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Procedural Textures Jian Huang, CS594, Fall 2002 This set of slides references slides used at Ohio State and “Texturing and modeling” by Ebert, et. al

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Procedural Textures Introduced by Perlin and Peachey (Siggraph 1989) look for book by Ebert et al: “Texturing and Modeling: A Procedural Approach” it’s a 3D texturing approach (can be used in 2D of course)

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What is procedural texture Procedural techniques are usually considered to be code segments or algorithms that specify some characteristic of a computer-generated model or effect Example: procedural texture for a marble surface does not use a scanned-in image to define the color values

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Why Use That? The most important and foremost reason: abstraction –Abstract complex scene into a function or an algorithm (I.e. procedure)

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Pros? Storage savings for details (compact) No fixed resolution, a great range of detail no matter how close you look Can cover arbitrarily large space Reduce the time of specifying the details from the programmer to computer Power to control parameters that meter meaningful concepts, e.g. the roughness of a mountain Flexibility, spend time on the essence of the object or phenomenon

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Cons? Very difficult to build and debug an implicit pattern description Surprise Slow to compute Aliasing A stochastic process

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Procedural Textures Gets around a bunch of problems of 2D textures –deformations/compressions –worrying about topology analogous to sculpting or carving

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Procedural Textures Object Density Function D(x) –defines an object, e.g. implicit description or inside/outside etc. Density Modulation Function (DMF) f i –position dependent –position independent –geometry dependent Hyper-texture: H(D(x),x) = f n (…f 2 (f 1 (D(x))))

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Procedural Textures Base DMF’s: –bias used to bend the Density function either upwards or downwards over the [0,1] interval. The rules the bias function has to follow are: bias(b,0)=0 bias(b,.5)=b bias(b,1)=1 The following function exhibits those properties: bias(b,t) = t^(ln(b)/ln(0.5)) b = 0.25 b = 0.75

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Procedural Textures –Gain The gain function is used to help shape how fast the midrange of an objects soft region goes from 0 to 1. A higher gain value means the a higher rate in change. The rules of the gain function are as follows: gain(g,0)=0 gain(g,1/4)=(1-g)/2 gain(g,1/2)=1/2 gain(g,3/4)=(1+g)/2 gain(g,1)=1

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Procedural Textures –Gain The gain function is defined as a spline of two bias curves: gain(g,t)= if (t<0.5) then bias(1-g,2*t) else 1- bias(1-g,2-2*2t)/2 G = 0.25G = 0.75

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Source of Randomness –Noise some strange realization that gives smoothed values between -1 and 1 creates a random gradient field G[i,j,k] (using a 3 step monte carlo process separate for each coordinate)

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Noise Set all integer lattice values to zero Randomly assign gradient (tangent) vectors

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Simple Noise Hermite spline interpolation Oscillates about once per coordinate Noisy, but still smooth (few high frequencies)

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Procedural Textures –Noise for an entry (x,y,z) - he does a cubic interpolation step between the dot product of G and the offset of the 8 neighbors of G of (x,y,z):

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Procedural Textures –turbulence creates “higher order” noise - noise of higher frequency, similar to the fractal brownian motion:

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Turbulence Increase frequency, decrease amplitude

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Turbulence The abs() adds discontinuities in the first derivative. Limit the sum to the Nyquist limit of the current pixel sampling.

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Density Function Models Radial Function (2D Slice)

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Density Function Models Modulated with Noise function.

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Density Function Models Thresholded (iso-contour or step function).

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Density Function Models Volume Rendering of Hypertextured Sphere

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Procedural Textures Effects (on colormap): –noise:

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Procedural Textures Effects (on colormap): –sum 1/f(noise):

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Procedural Textures Effects (on colormap): –sum 1/f(|noise|):

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Procedural Textures Effects (on colormap): –sin(x + sum 1/f( |noise| )):

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Procedural Textures Effects: –noisy sphere modify amplitude/frequency (Perlins fractal egg)

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Procedural Textures Summary:

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Procedural Textures Effects: –marble marble(x) = m_color(sin(x+turbulence(x))) –fire

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Procedural Textures Effects: –clouds noise translates in x,y

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Procedural Textures Many other effects!! –Wood, –fur, –facial animation, –etc.

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How do you render that? Rendering –solid textures keeps original surface map (x,y,z) to (u,v,w) –hypertexture changes surface as well (density function) volume rendering approach I.e. discrete ray caster

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Simple mesh for tile. So-so marble

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Procedural Textures Threshold to provide a sharp transition.

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Good Marble

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More bricks and other bumps.

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Wood Better marble as well.

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Knarly Marble Dude!!

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Decent Fire

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Other procedures

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