Book 3.7.1: No explanation given for the formulas

[dimitry-ishenko]

In chapter 7.1 we are told:

Given a directional PDF on the sphere (where $p(\omega) = f(\theta)$ ), the one dimensional PDFs on $\theta$ and $\phi$ are:

$$ a(\phi) = \frac{1}{2\pi} $$

$$ b(\theta) = 2\pi f(\theta)\sin(\theta) $$

But there is no explanation, how we've arrived at these formulas...

[hollasch]

I'll add this to the v4.0.0 milestone, but we'll probably run out of time.

[dimitry-ishenko]

While it's a bit of a show stopper for me (I like to understand everything I do), most people will probably just skimp over it. I just got back from vacation and will take another stab at it when I have a moment.