Efficient Computation of Smoothed Exponential Maps
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Date
2019
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© 2019 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd
Abstract
Many applications in geometry processing require the computation of local parameterizations on a surface mesh at interactive rates. A popular approach is to compute local exponential maps, i.e. parameterizations that preserve distance and angle to the origin of the map. We extend the computation of geodesic distance by heat diffusion to also determine angular information for the geodesic curves. This approach has two important benefits compared to fast approximate as well as exact forward tracing of the distance function: First, it allows generating smoother maps, avoiding discontinuities. Second, exploiting the factorization of the global Laplace–Beltrami operator of the mesh and using recent localized solution techniques, the computation is more efficient even compared to fast approximate solutions based on Dijkstra's algorithm.Many applications in geometry processing require the computation of local parameterizations on a surface mesh at interactive rates. A popular approach is to compute local exponential maps, i.e. parameterizations that preserve distance and angle to the origin of the map. We extend the computation of geodesic distance by heat diffusion to also determine angular information for the geodesic curves. This approach has two important benefits compared to fast approximate as well as exact forward tracing of the distance function: First, it allows generating smoother maps, avoiding discontinuities. Second, exploiting the factorization of the global Laplace–Beltrami operator of the mesh and using recent localized solution techniques, the computation is more efficient even compared to fast approximate solutions based on Dijkstra's algorithm.
Description
@article{10.1111:cgf.13607,
journal = {Computer Graphics Forum},
title = {{Efficient Computation of Smoothed Exponential Maps}},
author = {Herholz, Philipp and Alexa, Marc},
year = {2019},
publisher = {© 2019 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd},
ISSN = {1467-8659},
DOI = {10.1111/cgf.13607}
}