Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 529-539 |
| Seitenumfang | 11 |
| Fachzeitschrift | Visual Computer |
| Jahrgang | 28 |
| Ausgabenummer | 6-8 |
| Frühes Online-Datum | 26 Apr. 2012 |
| Publikationsstatus | Veröffentlicht - Juni 2012 |
Abstract
In this paper, we present a novel method for computing multiple geodesic connections between two arbitrary points on a smooth surface. Our method is based on a homotopy approach that is able to capture the ambiguity of geodesic connections in the presence of positive Gaussian curvature that generates focal curves. Contrary to previous approaches, we exploit focal curves to gain theoretical insights on the number of connecting geodesics and a practical algorithm for collecting these. We consider our method as a contribution to the contemporary debate regarding the calculation of distances in general situations, applying continuous concepts of classical differential geometry which are not immediately transferable in purely discrete settings.
ASJC Scopus Sachgebiete
- Informatik (insg.)
- Software
- Informatik (insg.)
- Maschinelles Sehen und Mustererkennung
- Informatik (insg.)
- Computergrafik und computergestütztes Design
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in: Visual Computer, Jahrgang 28, Nr. 6-8, 06.2012, S. 529-539.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Connecting geodesics on smooth surfaces
AU - Thielhelm, Hannes
AU - Vais, Alexander
AU - Brandes, Daniel
AU - Wolter, Franz Erich
PY - 2012/6
Y1 - 2012/6
N2 - In this paper, we present a novel method for computing multiple geodesic connections between two arbitrary points on a smooth surface. Our method is based on a homotopy approach that is able to capture the ambiguity of geodesic connections in the presence of positive Gaussian curvature that generates focal curves. Contrary to previous approaches, we exploit focal curves to gain theoretical insights on the number of connecting geodesics and a practical algorithm for collecting these. We consider our method as a contribution to the contemporary debate regarding the calculation of distances in general situations, applying continuous concepts of classical differential geometry which are not immediately transferable in purely discrete settings.
AB - In this paper, we present a novel method for computing multiple geodesic connections between two arbitrary points on a smooth surface. Our method is based on a homotopy approach that is able to capture the ambiguity of geodesic connections in the presence of positive Gaussian curvature that generates focal curves. Contrary to previous approaches, we exploit focal curves to gain theoretical insights on the number of connecting geodesics and a practical algorithm for collecting these. We consider our method as a contribution to the contemporary debate regarding the calculation of distances in general situations, applying continuous concepts of classical differential geometry which are not immediately transferable in purely discrete settings.
KW - Distance computation
KW - Focal curves
KW - Geodesics
KW - Homotopy method
KW - Shortest paths
UR - http://www.scopus.com/inward/record.url?scp=84861966409&partnerID=8YFLogxK
U2 - 10.1007/s00371-012-0681-4
DO - 10.1007/s00371-012-0681-4
M3 - Article
AN - SCOPUS:84861966409
VL - 28
SP - 529
EP - 539
JO - Visual Computer
JF - Visual Computer
SN - 0178-2789
IS - 6-8
ER -