The Ffmpeg afade filter is great but its documentation can be a little opaque if you have trouble figuring what a 'double-exponential sigmoid' curve is. This cheat sheet is here to help.
All curves were drawn in OS X's Grapher.app, with equations ported straight from afade's code. The Grapher file is included in repo for reference.
| afade argument | Meaning | Curve |
|---|---|---|
| tri | triangular, linear slope (default) |  |
| qsin | quarter of sine wave |  |
| hsin | half of sine wave |  |
| esin | exponential sine wave |  |
| log | logarithmic |  |
| ipar | inverted parabola |  |
| qua | quadratic |  |
| cub | cubic |  |
| squ | square root |  |
| cbr | cubic root |  |
| par | parabola |  |
| exp | exponential |  |
| iqsin | inverted quarter of sine wave |  |
| ihsin | inverted half of sine wave |  |
| dese | double-exponential seat |  |
| desi | double-exponential sigmoid |  |
| losi | logistic sigmoid |  |