Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization

Vincent Nivoliers, Dongming Yan, Bruno L. Lévy

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This paper introduces Voronoi squared distance minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function between the surface and the input mesh (SDM). This objective function is a generalization of the one minimized by centroidal Voronoi tessellation, and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh elements to best approximate the input, without estimating any differential quantities. Therefore, it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications of fitting quad meshes and polynomial surfaces to input triangular meshes are demonstrated. © 2012 Springer-Verlag London.
Original languageEnglish (US)
Pages (from-to)289-300
Number of pages12
JournalEngineering with Computers
Issue number3
StatePublished - Nov 6 2012

ASJC Scopus subject areas

  • Modeling and Simulation
  • Software
  • Engineering(all)
  • Computer Science Applications


Dive into the research topics of 'Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization'. Together they form a unique fingerprint.

Cite this