Homogeneous coordinates

Summary

Homogeneous coordinates describe a point of the projective space $\mathbb{P}^n$ by $n + 1$ numbers, not all zero, taken up to a common nonzero factor. They turn points at infinity into ordinary tuples, so that projective geometry can be done with linear algebra. Projective transformations become matrices, and curves become zero sets of homogeneous polynomials. They are standard in computer graphics, where translations and perspective become matrix products.