Polycube Shape Space

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...

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Bibliographic Details
Published in:Computer graphics forum Vol. 38; no. 7; pp. 311 - 322
Main Authors: Zhao, Hui, Li, Xuan, Wang, Wencheng, Wang, Xiaoling, Wang, Shaodong, Lei, Na, Gu, Xiangfeng
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.10.2019
Subjects:
Algorithms
CCS Concepts
Computing methodologies → Mesh models
Mathematics of computing → Graphs and surfaces
Mesh generation
Mesh geometry models
Optimization
Polyhedra
Theorems
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary: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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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13839