Polycube Shape Space
| dc.contributor.author | Zhao, Hui | en_US |
| dc.contributor.author | Li, Xuan | en_US |
| dc.contributor.author | Wang, Wencheng | en_US |
| dc.contributor.author | Wang, Xiaoling | en_US |
| dc.contributor.author | Wang, Shaodong | en_US |
| dc.contributor.author | Lei, Na | en_US |
| dc.contributor.author | Gu, Xianfeng | en_US |
| dc.contributor.editor | Lee, Jehee and Theobalt, Christian and Wetzstein, Gordon | en_US |
| dc.date.accessioned | 2019-10-14T05:08:15Z | |
| dc.date.available | 2019-10-14T05:08:15Z | |
| dc.date.issued | 2019 | |
| dc.description.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. | en_US |
| dc.description.number | 7 | |
| dc.description.sectionheaders | Voxels and Polycubes | |
| dc.description.seriesinformation | Computer Graphics Forum | |
| dc.description.volume | 38 | |
| dc.identifier.doi | 10.1111/cgf.13839 | |
| dc.identifier.issn | 1467-8659 | |
| dc.identifier.pages | 311-322 | |
| dc.identifier.uri | https://doi.org/10.1111/cgf.13839 | |
| dc.identifier.uri | https://diglib.eg.org:443/handle/10.1111/cgf13839 | |
| dc.publisher | The Eurographics Association and John Wiley & Sons Ltd. | en_US |
| dc.subject | Mathematics of computing | |
| dc.subject | Graphs and surfaces | |
| dc.subject | Computing methodologies | |
| dc.subject | Mesh models | |
| dc.subject | Mesh geometry models | |
| dc.title | Polycube Shape Space | en_US |