5|h@ }|it| BiL it Ut L? ˘L*)i h@* 5hu@Uit · 2013. 4. 23. · 5|h@ }|it| BiL_it Ut L? ˘L*)i_h@*...

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Transcript of 5|h@ }|it| BiL it Ut L? ˘L*)i h@* 5hu@Uit · 2013. 4. 23. · 5|h@ }|it| BiL_it Ut L? ˘L*)i_h@*...

Page 1: 5|h@ }|it| BiL it Ut L? ˘L*)i h@* 5hu@Uit · 2013. 4. 23. · 5|h@ }|it| BiL_it Ut L? ˘L*)i_h@* 5hu@Uit kL?h@_˘L*| ih @h!t5U4 it a?i c†bbH Devwudfw Jhrghvlf fxuyhv duh wkh ixqgdphqwdo

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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)

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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)