# Lecture 014

Why is mirrow flip left right but not up down?

Retro---.... refletion

// QUESTION: BRDF is per wavelengh right?

Light-camera duality. If you trace ray from eye to scene, it is the same as trace ray from scene to eye. Therefore, if you drop a water droplet into a pool surrounded by wave sensors, you can reconstruct the shape of droplet by calculation or by replay the wave in reverse direction.

Sometimes, we bake the $\frac{1}{\pi}$ is baked into the albedo texture, and sometinmes it is not. If we need to check whether is bakes, we can check whether the maximum is $\frac{1}{\pi}$ or $1$.

Using BRDF, we are assuming if we look at from anywhere along the line, the color is the same. This is assuming we have uniform distribution of the phase. However, layser shoots out Coherent Light, and therefore you can move your head front to back to observe different intensity.

\eta_i \sin(\theta_i) = \eta_t\sin(\theta_t)
\frac{\eta_i\sin(\theta_i)}{\eta_t} = \sin(\theta_t)
\frac{\eta_i\sin(\theta_i)}{\eta_t}\overset{?}{\geq} 1
F_r = \frac{1}{2}(r^2_{\parallel}+r^2_{\perp})

The parallel and perpendicular terms are given by:

r_{\parallel} = \frac{\eta_t\cos(\theta_i) - \eta_i\cos(\theta_t)}{\eta_t\cos(\theta_i)+\eta_i\cos(\theta_t)}
r_{\perp} = \frac{\eta_i\cos(\theta_i) - \eta_t\cos(\theta_t)}{\eta_i\cos(\theta_i)+\eta_t\cos(\theta_t)}

Therefore, for a dielectric material, the fraction of reflected light will be given by $F_r$, and the amount of transmitted light will be given by $1-F_r$.

Notes about atan2(y, x): Observe that normal atan(y/x) function cannot distinguish between 1st/3rd quadrant and 2nd/4th quadrant. This is because the atan() function only knows about the combined sign of y/x not the sign of x and sign of y. atan2(y, x) solves the issue by allowing you to provide x, y separately (not merged together), so that the information of the sign is kept. Normal atan() function is ranged from $-90^\circ \to 90^\circ$ while atan2() is ranged from $-180^\circ \to 180^\circ$.

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