Z-Y-X Euler Angles

Z-Y-X Euler Angles

Z-Y-X Euler Angles (or X-Y-Z fixed angles)
Rx'y'z' (a,b,c) =

[ cos(a)*cos(b), cos(a)*sin(b)*sin(c) - cos(c)*sin(a), sin(a)*sin(c) + cos(a)*cos(c)*sin(b)]
[ cos(b)*sin(a), cos(a)*cos(c) + sin(a)*sin(b)*sin(c), cos(c)*sin(a)*sin(b) - cos(a)*sin(c)]
[       -sin(b),                        cos(b)*sin(c),                        cos(b)*cos(c)]



X-Y-Z Euler Angles
Rz'y'x' (a,b,c) =

[                        cos(b)*cos(c),                       -cos(b)*sin(c),         sin(b)]
[ cos(a)*sin(c) + cos(c)*sin(a)*sin(b), cos(a)*cos(c) - sin(a)*sin(b)*sin(c), -cos(b)*sin(a)]
[ sin(a)*sin(c) - cos(a)*cos(c)*sin(b), cos(c)*sin(a) + cos(a)*sin(b)*sin(c),  cos(a)*cos(b)]

Rz'y'x' (c,b,a) =
[                        cos(a)*cos(b),                       -cos(b)*sin(a),         sin(b)]
[ cos(c)*sin(a) + cos(a)*sin(b)*sin(c), cos(a)*cos(c) - sin(a)*sin(b)*sin(c), -cos(b)*sin(c)]
[ sin(a)*sin(c) - cos(a)*cos(c)*sin(b), cos(a)*sin(c) + cos(c)*sin(a)*sin(b),  cos(b)*cos(c)]