Home

Multi-Dimensional Procedural Wave Noise

ACM Transactions on Graphics (TOG), Vol. 44, No. 4, Article XXX, August 2025
SIGGRAPH 2025, August 2025, Vancouver, Canada

Pascal Guehl1
Rémi Allègre2
Guillaume Gilet3
Basile Sauvage2
Marie-Paule Cani1
Jean-Michel Dischler2
1 LIX, Ecole Polytechnique, CNRS, Institut Polytechnique de Paris, France
2 ICube, Université de Strasbourg, CNRS, France
3 Université de Sherbrooke, Canada
Project Teaser

Wave noise is a new procedural noise that encompasses sparse convolution procedural noises like resp. Lewis, Gabor, and Phasor noises providing more efficient computation in higher dimensions (top row, resp. left to center). It also introduces various novel patterns (top row, two rightmost images), including a new cellular noise distinct from Worley’s cellular approach (right most). Retaining essential properties (infinite, resolution independent, compact [1KB per 3D example], fast to compute, and GPU-friendly), it supports diverse applications in Computer Graphics. Two examples are demonstrated: modeling volumetric materials with RGBA transfer functions (middle row), and surface materials mapped on arbitrary geometry with no UV coordinates using style transfer functions (bottom row). Transfer functions are on the left.

Abstract

While precise spectral control can be achieved through sparse convolution, corresponding state of the art noise models are typically too expensive for solid noise. We introduce an alternative, wave-based procedural noise model, fast enough to be used in any dimension. We express the noise in the spectral domain and then apply an inverse Fourier transform (FT), requiring the computation of a multidimensional integral. Our contribution is a novel, efficient way to perform this computation, using a sum of precomputed complex-valued hyperplanar wave-functions, oriented in random directions. We show that using suitable wave profiles and combination operators, our model is able to extend to 3D a number of Gaussian and non-Gaussian noises, including Gabor, by-example and Phasor noises, as well as generate novel cellular noises. Our versatile and controllable solid noise model is very compact, a key feature for complex power spectrum and animated noises. We illustrate this through the design of 2D, 3D, and 3D+t materials using color, transparency and style transfer functions.

Resources (Work In Progress: not finished yet!)

HAL (preprint): Articles Article (low res) Supp. doc (low res)
ACM: Article Supp. doc Supp. video
Tutorial (GUI) GitHub repository

Related Project(s)

Semi-Procedural Appearance Model for Controlling and Scaling Texture and Material Synthesis (Guehl 2022, PhD Thesis)
Semi-Procedural Textures Using Point Process Texture Basis Functions (Guehl et al. 2020, CGF, EGSR)