Barycentric Coordinates

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

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


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Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

flag flag flag flag flag flag Mathematics++: Selected Topics Beyond the Basic Courses (Student Mathematical Library) Kantor, Ida.

Chapters:

  1. Measure
  2. High Dimensional Geometry
  3. Fourier Analysis
  4. Representations of Finite Groups
  5. Polynomials
  6. Topology

Chapter 6 - Topology. Contains a relatively gentle introduction to homology.

 

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