Calculate direction angle from two vectors?

Question

Say I have two 2D vectors, one for an objects current position and one for that objects previous position. How can I work out the angular direction of travel?

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Answer 1

Still not sure what you mean by rotation matrices, but this is a simple case of getting an azimuth from a direction vector.

The complicated answer:

Normally you should pack a few conversion/utility functions with your 2D vectors: one to convert from X,Y (carthesian) to Theta,R (polar coordinates). You should also support basic vector operations like addition, substraction and dot product. Your answer in this case would be:

 double azimuth  =  (P2 - P1).ToPolarCoordinate().Azimuth;

Where ToPolarCoordinate() and ToCarhtesianCoordinate() are two reciprocal functions switching from one type of vector to another.

The simple one:

 double azimuth = acos ((x2-x1)/sqrt((x2-x1) * (x2-x1) + (y2-y1) * (y2-y1));
 //then do a quadrant resolution based on the +/- sign of (y2-y1) and (x2-x1)
 if (x2-x1)>0 {
   if (y2-y1)<0 {  azimuth = Pi-azimuth; } //quadrant 2
 } else 
 { if (y2-y1)> 0 {  azimuth = 2*Pi-azimuth;} //quadrant 4
    else  { azimuth = Pi + azimuth;} //quadrant 3
 }