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Ellipsoid Packing Structures on Freeform Surfaces
Author(s) -
Xu QunCe,
Deng Bailin,
Yang YongLiang
Publication year - 2018
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13550
Subject(s) - ellipsoid , isotropy , atomic packing factor , spheres , packing problems , surface (topology) , generalization , computer science , anisotropy , geometry , mathematics , algorithm , mathematical analysis , physics , nuclear magnetic resonance , quantum mechanics , astronomy
Designers always get good inspirations from fascinating geometric structures gifted by the nature. In the recent years, various computational design tools have been proposed to help generate cell packing structures on freeform surfaces, which consist of a packing of simple primitives, such as polygons, spheres, etc. In this work, we aim at computationally generating novel ellipsoid packing structures on freeform surfaces. We formulate the problem as a generalization of sphere packing structures in the sense that anisotropic ellipsoids are used instead of isotropic spheres to pack a given surface. This is done by defining an anisotropic metric based on local surface anisotropy encoded by principal curvatures and the corresponding directions. We propose an optimization framework that can optimize the shapes of individual ellipsoids and the spatial relation between neighboring ellipsoids to form a quality packing structure. A tailored anisotropic remeshing method is also employed to better initialize the optimization and ensure the quality of the result. Our framework is extensively evaluated by optimizing ellipsoid packing and generating appealing geometric structures on a variety of freeform surfaces.