Rotation - 2-D and 3-D transformations

Within 2-D rotation, an object is rotated via an angle θ along w.r.t. the origin. This angle is assumed to be +ive for anticlockwise rotation. There are two conditions for 2-D rotation, condition1- rotation regarding the origin and condition2 rotation about an arbitrary point.

If the rotation is made regarding to an arbitrary point, a set of basic transformation, that is composite transformation is needed. For 3-Dimentional rotation connecting 3-D objects, we require to identify both the angle of rotation and the axis of rotation, regarding such rotation has to be made. Now, we will see the condition1 and in the subsequent section we will see the condition2.