Given three distinct points in a projective line, a unique system of homogeneous coordinates exists such that the points have coordinates [1:0], [0:1], and [1:1]. Given a complete quadrangle of points in a projective plane, these can be uniquely assigned coordinates [1:0:0], [0:1:0], [0:0:1], and [1:1:1]. More generally, homogeneous coordinates can be assigned in this manner for n + 2 points in general position in a n-dimensional projective space.