Question

I want to calculate the angle between two lines formed by three points(one of the points is the point of intersection of the two lines) using inverse cosine function as follows:

CGFloat a = initialPosition.x - origin.x;
CGFloat b = initialPosition.y - origin.y;
CGFloat c = currentPosition.x - origin.x;
CGFloat d = currentPosition.y - origin.y;
CGFloat angle = (180/M_PI) * acosf(((a*c) + (b*d)) / ((sqrt(a*a + b*b)) * (sqrt(c*c + d*d))));

Unfortunately, acosf returns a value between 0 and pi only. How do I find a value between 0 and 2*pi (going, say, in the anti-clockwise manner)?

Answer 1

i don’t know what language you are using, but typically there is an atan2 function that gives you a value from the full 360 degrees. in this case you need to use it twice and then add a little additional logic.

some pseudocode will help clear things up:

initialAngle = atan2(initialPosition.y - origin.y, initialPosition.x - origin.x)
currentAngle = atan2(currentPosition.y - origin.y, currentPosition.x - origin.x)
# angle is measured from x axis anti-clock, so lets find the value starting from
# initial and rotating anti-clock to current, as a positive number
# so we want current to be larger than initial
if (currentAngle < initialAngle) {currentAngle += 2 pi}
# and then we can subtract
return currentAngle - initialAngle

i know this isn’t using acos, but that is multi-valued so to do so ends up using lots of logic about signs of differences that is bug-prone. atan2 is what you want.