Constrained Delaunay Tetrahedrization: A Robust and Practical Approach

Lorenzo Diazzi, Daniele Panozzo, Amir Vaxman, Marco Attene

Research output: Contribution to journalArticlepeer-review


We present a numerically robust algorithm for computing the constrained Delaunay tetrahedrization (CDT) of a piecewise-linear complex, which has a 100% success rate on the 4408 valid models in the Thingi10k dataset. We build on the underlying theory of the well-known tetgen software, but use a floating-point implementation based on indirect geometric predicates to implicitly represent Steiner points: this new approach dramatically simplifies the implementation, removing the need for ad-hoc tolerances in geometric operations. Our approach leads to a robust and parameter-free implementation, with an empirically manageable number of added Steiner points. Furthermore, our algorithm addresses a major gap in tetgen's theory which may lead to algorithmic failure on valid models, even when assuming perfect precision in the calculations. Our output tetrahedrization conforms with the input geometry without approximations. We can further round our output to floating-point coordinates for downstream applications, which almost always results in valid floating-point meshes unless the input triangulation is very close to being degenerate.

Original languageEnglish (US)
Article number181
JournalACM Transactions on Graphics
Issue number6
StatePublished - Dec 4 2023


  • numeric robustness
  • representability
  • volume meshing

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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