1. Generating well-shaped d-dimensional Delaunay Meshes
- Author
-
Xiang-Yang Li
- Subjects
General Computer Science ,Volume mesh ,Delaunay triangulation ,Computer Science::Computational Geometry ,Computational geometry ,Mathematics::Numerical Analysis ,d-dimensional meshes ,Theoretical Computer Science ,Combinatorics ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,Polygon mesh ,Circumscribed circle ,Well shaped ,Radius–edge ratio ,Mathematics ,ComputingMethodologies_COMPUTERGRAPHICS ,Constrained Delaunay triangulation ,Mesh generation ,Chew's second algorithm ,Aspect ratio ,Computer Science::Graphics ,Ruppert's algorithm ,Algorithms ,MathematicsofComputing_DISCRETEMATHEMATICS ,Computer Science(all) - Abstract
A d-dimensional simplicial mesh is a Delaunay triangulation if the circumsphere of each of its simplices does not contain any vertices inside. A mesh is well shaped if the maximum aspect ratio of all its simplices is bounded from above by a constant. It is a long-term open problem to generate well-shaped d-dimensional Delaunay meshes for a given polyhedral domain. In this paper, we present a refinement-based method that generates well-shaped d-dimensional Delaunay meshes for any PLC domain with no small input angles. Furthermore, we show that the generated well-shaped mesh has O(n) d-simplices, where n is the smallest number of d-simplices of any almost-good meshes for the same domain. Here a mesh is almost-good if each of its simplices has a bounded circumradius to the shortest edge length ratio.
- Published
- 2003
- Full Text
- View/download PDF