Discrete applied geometry

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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.