| Full text | |
| Author(s): |
Castelo, Antonio
;
Nakassima, Guilherme
;
Bueno, Lucas Moutinho
;
Gameiro, Marcio
Total Authors: 4
|
| Document type: | Journal article |
| Source: | COMPUTATIONAL & APPLIED MATHEMATICS; v. 43, n. 3, p. 23-pg., 2024-04-01. |
| Abstract | |
We present a Generalized Combinatorial Marching Hypercubes algorithm to compute a cell complex approximation of a manifold of any dimension and co-dimension, that is, a manifold of dimension n-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n-k$$\end{document} embedded into an n-dimensional space. The algorithm uses combinatorial and topological methods to avoid the use of expensive lookup tables and hence is efficient in higher dimensions. We illustrate the effectiveness of our algorithm in higher dimensions and compare its performance with a similar algorithm based on a simplicial decomposition of the domain. (AU) | |
| FAPESP's process: | 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision |
| Grantee: | Farid Tari |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 19/06249-7 - Applications of Computational and Topological Methods to Dynamical Systems |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 17/25631-4 - GEM data structure for triangulations |
| Grantee: | Lucas Moutinho Bueno |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |