Not seeing any vectors in your code. Used pixels instead...

Adapted Code

1. int numWater = 60000;
2. color bg = color(0);
3. color water = color(0,0,240);
4. color shape = color(255);
5.  
6. void setup() {
7.   size(800, 800);
8.   smooth();
9. }
10.  
11. void draw() {
12.   background(bg);
13.   translate(width/2, height/2);
14.   rotate(radians(frameCount/2));
15.  
16.   noStroke();
17.   fill(shape);
18.   beginShape();
19.   vertex( -150, -150 );
20.   vertex( -150, 150 );
21.   vertex( 150, 150 );
22.   vertex( 150, -150 );
23.   endShape();
24.  
25.   int waterFilled = 0;
26.   loadPixels();
27.   for (int i=pixels.length-1; i!=0; i--) {
28.     color c = pixels[i];
29.     if (c != bg && waterFilled < numWater) {
30.       pixels[i] = water;
31.       waterFilled++;
32.     }
33.   }
34.   updatePixels();
35. }

I thought that this could be resolve with vectors.
I'm trying to avoid to use pixel method because it drastically slow down the framerate.
I need this sketch in OPENGL or GLConstants.GLGRAPHICS mode with 10 rotating rectangles so if it possible with vectors that would be nice..
Stroke around a polygon produce unattractive results when strokeWeight is set in OPENGL mode.
How to avoid this jaggy edges?

The underlying idea is the same with pixels as it is with vectors, namely you have a fixed total area (amount of water). If you want to do it mathematically, you have as a constant the area of the polygon between the four water points. Furthermore you know the bottom two points of this water polygon are equal to the lowest two points of the rectangle. You know the top two points are of equal y and lie on the respective side-edges of the rectangle. So that's a lot of information. The only thing you need to find is which are the two lowest points and then the x and y position of both top points so that the area of the polygon is equal to the target area (amount of water). What may complicate this a bit is that you're using rotate and thus aren't actually changing the position of the vertices. But indeed vectors may come in handy, because if you create a vector from the rotation angle, perhaps it's easier to find the two bottom points. On the web you can find formulas to get the area of the polygon. Once you get those things it may fall into place...