## Sunday, October 21, 2007

### Probabilistic reflection/refraction

In the response to the previous post, Thomas said he would choose probabilistically. If you are sending many rays per pixel I definitely agree this is the way to go. I believe that approach was first suggested in Kajiya's 86 path tracing paper.

color trace(ray r, depth d)
color c
if (r hits scene at point p)
c = direct_light(p)
if (depth < maxdepth)
if (random < ks)
c+= trace(reflected_ray)
else
c+= trace(refracted_ray)
else
c = background(r)
return c

Note that the weighting is implicit; if you trace reflected_ray a fraction ks of the time, that is just like tracing it every time and weighting it by ks. And as Thomas said, the best images come when you use Fresnel equations.

## Wednesday, October 17, 2007

### Ray tree pruning

A time honored way to speed up your glass is to do "ray tree pruning" and you should do it if you aren't already. The way Whitted originally implemented his paper was like this:

color trace(ray r, depth d)
color c
if (r hits scene at point p)
c = direct_light(p)
if (depth < maxdepth)
c += ks*trace(reflected_ray) + kt*trace(refracted_ray)
else
c = background(r)
return c

If you hit glass that will be two branches per recursion level. The first efficiency improvement would be to only send the rays if ks and kt are non-zero. But that would not help you for glass. Instead, you need to kill whole paths down the recursion tree once they are sufficiently attenuated. For example, if kt=0.05, then after 3 transmissions the coefficient is (0.05)^3 and can be ignored. To implement this, you need to change the call to include an attenuation argument:

color trace(ray r, depth d, float atten)