Repository: DepositOnce – institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - RPRT
AU - Möhring, Rolf H.
AU - Müller-Hannemann, Matthias
PY - 1997
TI - Complexity and Modeling Aspects of Mesh Refinement into Quadrilaterals
DO - 10.14279/depositonce-14422
UR - http://dx.doi.org/10.14279/depositonce-14422
PB - Technische Universität Berlin
LA - en
AB - We investigate the following mesh refinement problem: Given a mesh of polygons in three-dimensional space, find a decomposition into strictly convex quadrilaterals such that the resulting mesh is conforming and satisfies prescribed local density constraints. We show that this problem can be efficiently solved by a reduction to a bidirected flow problem, if the mesh does not contain folding edges, that is, edges incident to more than two polygons. In addition, optimization criteria such as density, angles and regularity can be handled to some extent by this approach, too. The general case with foldings, however, turns out to be strongly NP-hard. For special cases of the density constraints, 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 foldings, we introduce a two-stage approach which first decomposes the whole mesh into components without foldings, and then uses minimum cost bidirected flows on the components in a second phase.
KW - mesh generation
KW - bidirected flows
KW - NP-completeness
KW - mesh decomposition
KW - Computer-Aided Design
ER -