n_bound_connect_3D {ashapesampler}

N Bound Connect 3D

Description

Function returns the minimum number of points to preserve the homology with an open cover of radius alpha.

Usage

n_bound_connect_3D(alpha, delta = 0.05, r = 1, rmin = 0.01, bound = "cube")

Arguments

alpha

radius of open balls around points

delta

probability of isolated point

r

radius of sphere, outer radius of shell, or length of cube side

rmin

inner radius of shell

bound

manifold from which points sampled. Options are sphere, shell, cube

Value

integer of minimum number of points needed

Examples

# For a cube with probability 0.05 of isolated points
n_bound_connect_3D(0.2, 0.05,0.9)
# For a sphere with probability 0.01 of isolated points
n_bound_connect_3D(0.2, 0.01, 1, bound="sphere")
# For a shell with probability 0.1 isolated points.
n_bound_connect_3D(0.2, 0.1, 1, 0.25, bound="shell")