Homogeneous Coordinate System

Question

What are the fundamental merits of using Homogeneous Coordinate System? Describe briefly?

Answer 1

Matrix symbolization is standard technique of implementing transformations in computer graphics. However unfortunately, we are not capable to symbolize all the transformations in a (2 x 2) matrix form; such as translation. Through using Homogeneous Coordinates System (HCS), we can symbolize all the transformations in matrix form. For translation of point (x,y) (x +| tx, y + ty ), it is not possible to symbolize this transformation in matrix form. But now in HCS, it is possible to symbolize.