Determine If Two Points Are Near

Question

I have the following:

bool AreNear(Point Old, Point Current)
{
    int x1 = Convert.ToInt32(Old.X);
    int x2 = Convert.ToInt32(Current.X);
    int y1 = Convert.ToInt32(Old.Y);
    int y2 = Convert.ToInt32(Current.Y);
    if (x1 == x2) {
        if (y1 == y2) {
            return true;
        }
    }
    return false;
}

I want to return true in the function if the current point is in 25 pixels radius of the old point. Can anyone tell me how to do that?

Answer 1

You can use the Pythagorean formula to calculate the distance between two points. In C#:

var d = Math.Sqrt(Math.Pow(x1 - x2, 2) + Math.Pow(y1 - y2, 2)) 

Why does this work? Have a look at the following diagram and remember that a^2 + b^2 = c^2 holds for right triangles:

Answer 2

Just calculate the square of the distance using Pythagoras' theorem, and compare to the square of the radius:

bool ComparePoints(Point Old, Point Current)
{
    int x1 = Convert.ToInt32(Old.X);
    int x2 = Convert.ToInt32(Current.X);
    int y1 = Convert.ToInt32(Old.Y);
    int y2 = Convert.ToInt32(Current.Y);
    int dx = x1 - x2;
    int dy = y1 - y2;
    return (dx*dx + dy*dy) < 25*25;
}