名：Computational Geometry
• 出版年：2012
• 期刊代码：18_09257721
• 类别：cp
• 出版时间：October, 2012
• 卷：45
• 期：8
• 页码：385-405
• 文件大小：1748 K

摘要

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.