Color-mapped Noise Vector Fields for Generating Procedural Micro-patterns

Abstract

Stochastic micro-patterns successfully enhance the realism of virtual scenes. Procedural models using noise combined with transfer functions are extremely efficient. However, most patterns produced today employ 1D transfer functions, which assign color, transparency, or other material attributes, based solely on the single scalar quantity of noise. Multi-dimensional transfer functions have received widespread attention in other fields, such as scientific volume rendering. But their potential has not yet been well explored for modeling micro-patterns in the field of procedural texturing. We propose a new procedural model for stochastic patterns, defined as the composition of a bi-dimensional transfer function (a.k.a. color-map) with a stochastic vector field. Our model is versatile, as it encompasses several existing procedural noises, including Gaussian noise and phasor noise. It also generates a much larger gamut of patterns, including locally structured patterns which are notoriously difficult to reproduce. We leverage the Gaussian assumption and a tiling and blending algorithm to provide real-time generation and filtering. A key contribution is a real-time approximation of the second order statistics over an arbitrary pixel footprint, which enables, in addition, the filtering of procedural normal maps. We exhibit a wide variety of results, including Gaussian patterns, profiled waves, concentric and non-concentric patterns.