torusUnif: Uniform Sample From The 3D Torus

In TDA: Statistical Tools for Topological Data Analysis

Uniform Sample From The 3D Torus

Description

The function torusUnif samples n points from the 3D torus, uniformly with respect to its surface.

Usage

  torusUnif(n, a, c)

Arguments

n	an integer specifying the number of points in the sample.
a	the radius of the torus tube.
c	the radius from the center of the hole to the center of the torus tube.

Details

This function torusUnif is an implementation of Algorithm 1 in the reference.

Value

The function torusUnif returns an n by 3 matrix of coordinates.

Author(s)

Fabrizio Lecci

References

Diaconis P, Holmes S, and Shahshahani M (2013). "Sampling from a manifold." Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton. Institute of Mathematical Statistics, 102-125.

See Also

circleUnif,sphereUnif

Examples

X <- torusUnif(300, a = 1.8, c = 5)
plot(X)

TDA documentation built on Feb. 16, 2023, 6:35 p.m.