Quading triangular meshes with certain topological constraints

Authors:
Linfa Lu;Xiaoyuan Qian;Xiquan Shi;Fengshan Liu
Affiliations:
School of Information Science & Technology, Sun Yat-sen University, China and Engineering Research Center of Digital Life, Ministry of Education of China, China and Key Laboratory of Digital Life, ...;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Department of Mathematical Sciences, Delaware State University, Dover, DE 19901, USA and School of Information Science & Technology, Sun Yat-sen University, China and Engineering Research Center o ...;Department of Mathematical Sciences, Delaware State University, Dover, DE 19901, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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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.