title: Formula to create simple MIDI velocity curves
body: <p>I'm trying to figure out a simple math formula that will allow me to apply various velocity curves to an incoming MIDI value. In the picture below, the starting x,y is (0,0) and ending x,y is (127,127). I'm trying to get a formula with a single variable that will allow me to produce simple expanded or contracted curves always bumping in the middle (by a degree of the variable). My input will be a value between 0 and 127, and my output will always be between 0 and 127. This seems like it should be easy, but my college calculus is escaping me at the moment.</p>
  
  <p><a href="https://i.stack.imgur.com/rzYQY.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/rzYQY.jpg" alt="enter image description here"></a></p>