My last post of this was all over the place so I am making a new one to explain this a little more clearly. With the decay and the inputs of distance from spacing weight, you can transform aim strain into a differential equation (you can do this with speed as well but I am focusing on aim). The input is the sum of distance over time multiplied by the dirac delta shifted to the time of the object for all the objects in the map. For sliders, I am adding a boxcar function multiplied by the slider velocity in pixels per milliseconds to the input function. I then calculate the differential equation with the new input function. For ease of calculation, I convoluded the new input function with the decay function already present (exponential).
The homogenous solution is just decay from the starting value. The particular solution is composed of two parts. One is the one that was also present in the last one, the one due to the distance between the two circles. The second part is the result of how much strain is added to the function due to the slider. I then took the slider portion function, evaluated it at the time of the end of the slider and added it to the strain function at the time of the end of the slider.
Easy Peasy
The homogenous solution is just decay from the starting value. The particular solution is composed of two parts. One is the one that was also present in the last one, the one due to the distance between the two circles. The second part is the result of how much strain is added to the function due to the slider. I then took the slider portion function, evaluated it at the time of the end of the slider and added it to the strain function at the time of the end of the slider.
Easy Peasy