Conference paper Open Access

High Quality Quadrilateral Mesh Generation Based on Meromorphic Quartic Differentials

Zheng, Xiaopeng; Shi, Xin; Wang, Chao; Zhu, Yiming; Luo, Zhongxuan; Lei, Na

Quadrilateral meshes generated for the industrial applications have to meet some special quality demands and it remains a tricky problem. We propose a novel method for high quality quad mesh generation based on the equivalence relation between quadrilateral meshes and meromorphic quartic differentials[1]. As long as more than one meromorphic quartic differential were obtained, the linear space extended by them is also available for us according to the meromorphic quartic differentials space theory. We can search the space for better quadrilateral mesh and the high quality mesh construction problem becomes a optimization problem. This paper gives the algorithm and carries out experiments under two different mesh quality constrains including mesh cell size constrain and feature lines constrain. The experimental results demonstrate the efficiency and efficacy of the algorithm.

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