How to calculate both positive and negative angle between two lines?

Question

There is a very handy set of 2d geometry utilities here.

The angleBetweenLines has a problem, though. The result is always positive. I need to detect both positive and negative angles, so if one line is 15 degrees "above" or "below" the other line, the shape obviously looks different.

The configuration I have is that one line remains stationary, while the other line rotates, and I need to understand what direction it is rotating in, by comparing it with the stationary line.

EDIT: in response to swestrup's comment below, the situation is actually that I have a single line, and I record its starting position. The line then rotates from its starting position, and I need to calculate the angle from its starting position to current position. E.g if it has rotated clockwise, it is positive rotation; if counterclockwise, then negative. (Or vice versa.)

How to improve the algorithm so it returns the angle as both positive or negative depending on how the lines are positioned?

Answer 1

That function is working in RADS

There are 2pi RADS in a full circle (360 degrees)

Thus I believe the answear you are looking for is simply the returned value - 2pi

If you are asking to have that one function return both values at the same time, then you are asking to break the language, a function can only return a single value. You could pass it two pointers that it can use to set the value of so that the change can persist after the frunction ends and your program can continue to work. But not really a sensible way of solving this problem.

Edit

Just noticed that the function actually converts the Rads to Degrees as it returns the value. But the same principle will work.

Answer 2

One 'quick and dirty' method you can use is to introduce a third reference line R. So, given two lines A and B, calculate the angles between A and R and then B and R, and subtract them.

This does about twice as much calculation as is actually necessary, but is easy to explain and debug.

Answer 3

Here's the implementation of brainjam's suggestion. (It works with my constraints that the difference between the lines is guaranteed to be small enough that there's no need to normalize anything.)

CGFloat angleBetweenLinesInRad(CGPoint line1Start, CGPoint line1End, CGPoint line2Start, CGPoint line2End) {
    CGFloat a = line1End.x - line1Start.x;
    CGFloat b = line1End.y - line1Start.y;
    CGFloat c = line2End.x - line2Start.x;
    CGFloat d = line2End.y - line2Start.y;

    CGFloat atanA = atan2(a, b);
    CGFloat atanB = atan2(c, d);

    return atanA - atanB;
}

I like that it's concise. Would the vector version be more concise?