What are homogeneous coordinates?

Homogeneous coordinates are coordinates used to represent the cartesian coordinate (x,y) as three - element vector.We represent each cartesian coordinate position (x,y) with the homogeneous coordinate triple (h.x, h.y, h) where h is any non - zero value.We can set h = 1.

Hence each two dimensional position (x,y) is represented as (x,y,1) in homogeneous coordinates.

Why do you need homogeneous coordinates?

Many graphics applications involve sequences of geometric transformations.The sequence of basic transformations can be expressed in matrix form as

P' = M1.P + M2

where M1 is a 2x2 matrix containing multiplicative terms and

M2 is a column matrix containing translational terms.

We can combine the multiplicative and translational terms in to a single matrix representation by expanding 2x2 matrices to 3x3 matrices.

To express any two dimensional transformation as a matrix multiplication, we represent each cartesian coordinate position with homogeneous coordinates.