Weighted distance maps computation on parametric three-dimensional manifolds

DOI10.1016/j.jcp.2007.01.009zbMath1122.65022OpenAlexW2115118342MaRDI QIDQ2381173

Michael M. Bronstein, Alexander M. Bronstein, Ron Kimmel

Publication date: 14 September 2007

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2007.01.009

zbMATH Keywords

viscosity solutionnumerical examplesHamilton-Jacobi equationsdistance mapgeodesic distanceeikonal equationsfast marchingfast sweepingwavefront propagationangle splittingparametric three-dimensional Riemannian manifolds

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) First-order nonlinear hyperbolic equations (35L60) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (7)

A fast sweeping method for eikonal equations on implicit surfaces ⋮ Legendre-transform-based fast sweeping methods for static Hamilton-Jacobi equations on triangulated meshes ⋮ A geodesic approach to calculating the information sets in dynamic search problems ⋮ Geometrical interpretations of continuous and complex-lamellar steady flows ⋮ Symmetries of the eikonal equation ⋮ DEVELOPMENT OF 3D NUMERICAL MANIFOLD METHOD ⋮ Riemannian Fast-Marching on Cartesian Grids, Using Voronoi's First Reduction of Quadratic Forms

Cites Work

• An efficient solution to the eikonal equation on parametric manifolds
• A fast sweeping method for static convex Hamilton-Jacobi equations
• Computing geodesic paths on manifolds
• Fast Sweeping Algorithms for a Class of Hamilton--Jacobi Equations
• Fast methods for the Eikonal and related Hamilton– Jacobi equations on unstructured meshes
• A fast sweeping method for Eikonal equations
• Efficient algorithms for globally optimal trajectories
• A fast marching level set method for monotonically advancing fronts.
• Fast Sweeping Methods for Eikonal Equations on Triangular Meshes
• Fast Sweeping Methods for Static Hamilton--Jacobi Equations
• Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces

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