|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