Composite Transformations - 2-d and 3-d Transformations

We can build complicated transformations as rotation regarding to an arbitrary point, mirror reflection about a line, and so on, via multiplying the fundamental matrix transformations. This process is termed as concatenation of matrices and the resulting matrix is often considered to as the composite transformation matrix. In composite transformation, an earlier transformation is pre-multiplied along with the next one.

Conversely, we can say that an order of the transformation matrices can be concatenated into a particular matrix. It is an effective procedure as it decreases since instead of applying initial coordinate position of an object to all transformation matrixes, we can find the final transformed position of an object via applying composite matrix to the first coordinate position of an object.  Conversely, we can say that a sequence of transformation matrix can be concatenated matrix in a particular matrix.  It is an effective procedure when it decreases computation since instead of applying initial coordinate position of an object to all transformation matrixes, we can acquire the last transformed position of an object via applying composite matrix to the first coordinate position of an object.