Signed L p-distance fields

Alexander Belyaev, Pierre Alain Fayolle, Alexander Pasko

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


We introduce and study a family of generalized double-layer potentials which are used to build smooth and accurate approximants for the signed distance function. Given a surface, the value of an approximant at a given point is a power mean of distances from the point to the surface points parameterized by the angle they are viewed from the given point. We analyze mathematical properties of the potentials and corresponding approximants. In particular, approximation accuracy estimates are derived. Our theoretical results are supported by numerical experiments which reveal the high practical potential of our approach.

Original languageEnglish
Pages (from-to)523-528
Number of pages6
JournalCAD Computer Aided Design
Issue number2
Publication statusPublished - Feb 2013
Externally publishedYes


  • Approximate distance functions
  • Generalized double potentials
  • Singular integrals


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