Constructing self-supporting surfaces with planar quadrilateral elements

Autor: Long Ma, Sidan Yao, Jianmin Zheng, Yang Liu, Yuanfeng Zhou, Shi-Qing Xin, Ying He
Přispěvatelé: School of Computer Science and Engineering
Rok vydání: 2022
Předmět:
Zdroj: Computational Visual Media. 8:571-583
ISSN: 2096-0662
2096-0433
DOI: 10.1007/s41095-021-0257-1
Popis: 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.
Databáze: OpenAIRE
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