Betweenness in affine spaces #
This file defines notions of a point in an affine space being between two given points.
Main definitions #
The segment of points weakly between
y. When convexity is refactored to support
abstract affine combination spaces, this will no longer need to be a separate definition from
segment. However, lemmas involving
-ᵥ will still be relevant after such a
refactoring, as distinct from versions involving
- in a module.
Suppose lines from two vertices of a triangle to interior points of the opposite side meet at
p lies in the interior of the first (and by symmetry the other) segment from a
vertex to the point on the opposite side.