Vtyjkyuk

I am search a math formula to solve this problem, preferably in C#

• A object should be to near smooth an other object and stop if reached the position of the destination object.


• The destination object can change the position before the second object reach and yet the moving is smooting again if possible.


• I need a min and max acceleration config

code example without smoothing

var x1 = 100;
var x2 = 50;

while (x1 >= x2)

 x2++;

update example base on the answer of vadim123

var minimum = 0.5;
var maximum = 5.0;
var frac = 1 / 20.0;

var x1 = 100.0;
var x2 = 50.0;

while (x1 >= x2)

 x2 = x2 + Math.Min(maximum, Math.Max(minimum, (x1 - x2) * frac));

I don't know C#, but here is some pseudocode. Let $MIN_V$ and $MAX_V$ be the minimum and maximum velocity, respectively. Let $FRAC$ be a smoothing coefficient, between $0$ and $1$, to be chosen for desired level of smoothing.

$$x2 = x2 + min(MAX_V, max(MIN_V, (x1-x2)*FRAC ))$$

Explanation: We will add $(x1-x2)*FRAC$ to $x1$ at each time step; if $FRAC=1/3$, then we will close one third of the distance at each time step. However, this is clipped to be within the max and min velocity. Without clipping, we go too fast at the start, and very very slow at the end (never arriving).