color = white * Noise(point)
	

	function boring_marble(point)
		x = point[1]
		return marble_color(sin(x))
	

	function marble(point)
		x = point[1] + turbulence(point)
		return marble_color(sin(x))
	

• This used for his marble vase

A Cellular Texture Basis Function
Steven Worley
Siggraph 1996

• Similar to Perlin, except adds new functions:
  • distributes pseudo-random points through space
  • F₁ = distance to closest point
    • slope discontinuity equivalent to Voronoi diagram
  • F₂ = distance to 2nd closest point
  • F₃ = distance to 3rd closest ...
• can do polka-dots, flagstone ....
• fractal version (multiple levels of resolution, like Perlin) can have detail at a wide range of scales

Pyramid-Based Texture Analysis/Synthesis
David Heeger & James Bergen
Siggraph 1995

• mainly 2D, non-directional 3D
• Builds statistics about a given texture (often scanned)
• Manipulates noise image to have same statistics
  • Histograms of frequency content for each direction, frequency band
• Why create new texture?
  • Can be arbitrarily large
  • Can be seamlessly tileable
  • Works well for noisy textures with non-distinguishable features.
  • Fails for distinguishable features, and correlation of high frequency over long distances, such as edges
• Steerable filters
  • A convolution kernel that picks up a certain frequency band in a certain direction
• Analyzing phase
  • We filter original image with a bank of these steerable filters, getting a pyramid of images of each frequency/direction
  • We build histograms of pixel intensities in each image
• Histogram-matching phase
  • We filter noise image with the same bank of these steerable filters, getting a pyramid of images of each frequency/direction
  • We build histograms of pixel intensities in each image
  • Compute a scaling function of pixel values for each of the images in the noise pyramid, so that it has the same histogram as corresponding source pyramid image
    
  • Collapse noise pyramid
    • filters not entirely indepent
    • This alters histograms
  • repeat Analyze-Match about 5 times

Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion
Greg Turk
Siggraph 1991

• Simulates the interaction of 2 (or more) chemicals
  They interact until they form a stable state
• Similar to how the embryo of a worm forms segments
• da/dt = F(a,b) + D_a * Grad(a)^2
• db/dt = G(a,b) + D_b * Grad(b)^2
  • G(a,b) is the reaction between chemicals a, b
  • D_b is the diffusion constant for b
  • Grad(b)^2 is local gradient of b's concentration, which affects its diffusion speed
• Map chemical concentrations to a texture (color, bump, etc)

Flow and Changes in Appearance
Julie Dorsey et. al.
Siggraph 1996

• 2D
• Simulate water flow as a particle system
  • factors: gravity, friction, wind, roughness ...
  • parameters:
    • rendering: diffuse color, specular color, shininess
    • simulation: roughness, absorption, absorptivity
    • deposits: diffuse color, adhesion rate, solubility rate
• Rendering: Deposits alpha blended over surface

Cellular Texture Generation
Kurt W Fleischer et. al.
Siggraph 1995

• 2D
• Cellular particle simulator
  • Uses differential equations to place the cells
  • Constraints specified as energy functions to be minimized, e.g.:
    • Go to the object surface
    • Die if too far from surface
    • Align an axis with a vector field
    • Adhere to other cells
    • Divide until surface is covered
    • Set size relative to surface feature size
    • Reaction-diffusion
• Parameterized particle-to-geometry converter
  • Converts cell parameters to tiny textured polygons
• Rendered -- lots of polygons