Geodesic Flow on Polyhedral Surfaces

  • Konrad Polthier
  • Markus Schmies
Part of the Eurographics book series (EUROGRAPH)


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.


Wave Front Concentric Circle Conjugate Point Geodesic Flow Injectivity Radius 
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Copyright information

© Springer-Verlag/Wien 1999

Authors and Affiliations

  • Konrad Polthier
    • 1
  • Markus Schmies
    • 1
  1. 1.Technische Universität BerlinFrance

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