Relative cardinal direction of two coordinates

Question

Following enum is defined:

public enum Direction
{
    North,
    South,
    East,
    West,
    Northeast,
    Northwest,
    Southeast,
    Southwest,
    Undefined
}

Given two sets of coordinates in two-dimensional space, I'd like to determine the relative cardinal direction from Point 2 to 1.

Examples:

• P1(1,1) and P2(0,1) returns Direction.North as P2 is north of P1
• P1(1,1) and P2(5,4) returns Direction.Southeast
• P1(1,1) and P2(1,1) returns Direction.Undefined

My current approach involves a bunch of conditions, i.e.

if (P1.X == P2.X)
{
    // either North, South or Undefined
    if (P1.Y < P2.Y)
        return Direction.South;
    else if (P1.Y > P2.Y)
        return Direction.North,
    else
        return Direction.Undefined;
}
else if (P1.Y == P2.Y)
{
    ...
}
else 
{
    ...
}

I'm seeking a shorter and more elegant solution.

Answer 1

My 3 cents - i'm waiting for improvements

Here is the enum:

public enum Direction
{
    North = 0,
    South = 4,
    East = 6,
    West = 2,
    Northeast = 7,
    Northwest = 1,
    Southeast = 5,
    Southwest = 3,
    Undefined = -1
}

and the conversion goes as:

public static Direction GetDirection(Point p1, Point p2) {
    double angle = Math.Atan2(p2.Y - p1.Y, p2.X - p1.X);
    angle += Math.PI;
    angle /= Math.PI / 4;
    int halfQuarter = Convert.ToInt32(angle);
    halfQuarter %= 8;
    return (Direction)halfQuarter;
}

It does not return Direction.Undefined however, because

if y is 0 and x is 0, θ = 0.

(from https://msdn.microsoft.com/library/system.math.atan2(v=vs.110).aspx)