Journal Article10.1007/S00371-012-0681-4
Connecting geodesics on smooth surfaces
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TL;DR: This paper presents a novel method for computing multiple geodesic connections between two arbitrary points on a smooth surface based on a homotopy approach that is able to capture the ambiguity of geodesIC connections in the presence of positive Gaussian curvature that generates focal curves.
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Abstract: In this paper, we present a novel method for computing multiple geodesic connections between two arbitrary points on a smooth surface. Our method is based on a homotopy approach that is able to capture the ambiguity of geodesic connections in the presence of positive Gaussian curvature that generates focal curves.
Contrary to previous approaches, we exploit focal curves to gain theoretical insights on the number of connecting geodesics and a practical algorithm for collecting these.
We consider our method as a contribution to the contemporary debate regarding the calculation of distances in general situations, applying continuous concepts of classical differential geometry which are not immediately transferable in purely discrete settings.
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Jos Stam
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TL;DR: To compute the shortest path between two given points, a lower-bound property of the approximate geodesic algorithm is used to efficiently prune the frontier of the MMP algorithm, thereby obtaining an exact solution even more quickly.
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