Discrete applied geometry

结构的刚性和灵活性是其功能和设计的核心。这适用于生物分子(预测功能和药物设计的蛋白质灵活性)、材料科学(例如，用于提炼重油的人造沸石)、人类建造结构、设计的机构(机构的路径)，以及CAD中几何配置的独立性(影响稳定和高效的CAD程序的设计)和计算机图形(如何在计算机中处理几何约束)。这项研究使用组合学和几何学来分析结构的哪些部分是刚性的，哪些是柔性的。在某些情况下，我们想要的不仅仅是最低限度的刚性--我们想要的是稳定或全球刚性。这适用于研究分子的微小波动，或者避免替代形式的分子(可能导致疾病或药物反应)，以及构建的结构，如果一个支撑成员薄弱，这些结构不会失效。

The rigidity and flexibility of structures are central to their function and their design. This holds for biomolecules (protein flexibility for predicting function and for drug design), material science (e.g. artificial zeolites for refining heavy oil), for human build structures, for designed mechanisms (paths of mechanisms), and for independence of geometric configurations in CAD (impacting the design of stable and efficient CAD programs) and computer graphics (how geometric constraints are handled inside a computer). This study uses combinatorics and geometry to analyze what portions of a structure are rigid and which are flexible. In some situations, we desire more than minimal rigidity - we desire stability or global rigidity. This is true in the study of small fluctuations in molecules, or avoiding alternative forms of molecules (which can cause disease or drug reactions) as well as built structures which should not fail if one bracing member is weak.