Exact Geosedics and Shortest Paths on Polyhedral Surface
Polimeni, Jonathan R.
Schwartz, Eric L.
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We present two algorithms for computing distances along a non-convex polyhedral surface. The ﬁrst algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimalgeodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface ﬂattening methods that accurately transform curved manifolds into ﬂat representations.