Algorithms for solid noise synthesis

A solid noise is a function that defines a random value at each point in space. Solid noises have immediate and powerful applications in surface texturing, stochastic modeling, and the animation of natural phenomena.Existing solid noise synthesis algorithms are surveyed and two new algorithms are presented. The first uses Wiener interpolation to interpolate random values on a discrete lattice. The second is an efficient sparse convolution algorithm. Both algorithms are developed for model-directed synthesis, in which sampling and construction of the noise occur only at points where the noise value is required, rather than over a regularly sampled region of space. The paper attempts to present the rationale for the selection of these particular algorithms.The new algorithms have advantages of efficiency, improved control over the noise power spectrum, and the absence of artifacts. The convolution algorithm additionally allows quality to be traded for efficiency without introducing obvious deterministic effects. The algorithms are particularly suitable for applications where high-quality solid noises are required. Several sample applications in stochastic modeling and solid texturing are shown.