Question

I am currently trying to implement a virtual arcball in OpenGL utilizing GLUT library.
As of now I am calculating the axis of rotation and angle of rotation by doing standard arcball computation on old and new coordinates of the mouse. But I want to obtain the angle theta1, theta2, theta3 , such that rotation of the object about X axis by theta1 , about Y axis by theta2 and about Z axis by theta3 would yield the same effect as before.

Answer 1

What you want is to go from axis-angle two three Euler angles. Look into wikipedia rotation conversions . There you can go from axis-angle to quarternion and then to euler angles, or alternatively via the full 3×3 rotation matrix.

Look also into what is called the Rodrigues parameters to help in the conversion. To first rotate about X, then Y and then Z you want to do RZ(t3)*RY(t2)*RX(t1).

In your case it might be easier to construct the 3×3 rotation matrix and use OpenGL to transform the modelview based on the matrix, instead of the 3 sequential rotations.