Smallest turning angle

Question

I know it's probably been answered, but my google-fu is failing me today...

I have two 2D points; A and B
A has a known Heading. The X and Y coordinates are always positive, if that helps at all.

What I would like to do is figure out the angle that A needs to turn in order for the Heading to be pointing toward B. Once I know the turn angle, figuring out if it's the smallest (i.e. is turning left quicker than turning right, or vice versa) is easy.

Are these points in the plane? Or in 3-space? Are they given in terms of Cartesian coordinates? — Nick Matteo, Sep 24 '14 at 01:43

score 1 · Answer 1 · answered Sep 24 '14 at 01:54

If your points are in the plane, and given by Cartesian coordinates $A = (x_1,y_1)$, $B = (x_2,y_2)$, then the heading from $A$ to $B$ is $\tan^{-1}(\frac{y_2 - y_1}{x_2 - x_1})$. Unfortunately, this does a bad job of distinguishing directions when the differences aren't positive. If you have access to atan2, a function provided by many programming languages, it provides the correct angle in all cases via $\operatorname{atan2}(y_2 - y_1,x_2 - x_1)$.

If $A$ already has heading $\theta$, relative to the positive $x$-direction, then it needs to turn $\operatorname{atan2}(y_2 - y_1,x_2 - x_1) - \theta$.

Smallest turning angle

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