Noise, Turbulence, and Texture

Dr. Matthew O. Ward
Computer Science Department
WPI

Random Numbers in Graphics

• Random variation adds realism

• Random numbers can be used on all graphical attributes (location, color, normals, transparency, motion)

• Many natural phenomena are composed of a combination of structure and randomness

Just Call random()

• We can simply call random() with an appropriate value range and distribution

• This doesn't provide any continuity between adjacent points

• Can lead to "bubbling" effect when animated

Fields of Random Noise

• Generate a fixed grid of random numbers (1-D, 2-D, ....) of size N in each dimension

• Assuming a single continuous dimension in data space with variable T

  

  

  

• noise(T) is influenced by noise() and noise()

Linear Interpolation

This gives smooth transitions between nodes, but only 0th order continuity at nodes.

Easy to extend to arbitrary dimensions.

Polynomial Fits are Better

• Can fit quadratic or cubic curves to fill in between nodes (treat random number as a dimension)
• Can use nodes as control points for splines
• Can assign gradients at nodes and use Hermite curves

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.

Using Turbulence

1. Start with a simple regular structure (e.g. a curve)

2. Impose turbulence on values

   

   or

3. Need to modify range of turbulence to fit structure

4. Need to play with degree and scale of turbulence

Applications

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.

Conclusions

• Lots of interesting effects can be gained by adding turbulence

• Need to play with degree and scale to get most realistic images

• Ties together a lot of topics in graphics (fractals, texture, color, curves)