Integrating multiple raymarching samples

Question

Let's say I'm using raymarching to render a field function. (This on the CPU, not the GPU.) I have an algorithm like this crudely-written pseudocode:

pixelColour = arbitrary;
pixelTransmittance = 1.0;
t = 0;
while (t < max_view_distance) {
  point = rayStart + t*rayDirection;
  emission, opacity = sampleFieldAt(point);
  pixelColour, pixelTransmittance =
      integrate(pixelColour, pixelTransmittance, emission, absorption);
  t = t * stepFactor;
}
return pixelColour;

The logic is all really simple... but how does integrate() work?

Each sample actually represents a volume in my field, not a point, even though the sample is taken at a point; therefore the effect on the final pixel colour will vary according to the size of the volume.

I don't know how to do this. I've had a look around, but while I've found lots of code which does it (usually on Shadertoy), it all does it differently and I can't find any explanations of why. How does this work, and more importantly, what magic search terms will let me look it up on Google?

...after spending quite some time doing research on the web, I got really excited for a moment when I found what looked like a really promising article on the subject. Turned out it was this question. Bah. — David Given, May 27 '14 at 21:29

score 0 · Answer 1 · answered May 27 '14 at 23:10

It's the Beer-Lambert law, which governs extinction through participating homogenous media. No wonder I was unable to find any keywords which worked.

There's a good writeup here, which tells me almost everything I need to know, although it does rather gloss over the calculation of the phase functions. But at least now I know what to read up on.

Integrating multiple raymarching samples

1 Answers1