Stealthy Blue Noise

Blue noise point sets are both hyperuniform (large-scale density fluctuations suppressed) and disordered, filling space evenly without introducing regular patterns. This makes them perceptually favorable, well suited to numerical integration, and effective for aliasing-free sampling. We borrow insights from the study of hyperuniform point sets in condensed matter physics and show that optimizing the disordered ground states of stealthy potentials yields blue noise that saturates the spectral-gap limit. Such point sets can be obtained by plain gradient descent, without early stopping. Using bond-orientational order parameters from the study of 2D melting, we map the Pareto frontier between uniformity and disorder, giving a real-space characterization that complements the standard spectral view of blue noise. We extend the method to non-Euclidean manifolds, combine stealthy losses over unions of point sets to construct multi-class blue noise that enables runtime-adjustable variable-density sampling, and apply reprojective constraints so that such point sets can be stored as textures. Finally, we generalize the loss from suppressing Fourier modes to matching arbitrary spectral targets, and introduce a spatially-varying frequency budget that scales each point's constrained modes by local density, enabling stippling that maintains consistent visual quality at all densities without crystallization artifacts.