1. Fast Marching Methods.
- Author
-
Sethian, J. A.
- Subjects
MATHEMATICAL models ,ALGORITHMS ,COMPUTATIONAL complexity ,EQUATIONS ,MATHEMATICAL geography ,MATHEMATICS - Abstract
Fast Marching Methods are numerical schemes for computing solutions to the nonlinear Eikonal equation and related static. HamiltonJacobi equations. Based on entropy-satisfying upwind schemes and fast sorting techniques, they yield consistent, accurate, and highly efficient algorithms. They are optimal in the sense that the computational complexity of the algorithms is O(N log N), where N is the total number of points in the domain. The schemes are of use in a variety of applications, including problems in shape offsetting, computing distance from compiles curves and surfaces, shape-from-shading, photolithographic development, computing first arrivals in seismic travel times, construction of shortest geodesies on surfaces, optimal path planning around obstacles, and visibility and reflection calculations. In this paper, were review the development of these techniques, including the theoretical and numerical underpinnings; provide details of the computational schemes, including higher order versions; and demonstrate the techniques in a collection of different areas. [ABSTRACT FROM AUTHOR]
- Published
- 1999
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