Approximation of 3D objects by piecewise linear geometric interpolants of their 1D cross-sections

Nira Dyn, Elza Farkhi, Shirley Keinan

Research output: Contribution to journalArticlepeer-review


In this paper we introduce a method for reconstruction of 3D objects from their 1D parallel cross-sections by set-valued interpolation. We regard a 3D object as the graph of a set-valued function defined on a planar domain, with the given 1D cross-sections as its samples. The method is based on a triangulation T of the sampling points in the planar domain and it is modular: for each triangle in T the corresponding 1D cross-sections are geometrically interpolated by a union of polyhedrons. The union of these interpolants over all triangles of T constitutes the approximating 3D object. Properties of this approximation are studied, in particular we derive the approximation order of the error, measured by the symmetric difference metric.

Original languageEnglish
Article number112466
JournalJournal of Computational and Applied Mathematics
StatePublished - Apr 2020


  • 1D samples
  • Approximation order
  • Bivariate set-valued functions
  • Interpolation
  • Reconstruction of 3D objects
  • Symmetric difference metric

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics


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