Dr. Matthew O. Ward
Computer Science Department
Random Numbers in Graphics
Just Call random()
Fields of Random Noise
This gives smooth transitions between nodes, but only 0th order continuity at nodes.
Easy to extend to arbitrary dimensions.
Polynomial Fits are Better
Here is an example of a random field using Catmull-Rom splines for interpolation.
Noise is Good, Turbulence is Better
We can impose self-similarity on noise to add scale-invariance. The turbulence at a point is created by summing the noise at that point with scaled down noise values at other points.
where k is the smallest integer for which is greater than the size of a pixel in real coordinates. This is very similar to fractal surface generation, giving a visual impression of brownian motion.
Here is an example of a turbulent field using the random field as a basis. I show it using grey scale and a random color map.
Marble Texture: Add turbulence to sine wave, use a curve through color space instead of a ramp
Here is an example of a sine wave with added turbulence. I show it using grey scale and a random color map.
Tree Bark: Add turbulence to a sawtooth wave and use to bump map surface
Stars: Intensity of points based on distance to the center. Add turbulence to this distance. Here is an example of a star with added turbulence.
Flames: Compute intensity of point based on distance from center in x. Scale it based on distance in y. Add turbulence. Use 3-D turbulence to animate. Here is an example of a flame with added turbulence.