Generating Textures for Arbitrary Surfaces Using Reaction-Diffusion

For all but the most simple geometric models it is difficult to find a mapping from a two-dimensional texture space to the surface of a model that does not distort the texture. This paper introduces a method of texture synthesis where such a mapping is not necessary because the texture is generated directly on the surface of the model. No assignment of texture coordinates to polygon vertices is needed. We describe how to generate a mesh of points on a polyhedral model using a relaxation process and how this mesh is used to generate textures. There is no distortion from such a texture because the geometry of the texture matches the geometry of the model. These textures can be rendered free of artifacts resulting from the discrete nature of the underlying mesh or due to aliasing of the texture features. Such textures can also be used as bump maps. We demonstrate how a pattern formation mechanism called reaction- diffusion can be simulated on a such mesh to create a variety of patterns found in nature. Reaction-diffusion is an addition to the growing collection of procedural methods found in the texture synthesists toolbox. Biologists have shown how the chemical mechanism of reaction-diffusion can be used to form simple spotted and striped patterns.