The function alphaShapeDiag
computes the persistence diagram of the alpha shape filtration built on top of a point cloud in 3 dimension.
1  alphaShapeDiag(X, library = "GUDHI", printProgress = FALSE)

X 
an n by d matrix of coordinates, used by the function 
library 
Currently only the library "GUDHI" can be used to compute the persistence diagram. 
printProgress 
if 
The function alphaShapeDiag
constructs the alpha shape filtration, using the C++ library GUDHI.
See refereneces.
The function alphaShapeDiag
returns a list with the following elements:
diagram 
an object of class 
Jisu Kim and Vincent Rouvreau
Fischer K (2005). "Introduction to Alpha Shapes."
Edelsbrunner H, Mucke EP (1994). "Threedimensional Alpha Shapes." ACM Trans. Graph.
Maria C (2014). "GUDHI, Simplicial Complexes and Persistent Homology Packages." https://project.inria.fr/gudhi/software/
Morozov D (2008). "Homological Illusions of Persistence and Stability." http://www.mrzv.org/publications/thesis/phd/
Edelsbrunner H, Harer J (2010). "Computational topology: an introduction." American Mathematical Society.
summary.diagram
, plot.diagram
, alphaComplexDiag
, gridDiag
, ripsDiag
1 2 3 4 5 6 7 8  # input data generated from sphere
XX < sphereUnif(n = 500, d = 2)
# persistence diagram of alpha shape
DiagAlphaShape < alphaShapeDiag(X = XX, printProgress = TRUE)
# plot
plot(DiagAlphaShape[["diagram"]])

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