Capacity-Constrained Delaunay Triangulation for point distributions

Yin Xu, Ligang Liu, Craig Gotsman, Steven J. Gortler

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


Sample point distributions possessing blue noise spectral characteristics play a central role in computer graphics, but are notoriously difficult to generate. We describe an algorithm to very efficiently generate these distributions. The core idea behind our method is to compute a Capacity-Constrained Delaunay Triangulation (CCDT), namely, given a simple polygon P in the plane, and the desired number of points n, compute a Delaunay triangulation of the interior of P with n Steiner points, whose triangles have areas which are as uniform as possible. This is computed iteratively by alternating update of the point geometry and triangulation connectivity. The vertex set of the CCDT is shown to have good blue noise characteristics, comparable in quality to those of state-of-the-art methods, achieved at a fraction of the runtime. Our CCDT method may be applied also to an arbitrary density function to produce non-uniform point distributions. These may be used to half-tone grayscale images.

Original languageEnglish (US)
Pages (from-to)510-516
Number of pages7
JournalComputers and Graphics (Pergamon)
Issue number3
StatePublished - Jun 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • General Engineering
  • Human-Computer Interaction
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


  • Blue noise
  • Capacity-Constrained Delaunay Triangulation (CCDT)
  • Minimal area variance
  • Poisson disk distribution


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