The Cheat Sheet

Graphics

FoV Conversions

$$f_x=2\;\arctan\left(\tan\left(\frac{1}{2}\frac{w}{h}f_y\right)\right)$$
$$f_y=2\;\arctan\left(\tan\left(\frac{1}{2}\frac{h}{w}f_x\right)\right)$$

Audio

Gain and Attenuation

Given $g$ as linear gain in the range $(0,1]$ and $a$ as attenuation in $dB$. Keep in mind that $\log _{10}(g)$ approaches negative infinity as $g$ approaches zero – avoid computing the log for small gain values and just return something like $-96dB$ (silence). As a useful reference points, $a=-6dB$ for $g=0.5$, roughly.

$$a=20\;\log _{10}(g)$$
$$g=10^{a/20}$$

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