Pathway XVIII

ΔAffine geometry and simplices

Barycentric coordinates. A simplex is the convex hull of affinely independent points.

1. 01The simplexA 2-simplex is a triangle. Every interior point is a unique convex combination of the vertices.4 min
2. 02Affine geometryForget distances and angles. Parallelism and barycenters remain — affine combinations.4 min
3. 03Euclidean simplicesPut the inner product back. A triangle has a circumcircle, an orthocenter, and Pythagoras.4 min