Distance function and extension in normal direction for implicitly defined interfaces

Abstract

In this paper we present a novel application of extrapolation pro- cedure for three popular numerical algorithms to compute the distance func- tion for an interface that is given only implicitly. The methods include the fast marching method [8], the fast sweeping method [10] and the linearization method [3]. The extrapolation procedure removes the necessity of a special ini- tialization procedure for the grid nodes next to the interface that is used so far with the methods, thus it represents a natural extension of these methods. The extrapolation procedure can be used also for an extension of a function that is defined only locally on the interface in the direction given by the gradient of distance function [2].