A homogeneous formulation for lines in 3 space

Abstract

Homogeneous coordinates have long been a standard tool of computer graphics. They afford a convenient representation (for) various geometric quantities in two and three dimensions. The representation of lines in three dimensions has, however, never been fully described. This paper presents a homogeneous formulation for lines in 3 dimensions as an anti-symmetric 4x4 matrix which transforms as a tensor. This tensor actually exists in both covariant and contravariant forms, both of which are useful in different situations. The derivation of these forms and their use in solving various geometrical problems is described.