@Article{balasubramanian2008exact,
author = {M. Balasubramanian and J. R. Polimeni and E. L.
Schwartz},
title = {Exact Geodesics and Shortest Paths on Polyhedral
Surfaces},
journal = {IEEE Transactions on Pattern Analysis and Artificial
Intelligence (PAMI)},
year = 2009,
volume = {31},
number = {6},
pages = {1006-10016},
key = {geodesics},
abstract = {We present two algorithms for computing distances along convex and
non-convex polyhedral surfaces. 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
minimal-geodesic 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.},
volume = {In Press},
url = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2008.213},
DOI = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2008.213},
datestr = 20081230,
}