Quading triangular meshes with certain topological constraints |
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Authors: | Linfa Lu Xiaoyuan Qian Xiquan Shi Fengshan Liu |
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Institution: | a School of Information Science & Technology, Sun Yat-sen University, Chinab Engineering Research Center of Digital Life, Ministry of Education of China, Chinac Key Laboratory of Digital Life, Ministry of Education of China, Chinad Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, Chinae Department of Mathematical Sciences, Delaware State University, Dover, DE 19901, USA |
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Abstract: | In computer graphics and geometric modeling, shapes are often represented by triangular meshes (also called 3D meshes or manifold triangulations). The quadrangulation of a triangular mesh has wide applications. In this paper, we present a novel method of quading a closed orientable triangular mesh into a quasi-regular quadrangulation, i.e., a quadrangulation that only contains vertices of degree four or five. The quasi-regular quadrangulation produced by our method also has the property that the number of quads of the quadrangulation is the smallest among all the quasi-regular quadrangulations. In addition, by constructing the so-called orthogonal system of cycles our method is more effective to control the quality of the quadrangulation. |
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Keywords: | Computational topology Fundamental group Tight orthogonal homotopic basis Mesh quading Quasi-regular quadrangulation T-shirt |
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