Rotation about Arbitrary AxisWhen the object is rotated about an axis that is not parallel to any one of coordinate axis, i.e., x, y, z. Then additional transformations are required. First of all, alignment is needed, and then the object is being back to the original position. Following steps are required
Matrix for representing threedimensional rotations about the Z axisMatrix for representing threedimensional rotations about the X axisMatrix for representing threedimensional rotations about the Y axisFollowing figure show the original position of object and position of object after rotation about the xaxis 5. Apply inverse translation to bring rotation axis to the original position. For such transformations, composite transformations are required. All the above steps are applied on points P' and P".Each step is explained using a separate figure. Step1: Initial position of P' and P"is shown Step2: Translate object P' to origin Step3: Rotate P" to z axis so that it aligns along the zaxis Step4: Rotate about around z axis Step5: Rotate axis to the original position Step6: Translate axis to the original position.
Next TopicInverse Transformations
