PROCEDURAL TEXTURES

SOLID TEXTURES
-- [Peachey'85], [Perlin'85], [Perlin'89]
-- Some visual objects have no obvious surfaces!!
-- We cannot scan 3-D textures in!
-- These are difficult to generate in general.
-- Even if we could, it is expensive to store them.
-- Achievable effects: marble, hair, fur, fire, glass, fluid flow, erosion, etc.

HOW TO CREATE WOOD
-- Create a 1-Dim texture

GLfloat tex[s] = { 1.0, 1.0, 0.0, 0.0, 0.0, 0.0};

-- Create a 2-Dim texture

Tex(s,t) = tex( \sqrt{s^2 + t^2});

-- Create a 3-Dim texture

TEX(s,t,r) = Tex(s,t);

We can generate a 2-dimensional texture map from TEX(s,t,r), to be used in OpenGL functions.
-- We should allow ourselves some arbitrary transformation of the (s,t,r) parameters.

MORE REALISM:

Tex(s,t) = tex(     \sqrt{s^2 + t^2} +     d_1 \sin (c_1 \arctan(s/t)) +     d_2 \sin (c_2 \arctan(s/t)) )

where c_1 << c_2, and d_i are small.

TEX(s,t,r) = Tex(s + e_1 \sin(f_1 r), t + e_2 \sin( f_2 r + g) )

where e_i, f_i are small, and g arbitrary.

SOLID NOISE
-- DESIRED PROPERTIES of NOISE(s,t,r)

1. Statistical invariance under rigid transformation
   (-- so appearance is invariant under motions)
2. Narrow bandpass limit
   (-- so we can sample the noise function without alias effects)

TURBULENCE
-- This is the basis for many other effects
-- E.g., we can add noise to TEX(s,t,r).
-- An implementation of Perlin's turbulence
-- The implementation computes, for a position p in Euclidean space (of any dimension):

turbulence(p) = \sum_{i=0}^k | noise(2^i. p) / 2^i |.

-- Note: the term noise(2p)/2 is varying twice as fast as noise(p) but has half the amplitude. This is typical of fractal-like objects.