This package allows users to use Freudenthal triangulation for functional value approximation.

Specifically it allows the user to find the simplex of a point x in Freudenthal space and the barycentric coordinates of that point with respect to the its simplex.

Start Julia and run the following command:

Pkg.add("FreudenthalTriangulation")

To use the FreudenthalTriangulation module, begin your code with

using FreudenthalTriangulation

To find the vertices of the simplex around a point x in Freudenthal space, run

V = freudenthal_simplex(x)

Then to find barycentric coordinates of x with respect to the simplex, run

coords = barycentric_coordinates(x, V)

Note that these vertices must be in the same order as provided by freudenthal_simplex.

To calculate the simplex and the barycentric coordinates with one function, run

V, coords = freudenthal_simplex(x, V, coords)

so that V will be filled with the simplex vertices in the Freudenthal space and coords will be filled with the associated coordinates.

For these functions the requirements are

• x::Vector{Float64} The point in Freudenthal space
• V::Vector{Vector{Float64}} The vertices of the simplex around x in Freudenthal space
• coords::Vector{Float64} The barycentric coordinates of x with respect to the simplex

Contributors to this package include Mykel Kochenderfer and Sidhart Krishnan