Advantage of Initiating the Matrix Form of Translation
The advantage of initiating the matrix form of translation is as it expresses the operations on complicated objects that are we can now build complicated transformations via multiplying the basic matrix transformations. Conversely, we can see that a sequence of transformation matrices can be concatenated in a particular matrix. It is an effectual procedure as it decreases the computation since instead of applying first coordinate position of an object to all transformation matrixes; we can acquire the last transformed position of an object by applying composite matrix to the first coordinate position of an object. Standard method of implementing transformations in computer graphics is Matrix illustration.
Hence, from the point of view of matrix multiplication, along with the matrix of translation, another basic transformation as scaling, reflection and rotation etc, can also be illustrates as 3x3 homogeneous coordinate matrices. It can be accomplished via augmenting the 2x2 matrices along with a third row (0,0,x) and a third column, which is: