Polycube Shape Space
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Date
2019Author
Zhao, Hui
Li, Xuan
Wang, Wencheng
Wang, Xiaoling
Wang, Shaodong
Lei, Na
Gu, Xianfeng
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Show full item recordAbstract
There are many methods proposed for generating polycube polyhedrons, but it lacks the study about the possibility of generating polycube polyhedrons. In this paper, we prove a theorem for characterizing the necessary condition for the skeleton graph of a polycube polyhedron, by which Steinitz's theorem for convex polyhedra and Eppstein's theorem for simple orthogonal polyhedra are generalized to polycube polyhedra of any genus and with non-simply connected faces. Based on our theorem, we present a faster linear algorithm to determine the dimensions of the polycube shape space for a valid graph, for all its possible polycube polyhedrons. We also propose a quadratic optimization method to generate embedding polycube polyhedrons with interactive assistance. Finally, we provide a graph-based framework for polycube mesh generation, quadrangulation, and all-hex meshing to demonstrate the utility and applicability of our approach.
BibTeX
@article {10.1111:cgf.13839,
journal = {Computer Graphics Forum},
title = {{Polycube Shape Space}},
author = {Zhao, Hui and Li, Xuan and Wang, Wencheng and Wang, Xiaoling and Wang, Shaodong and Lei, Na and Gu, Xianfeng},
year = {2019},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.13839}
}
journal = {Computer Graphics Forum},
title = {{Polycube Shape Space}},
author = {Zhao, Hui and Li, Xuan and Wang, Wencheng and Wang, Xiaoling and Wang, Shaodong and Lei, Na and Gu, Xianfeng},
year = {2019},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.13839}
}