  We propose a fast and scalable algorithm to project a given density on a set
of structured measures defined over a compact 2D domain. The measures can be
discrete or supported on curves for instance. The proposed principle and
algorithm are a natural generalization of previous results revolving around the
generation of blue-noise point distributions, such as Lloyd's algorithm or more
advanced techniques based on power diagrams. We analyze the convergence
properties and propose new approaches to accelerate the generation of point
distributions. We also design new algorithms to project curves onto spaces of
curves with bounded length and curvature or speed and acceleration. We
illustrate the algorithm's interest through applications in advanced sampling
theory, non-photorealistic rendering and path planning.
