Post by baris kazarHi Roger,-
yes, this is one step closer to what i need but not
x=(1,0,0); y=(1,0,1) and z=(1,0-1)
let's call the angle between x and y theta.
Then i wanna get 2pi-theta for the angle between x and z.
i dont have access y and z at the same time.
hope that this problem statement is clear.
Thanks much for your reply
Best regards
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You will have to try harder to explain your problem, if I am to understand
you, Baris. The example you gave has x, y, and z all in the same plane. You
didn't state previously that all your vectors are coplanar. Are they? But
whether they are or not, this doesn't explain how you would define the angle
theta between x and y. It could be plus pi/4 or it could be minus pi/4 (or
7/4*pi.) Which one would you choose and according to what criterion? It
would depend on which side of the plane, in this case the x-z plane, is
regarded as its positive side - along the plus y-axis, or along the negative
side of the y-axis. Also it depends on whether you are moving from x
towards y or from y towards x if you are adhering to right-hand cross
product direction conventions.
Select two arbitrary vectors in three-dimensional space (x1,y1,z1) and
(x2,y2,z2) and try to think of a consistent way of defining the angle between
them without reference to any other vector that would allow this quantity to
range over the full four quadrants, 0 to 2*pi. I think you will find this a
difficult thing to do in any way that could reasonably be considered canonical.
In two dimensions, there is a clearly defined counterclockwise direction from
vector x to vector y which would give you the range you desire. In three
dimensions, you lose the sense of what is a "counterclockwise" direction. You
can go from x to y along either of two great circle paths and one direction will
give the supplement angle to the opposite direction. If you always select the
shortest path, then your angle range is restricted to [0,pi].
If one vector of each pair is restricted to a particular fixed vector, as your
previous wordage seemed to imply, I still don't see what criterion you wish to
use to define these angles. For example, you can move from the fixed vector
by one degree in all possible directions giving a cone, but which half of these
angles should be adjusted so as to be the supplements (that is 359 degrees,)
of those on the opposite side? If you are restricting your vectors to all be
coplanar, then which side of such a plane is to be considered its "positive"
side?
Roger Stafford