I'm trying to get a slow in, slow out animation.  The below example code works, but I'd like to get something that is a little slower on the in and out, while maintaining a quick middle.  Something like the Cubic in/out easing on the Ani library.  Any suggestions?

1. float movementpos = 0;
2. float startx = 200;
3. float starty = 200;
4. float x = 200;
5. float y = 200;
6. float endx, endy;
7. boolean startmovement;
8. void setup() {
9.   size(400, 400);
10.   smooth();
11. }
12. void draw() {
13.   background(0);
14.   if (startmovement) {
15.     moveme();
16.   }
17.   ellipse(x, y, 20, 20);
18. }
19. void moveme() {
20.   float movepos =  (cos(movementpos)-1)/-2;
21.   x = lerp(startx, endx, movepos);
22.   y = lerp(starty, endy, movepos);
23.   movementpos += (TWO_PI/100.0);
24.   if (degrees(movementpos) > 180) {
25.     x = endx;
26.     y = endy;
27.     startx = endx;
28.     starty = endy;
29.     startmovement = false;
30.   }
31. }
32. void mouseClicked() {
33.   startx = x;
      starty = y;
    
34.   endx = mouseX;
35.   endy = mouseY;
36.   movementpos = 0;
37.   startmovement = true;
38. }