A polynomial algorithm for b-matchings: an alternative approach
Information Processing Letters
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Finite element mesh generation methods: a review and classification
Computer-Aided Design
LEDA: a platform for combinatorial and geometric computing
Communications of the ACM
Empirical design of geometric algorithms
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Combinatorics helps for hexahedral mesh generation in CAD
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Improving the surface cycle structure for hexahedral mesh generation
Proceedings of the sixteenth annual symposium on Computational geometry
Implementing weighted b-matching algorithms: towards a flexible software design
Journal of Experimental Algorithmics (JEA)
Implementing weighted b-matching algorithms: insights from a computational study
Journal of Experimental Algorithmics (JEA)
Implementing Weighted b-Matching Algorithms: Insights from a Computational Study
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
On the Differences between ``Practical'' and ``Applied''
WAE '00 Proceedings of the 4th International Workshop on Algorithm Engineering
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Quadrilateral surface meshes without self-intersecting dual cycles for hexahedral mesh generation
Computational Geometry: Theory and Applications
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We investigate a problem arising in the computer-aided design of cars, planes, ships, trains, and other motor vehicles and machines: refine a mesh of curved polygons, which approximates the surface of a workpiece, into quadrilaterals so that the resulting mesh is suitable for a numerical analysis. This mesh refinement problem turns out to be strongly NP-hardIn commercial CAD systems, this problem is usually solved using a greedy approach. However, these algorithms leave the user a lot of patchwork to do afterwards. We introduce a new global approach, which is based on network flow techniques. Abstracting from all geometric and numerical aspects, we obtain an undirected graph with upper and lower capacities on the edges and some additional node constraints. We reduce this problem to a sequence of bidirected flwo problems (or, equivalently, to b-matching problems). For the first time, network flow techniques are applied to a mesh refinement problem.This approach avoids the local traps of greedy approaches and yields solutions that require significantly less additional patchwork.