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  • $\begingroup$ Very nice solution, answering my (implied) question on a "good" parameterization of the curve for the purpose of interpolation. Thanks! I'll mark this as my best answer. $\endgroup$ Commented Jul 29, 2016 at 17:02
  • $\begingroup$ The code in your question used chord-length parametrization (corresponding to setting a to 1 in parametrizeCurve[]), which should also work; the snag you hit into was that you did not permute the points so that the cusp is at the start and end. But Lee shows that centripetal parametrization is often a more "natural" choice for many configurations. $\endgroup$ Commented Jul 29, 2016 at 17:06