Constructing self-supporting surfaces with planar quadrilateral elements
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...
| Main Authors: | , , , , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/160723 |
| _version_ | 1824456085075918848 |
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| author | Ma, Long Yao, Sidan Zheng, Jianmin Liu, Yang Zhou, Yuanfeng Xin, Shi-Qing He, Ying |
| author2 | School of Computer Science and Engineering |
| author_facet | School of Computer Science and Engineering Ma, Long Yao, Sidan Zheng, Jianmin Liu, Yang Zhou, Yuanfeng Xin, Shi-Qing He, Ying |
| author_sort | Ma, Long |
| collection | NTU |
| description | 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. |
| first_indexed | 2025-02-19T03:48:29Z |
| format | Journal Article |
| id | ntu-10356/160723 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:48:29Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1607232022-08-01T08:27:35Z Constructing self-supporting surfaces with planar quadrilateral elements Ma, Long Yao, Sidan Zheng, Jianmin Liu, Yang Zhou, Yuanfeng Xin, Shi-Qing He, Ying School of Computer Science and Engineering Engineering::Computer science and engineering Self-Supporting Surfaces Planar Quadrilateral Meshes 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. Ministry of Education (MOE) Published version This work was partially supported by National Natural Science Foundation of China (62172257, 61802228), Singapore Ministry of Education (T2EP20220-0014), and the RIE2020 Industry Alignment Fund–Industry Collaboration Projects (IAF–ICP) Funding Initiative, as well as cash and in-kind contribution from the industrial partner, Rolls-Royce. 2022-08-01T08:27:35Z 2022-08-01T08:27:35Z 2022 Journal Article 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. https://dx.doi.org/10.1007/s41095-021-0257-1 2096-0433 https://hdl.handle.net/10356/160723 10.1007/s41095-021-0257-1 2-s2.0-85129873998 4 8 571 583 en T2EP20220-0014 Computational Visual Media © 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 http://creativecommons.org/licenses/by/4.0/. application/pdf |
| spellingShingle | Engineering::Computer science and engineering Self-Supporting Surfaces Planar Quadrilateral Meshes Ma, Long Yao, Sidan Zheng, Jianmin Liu, Yang Zhou, Yuanfeng Xin, Shi-Qing He, Ying Constructing self-supporting surfaces with planar quadrilateral elements |
| title | Constructing self-supporting surfaces with planar quadrilateral elements |
| title_full | Constructing self-supporting surfaces with planar quadrilateral elements |
| title_fullStr | Constructing self-supporting surfaces with planar quadrilateral elements |
| title_full_unstemmed | Constructing self-supporting surfaces with planar quadrilateral elements |
| title_short | Constructing self-supporting surfaces with planar quadrilateral elements |
| title_sort | constructing self supporting surfaces with planar quadrilateral elements |
| topic | Engineering::Computer science and engineering Self-Supporting Surfaces Planar Quadrilateral Meshes |
| url | https://hdl.handle.net/10356/160723 |
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