A Constrained Resampling Strategy for Mesh Improvement. (14th August 2017)

• Record Type: Journal Article
• Authors: Abdelkader, Ahmed; Mahmoud, Ahmed H.; Rushdi, Ahmad A.; Mitchell, Scott A.; Owens, John D.; Ebeida, Mohamed S.
• Is Part Of: Computer graphics forum. Volume 36:Number 5(2017)
• Page Start: 189
• Page End: 201
• Publication Date: 2017-08-14
• Subjects: Categories and Subject Descriptors (according to ACM CCS) -- I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.13256
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract: 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.