A Constrained Resampling Strategy for Mesh Improvement

作者：Abdelkader Ahmed; Mahmoud Ahmed H; Rushdi Ahmad A; Mitchell Scott A; Owens John D; Ebeida Mohamed S^*

来源：Computer Graphics Forum, 2017, 36(5): 189-201.

DOI：10.1111/cgf.13256

In many geometry processing applications, it is required to improve an initial mesh in terms of multiple quality objectives. Despite the availability of several mesh generation algorithms with provable guarantees, such generated meshes may only satisfy a subset of the objectives. The conflicting nature of such objectives makes it challenging to establish similar guarantees for each combination, e.g., angle bounds and vertex count. In this paper, we describe a versatile strategy for mesh improvement by interpreting quality objectives as spatial constraints on resampling and develop a toolbox of local operators to improve the mesh while preserving desirable properties. Our strategy judiciously combines smoothing and transformation techniques allowing increased flexibility to practically achieve multiple objectives simultaneously. We apply our strategy to both planar and surface meshes demonstrating how to simplify Delaunay meshes while preserving element quality, eliminate all obtuse angles in a complex mesh, and maximize the shortest edge length in a Voronoi tessellation far better than the state-of-the-art.

• 出版日期2017-8