Name
Abstract | ||
|---|---|---|
A mesh is the discretization of a geometric domain into small, simple shapes. The focus of this project is the generation of strictly convex quadrilateral (quad) meshes with provable quality guarantees through the conversion of good quality triangle meshes of planar straight line graphs. The conversion is achieved with an algorithm that uses the dual graph of the input triangulation to quadrangulate small groups of triangles at a time [1,3,4]. A specific goal of the project is proving an upper bound on the aspect ratios of all quads in the mesh. We implement two different metrics to measure the aspect ratios of the quads in the generated meshes. The first metric simply takes the ratio of the longest edge to the shortest edge for each quad. The disadvantage of this method is that it does not take into account the angle measures of the quads. The second approach, a method developed by John Robinson [2], utilizes both edge lengths and angle measures to calculate aspect ratio. We develop code to produce empirical results for both metrics of aspect ratio measurement and histogram plots showing the distribution of quad aspect ratios in a given mesh. With these experimental results, we aim to prove that, given a good quality input triangle mesh with a minimum angle bound, we can give a provably good upper bound on aspect ratio for the resulting quad mesh. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1145/3017680.3022461 | SIGCSE |
Keywords | Field | DocType |
Mesh Generation, Quadrilateral, Aspect Ratio | Aspect ratio (image),Polygon mesh,Upper and lower bounds,Computer science,Algorithm,Dual graph,Triangulation (social science),Quadrilateral,Multimedia,Mesh generation,Triangle mesh | Conference |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christopher Gillespie | 1 | 0 | 0.34 |
| Mark Moore | 2 | 0 | 0.34 |
| Colin Brown | 3 | 0 | 0.34 |