How to calculate the angle of a vector from the vertical?

Question

Im trying to find out the angle (in degrees) between two 2D vectors. I know I need to use trig but I\'m not too good with it. This is what I\'m trying to work out (the Y axi

Answer 1

It looks like Niall figured it out, but I'll finish my explanation, anyways. In addition to explaining why the solution works, my solution has two advantages:

• Potential division by zero within atan2() is avoided
• Return value is always positive in the range 0 to 360 degrees

atan2() returns the counter-clockwise angle relative to the positive X axis. Niall was looking for the clockwise angle relative to the positive Y axis (between the vector formed by the two points and the positve Y axis).

The following function is adapted from my asteroids game where I wanted to calculate the direction a ship/velocity vector was "pointing:"

// Calculate angle between vector from (x1,y1) to (x2,y2) & +Y axis in degrees.
// Essentially gives a compass reading, where N is 0 degrees and E is 90 degrees.

double bearing(double x1, double y1, double x2, double y2)
{
    // x and y args to atan2() swapped to rotate resulting angle 90 degrees
    // (Thus angle in respect to +Y axis instead of +X axis)
    double angle = Math.toDegrees(atan2(x1 - x2, y2 - y1));

    // Ensure result is in interval [0, 360)
    // Subtract because positive degree angles go clockwise
    return (360 - angle) %  360;
}