Announcements Written Assignment 2 is due 3 8 Computer Graphics 15 462 1 Advanced Texturing Bump Bump Mapping Mapping Displacement Displacement Mapping Mapping Environment Environment Mapping Mapping Procedural Procedural Textures Textures Shirley Chapter 11 COMPUTER GRAPHICS 15 462 03 06 07 Computer Graphics 15 462 2 Uses for Texture Mapping Heckbert 1986 Use texture to affect a variety of parameters surface color Catmull 1974 surface reflectance normal vector geometry transparency light source radiance Computer Graphics 15 462 color radiance of each point on surface reflectance coefficients kd ks or nshiny bump mapping Blinn 1978 displacement mapping transparency mapping clouds Gardener 1985 environment mapping Blinn 1978 3 Fine Surface Detail http www siggraph org education materials HyperGraph mapping bumpmap htm How can we model this level of detail Computer Graphics 15 462 4 Bump Mapping Basic texture mapping paints on to a smooth surface How do you make a surface look rough Option 1 model the surface with many small polygons Option 2 perturb the normal vectors before the shading calculation Real Bump Sphere w Diffuse Texture Map Computer Graphics 15 462 Flat Plane Fake Bump Bump Map 5 Sphere w Diffuse Texture Bump Map Why Does this Work Which spots bulge out and which are indented The human visual system is hard coded to expect light to come from above the sun Computer Graphics 15 462 6 Implementing Bump Mapping At each point displace the normal by some amount to change lighting Displacements stored in bump map texture image blackboard Computer Graphics 15 462 7 Demo Bump Mapping is a Hack What anomalies do you see in the image below Greg Turk Computer Graphics 15 462 8 Displacement Mapping Use texture map to displace each point on the surface Texture value gives amount to move in direction normal to surface How is this better worse than bump mapping Computer Graphics 15 462 9 Demo Environment Mapping Very shiny objects show reflections of their surroundings To do this properly we use ray tracing to calculate multiple bounces That s a lot of computation how can we fake it Use a pre rendered environment Won t support inter object reflections Computer Graphics 15 462 10 Environment Mapping Spherical Imagine that object is surrounded by an infinitely large sphere Calculate reflection vector project on to sphere Need a seamless texture for the sphere blackboard Jerome Dewhurst Computer Graphics 15 462 11 Environment Mapping Cube Map Same idea as spherical map but with 6 textures forming a cube OpenGL supports both methods of environment mapping glEnable GL TEXTURE CUBE MAP EXT glEnable GL TEXTURE GEN S glEnable GL TEXTURE GEN T What are the advantages disadvantages of each method Computer Graphics 15 462 12 Demo Color Mapping Mapping from R R3 specifically from 0 1 0 1 3 Allows us to convert scalar valued functions to colors Option 1 Color table 0 0 2 0 2 0 4 0 4 0 6 0 6 0 8 0 8 1 0 Abrupt transitions but dead simple to implement Option 2 Color spline Linear cubic C R Hermite interpolation between colors Can create both sharp transitions and smooth gradients Computer Graphics 15 462 13 Procedural Textures What if we want to generate textures procedurally To save space To get effects not possible with photographic textures solid texture To animate textures To get the correct texture scale Basic procedural textures are regular boring Built with periodic functions like sin cos Need to add interestingness to textures Disturb the regularity of basic textures Computer Graphics 15 462 14 Perlin Noise Random perturbation function with the following characteristics Repeatable function of x y z input Known range 1 1 Band limited coherent No obvious periodicity Stationary Isotropic Perlin Noise White Noise Computer Graphics 15 462 15 Perlin Noise Algorithm Perlin Noise is also known as gradient noise Gradient value at each integer point in the 3 space lattice Gradient determined by repeatable hash of floor x floor y floor z Take dot product of each gradient with distance to lattice point Weighted average using ease function 6t5 15t4 10t3 http mrl nyu edu perlin noise Computer Graphics 15 462 16 blackboard Turbulence Noise has a range of 1 1 must convert to 0 1 Can scale noise using 0 5 noise 1 abs noise creates dark veins at zero crossings Computer Graphics 15 462 17 Octaves of Noise Feature size of basic Perlin noise is relatively uniform Sum multiple calls to noise scaling input Typically we scale the input by 2i Number of iterations number of octaves 1 8 Octaves of Turbulence Computer Graphics 15 462 18 Using Noise Clouds noise point offset intensity Fire abs noise3 point offset Marble sin offset turbulence point Wood noise point scale int noise point scale Animated texture add time varying offset vector to point Computer Graphics 15 462 19 Demo Reaction Diffusion Witkin Kass 91 Originally developed by Alan Turing as a way to model morphogenesis Two or more morphogens whose concentration varies over a 2D grid Concentration affected by Decay of morphogens Movement of morphogen from areas of high concentration to low diffusion Interactions between morphogens which create and destroy them reaction blackboard Computer Graphics 15 462 20 Reaction Diffusion R Functions Difference in concentrations giraffe markings Max of differences 3 morphogens maze like Difference of abs 3 morphogens woven twigs Computer Graphics 15 462 21 Video Reaction Diffusion Varying anisotropy by curvature or location allows for more complicated effects Zebra s stripes wrap correctly Girrafe s pattern is larger on smooth areas Turk Computer Graphics 15 462 22 Cellular Textures Worley Based on the idea that there are feature points in 3space and we care about the distance to the nth closest feature Fi x y is the distance to the ith closest randomly distributed feature F1 Computer Graphics 15 462 F2 23 F3 Cellular Texture Variations Cellular texture algorithm very hackable Change distribution of feature points Fractal sum of multiple octaves water tin foil Linear nonlinear combinations of Fis Unique ID number per feature point flagstones Different distance metrics Manhattan super quadratic F2 F1 Computer Graphics 15 462 Manhattan Distance 24 Announcements Written Assignment 2 is due 3 8 Computer Graphics 15 462 25
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