| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Sao Carlos, SP - Brazil
[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 - USA
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | COMPUTERS & GRAPHICS-UK; v. 102, p. 67-77, FEB 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
We propose a Combinatorial Marching Hypercubes (CMH) algorithm to approximate manifolds of any dimension by a collection of cells. Our algorithm is a generalization of the renowned Marching Cubes Algorithm, which approximates surfaces by a set of polygons. The size and complexity of the manifolds, as well as their approximations, grow exponentially with their dimensions. In order to make our algorithm feasible in higher dimensions, we use a set of efficient techniques that rely on topology and enumeration concepts, which do not require the use of lookup tables. We also propose an extension to CMH, the Combinatorial Continuation Hypercubes (CCH), that uses a continuation method to avoid processing empty spaces. We implemented and compared our algorithm with a similar algorithm based on hypertetrahedra. We present empirical results for manifolds of up to five dimensions. (C) 2021 Elsevier Ltd. All rights reserved. (AU) | |
| 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: | 19/06249-7 - Applications of Computational and Topological Methods to Dynamical Systems |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |
| 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: | 17/25631-4 - GEM data structure for triangulations |
| Grantee: | Lucas Moutinho Bueno |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |