1.
Check the first property of linearity:
Therefore, , so the transformation is nonlinear.
2.
Check the first property of linearity:
Check the second property of linearity:
Constructing the induced matrix is a simple matter of applying the transformation to the columns of the identity matrix. The result is shown below:
3.
The operation is not linear, since it involves translation, although it could be made linear under homogeneous coordinates.
4.
Define parent-child relationships between all the polygons composing the character such that the transformation of a parent will always be applied to the children (through matrix concatenation).
5.
6.
The transformation we seek is , since this effectively reflects the point off the x-axis. To get the induced matrix, we apply this transformation to the columns of the
identity matrix. The result is shown below: