Homogeneous coordinates

If we consider $A=(1,2,3)$ we don't know whether it represents a point or a vector. Homogenous coordinates have one more dimension $w$ for that:

• $w=0$ when A is a vector: $A=(1, 2, 3, 0)$
• $w=1$ when A is a point: $A=(1,2,3,1)$

Adding two vectors will be a vector, subtracting two points will return a vector.