Computation of the signed distance function to a discrete contour on adapted triangulation

In this paper, we propose a numerical method for computing the signed distance function to a discrete domain, on an arbitrary triangular background mesh. It mainly relies on the use of some theoretical properties of the unsteady Eikonal equation. Then we present a way of adapting the mesh on which computations are held to enhance the accuracy for both the approximation of the signed distance function and the approximation of the initial discrete contour by the induced piecewise affine reconstruction, which is crucial when using this signed distance function in a context of level set methods. Several examples are presented to assess our analysis, in two or three dimensions.