-1, 0, 0, 0
0, 1, 0, 0
0, 0, -1, 0
0, 0, 0, 1
will do a 180 degree rotation arround the y-Axis. No mirroring but a -1 at M00.
Transformation Matrix is nothing i deal with every day… as fare is i remember you have to calculate the determinant of the upper left 3x3 Matrix (+ or - ) …
this is mentioned here - stackexchange
@menno is a clever guy and may know !
if you find some nice resource that explains matrices in a accessible way for the design-World… please post it.
If you re on the programming side and want a more graphic solution:
use two vectors a,b, and their crossproduct c.
apply the transformation to a b c
create a second crossproduct “test” and compare it to transformed c.
if the angle is more then Pi/2 the right-hand rule is destroyed and the transformation is doeing reflection…
(but any mathematician will have a nicer solution for sure…)
hope that helps. kind regards -tom