Where and how Ruppert’s algorithm fails
Several examples are given to demonstrate non-termination of Ruppert’s Delaunay refinement algorithm for triangular mesh generation exploring the relationship between the minimum angle in the input and the minimum allowable angle in the output. These examples show non-termination despite requiring a...
| Published in: | Examples and Counterexamples |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-11-01
|
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X22000118 |
| _version_ | 1857000703206096896 |
|---|---|
| author | Alexander Rand |
| author_facet | Alexander Rand |
| author_sort | Alexander Rand |
| collection | DOAJ |
| container_title | Examples and Counterexamples |
| description | Several examples are given to demonstrate non-termination of Ruppert’s Delaunay refinement algorithm for triangular mesh generation exploring the relationship between the minimum angle in the input and the minimum allowable angle in the output. These examples show non-termination despite requiring a minimum output angle of less than 30° which is smaller than the value generally observed in practice. For input containing only points, an example demonstrates failure of the algorithm with a minimum angle of 30° showing that the theoretical analysis in that context is sharp. |
| format | Article |
| id | doaj-art-059c550fe28449b39c1444d0119f79fc |
| institution | Directory of Open Access Journals |
| issn | 2666-657X |
| language | English |
| publishDate | 2022-11-01 |
| publisher | Elsevier |
| record_format | Article |
| spelling | doaj-art-059c550fe28449b39c1444d0119f79fc2025-08-19T19:50:12ZengElsevierExamples and Counterexamples2666-657X2022-11-01210006910.1016/j.exco.2022.100069Where and how Ruppert’s algorithm failsAlexander Rand0Siemens Digital Industries Software, 10800 Pecan Park Blvd, Austin, TX 78750, United States of AmericaSeveral examples are given to demonstrate non-termination of Ruppert’s Delaunay refinement algorithm for triangular mesh generation exploring the relationship between the minimum angle in the input and the minimum allowable angle in the output. These examples show non-termination despite requiring a minimum output angle of less than 30° which is smaller than the value generally observed in practice. For input containing only points, an example demonstrates failure of the algorithm with a minimum angle of 30° showing that the theoretical analysis in that context is sharp.http://www.sciencedirect.com/science/article/pii/S2666657X22000118Computational geometryMesh generationDelaunay triangulation |
| spellingShingle | Alexander Rand Where and how Ruppert’s algorithm fails Computational geometry Mesh generation Delaunay triangulation |
| title | Where and how Ruppert’s algorithm fails |
| title_full | Where and how Ruppert’s algorithm fails |
| title_fullStr | Where and how Ruppert’s algorithm fails |
| title_full_unstemmed | Where and how Ruppert’s algorithm fails |
| title_short | Where and how Ruppert’s algorithm fails |
| title_sort | where and how ruppert s algorithm fails |
| topic | Computational geometry Mesh generation Delaunay triangulation |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X22000118 |
| work_keys_str_mv | AT alexanderrand whereandhowruppertsalgorithmfails |