[Hill:
217-222. Foley & van Dam: p. 201-208, 213-217]
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 transformations defined above can be
rewritten using 4x4 matrices and homogeneous coordinates. The general form of
the matrix is:
The expressions derived earlier correspond to the following transformation
matrices.
