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Geometry Of Discrete And Continuous Bounded Surfaces, Kyung Eun Kim

Dissertations - ALL

We work on reconstructing discrete and continuous surfaces with boundaries using length constraints. First, for a bounded discrete surface, we discuss the rigidity and number of embeddings in three-dimensional space, modulo rigid transformations, for given real edge lengths. Our work mainly considers the maximal number of embeddings of rigid graphs in three-dimensional space for specific geometries (annulus, strip). We modify a commonly used semi-algebraic, geometrical formulation using Bézout's theorem, from Euclidean distances corresponding to edge lengths. We suggest a simple way to construct a rigid graph having a finite upper bound. We also implement a generalization of counting embeddings for …