Avoid floating-point precision error in algorithm

Question

In my 2D physics simulation (Java) I calculate the center of a convex polygon as follows, where the parameter area is the enclosed area of the polygon calculated before.

private Vector2d calculateCenterOfMass(double area) {
    Vector2d center = new Vector2d(0, 0);

    for (int i = 0; i < vertices.length; i++) {
        int j = (i + 1) % vertices.length;
        double factor = (vertices[i].x * vertices[j].y
                       - vertices[j].x * vertices[i].y);
        center.x += (vertices[i].x + vertices[j].x) * factor;
        center.y += (vertices[i].y + vertices[j].y) * factor;
    }
    center.scale(1 / (area * 6));

    return center;
}

I further have a polygon with the following points I use the function to calculate the center of mass of:

Vector2d [x=325.20399446366355, y=400.0, length=515.5168649182318]
Vector2d [x=375.20399446366355, y=400.0, length=548.4323453822622]
Vector2d [x=375.20399446366355, y=450.0, length=585.8993407245727]
Vector2d [x=325.20399446366355, y=450.0, length=555.2095442399406]

As you can see just by looking at the y values the center must be at y=425.0. Due to floating point magic the y value becomes 425.00000000000017 instead. The area given as parameter has the exact value 2500.0.

How can I avoid this and get my expected 425.0?

You should read What Every Computer Scientist Should Know About Floating-Point Arithmetic — hivert
– hivert, Commented Mar 4, 2014 at 9:29
If you don't need that much precision you can just round the number to, say, 2 decimal places... — assylias
– assylias, Commented Mar 4, 2014 at 9:41

Manuel · Accepted Answer · 2014-03-04 09:31:29Z

3

BigDecimal could help, but I would suggest reading the whole answer.

Floating point errors are 'normal' in a sense, that you cannot store every floating point number exact within a variable. There are many resources out there how to deal with this problem, a few links here:

If you do not know what the actual problem is check this out.
What Every Computer Scientist Should Know About Floating-Poit Arithmetic
IEEE floating point
To give you an idead how to work: Quantity Pattern

answered Mar 4, 2014 at 9:31

Manuel

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1 Comment

Sebastian Barth Over a year ago

Your links really helped to understand the problem. So you will get the mark! I end up with a cast to float and back to double. That rounds my numbers in respect to the magnitude of the value with float precision. Do you have any idea how I can reach a higher precision (float < X < double) since float is still very inaccurate.

Gordon Mohrin · Accepted Answer · 2014-03-04 15:38:13Z

1

Use Double to calculate and Long to store.

answered Mar 4, 2014 at 15:38

Gordon Mohrin

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