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Main Title: High Quality Quadrilateral Surface Meshing Without Template Restrictions: A New Approach Based on Network Flow Techniques
Author(s): Müller-Hannemann, Matthias
Type: Research Paper
Abstract: We investigate a purely combinatorial approach to the following mesh refinement problem: Given a coarse mesh of polygons in three-dimensional space, find a decomposition into well-shaped quadrilaterals such that the resulting mesh is conforming and satisfies prescribed local density constraints. We present a new approach based on network flow techniques. In particular, we show that this problem can efficiently be solved by a reduction to a minimum cost bidirected flow problem, if the mesh does not contain branching edges, that is, edges incident to more than two polygons. This approach handles optimization criteria such as density, angles and regularity. In our model we get rid of restrictions on the set of feasible solutions imposed by templates. On the other hand, we still use advantages of general templates with respect to mesh quality for the individual refinement of the mesh polygons. For meshes with branchings, the problem is feasible if and only if a certain system of linear equations over GF(2) has a solution. To enhance the mesh quality for meshes with branchings, we introduce a two-stage approach which first decomposes the whole mesh into components without branchings, and then uses minimum cost bidirected flows on the components in a second phase. We report on our computational results which indicate that this approach usually leads to a very high mesh quality.
Subject(s): quadrilateral surface meshes
non-manifold surfaces
mesh decomposition
bidirected flows
mesh smoothing
Issue Date: 1997
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 1997, 561
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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