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10. A Sample Material

In this chapter, we will implement a sample Material. This Material creates the effect of patchy fog by adding together three octaves of Perlin noise, and using the result to adjust the transparency. It includes a number of adjustable parameters: the color and thickness of the fog, how strongly it scatters light, and whether it casts shadows.

The full source code is found in PatchyFog.java. Here is the getMaterialSpec() method:

public void getMaterialSpec(MaterialSpec spec, double x, double y, double z, double xsize, double ysize, double zsize, double t)
{
  double size = 1.0, scale = 1.0;
  float d = 0.0f;

  for (int i = 0; i < 3 && xsize < size && ysize < size && zsize < size; i++)
    {
      d += (float) (size*Noise.value(x*scale+123.456, y*scale+123.456, z*scale+123.456));
      size *= 0.5;
      scale *= 2.0;
    }
  d = 0.5f*d + 1.0f - thickness;
  if (d > 1.0f)
    d = 1.0f;
  else if (d < 0.0f)
    d = 0.0f;
  spec.transparency.setRGB(d, d, d);
  spec.color.copy(color);
  if (scattering > 0.0f)
    {
      d = scattering*(1.0f-d);
      spec.scattering.setRGB(d, d, d);
      spec.eccentricity = 0.0;
    }
}

There are a number of important things to notice about this method:

Each octave of noise has half the amplitude and twice the frequency of the previous one. This is a fairly common arrangement, but certainly not the only possible one. Other ratios will give different characters to the fog.
Notice that we add 123.456 to each coordinate. This has the effect of offsetting each octave of noise by a different amount. This is critical, since Perlin noise is equal to zero whenever x, y, and z are all integers. Without this offset, the zeros from different octaves would coincide and there would be a regular lattice of zeros in the summed noise function. There are other ways of accomplishing this, such as multiplying the frequency by something slightly different from 2, or applying a different rotation to each noise octave.
We use a very simple form of antialiasing: we simply omit any octaves whose variation is on a scale shorter than the maximum of xsize, ysize, and zsize. Obviously, there are more sophisticated things we could do.
The line
```
d = 0.5f*d + 1.0f - thickness;
```
is somewhat arbitrary. We want thickness values in the range [0, 1] to cover the range of useful materials, from very thin and wispy to almost totally opaque, and this function is empirically found to give good results.
Notice that if scattering = 0, we do not bother setting the scattering color or eccentricity. This is because the isScattering() method is implemented as follows:
```
public boolean isScattering()
{
  return (scattering > 0.0f);
}
```
If scattering = 0, then isScattering returns false and the renderer ignores the scattering color.

Here is what the PatchyFog Material looks like when rendered:

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