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We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain.
The solution of partial differential equations by means of electrical networks
MacNeal, R · 1949
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On the behavior of the fundamental solution of the heat equation with variable coefficients
Varadhan, S. R. S · 1967
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The discrete geodesic problem
Mitchell, J · 1987
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Hodge decomposition: a method for solving boundary value problems
Schwarz, G · 1995
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Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Science
Sethian, J · 1996
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Weighted eno schemes for hamilton-jacobi equations
Jiang, G · 1997
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Heat Kernel Asymptotics and the Distance Function in Lipschitz Riemannian Manifolds
Norris, J · 1997
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Fast Marching Methods on Triangulated Domains
Kimmel, R · 1998
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Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces
Memoli, F · 2001
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An as-short-as-possible intro. to the MLS method for scattered data approximation and interpolation
Nealen, A · 2004
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Analysis of the cut locus via the heat kernel
Neel, R · 2004
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Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems
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Heat Kernel Comparison on Alexandrov Spaces with Curvature Bounded Below
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Discrete Differential Forms for Computational Modeling
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Parallel algorithms for approximation of distance maps on parametric surfaces
Weber, O · 2008
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Approximating gradients for meshes and point clouds via diffusion metric
Luo, C · 2009
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Lipman, Y · 2010
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Discrete Laplacians on General Polygonal Meshes
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