Geodesic Flow on Polyhedral Surfaces

Polthier, Konrad; Schmies, Markus

Geodesic Flow on Polyhedral Surfaces

Files

10_Polthier.pdf (3.43 MB)

Date

1999

Authors

Polthier, Konrad
Schmies, Markus

Publisher

Springer and The Eurographics Association

Abstract

On a curved surface the front of a point wave evolves in concentric circles which start to overlap and branch after a certain time. This evolution is described by the geodesic flow and helps us to understand the geometry of surfaces. In this paper we compute the evolution of distance circles on polyhedral surfaces and develop a method to visualize the set of circles, their overlapping, branching, and their temporal evolution simultaneously. We consider the evolution as an interfering wave on the surface, and extend isometric texture maps to efficiently handle the branching and overlapping of the wave.

        @inproceedings{10.2312:vissym19991009
,
booktitle = {VisSym99: Joint Eurographics - IEEE TCVG Symposium on Visualization
},
editor = {Gröller, E., Löffelmann, H., Ribarsky, W.
},
title = {{Geodesic Flow on Polyhedral Surfaces
}},
author = {Polthier, Konrad and 
Schmies, Markus
},
year = {1999
},
publisher = {Springer and The Eurographics Association
},
ISSN = {EG: 1727-5296
Springer: 0946-2767
},
ISBN = {978-3-7091-6803-5
},
DOI = {10.2312/vissym19991009
}
}