Description Usage Arguments Details Examples

These functions generate uniform samples from Klein bottles in 4-dimensional space, optionally with noise.

1 2 3 4 5 | ```
sample_klein_tube(n, ar = 2, sd = 0)
sample_klein(n, ar = 2, sd = 0)
sample_klein_flat(n, ar = 1, bump = 0.1, sd = 0)
``` |

`n` |
Number of observations. |

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

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

`bump` |
Bump constant for the flat torus-based Klein bottle. |

(Details.)

1 2 3 4 5 6 7 | ```
# Klein bottle tube embedding in 4-space
x <- sample_klein_tube(120, sd = .05)
pairs(x, asp = 1, pch = 19, cex = .5)
# Klein bottle flat torus-based embedding in 4-space
x <- sample_klein_flat(120, sd = .05)
pairs(x, asp = 1, pch = 19, cex = .5)
``` |

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