Polycube Shape Space

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Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
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.
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@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
} }
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