## 2010-09-02

### A personal annotations of Veach's thesis (17) pp.227-240

p.227 Probability density

When I calculate the probability density p(\overline{x}) of given path \overline{x}, density is

In p.228, the author said that it is also possible to directory compute the P. I thought this is just replace p with P and I fail to see how we could compute it. Here P is a density of samples, that I should decide it. This mean I could compute directory. For example, if I sample uniformly, then the density becomes uniform. In a sense, I need to decide it or if I choose a method, then it automatically chosen. Therefore, there is no more explanation here. But it is actually difficult part for me.

p.232 BSDF's value is less than infinity

BSDF is a sort of transfer function (signal processing sense), that is the ratio of input light and output light. Therefore, I thought why this can be infinity. I totally forgot this is a density function. In this case, total reflection gives you the Dirac delta, therefore, the value is infinite. There are some cases the value becomes more than 1. But in any cases, if we integrate in some domain, this should be equal or less than 1.

p.236 Scattering events at Psi_L and Psi_W

This is a cool idea. We consider the light source is a reflector that its light source is infinitely close. If we think as like this, every scene element can be a reflection surface. No need to think the light source is a special case. For example, a object emits light case is not the special case anymore.

One of the Feynman's books (I think it is Surely You're Joking, Mr. Feynman!) has an episode. Feynman tried to model an electron as self affecting particle. Since the center of the electron seems singular point of the electro magnetic field. He tried to get rid of this singularity. I think he wrote the idea doesn't work unfortunately, but, this Veach's idea just reminded me this story.

p.240 Chains

I think the chain here explained is
But he did not write this in his notation. I just wonder why he did not write that in this way. Or I might be wrong.

Acknowledgements
Thanks to Leo and Daniel to give me the answer regarding with my questions of these pages.