TABLE III

             Two-Dimensional Transformation Matrices



Translation Matrix:

      __       __
     |           |
     | 1   0   0 |
     |           |       Tx = amount to translate in X dimension
     | 0   1   0 |       
     |           |       Ty = amount to translate in Y dimension
     | Tx  Ty  1 |       
     |__       __|



Scaling Matrix:

      __       __
     |           |
     | Sx  0   0 |
     |           |       Sx = scaling factor in X dimension
     | 0   Sy  0 |       
     |           |       Sy = scaling factor in Y dimension
     | 0   0   1 |       
     |__       __|



Rotation Matrix:

      __              __
     |                  |
     |  cosų   sinų   0 |     
     |                  |     ų =  angle to rotate
     | -sinų   cosų   0 |          (counter-clockwise)
     |                  |     
     |   0      0     1 |
     |__              __|