How to keep the sum of an Array with three or more values equal

Eluxiver

I have a bit of a math problem and I can't seem to find an easy solution.

I want to make a function that easily changes the other values in the array if one value of that array changes. (Mathematically something like this (X+Y+Z = 1) And I can think of two versions of this problem/function but I can't find a neat solution for any of them.

One solution is that if I change one value, all the other values have to change too so it doesn't exceed or go below 1 (for example I have (0.3, 0.3, 0.4) and I change the first value to 0.2 the difference gets split over the other two values resulting in (0.2, 0.35, 0.45).

Another solution could be that I specify which value is linked to another value (so only two values are linked, or more if I have more than three values in the array) (for example if I have (0.3, 0.3, 0.4) and I say that the first two values are "linked" , when I then change the first value to 0.2 I get (0.2, 0.4, 0.4).

This looks like a easy problem but I can't find a simple solution. I want to be able to change the size of the array later on without changing the programming.

Does anyone have an idea? Or a mathematical formula that solves this easily? What would be very neat is if I could specify the relation between different values in the array so if one changes I can give a percentage of how much the other values are linked and need to change (for example 0% is no link so no change, 100% is a 1on1 link so if one value changes the other changes equally)

This must be something simple but I can't seem to wrap my head around it. Thanks.

GoToLoop

My idea is to create a class to tightly control the add() & sub() processes! Here's my draft: :>

/** 
 * XYZequals1 (v1.4)
 * by GoToLoop (2014/Jan)
 *
 * forum.processing.org/two/discussion/2280/
 * how-to-keep-the-sum-of-an-array-with-three-or-more-values-equal
 */

class XYZ {
  static final int MAX = 1;
  //static final int MIN = -MAX;
  static final int MIN = 0;

  final float[] xyz = {
    .3, .3, .4
  };

  XYZ(float x, float y, float z) {
    x = constrain(x, MIN, MAX);
    y = constrain(y, MIN, MAX);
    z = constrain(z, MIN, MAX);

    if (x + y + z != 1)  return;

    xyz[0] = x;
    xyz[1] = y;
    xyz[2] = z;
  }

  void add1Tenth(int idx) {
    if (idx < 0 || idx > 2 || xyz[idx] + .1 > MAX)  return;
    for (int i = 0; i != 3; xyz[i] += i++ == idx? .1 : -.05);
  }

  void sub1Tenth(int idx) {
    if (idx < 0 || idx > 2 || xyz[idx] - .1 < MIN)  return;
    for (int i = 0; i != 3; xyz[i] += i++ == idx? -.1 : .05);
  }

  float sum() {
    return xyz[0] + xyz[1] + xyz[2];
  }

  String toString() {
    return "x=" + xyz[0] + " + y=" + xyz[1]
      + " + z=" + xyz[2] + " = " + sum();
  }
}

Eluxiver

Thanks, I definitely like the idea for an add and subtracts method, I will work on it a bit more with your code as a base to fit it in my program.