Procedural Texturing
David S. Ebert
September 2000
Marble Vase by Ken Perlin, 1985
Traditional Texture Mapping (Ed
Catmull 1974) :
Use of scanned in photograph or pre-computed
information to "wrap" around an object to simulate greater complexity.
Advantages:
Less complex models
Easy to acquire photos ??
Disadvantages:
Storage
Aliase prone
Photos already have illumination calculations done
Mapping complex
Example
Procedural Texturing (Gardner 1984, Peachey, Perlin 1985)
Procedural Techniques:
Definition
-
use of code segments or algorithms to generate object
description, attribute, motion, etc.
Advantages:
-
detail on demand
-
flexibility
-
data amplification
-
parametric control
-
2D Procedural Textures:
-
space savings
-
adaptability to geometry
-
more efficient ?? -- Sometimes
-
Example 2D Procedural Texture:
Sample_Procedure(x,y,color)
{
static
int first=1;
color.r=color.g=color.b=0;
if(first)
{ first=0;
for (i=0; i < 20; i++)
{
center[i].x = drand48()*10;
center[i].y = drand48()*10;
radius[i] = drand48*.5; radius[i] *=radius[i];
color[i].r = drand48(); color[i].g=drand48();
color[i].b=drand48();
}
}
for (i=0;
i < 20; i++)
{
dist_sq = (center[i].x-x)*(center[i].x-x) +
(center[i].y-y)*(center[i].y-y)
if (dist_sq < radius[i])
color=color[i];
break;
}
}
Solid Texturing
-
3D texture space
-
Mapping is now simple affine transformation
-
Can use 3D scanned images (CT, MR, ...)
-- excessive memory cost
-
Appeared in 1985 by Peachey, Perlin; (also in 1984
by Gardner)
-
Object Carving
Applying texture function is like carving away the defining
space
-
Natural for object made from solid material
Examples:
-
Solid Texturing Procedures (Toolbox)
-
Primitives
-
trigonometric functions
-
noise
-
turbulence
-
bombing
-
bias/gain
-
cellular functions
-
...
Trigonometric Functions
example:
-
sin(y) -- horizontal stripes
- color.r = color.g =color.b = sin(pnt.y);
- sin(pnt.x) = vertical stripes
-
-
tan -- Can be used for wood
Vertical cylinder
- r1 = sqrt (u2 + w2
Add variation
- r2 = r1 + 2 sin(a*theta + v/b)
where
- theta = tan-1(u/w)
and v varies with height. Do mod on r2
to get cylinder colors. Could also do sin of r2, but
still too regular.
-
exponential -- More natural falloff than linear falloff
-
splines - smooth transitions, 2nd dreivative
continuity
-
power function
Stochastic Procedures
Noise
-
simulation of uncorrelated random noise
-
desired properties
-
statistical invariance under rotation
-
statistical invariance under translation
-
narrow bandpass limit in frequency to allows anti-aliasing
-
Perlin's Lattice Noise implementation
-
integer lattice w/ random values at each point
-
values not at lattice points are interpolated
-
replicate to fill 3 space
-
interpolation can be
-
Perlin's Gradient Noise
-
integer lattice w/ random unit vectors at each point
-
values not at lattice points are interpolated, using
gradients as spline coefficients
-
Less regularity artifacts
-
Example:
- J. P. Lewis gives better noise functions
- Peachey gives several implementation
-
- value noise
-
- gradient noise
-
- sparse convolution noise
-
- spectral synthesis (Fourier)
-
Scaling Noise Space - Change frequency of repetition of
noise lattice, can also change amplitude
Turbulence
-
produce 1/f frequency distribution
-
turbulence(pt) = noise(pt) + 1/2 noise(2*pt) + 1/4 noise(4*pt) +
....
Examples
value = (sin ( point.y + turbulence(point)) +1) *.5;
color = spline (white, blue, value);
A Simple example of adding noise for marble:
Wood - use above plus turbulence added to point
Some examples of using turbulence to create the
actual object geometry/density procedurally
Nice Java Applet by
Justin Legakis
Nice
Procedural Texture Page
Ken Perlin's
Hypertexture Page
Can Apply To Other Attributes
Bump Mapping - Texture Map the Normal
to the Surface
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