| Autor: | Nicolas Szafran, Valérie Pham-Trong, Luc Biard |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Discrete mathematics
Surface (mathematics) Geodesic Applied Mathematics Mathematical analysis 020207 software engineering 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Longest path problem Euclidean shortest path Computer Science::Graphics Path length Parametric surface Shortest path problem 0202 electrical engineering electronic engineering information engineering Net (polyhedron) 0101 mathematics ComputingMethodologies_COMPUTERGRAPHICS Mathematics |
| Zdroj: | Numerical Algorithms. 26:305-315 |
| ISSN: | 1017-1398 |
| DOI: | 10.1023/a:1016617010088 |
| Popis: | We present two numerical methods to approximate the shortest path or a geodesic between two points on a three-dimensional parametric surface. The first one consists of minimizing the path length, working in the parameter domain, where the approximation class is composed of Bezier curves. In the second approach, we consider Bezier surfaces and their control net. The numerical implementation is based on finding the shortest path on the successive control net subdivisions. The convergence property of the Bezier net to the surface gives an approximation of the required shortest path. These approximations, also called pseudo-geodesics, are then applied to the creation of pseudo-geodesic meshes. Experimental results are also provided. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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