PDA

View Full Version : Converting Euler Angles to a Matrix



Sarah22
05-10-2010, 07:45 PM
I don't understand what happen here.

http://img13.imageshack.us/img13/6995/quaternionquestion.png

Why is it [ cos h 0 sin h ] on the first row? Isn't it should be [ cos h 0 -sin h ] ?


It explains here but still didn't understand what it stated. Can anyone here explain it more. Proving will really help.

http://img140.imageshack.us/img140/1705/quaternionquestion2.png

Thank you
Sarah

Kelvin
05-10-2010, 11:05 PM
Looks OK to me.

Given the property of sin:
sin(-a) = -sin(a)

we simplify -sin(-h):

-sin(-h) = --sin(h) = sin(h)

Dark Photon
05-11-2010, 04:44 AM
I don't understand what happen here.
http://img13.imageshack.us/img13/6995/quaternionquestion.png
Why is it [ cos h 0 sin h ] on the first row? Isn't it should be [ cos h 0 -sin h ] ?
Yeah, been there done that ;) That's definitely the pattern visually. But here's the deal:

Rotate about X axis = rotate from Y axis to Z axis
Rotation about Y axis = rotate from Z axis to X axis
Rotation about Z axis = rotate from X axis to Y axis

Notice anything strange? Yeah, the positive rotation direction on the 2nd one (the one you're asking about), goes backwards in the alphabet. Since X, Y, and Z are assigned columns 0, 1, and 2 and rows 0,1, and 2, this has the effect of making it look like the minus signs on the sin expressions are flopped.

What happened is that the starting point for our little 2x2 cos/-sin sin/cos matrix is cell 2,2 (Z,Z), and it wraps around the right and bottom edges of the upper-left 3x3, giving the appearance of flopping the signs on the sins.