2D coordinate normalization

Question

I need to implement a function which normalizes coordinates. I define normalize as (please suggest a better term if Im wrong):

Mapping entries of a data set from their natural range to values between 0 and 1.

Now this was easy in one dimension:

    static List<float> Normalize(float[] nums)
    {
        float max = Max(nums);
        float min = Min(nums);
        float delta = max - min;

        List<float> li = new List<float>();
        foreach (float i in nums)
        {
            li.Add((i - min) / delta);
        }
        return li;
    }

I need a 2D version as well and that one has to keep the aspect ratio intact. But Im having some troubles figuring out the math.

Although the code posted is in C# the answers need not to be.

Thanks in advance. :)

Answer 1

It seems you want each vector (1D, 2D or ND) to have length <= 1.
If that's the only requirement, you can just divide each vector by the length of the longest one.

double max = maximum (|vector| for each vector in 'data');
foreach (Vector v : data) {
    li.add(v / max);
}

That will make the longest vector in result list to have length 1.

But this won't be equivalent of your current code for 1-dimensional case, as you can't find minimum or maximum in a set of points on the plane. Thus, no delta.