I began working on this code with the purpose of changing the speed of a motor or the brightness of LEDs exponentially.
The reason of wanting to change the PWM exponentially is due to using a keyboard to control an Arduino. With a keyboard there could be only be two states (on or off) when pressing keys. However, I wanted to change the PWM as time passes while the key is pressed. A linear change of PWM is good enough for changing the speed of a motor. Though, it is not enough for changing the brightness of the LEDs; it "does not feel right." I think that exponential change in PWM would better suited to change the brightness of LEDs since often I want to make small changes in the brightness of the LED if the key is pressed momentarily. But if the is key pressed longer I would like increase the PWM faster. That is, small rate of change at first and large rate of change as time passes.
So I though about a g 6BC4 raph that looked more or less like this:
I used targets and ticks as means to achieve the desired exponential change in PWM. When a key is pressed a target is set. For instance, if key Q is set to be the key that increases a LED's PWM then while this key is pressed, a target of 255 is set. Once there is a target different to the current PWM, a counter I call tick will be updated every certain amount of time. The PWM of the motor increases towards target every time the counter tick updates.
Using this method the graph of PWM vs time would look like this:
a*e^(b*x) + c
where a, b, c are constants used to change the graph of the exponential change in PWM.