TDA (version 1.6.2)

alphaShapeFiltration: Alpha Shape Filtration in 3d

Description

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

Usage

alphaShapeFiltration(
    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

a string specifying which library to compute the Alpha Shape filtration. The user can use the library "GUDHI", and is also the default value.

printProgress

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

Value

The function alphaShapeFiltration returns a list with the following elements:

cmplx

a list representing the complex. Its i-th element represents the vertices of i-th simplex.

values

a vector representing the filtration values. Its i-th element represents the filtration value of i-th simplex.

increasing

a logical variable indicating if the filtration values are in increasing order (TRUE) or in decreasing order (FALSE).

coordinates

a matrix representing the coordinates of vertices. Its i-th row represents the coordinate of i-th vertex.

Details

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

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

alphaShapeDiag, filtrationDiag

Examples

# NOT RUN {
# input data generated from sphere
X <- sphereUnif(n = 20, d = 2)

# alpha shape filtration
FltAlphaShape <- alphaShapeFiltration(X = X, printProgress = TRUE)
# }