alphaShapeDiag: Persistence Diagram of Alpha Shape in 3d

Description Usage Arguments Details Value Author(s) References See Also Examples

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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