HIGH QUALITY QUADRILATERAL SURFACE MESHING WITHOUT TEMPLATE RESTRICTIONS: A NEW APPROACH BASED ON NETWORK FLOW TECHNIQUES

MATTHIAS MÜLLER–HANNEMANN
2000 International journal of computational geometry and applications  
We investigate the following mesh re nement problem: Given a mesh of polygons in three-dimensional space, nd a decomposition into strictly convex quadrilaterals such that the resulting mesh is conforming and satis es prescribed local density constraints. We show that this problem can e ciently be solved by a reduction to a minimum cost bidirected ow problem, if the mesh does not contain branching edges, that is, edges incident to more than two polygons. This approach handles optimization
more » ... a such as density, angles and regularity, too. 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 rst decomposes the whole mesh into components without branchings, and then uses minimum cost bidirected ows 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.
doi:10.1142/s0218195900000176 fatcat:ixtmu3foxjhpviunumpphrisai