Distance between vectors

This is the second installment of “stuff I wrote before but I really want to have on my own website”. I wrote this in 2020 and I still find it useful to refresh my memory every now and then.

I’m no math man, so don’t @ me. Unity has some cool methods that perform basic operations, but from time to time I want to understand what it actually does. This is one such example.

To find the distance between two vectors you need the following formula:

√((vx-kx)²+(vy-ky)²+(vz-kz)²)

Let’s break it down using an example where we have two vectors v and k.

v = (0, 0, 0) and k = (3, 4, 0)

Giving us:

• √((0–3)²+(0–4)²+(0–0)²)
• √((–3)²+(–4)²+(0)²)
• √(9+16+0)
• √25

Distance = 5

Sooo, code?

Sure. Here’s how you could implement your very own distance function:

public class BigMathMan
{
    public float Square(float value)
    {
        return value * value;
    }

    public float Distance(Vector3 from, Vector3 to)
    {
        return Mathf.Sqrt(
            Square(from.x - to.x) +
            Square(from.y - to.y) +
            Square(from.z - to.z)
        );
    }
}

Or if you’re using Unity just use Vector3.Distance() I guess. But now you know!