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arXiv · 1811.12604

Metric Based Quadrilateral Mesh Generation

Wei Chen·Xiaopeng Zheng·Jingyao Ke·Na Lei·Zhongxuan Luo·Xianfeng Gu
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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 $\{e^{ik\pi/2}\}$, 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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Wei Chen, Xiaopeng Zheng, Jingyao Ke, Na Lei, Zhongxuan Luo, Xianfeng Gu. 2018-11-30. Metric Based Quadrilateral Mesh Generation. https://arxiv.org/abs/1811.12604

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