Description Usage Arguments Details References Examples

These functions generate uniform samples from configurations of tori of primary radius 1 in 3-dimensional space, optionally with noise.

1 2 3 4 5 | ```
sample_torus_tube(n, ar = 2, sd = 0)
sample_tori_interlocked(n, ar = 2, sd = 0)
sample_torus_flat(n, ar = 1, sd = 0)
``` |

`n` |
Number of observations. |

`ar` |
Aspect ratio for tube torus (ratio of major and minor radii) or flat torus (ratio of scale factors). |

`sd` |
Standard deviation of (independent multivariate) Gaussian noise. |

The function `sample_torus_tube()`

uses the tubular parameterization into
3-dimensional space documented at
MathWorld.

The function `sample_torus_flat()`

uses a flat parameterization (having zero
Gaussian curvature) into 4-dimensional space, as presented on
Wikipedia.

The function `sample_tori_interlocked()`

samples from two tubular tori
interlocked in the same way as `sample_circles_interlocked()`

.

All uniform samples are generated through a rejection sampling process as described by Diaconis, Holmes, and Shahshahani (2013).

P Diaconis, S Holmes, and M Shahshahani (2013) Sampling from a Manifold.
*Advances in Modern Statistical Theory and Applications: A Festschrift in
honor of Morris L. Eaton*, 102–125. doi: 10.1214/12-IMSCOLL1006

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