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Mapping, Texture Bump Mapping, OpenGL CS116B Chris Pollett May 2, 2004. Outline Surface Texture Mapping Texture Reduction Patterns Procedural Texturing Methods Bump Mapping Frame Mapping OpenGL Surface Texture Mapping Texture Space (s,t) Object Space (u,v) parametrization of a surface (x(u,v), y(u,v), z(u,v)) transformation Image Space: (x,y) Pixel Coordinates texture surface transformation viewing and projection Typically, the texture space and the object space are rectangles so can map using the equations: u(s,t) = a_u*s+b_u*t +c_u v(s,t) = a_v*s =b_v*t +c_u. The object space to image space mapping depends on the surface we are parametrizing. For example, for a cylinder we might use x=r*cos u, y=r*cos u, z=v. We can map either from texture space to image space (texture scanning) by composition or can map reverse direction (pixel-order scanning). The latter is useful to avoid pixel round off errors. Volume Texturing Similar to surface texturing except now texture is 3D. So given by 3 coordinates (s,t,r). Might want to do for cut-away displays, scenes like inside a fish-tank,etc. Texture Reduction Patterns As objects get far away, it doesn t make sense to do lots of calculations to apply a texture to them. It also can cause distortion in how the texture looks. To avoid this we can create different textures of different levels of detail to use depending on the scale of the object. These texture reduction are patterns often called MIP maps (multum in parvo). Procedural Texturing Methods Another technique for adding a texture pattern to an object is to use a procedural definition for the textures that are to be applied. That is have a little program that calculates something that looks like wood graining, marble, etc. Bump Mapping Texture are not very effective when trying to model rough surfaces such as oranges, strawberries, or raisins. The problem is the light intensity given in a texture for such an object does not depend on the light in the scene. But these objects change a lot according to the lighting. Bump mapping is a technique to make realistic bumpy surfaces that can be used instead. More Bump Mapping Let P(u,v) be a point on a surface. Then N = Pu x Pv is the normal at (u,v). Let n= N/|N|. We can add a bump to the surface using an equation: P (u,v) =P(u,v) + b(u,v)n. Here b(u,v) is a bump function. Can show the perturbed normal is now approximately: N = N + bv(Pu x n) + bu(Pv x n) We now use this normal to do our lighting calculations. Frame Mapping This is an extension to bump mapping. We not only perturb the surface normal, we also perturb the local coordinate system at the point. To do this we tweak the tangent vector T and calculate a binormal as B= T x N. This is useful in modeling anisotropic surfaces, such as wood grains, cross threading in clothing, and streaks on marbles.

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