Persistence Diagram of Alpha Shape in 3d

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Description

The function alphaShapeDiag computes the persistence diagram of the alpha shape filtration built on top of a point cloud in 3 dimension.

Usage

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alphaShapeDiag(X, library = "GUDHI", printProgress = FALSE)

Arguments

X

an n by d matrix of coordinates, used by the function FUN, where n is the number of points stored in X and d is the dimension of the space. Currently d should be 3.

library

Currently only the library "GUDHI" can be used to compute the persistence diagram.

printProgress

if TRUE, a progress bar is printed. The default value is FALSE.

Details

The function alphaShapeDiag constructs the alpha shape filtration, using the C++ library GUDHI. See refereneces.

Value

The function alphaShapeDiag returns a list with the following elements:

diagram

an object of class diagram, a P by 3 matrix, where P is the number of points in the resulting persistence diagram. The first column stores the dimension of each feature (0 for components, 1 for loops, 2 for voids, etc). Second and third columns are Birth and Death of the features.

Author(s)

Jisu Kim and Vincent Rouvreau

References

Fischer K (2005). "Introduction to Alpha Shapes."

Edelsbrunner H, Mucke EP (1994). "Three-dimensional 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.

See Also

summary.diagram, plot.diagram, alphaComplexDiag, gridDiag, ripsDiag

Examples

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# 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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