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