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# 3D Textures

3D Textures. Soon Tee Teoh CS 116B. 2D Texture Maps in Ray-Tracing. We have seen 2D texture-mapping in OpenGL. How do we do 2D texture mapping in ray-tracing?

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## 3D Textures

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1. 3D Textures Soon Tee Teoh CS 116B

2. 2D Texture Maps in Ray-Tracing • We have seen 2D texture-mapping in OpenGL. • How do we do 2D texture mapping in ray-tracing? • Simply generate the (s,t) texture coordinates from the surface coordinates of the object, and read from the texture map to get the color. z t Wrapping a texture around a cylinder t = z s = q/360 q s

3. 3D Texture Maps in Ray-Tracing • A 2D texture map is a pattern that is pasted onto a surface. • A 3D texture map defines a color at each 3D coordinate (x,y,z). • 3D texture also called solid texture. • For example, a 3D wood texture or marble texture can be defined. • When mapped onto 3D geometry, it is as though the 3D geometry has been carved out of the wood or marble material.

4. Functional 3D Texture Definition • Whether in 2D or 3D, the texture pattern can be either defined by a function or by some 2D or 3D data. • Let’s try to generate some nice 3D textures functionally. • The texture function can be generalized as f, where f(x,y,z) = (r,g,b) • In other words, given 3D coordinates, the texture function returns a color.

5. Noise and Turbulence • Ken Perlin’s SIGGRAPH 85 paper An Image Synthesizer introduces 3D texture-mapping, and also suggests an approach to generate interesting 3D textures. • The method uses noise and turbulence. • The noise function is a continuous function that varies in 3D space at uniform frequency. • Simple noise function: • Create a 3D grid. • Generate a random number at each grid point. • Use tri-linear interpolation to get value at any position. • Turbulence: Obtained by mixing several noise functions together turb(s,x,y,z) = noise(sx,sy,sz)/2 + noise(2sx,2sy,2sz)/4 + noise(4sx,4sy,4sz)/8 where s is the scaling factor • A more general formula for turb is: • You get the above example by setting N=3, a=b=2 N-1 noise (sbix, sbiy, sbiz) ai+1 turb(s,x,y,z) = S i=0

6. Noise and Turbulence Turbulence Noise Scale: 4 3 2 1

7. Marble Texture Function • Marble function: marble(x,y,z) = undulate(sin(z + A turb(s,x,y,z))) where A and s are parameters the user can set to control the appearance of the marble • The undulate function is a spline-shaped function that the user can define undulate(u) u

8. Wood Texture Function • A simple wood texture with concentric rings around the center rings(r) = ((int)r) % 2 where r = sqrt(x2+y2) to make rings about the z-axis • The value of the function jumps between 0 and 1 • Next: Rings of thickness M. Function jumps between D and D+A • wood(x,y,z) = D + A x rings(r/M) • Next: Add some “wobble” to the rings wood(x,y,z) = D + A x rings(r/M + K sin (q/N)) where q is the angle about the z axis, and D, A, M, K and N are user-defined parameters to control the appearance of the texture • Next: Add a twist to the wood grain wood(x,y,z) = D + A x rings(r/M + K sin (q/N + Bz)) where B is also a user-defined parameter

9. 3D Textures in OpenGL • Using 3D Textures in OpenGL is a straight-forward extension of 2D textures. • The following functions should look familiar. glTexImage3D(GL_TEXTURE_3D, 0, GL_RGBA, texWidth, texHeight, texDepth, 0, dataFormat, dataType, volTexArray); glEnable(GL_TEXTURE_3D); glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_MAG_FILTER, GL_NEAREST); glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_MIN_FILTER, GL_NEAREST); glTexCoord3f(sCoord, tCoord, rCoord);

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