5|h@ }|it| BiL it Ut L? ˘L*)i h@* [email protected]/polthier/articles/straightest/...5|h@...

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  • 382 Appendix: Color Plates

    Fig. 29. Geodesics on a smooth surface and di�erent local minimizers. (Polthier,Schmies, p. 137)

    Fig. 30. Straightest geodesic through the vertex of a polyhedral surface and an

    unfolding of the adjacent faces to a planar domain. (Polthier, Schmies, p. 142)

  • Appendix: Color Plates 383

    Fig. 31. Comparison of geodesic Euler (blue, stepsize h) and geodesic Runge-Kuttamethod (green, stepsize 4h) on a polyhedral surface. The particle traces are piece-wise straightest geodesics. (Polthier, Schmies, p. 149)

    Fig. 32. Straightest geodesics uniquely solve the initial value problem for geodesicson polyhedral surfaces and are suitable tool for the numerical study of discrete

    ows. The front of a point wave on a polyhedral surface follows straightest geodesics.(Polthier, Schmies, p. 149)