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Subject: Re: Angle between two vectors
Date: Wed, 12 Oct 2011 18:54:26 +0000 (UTC)
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"Roger Stafford" wrote in message <fjm4u4$i8o$1@fred.mathworks.com>...
> "salih tuna" <salihtuna@gmail.com> wrote in message <fjlrpl$gii
> $1@fred.mathworks.com>...
> > Hi,
> > thanks a lot for your reply. yes they are in 2d, sorry i
> > forgot to mention.
> > i tried to apply the formula but i am getting wrong result.
> > for example i want to calculate the angle between a = [1 1]
> > and b = [0 -1] which is 225 degrees. with this formulae i
> > got 243.4. i couldn't see where i am doing the mistake.
> > thanks a lot in advance
> > salih
> > 
> > "Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid>
> > wrote in message <fjk0tg$jli$1@fred.mathworks.com>...
> > >  angle = mod(atan2(y2-y1,x2-x1),2*pi); % Range: 0 to 2*pi
> --------
>   I certainly owe you an apology, Salih.  That formula I gave you is very, very 
> wrong.  I can't imagine what I was thinking about when I wrote it.  Chalk it up 
> to momentary insanity!  :-)  The correct computation should be as follows.
> 
>   Assuming a = [x1,y1] and b = [x2,y2] are two vectors with their bases at the 
> origin, the non-negative angle between them measured counterclockwise 
> from a to b is given by
> 
>  angle = mod(atan2(x1*y2-x2*y1,x1*x2+y1*y2),2*pi);
> 
>   As you can see, this bears a close relationship to the three-dimensional 
> formula I wrote last July 10.  The quantities, x1*y2-x2*y1 and x1*x2+y1*y2 
> are, respectively, the sine and cosine of the counterclockwise angle from 
> vector a to vector b, multiplied by the product of their norms - that is, their 
> cross product and the dot product restricted to two dimensions.  The 'atan2' 
> function then gives the angle between them ranging from -pi to +pi, and the 
> 'mod' operation changes this so as to range from 0 to 2*pi, as you requested.
> 
> Roger Stafford
> 
> 

Hate to belabor this thread, but I'm not getting the above equation to work.  It works for the one test case you mention in a later thread a=(1,1) and b=(0,-1), but not much else.  For example a=(0,1) and b=(1,0) gives 180.  I can get the angle easily by using atan2(x2,y2) - atan2(x1,y1) but I haven't thought of a clever way to deal with wrapping without using a couple of if-then statements.  (I want the answer to fall between -180 and 180)

thanks.