Derivation of Transformations

translation
scaling
shear
rotation

Note: A positive rotation about the z-axis is defined as one that rotates from the positive x-axis to the postive y-axis. We can similarly define rotations about the other two axes. These definitions hold for both RHCS and LHCS.

• about x-axis: positive y to positive z
• about y-axis: positive z to positive x
• about z-axis: positive x to positive y

Transformation Matrices

The expressions derived earlier correspond to the following transformation matrices.