Am 19.08.2013 03:23, schrieb Bald Eagle:
> ARrrrrrgh.
> I would have thought that VangleD( <0, 0, 0>, <8, 8, 0>) would return 45
> degrees.
> Instead it returns 90.
> VangleD( <8, 0, 0>, <8, 8, 0>) returns 45 degrees.
>
> So, it's not the angle between the "vectors" that it returns, but the angle
> formed by the Vector described by the two points, and an axis?

Well, I guess I'll resort to my standard answer again: "Um... no, not 
really." :-)

Note that <0,0,0> has no direction, so the angle between it and any 
other given vector is poorly defined. The function has to return 
/something/, and it decides to return 90 because it's just as good or 
bad as any other answer in that situation.

You can interpret the function in two ways:

(i) The function gives the angle between two direction vectors; to 
understand what the angle between two vectors is, imagine both vectors 
to be in the same plane (you can easily do this with any direction 
vector because by definition a direction vector has no associated 
location in space, just the direction and magnitude); the angle between 
the two vectors is the rotation in that common plane that, when applied 
to A, will reorient it to be collinear with vector B.

(ii) The function gives the angle between two location vectors; this is 
equivalent to drawing two rays from the origin, one through each of the 
points defined by the location vectors A and B, and - in the plane 
defined by those two points and the origin - measuring the angle between 
the two rays.

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