All-quad meshing without cleanup. (April 2017)

• Record Type: Journal Article
• Authors: Rushdi, Ahmad A.; Mitchell, Scott A.; Mahmoud, Ahmed H.; Bajaj, Chandrajit C.; Ebeida, Mohamed S.
• Is Part Of: Computer aided design. Volume 85(2017)
• Page Start: 83
• Page End: 98
• Publication Date: 2017-04
• Subjects: All-quadrilateral meshing -- Guaranteed quality -- Sharp features; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2016.07.009
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: We present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometry–quadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning we have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.