Polyhedra Fabrication Through Mesh Convexification: A Study of Foldability of Nearly Convex Shapes
Zhonghua Xi and Jyh-Ming Lien
Abstract
A polyhedron can be unfolded to a net, i.e., an unfolding without overlapping, by carefully cutting along the surface. If the cuts are restricted only on the edges of the polyhedron, where should the cuts be? This is called an edge-unfolding problem, which has been extensively studied in the literature for centuries. Although several promising properties have been discovered, several recent preliminary works show that no valid net exists even for certain simple non-convex polyhedra. Therefore, we propose to convexify the input polyhedron before unfolding. More specifically, we remove local concave surface features via inflation simulation. We then eliminate global concave structure features by segmenting the polyhedron to a small number of part-aware and nearly convex components. Then the net for each nearly convex component can be obtained. We further show that convexified shapes can be continuously folded and can be easily realized by a physical self-folding machine Our experimental results show that the proposed convexification approaches can reduce the computation time by several folds.Publication
Polyhedra Fabrication Through Mesh Convexification: A Study of Foldability of Nearly Convex Shapes, Zhonghua Xi and Jyh-Ming Lien, International Design and Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE), ASME, Aug. 2017
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Web Site / Paper(pdf) / BibTeX