Homogeneous coordinates are another way to represent points to simplify the way in which we express affine transformations. Normally, book-keeping would become tedious when affine transformations of the form
are composed. With homogeneous coordinates, affine transformations become matrices, and composition of transformations is as simple as matrix multiplication. With homogeneous coordinates, a point is augmented with a 1, to form
All points represent the same point
OR We have to use 3×3 transformation matrix instead of 2×2 transformation matrix. To convert a 2×2 matrix to 3×3 matrix, we have to add an extra dummy coordinate W. In this way, we can represent the point by 3 numbers instead of 2 numbers, which is called Homogenous Coordinate system.
Homogeneous coordinates are used extensively in computer vision and graphics because they allow common operations such as translation, rotation, scaling and perspective projection to be implemented as matrix operations 3D graphics hardware can be specialized to perform matrix multiplications on 4x4 matrices.