homogeneous coordinates

Representing a 2D or 3D point with one extra coordinate so translation becomes a matrix multiply like every other transform.

Homogeneous coordinates append an extra coordinate to a point -- $(x,y)\to(x,y,1)$ in 2D -- so that translation, previously an addition, becomes a matrix multiplication alongside rotation, scaling, and shear, letting every affine or projective transform be represented as a single matrix. A homogeneous point $(x_h,y_h,w)$ with $w\neq 1$ recovers its true Cartesian location via the perspective divide, $(x_h/w,\ y_h/w)$ .

Examples

The homogeneous point $(6,9,3)$ recovers its true 2D location $(2,3)$ once divided through by its own last coordinate.