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Generalized Regular Quadrilateral Mesh Generation based on Surface Foliation

Lei, Na, Xiaopeng Zheng, Hang Si, Zhongxuan Luo, Xianfeng Gu

Proceedings, 26th International Meshing Roundtable, Elsevier, Science Direct, September 18-21 2017

INTERNATIONAL
MESHING
ROUNTABLE

26th International Meshing Roundtable
Barcelona, Spain
September 18-21, 2017

Na Lei, Dalian University of Technology, CN, nalei@dlut.edu.cn
Xiaopeng Zheng, Dalian University of Technology, CN, shawnxpzheng@gmail.com
Hang Si, Weierstrass Institute for Applied Analysis and Stochastics, DE, Hang.Si@wias-berlin.de
Zhongxuan Luo, Dalian University of Technology, CN,
Xianfeng Gu, Stony Brook University, US, gu@cs.stonybrook.edu

Abstract
This work introduces a novel algorithm for quad-mesh generation based on surface foliation theory. The algorithm is based on the equivalence among colorable quad-meshes, measure foliations and holomorphic differentials. The holomorphic differentials can be obtained by graph-valued harmonic maps. The algorithm has several merits: it can be applied for surfaces with general topologies; the resulting quad-meshes have global tensor product structure and the least number of singularities; the algorithmic pipeline is fully automatic. The experimental results demonstrate the efficiency and efficacy of the proposed method.

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