Capacity-Constrained Delaunay Triangulation for point distributions

• Published in: Computers & graphics Vol. 35; no. 3; pp. 510 - 516
• Main Authors: Xu, Yin, Liu, Ligang, Gotsman, Craig, Gortler, Steven J.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2011
• Subjects: Blue noise; Capacity-Constrained Delaunay Triangulation (CCDT); Computer graphics; Delaunay triangulation; Density; Mathematical analysis; Minimal area variance; Noise; Poisson disk distribution; Spectra; State of the art; Poisson disk distribution; Minimal area variance; Blue noise; Capacity-Constrained Delaunay Triangulation (CCDT)
• ISSN: 0097-8493; 1873-7684
• DOI: 10.1016/j.cag.2011.03.031

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. [Display omitted] ► We develop a method that efficiently generates point distribution with blue noise property in a planar domain.► The Delaunay triangulation of the point set has as much uniform triangle areas as possible.► The resulting point set has good blue noise property which is comparable with the current best method and performs an order of magnitude faster than it.► We introduce the density function in the method and produce non-uniform distribution.