Coordinate system conversion

It sounds like you're looking for the following indirect permutation matrix:

0   0  -1   0-1  0   0   00   1   0   00   0   0   1

Admiral

Thanks, but how did you come up with that matrix?

Assuming I know the coordinate systems I want to go from->to, how do I create such a matrix?

There's a clever little trick you can use to come up with these permutation matrices. In the source system, let x correspond to the first column, y correspond to the second column, and z correspond to the third column, and let x/y/z in the destination system correspond to the rows. We see that x+ is "right" in the source system. What is "right" is the destination system? If y+ is left, then y- is right. So we're going from x+ -> y-, which is a -1 in the first column, second row. For "up", we go from y+ -> z+, so that's a +1 in the second column, third row. For "out", we go from z+ -> x-, so that's a -1 in the third column, first row. Basically, you figure out the orientations for x+/y+/z+ in the source system (which happen to be "right", "up", and "out", but could have just as easily been "right", "down", "in" for an arbitrary system), and match those up in the destination system. This will tell you which rows and columns have +1/-1.

Note that, depending on whether you use row vectors, or column vectors, the words "column" and "row" may need to be interchanged in Zipster's explanation. For more information, see my article on matrix representations.

Thanks for the explanation! I see the pattern now.