Barycentric Coordinates

Imagine that we have a line segment between two verticies, v1 and v2.

For simplicity lets choose coordinates so that v₁ and v₂ are 1 unit apart.

Any point on that line segment can therefore be specified as follows:

(1- λ)v₁ + λ v₂

where: λ is a real number between 0 and 1.

A note about Points and Vectors Usually I make a distinction between points and vectors where we cannot do arithmetic on points. So, for instance, it does not make sence to add two points together. Vectors are transforms on points and it does make sence to add togther two vectors or to multiply a vector by a scaler. On this page I may blur this distinction a bit.

We can expand this construction to

EuclideanSpace

home

This page discusses implementing geometric simplicial complexes using the Axiom/FriCAS computer algebra system.

This page concentrates on barycentric coordinates, for a more general discussion of both geometric and abstract (combinatorial) versions of simplicial complexes start on this page first.

My code for this page is on github here.

Theory

This page is about code I have implemented for algebraic topology structures. For a more theoretical explanation see the page here.