Metric Based Quadrilateral Mesh Generation

2018/11/30 by Chen, Wei, Zheng, Xiaopeng, Ke, Jingyao +3
#Computational Geometry (cs.CG) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.1811.12604

Abstract

This work proposes a novel metric based algorithm for quadrilateral mesh generating. Each quad-mesh induces a Riemannian metric satisfying special conditions: the metric is a flat metric with cone signualrites conformal to the original metric, the total curvature satisfies the Gauss-Bonnet condition, the holonomy group is a subgroup of the rotation group \e^ikπ/2\, furthermore there is cross field obtained by parallel translation which is aligned with the boundaries, and its streamlines are finite geodesics. Inversely, such kind of metric induces a quad-mesh. Based on discrete Ricci flow and conformal structure deformation, one can obtain a metric satisfying all the conditions and obtain the desired quad-mesh. This method is rigorous, simple and automatic. Our experimental results demonstrate the efficiency and efficacy of the algorithm.

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