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Show HN: Reusable, spectraly shaped Blue Noise point clouds

By adec314 2 min read 0 views 0 comments

Blue noise is the task of sampling a collection of points optimally placed to cover space randomly yet uniformly.-randomly: no periodic pattern or undesired ordered structure, to prevent aliasing effects.-uniformly: no empty regions, clusters... that would unavoidably appear by just using a raw random generator because of natural fluctuations.In spectral language, one can take the Fourier transform of the point cloud. For a blue noise, it's amplitude should be:- 0 or small at low frequencies. This ensures long-range order.- 1 or not too big at high frequencies (short-range disorder).Hence blue noise: Imagine sending light on the point cloud; in some abstract sense, only the blue (high frequency) will pass through.Many popular algorithms can sample blue noise: Poisson disks, void and clusters, Lloyd relaxation... but the bluest blue noise (those that show up as a hard 0-1 spectral step) comes from the most basic, brute-force algorithm you can imagine. Take points from a purely random generator, compare the Fourier transform with the 0-1 target, launch gradient descent... and wait. Wait because it has O(N^2) complexity. Well, it turns out in 2D / 3D, advanced fast Fourier techniques…

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