Straightest geodesics on polyhedral surfaces

  title={Straightest geodesics on polyhedral surfaces},
  author={Konrad Polthier and Markus Schmies},
  booktitle={SIGGRAPH Courses},
Geodesic curves are the fundamental concept in geometry to generalize the idea of straight lines to curved surfaces and arbitrary manifolds. On polyhedral surfaces we introduce the notion of discrete geodesic curvature of curves and define straightest geodesics. This allows a unique solution of the initial value problem for geodesics, and therefore a unique movement in a given tangential direction, a property not available in the well-known concept of locally shortest geodesics.An immediate… CONTINUE READING
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