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Full-Text Articles in Physical Sciences and Mathematics
Unfolding Convex Polyhedra Via Radially Monotone Cut Trees, Joseph O'Rourke
Unfolding Convex Polyhedra Via Radially Monotone Cut Trees, Joseph O'Rourke
Computer Science: Faculty Publications
A notion of "radially monotone" cut paths is introduced as an effective choice for finding a non-overlapping edge-unfolding of a convex polyhedron. These paths have the property that the two sides of the cut avoid overlap locally as the cut is infinitesimally opened by the curvature at the vertices along the path. It is shown that a class of planar, triangulated convex domains always have a radially monotone spanning forest, a forest that can be found by an essentially greedy algorithm. This algorithm can be mimicked in 3D and applied to polyhedra inscribed in a sphere. Although the algorithm does …
Geometric Deformations Of Sodalite Frameworks, Ciprian Borcea, Ileana Streinu
Geometric Deformations Of Sodalite Frameworks, Ciprian Borcea, Ileana Streinu
Computer Science: Faculty Publications
In mathematical crystallography and computational materials science, it is important to infer flexibility properties of framework materials from their geometric representation. We study combinatorial, geometric and kinematic properties for frameworks modeled on sodalite.