nd_surface: Calculate area of the n-dimensional hypersphere

In hosscine/phacm: The R Package for Analyzing Persistent Homology and Cycles of Manifold

Description

Threshold for n-dimensional persistence is must be magnified by considering difficulty of forming n-dimensional hypersphere. In paticular, use threshold multipuled by nd_surface(1) / nd_surface(n).

Usage

nd_surface(n)

Arguments

n	dimension.

Details

The unit circle is a 1-dimensional hole and its surface area is 2 * pi. Then, the unit sphere is a 2-dimensional hole and its surface area is 4 * pi. To form both the unit circle and the unit sphere with data points having the same surface variance, the unit sphere must have twice as many data points as the unit circle.

Value

area of n-dimensional superplane.

hosscine/phacm documentation built on May 23, 2019, 1:46 p.m.