Procedural Texture Synthesis

Patterns from Algorithms

Procedural Synthesis

• The basic problem: Worlds are big.– To create models and textures for even fairly small

worlds takes ages, if you do it by hand.

• Idea: write down the rules of the world, and a program can create the content.

• Philosophy of algorithmic synthesis: proceduralism.

[World of Warcraft, 2004-2010]

[Oblivion, 2006]

Procedural Texture

• Simplest form: function evaluation– T(x,y) = ?

• Instead of accessing texture memory, directly compute the texture value

• Pro: saves memory, bus• Con: need the algorithm– and, need a shader, but normally would have that

anyway

Proceduralism vs Reuse

• Reuse: simple repetition of models, textures

• Proceduralism: new models, textures by rerunning algorithm with different inputs– trivially, different random seed

Sophisticated reuse

• Use small pieces – reuse not so obvious– "Lego blocks"

• Modular design: blocks are big (e.g., section of tunnel) – might be OK in industrial fiction

• "divine corpse" for monsters, architecture• Penrose tiles, Wang tiles for texture, terrain– Reuse with rotation, less apparent– city setting: regular layout

Texture Synthesis Primitives

• Building blocks for textures:– noise– Perlin noise– Voronoi cells– many others

• Rosalind Picard: "a society of models"

Texture Basis

• "basis functions" for texture• primitive functions used as foundation for specific

functions aimed at specific effects• Perlin noise: "the function that launched a thousand

textures"

Noise

• Simple and straightforward:– N(x,y) = random(range)

• Introduces much-needed randomness• But:– lacks coherence– cannot be sensibly subsampled, supersampled

Perlin Noise

• Ken Perlin, 1985

• random 4-vector at each node on an integer lattice:{a,b,c,d}[x][y][z]

Noise[x][y][z] = d[x][y][z] if x,y,z are integersotherwise, interpolate ax+d, by+d, cz+d using spline

2t^3 – 3t^2

DNoise

• Noise() is a scalar• Can get vector-valued function (for bump

mapping, say) by taking the gradient of Noise()

Multiresolution Noise

• Different signals at different scales• Fractals: clouds, mountains, coastlines

1/2 1/4 1/8 1/16 sum

Multiresolution Noise

• aka "turbulence"• FNoise(x,y,z) = Σ((2-i)*Noise(x*2i…))

• Extremely common formulation – so common that many mistake it for the basic noise primitive

Attributes of Perlin Noise

• Reproducible• Coherent• Continuous in first derivative• Arbitrary resolution

• Used as input to other functions

Perlin Marble

• texture = cos(x + a*Noise(x,y))– or, texture = cos(x + a*Turb(x,y))

• properly renormalized, of course!• purple/white color map• value of parameter a says how noisy the

marble is

Cellular Texture

• “Worley texture”, Worley 1996• Based on the Voronoi diagram: partition of

plane according to nearest point• Use nth-order distances (closest, second

closest…) as basis

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Combining distances

• Having normalized distances, can combine– say D1, D2, D3, D4

• Take (say) 2*D1 – D3• Linear transformation given by 4 coefficients:– C1D1 + C2D2 + C3D3 + C4D4

• manipulate coefficients to obtain effects