Sampling Lissajous and Fourier Knots

@article{Boocher2009SamplingLA,
  title={Sampling Lissajous and Fourier Knots},
  author={Adam Boocher and Jay Daigle and J. Hoste and W. Zheng},
  journal={Experimental Mathematics},
  year={2009},
  volume={18},
  pages={481 - 497}
}
A Lissajous knot is one that can be parameterized as , where the frequencies n x , n y , and n z are relatively prime integers and the phase shifts ϕ x , ϕ y , and ϕ z are real numbers. Lissajous knots are highly symmetric, and for this reason, not all knots are Lissajous. We prove several theorems that allow us to place bounds on the number of Lissajous knot types with given frequencies and to efficiently sample all possible Lissajous knots with a given set of frequencies. In particular, we… Expand
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