- #1

TerryW

Gold Member

- 168

- 6

I've worked through the maths and produced the matrices by multiplying the three individual rotation matrices, (no problem there) but I have been trying to work out what is actually going on. I have ended up with a 3x3 matrix which I believe is giving me the new co-ordinates of the new axes (now X'Y'Z') in terms of the original axes XYZ. after a rotation around a vector n

_{x}n

_{y}n

_{z}. The X component of X' is cos n

_{y}t*cos n

_{z}t. Well this looks fine because it is the same as you will find in lots of places in Wikipedia. The only problem I have is that I then went on to try to derive the same results using pure geometry I arrived at a different formula, which is not necessarily a problem because it is a different process, a single rotation rather than three separate rotations. But the numerical results should be the same. So I built a spreadsheet to compare my geometric result with the matrix result and I also made a cube and stuck a skewer through it to see what really happens.

I chose the vector (1, 0.6, 0.8) as the axis of rotation.

My geometric formula looks to come up with the correct result, the X' axis (1,0,0) is back to where it started after a rotation of 2π. The corresponding result for the rotation matrix is an X co-ordinate of 0.8413! Moreover, the rotation matrix result produces some negative values for the X co-ordinate, but there is nowhere during its rotation that the original point (1,0,0) ventures into negative territory when I spin my cube around the skewer.

I must be getting something wrong somewhere but I can't see it - can anyone help?

TerryW