How to calculate rotation axis and angle?

Question

I am trying to rotate a model in 3D so that it faces the right direction. The rotation I want is fairly trivial and can be broken down into two steps:

1. Rotate the model 90 degrees on its x-axis.
2. Rotate the model 180 degrees on its z-axis (relative to the first rotation).

The way to set a model's rotation in the framework I'm using (openFrameworks) is by calling its setRotation method. This method takes an angle, as well as floats x, y and z that specify the axis of rotation. How do I calculate the axis of rotation and angle for this particular rotation? I can't rotate the model two times sequentially because any call to setRotation overwrites previous rotations.

Please let me know if I can provide more information or clarity.

EDIT: In case anyone has the same question, this post helped me a lot.

Answer 1

weird that you can not apply more then one transform ... maybe you just use wrong function but anyway:

If you have direct access to transform matrix (or by get,set)

1. google for transform matrices if you do not have the knowledge
   • I suspect you are using 4x4 homogenous cartesian transform matrices
   • transform matrix anatomy
2. generate first rotation matrix and store it to M1
   • can use the setRotation for that
3. generate second rotation matrix and store it to M2
4. multiply them M=M1*M2
5. use this M instead of setRotation

If yo do not have the direct access to transform matrix and have to use just the setRotation

• in that case you have to use quaternion which is the 4D vector you call the setRotation with
• google for quaternion math and find the application of 2 rotations
• I do not use them so I can not help with that but there are also equations out there
• which converts 3x3 rotation matrix into quaternion and back
• so you can still use the algorithm above
• obtain M
• extract the rotation matrix from it (it is just sub matrix you omit last row and column)
• compute quaternion from it
• and call setRotation with the result