Posted by B. Douglas Ward on March 29, 2001 at 10:25:48:
In Reply to: Re: Matrix file posted by bob cox on March 28, 2001 at 11:22:06:
Bob:
I don't understand what you're getting at. Are you saying that Phoebe should
use the inverse of the rotation matrix?
Part of the confusion is that the same rotation can be specified in different
ways.
For example, if we consider the coordinate axes as fixed, and if the
head executes a pure rotation of angle r about the z-axis, then a fixed point
on the head is mapped to the new location (in original coordinates) by:
+cos(r).-sin(r)..0
+sin(r).+cos(r)..0
...0......0......1
However, if we consider a new coordinate system as rotating with the head,
then a fixed point in space in the old coordinate system is mapped to the
new coordinate system by:
+cos(r).+sin(r)..0
-sin(r).+cos(r)..0
...0......0......1
Presumably, it is the latter matrix that would be used to transform the input
dataset to the output dataset.
Of course, without knowing the definition of Phoebe's original 4x4 matrix,
I can't say for sure. Perhaps they are using quaternions.
Doug Ward