1 - AlphaStructures.jl

AlphaStructures.jl is a Julia library that provides some tool for point cloud analysis.

With AlphaStructures.jl you can:

• evaluate the $\alpha$-Shape of a point cloud
• compute the $\alpha$-Filtration of a point cloud
• build the $\alpha$-Complex of a point cloud
• find some basics about Persistent Homology evaluation of a cloud of points

In this documentation we present the problem and the related solution we have implemented so far both from the mathematical [EM92] and the computer science [Ede14] point of view.

Dependencies

AlphaStructures.jl has the following dependeces:

• Combinatorics.jl by Julia Math
• DataStructures.jl by Julia Collections
• LinearAlgebraicRepresentation by CVD Lab
• Triangle.jl by CVD Lab

and as additional dependece:

• ViewerGL by CVD Lab

Docstrings conventions

• Bold is used to point out theory concepts.
• Monospace is used for everything code related.