On Fri, 11 Jan 2002 12:14:50 -0000, "Alexandre Bento Freire"

>The problem is that x may be positive and y negative, and z negative.

>That is there one scale per axis

Then you are asking a question that has no well defined answer,

unless you are talking about a pure nonuniform scaling with no

rotation at all. Here's an example that proves it: Reflection in

the xy plane (i.e., a z scale of -1) concatenated with reflection in

the xz-plane (i.e. a y scale of -1) produces exactly the same result

as rotation of 180 degrees about the x axis with no reflections at

all.

Ron

>> Find the determinant of the 3x3 non-translation portion of the matrix.

>> This value is:

>> det = (xy*yz - xz*yy)*zx + (xz*yx - xx*yz)*zy + (xx*yy - xy*yx)*zz

>> I think the determinant of the transpose is the same, so it doesn't matter

>> whether you address your matrix by rows first or columns first.

>> The sign of the determinant is the sign of the scale.