Analysis of a polytopal complex based on convex diagonalizations, suggesting new avenues in visibility theory.
Given an arbitrary simple polygon, we construct a polytopal complex analogous to the associahedron based on its convex diagonalizations. This polytopal complex is shown to be contractible, and a geometric realization is provided based on the theory of secondary polytopes. We then reformulate a combinatorial deformation theory in terms of visibility and presents some open problems.
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Devadoss et al. (2012) studied this question.
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