High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains
Journal of Computational Physics
SIAM Review
An $\cal O(N)$ Level Set Method for Eikonal Equations
SIAM Journal on Scientific Computing
Exploration of a cluttered environment using Voronoi Transform and Fast Marching
Robotics and Autonomous Systems
Exploration of 2D and 3D Environments using Voronoi Transform and Fast Marching Method
Journal of Intelligent and Robotic Systems
Hi-index | 7.30 |
A new front marching algorithm for solving the eikonal equation is presented. An important property of the algorithm is that it can be used on nodes that are located on highly distorted grids or on nodes that are randomly located. When the nodes are located on an orthogonal grid, the method is first-order accurate and is shown to be a generalization of the front marching algorithm in (Proc. Natl. Acad. Sci. 93 (4) (1996) 1591). The accuracy of the method is also shown to be dependent on the principle curvature of the wave front solution. Numerical results on a variety of node configurations as well as on shadow, nonconvex and nondifferentiable solutions are presented.