Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


osu1155212604.pdf (2.7 MB)

ETD Abstract Container

Abstract Header

Quality delaunay meshing of polyhedral volumes and surfaces

Ray, Tathagata
http://rave.ohiolink.edu/etdc/view?acc_num=osu1155212604

Abstract Details

2006, Doctor of Philosophy, Ohio State University, Computer and Information Science.
Many applications such as finite element methods, computer graphics, and numerical simulations require meshing a surface or the volume enclosed by one in three dimensions. We consider polyhedral surfaces and volumes and mesh them with Delaunay refinement. We present four algorithms, QUALMESH, POLYSURFMESH, WQUALMESH, and SURFREMESH. The first one, QUALMESH, computes a Delaunay mesh of the volume enclosed by an input polyhedron possibly with small input angles. The generated mesh conforms to the input, and the circumradius to shortest edge ratio, also called radius-edge ratio, of most of the tetrahedra in the output mesh are bounded above by a constant. Some of the output tetrahedra do remain “bad”, but they are only in the vicinity of small input angles. Second, we present POLYSURFMESH, a modification of the QUALMESH algorithm, to generate a triangular surface mesh of an input polyhedra such that the output mesh conforms to every vertex, edge, and facet of the input and the radius-edge ratio of most of the triangles are bounded from above. Those triangles which are “bad” also remain in the vicinity of sharp input angles. One deficiency of QUALMESH is that its output mesh might have a particular kind of bad tetrahedra called slivers. The third algorithm, WQUALMESH extends QUALMESH using the weighted Delaunay triangulation to remove most of the slivers from the output of QUALMESH. Some of the slivers do remain in the output but they are again only in the vicinity of sharp angles. Finally, SURFREMESH remeshes a polygonal surface approximating a smooth surface. The output surface is guaranteed to be homeomorphic to the input, and the output triangles have bounded radius-edge ratio. This algorithm starts with a few points chosen from the input surface and gradually builds the entire surface to satisfy user-defined thresholds for parameters capturing the geometric closeness to the input surface. These parameters allow the user to extract the surface at different levels of detail. Implementation results of all the algorithms are presented, and they corroborate with the theory.
Tamal Dey (Advisor)
162 p.
Computer Science
Mesh generation; Computational geometry

Recommended Citations

Citations

  • Ray, T. (2006). Quality delaunay meshing of polyhedral volumes and surfaces [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1155212604

    APA Style (7th edition)

  • Ray, Tathagata. Quality delaunay meshing of polyhedral volumes and surfaces. 2006. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1155212604.

    MLA Style (8th edition)

  • Ray, Tathagata. "Quality delaunay meshing of polyhedral volumes and surfaces." Doctoral dissertation, Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1155212604

    Chicago Manual of Style (17th edition)

osu1155212604
1,082
© 2006, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.