Procedural Texture Synthesis

1. Procedural Texture Synthesis Patterns from Algorithms

2. 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.

3. [World of Warcraft, 2004-2010]

4. [Oblivion, 2006]

5. 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

6. Proceduralismvs Reuse • Reuse: simple repetition of models, textures • Proceduralism: new models, textures by rerunning algorithm with different inputs • trivially, different random seed

7. 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

11. Texture Synthesis Primitives • Building blocks for textures: • noise • Perlin noise • Voronoi cells • many others • Rosalind Picard: "a society of models"

12. 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"

13. Noise • Simple and straightforward: • N(x,y) = random(range) • Introduces much-needed randomness • But: • lacks coherence • cannot be sensibly subsampled, supersampled

15. 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 integers otherwise, interpolate ax+d, by+d, cz+d using spline 2t^3 – 3t^2

17. DNoise • Noise() is a scalar • Can get vector-valued function (for bump mapping, say) by taking the gradient of Noise()

18. 1/2 1/4 1/8 1/16 Multiresolution Noise • Different signals at different scales • Fractals: clouds, mountains, coastlines sum

19. 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

21. Attributes of Perlin Noise • Reproducible • Coherent • Continuous in first derivative • Arbitrary resolution • Used as input to other functions

23. 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

28. 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

31. v1 v3 v2 v4

32. v1 v3 v2 v4

33. 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