[Cst-1b] 99.6.4 Graphics / Mistake in example

[M.Y.W.Y.B.]

--On Sonntag, 28. Mai 2000, 17:31 +0100 "M.Y.W.Y.B."
<mywyb2@hermes.cam.ac.uk> wrote: 
> Nathan: I can't figure out how you got 76.66 degrees about z-axis. In the
> reverse transformation that must have been your first rotation, so either
> you rotated the transformed cone onto the xz plane (-53.13 degrees or
126.87
> degrees) or onto the yz plane (36.87 degrees or -143.13 degrees).


Ah, I think I know what the mistake was: 
you calculated arccos(3/|d|)=76.66 degrees, where |d| = length of the
direction vector = 13

But that is the angle between the direction vector and the x-axis! What you
want is the angle between the direction vector projected onto the xy-plane
and the x-axis.

So the angle is arccos(3/|d'|)=53.13 degrees, where |d'| = length of the
direction vector projected onto the xy-plane = |(3,4,0)| = 5.
Or even easier arctan(y/x)=arctan(4/3)=53.13
Now the rotation is clockwise, so actually the angle is -53.13 in the
reverse transformation.


Mo