document: Algorithms regarding distance fields go back to the level set equation. The level set method was presented by Osher and Sethian [20] who described the temporal propagation of moving interfaces by numerical methods solving the Hamilton–Jacobi equation. This is performed by a finite difference scheme working on a rectangular grid in two or three dimensions. Information on normal vectors and curvature can be obtained. The fast marching method [21] provides an efficient numerical scheme of complexity nlogn to compute the support values on the grid. It is a reinterpretation of the propagation process, i.e. the time where the interface passes a certain grid point is influenced only by those neighboring grid points which are previously passed by the interface. An overview on the theory of level set and fast marching methods and their applications to problems of various areas are given in [22,23], for example shape offsetting, computing distances, photolithography development, seismic travel times, etc. Distance fields are a special case of the level set equation where the absolute value of the advection velocity is 1.
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