1.5.3. Exemplary Computation

In this chapter we first combine a scaling operation with a translation operation. The new matrix is then combined with a rotation. Surely that these steps could be merged to one operation. But by looking at these steps separately it is easier to understand the whole operation.

Combination of Scaling and Translation:

Combination of the new matrix and rotation:

Now we make the same steps with exemplary numbers. First we combine the scaling operation (parameters: s_x=3 and s_y = 3) with a translation (parameters: d_x=2 and d_y = 4):

And now we integrate the rotation considering an angle A = 90^o:

The transformation matrix including scaling, translation and rotation can now be applied to any arbitrary point:

Using a point with the coordinates x=3 and y=2 the computation looks like this: