组合数学与CAD系统的刚性
Combinatorics and the Rigidity of CAD Systems
摘要：
我们研究了车身和CAD框架的刚度，这些框架捕获了3D机械工程CAD软件中使用的大多数几何约束。我们提出了一个组合表征的通用最小刚度的一个子集的身体和CAD框架中，我们对待20的21个身体和CAD的约束，省略了点的重合。虽然为数不多的经典组合特征的刚性集中在点之间的距离约束，这是第一个结果，同时解决重合，角度和距离约束。我们的结果表示在一个图的分割成边不相交的生成树。这种组合的方法提供了理论基础的确定性算法的发展（将不依赖于数值方法），用于分析车身和cad框架的刚度。
英文摘要：
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.
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