, Volume 49, Issue 3, pp 193–219 | Cite as

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.


Signed distance function Eikonal equation Level set method Anisotropic mesh adaptation 1-finite elements interpolation 

Mathematics Subject Classification (2000)

65M25 65M50 35F20 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Centre de Mathématiques Appliquées (UMR 7641)Ecole PolytechniquePalaiseauFrance
  2. 2.Renault DREAM-DTAAGuyancourtFrance
  3. 3.Laboratoire J.-L. LionsUPMC Univ Paris 06, UMR 7598ParisFrance

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