This paper presents a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential equation for a propagating level set function and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. The method is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufacturing, and arrival time problems in control theory. The paper describes and tests a numerical algorithm for tracking the evolution of interfaces. The technique applies in the case of a front propagating normal to itself with a speed F that depends only on position and is always either positive or negative. The applications of such a technique include some global illumination problems and problems from control theory, as well as surface advancement in lithographic development and isotropic etching and deposition in the manufacturing of microelectronic structures. The method is based on the level set formulation, which views the interface as the zero level set of a function. The evolution equation for the interface is given by $ \phi_{t}+F|\nabla\phi|=0 $. This equation is solved using a fast marching level set method, which is a computationally efficient technique that only works in a narrow band around the interface. The method is shown to produce accurate results for a variety of problems, including lithographic development and isotropic etching and deposition. The algorithm is efficient and has been tested on a variety of problems, including a parameter study on a Sparc 10 workstation. The method is also shown to be applicable to a wide range of problems, including control theory, etching/deposition/lithography, and global illumination. The paper concludes with a discussion of the applications and potential extensions of the method.This paper presents a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential equation for a propagating level set function and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. The method is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufacturing, and arrival time problems in control theory. The paper describes and tests a numerical algorithm for tracking the evolution of interfaces. The technique applies in the case of a front propagating normal to itself with a speed F that depends only on position and is always either positive or negative. The applications of such a technique include some global illumination problems and problems from control theory, as well as surface advancement in lithographic development and isotropic etching and deposition in the manufacturing of microelectronic structures. The method is based on the level set formulation, which views the interface as the zero level set of a function. The evolution equation for the interface is given by $ \phi_{t}+F|\nabla\phi|=0 $. This equation is solved using a fast marching level set method, which is a computationally efficient technique that only works in a narrow band around the interface. The method is shown to produce accurate results for a variety of problems, including lithographic development and isotropic etching and deposition. The algorithm is efficient and has been tested on a variety of problems, including a parameter study on a Sparc 10 workstation. The method is also shown to be applicable to a wide range of problems, including control theory, etching/deposition/lithography, and global illumination. The paper concludes with a discussion of the applications and potential extensions of the method.