Research Article

Geodesics on Point Clouds

Figure 7

Comparison of the approximate geodesic paths and the corrected ones. The 5 sources are marked as . (a) The approximated geodesic paths computed using Algorithm 1 described in Section 3.1; (b) the corrected geodesic paths by the geodesic correction procedure described in Section 3.3; (c) both approximate and corrected geodesic paths are depicted together, where the magenta curves represent the corrected paths, while the black ones represent the approximate paths; (d) the solid curve (yellow) represents the approximate geodesic path, while the dashed curve (yellow) represents the corrected path. The bold solid curve (black) is the other geodesic.
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(d)