Back to Applied Geometry homepage Blue Noise through Optimal Transport
Fernando de Goes
Katherine Breeden
Victor Ostromoukhov
Mathieu Desbrun
Caltech Stanford Lyon 1 U./CNRS-LIRIS Caltech

ACM Transactions on Graphics 31(6) (SIGGRAPH Asia 2012)

julia pointset zebra

We present a fast, scalable algorithm to generate high-quality blue noise point distributions of arbitrary density functions. At its core is a novel formulation of the recently-introduced concept of capacity-constrained Voronoi tessellation as an optimal transport problem. This insight leads to a continuous formulation able to enforce the capacity constraints exactly, unlike previous work. We exploit the variational nature of this formulation to design an efficient optimization technique of point distributions via constrained minimization in the space of power diagrams. Our mathematical, algorithmic, and practical contributions lead to high-quality blue noise point sets with improved spectral and spatial properties.


Published version Supplemental Material Widget of our Blue Noise code
Paper [PDF] Supplemental Material [PDF] Source Code []

pointsets ramp Stippling
Point Sets   Quadratic Ramp  Stippling

    title = {Blue Noise through Optimal Transport},
    author = {F. de Goes and K. Breeden and V. Ostromoukhov and M. Desbrun},
    journal = {ACM Trans. Graph. (SIGGRAPH Asia)},
    volume= {31},
    issue = {6},
    year = 2012,