Texturing Surfaces Using Reaction - Diffusion

This dissenation introduces a new method of creating computer graphics textures that is based on simulaling a biological model of pa11em formation known as reaction-diffusion. Applied mathematicians and biologistli have shown how simple reaction-diffusion systems can create pan ems of spots or stripes. Here we demonstr.lte that the range of patterns created by reaction-dtffusion can be greatly expanded by cascading two or more reaction-d iffusion systems. Cascaded systems can produce such complex paucms as the clusters of spots found on leopards and the mixture of spots and stripes found on ccnain squirrels. This disscnalion also presents a method for simulating reaction-diffusion systems directly on the surface of any given polygonal model. This IS done by creating a mesh for simulation that is specifically fit to a p<tnicular model. Such .a mesh is created by first randomly distribuLing points ovcnhc surface of the model and causing these pomts to repel one another so that they are evenly spaced over the surface. TI1en a mesh cell is crea ted around each point by finding the Vorono• region for each pomt within a local planar approximation 10 the surface. Reaction-diffusion systems can then be simulated on this mesh of cells. The chemical concenrrauons resulting from such a simulation can be convened to color values tO crea te a texture. Textures erentcd by simulation on a mesh do not have the problems of texture distonion or seams between parches that are arofacrs of some other methods of texturing. Two methods of rendering thes;: synthetic textures are pres;:nred. The first method uses a new surface of triangles that closely matches the original model. but whos;: veniccs are taken from the cells of the simulauon mesh. These venices are assigned colors based on the simulation values. and this re-Lilt:d model can be rapidly displayed on a graphics workstation. A higherquality image can be created by eomputingeach pixel's color value using a weigh ted average of the chemical coneenrration at nearby mesh points. Using a smooth cubic weighting function gives a satisfactory reconstruction oi the underlying function specified by the values at the mesh pointS. Several low-pass filtered versions of the texrure are used to avoid aliasing when the textured object covers a small ponion of the screen. The propercolorvalueat a pixel is found by selec£ing from the appropriately filtered level.