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Title: Constructing self-supporting surfaces with planar quadrilateral elements
Authors: Ma, Long
Yao, Sidan
Zheng, Jianmin
Liu, Yang
Zhou, Yuanfeng
Xin, Shi-Qing
He, Ying
Keywords: Engineering::Computer science and engineering
Issue Date: 2022
Source: Ma, L., Yao, S., Zheng, J., Liu, Y., Zhou, Y., Xin, S. & He, Y. (2022). Constructing self-supporting surfaces with planar quadrilateral elements. Computational Visual Media, 8(4), 571-583.
Project: T2EP20220-0014 
Journal: Computational Visual Media 
Abstract: We present a simple yet effective method for constructing 3D self-supporting surfaces with planar quadrilateral (PQ) elements. Starting with a triangular discretization of a self-supporting surface, we first compute the principal curvatures and directions of each triangular face using a new discrete differential geometry approach, yielding more accurate results than existing methods. Then, we smooth the principal direction field to reduce the number of singularities. Next, we partition all faces into two groups in terms of principal curvature difference. For each face with small curvature difference, we compute a stretch matrix that turns the principal directions into a pair of conjugate directions. For the remaining triangular faces, we simply keep their smoothed principal directions. Finally, applying a mixed-integer programming solver to the mixed principal and conjugate direction field, we obtain a planar quadrilateral mesh. Experimental results show that our method is computationally efficient and can yield high-quality PQ meshes that well approximate the geometry of the input surfaces and maintain their self-supporting properties.
ISSN: 2096-0433
DOI: 10.1007/s41095-021-0257-1
Schools: School of Computer Science and Engineering 
Rights: © 2022 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SCSE Journal Articles

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