- Generating Textures on Arbitrary Surfaces...

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Introduction Texture mapping was introduced in [Catmull 74] as a method of adding to the visual richness of a computer generated image without adding geometry. There are three fundamental issues that must be addressed to render textures. First, a texture must be acquired. Possibilities include creating a texture procedurally, painting a texture, or digitally scanning a texture from a photograph. Next, we need to define a mapping from the texture space to the space of the model to be textured. Defining this mapping should not require a great deal of a user’s time. This mapping should not noticeably distort the texture. Finally, we require a method of sampling the texture during rendering so that the final image contains no artifacts due to aliasing or resulting from the underlying texture representation [Heckbert 89]. These three issues are often interrelated, and this is true of the techniques in this paper. This paper explores a procedural method for texture synthesis and also introduces a new method for fitting a texture to a surface. Either of these techniques can be used separately, but the examples given here shows the strength of using them together to produce natural textures on complex models. After a discussion of previous texturing methods, the majority of the paper is divided into two parts, one for each of these topics. The first part of this paper describes a chemical mechanism for pattern formation know as reaction-diffusion . This mechanism, first described in [Turing 52], shows how two or more chemicals that diffuse across a surface and react with one another can form stable patterns. A number of researchers have shown how simple patterns of spots and stripes can be created by reaction-diffusion systems [Bard 81; Murray 81; Meinhardt 82]. We begin by introducing the basics of how a reaction-diffusion system can form simple patterns. We then introduce new results that show how more complex patterns can be generated by having an initial pattern set down by one chemical system and further refined by later chemical systems. This widens the range of patterns that can be generated by reaction- diffusion to include such patterns as the rosettes found on leopards and the multiple-width stripes found on some fish and snakes. These patterns could be generated on a square grid and then mapped onto an object’s surface using traditional techniques, but there are advantages to synthesizing the pattern directly on the surface to be textured in a manner that will be described next. The second part of this paper presents a method of generating a mesh over the surface of a polyhedral model that can be used for texture synthesis. The approach uses relaxation to evenly distribute points across the model’s surface and then divides the surface into cells centered at these points. We can simulate reaction-diffusion systems directly on this mesh to create textures. Because there is no mapping from texture space to the object, there is no need to assign texture Abstract
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This document was uploaded on 01/05/2012.

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