2.1 Affine and convex sets
2.1.1 Lines and line segments
Suppose x1 ≠ x2 are two points in Rn. Points of the form
where θ ∈ R, form the line passing through x1 and x2. The parameter value θ = 0 corresponds to y = x2, and the parameter value θ = 1 corresponds to y = x1. Values of the parameter θ between 0 and 1 correspond to the (closed) line segment between x1 and x2.
Expressing y in the form
gives another interpretation: y is the sum of the base point x2 (corresponding to θ = 0) and the direction x1 − x2 (which points from ...