“Wavelet noise” by Cook and DeRose

Noise functions are an essential building block for writing procedural shaders in 3D computer graphics. The original noise function introduced by Ken Perlin is still the most popular because it is simple and fast, and many spectacular images have been made with it. Nevertheless, it is prone to problems with aliasing and detail loss. In this paper we analyze these problems and show that they are particularly severe when 3D noise is used to texture a 2D surface. We use the theory of wavelets to create a new class of simple and fast noise functions that avoid these problems.

1. Abramowitz, M., and Stegun, I. A. 1970. Error function and fresnel integrals. In Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, ch. 7.1.1, 297.Google Scholar
2. Chui, C. K. 1992. An introduction to wavelets. Academic Press Professional, Inc., San Diego, CA, USA. Google ScholarDigital Library
3. Farin, G. 2002. Curves and surfaces for CAGD: a practical guide, 5th ed. Morgan Kaufmann Publishers Inc. Google ScholarDigital Library
4. Knuth, D. E. 1997. The Art of Computer Programming, third ed., vol. 2. Addison-Wesley. Google ScholarDigital Library
5. Lewis, J. P. 1989. Algorithms for solid noise synthesis. In SIGGRAPH ’89: Proceedings of the 16th annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 263–270. Google ScholarDigital Library
6. Malzbender, T. 1993. Fourier volume rendering. ACM Transaction on Graphics 12, 3 (July), 233–250. Google ScholarDigital Library
7. Peachey, D. 2003. Building procedural textures. In Texturing and Modeling: A Procedural Approach, third ed. Morgan Kaufmann Publishers Inc., ch. 2.Google Scholar
8. Perlin, K., and Velho, L. 1995. Live paint: painting with procedural multiscale textures. In SIGGRAPH ’95: Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 153–160. Google ScholarDigital Library
9. Perlin, K. 1985. An image synthesizer. In SIGGRAPH ’85: Proceedings of the 12th annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 287–296. Google ScholarDigital Library
10. Perlin, K. 2002. Improving noise. In SIGGRAPH ’02: Proceedings of the 29th annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 681–682. Google ScholarDigital Library
11. Stollnitz, E., DeRose, T., and Salesin, D. 1996. Wavelets for Computer Graphics. Morgan Kaufmann Publishers. Google ScholarDigital Library