Title of Paper:Quadrilateral mesh generation I : Metric based method

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Date of Publication:2019-11-01

Journal:COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Included Journals:EI、SCIE

Volume:356

Page Number:652-668

ISSN No.:0045-7825

Key Words:Quadrilateral mesh; Flat Riemannian metric; Geodesic; Discrete Ricci flow; Conformal structure deformation

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 singularities 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)}, 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. (C) 2019 Elsevier B.V. All rights reserved.