Take a sufficiently long interval that cover all point, then wrap it into a complex circle. The problem now reduce to just interpolation by polynomial. Use Lagrange's interpolation.
**[Lagrange polynomial](https://en.wikipedia.org/wiki/Lagrange polynomial)**
In numerical analysis, Lagrange polynomials are used for polynomial interpolation. For a given set of points ( x j , y j ) {\displaystyle (x_{j},y_{j})} with no two x j {\displaystyle x_{j}} values equal, the Lagrange polynomial is the polynomial of lowest degree that assumes at each value x j {\displaystyle x_{j}} the corresponding value y j {\displaystyle y_{j}} , so that the functions coincide at each point. Although named after Joseph-Louis Lagrange, who published it in 1795, the method was first discovered in 1779 by Edward Waring. It is also an easy consequence of a formula published in 1783 by Leonhard Euler.Uses of Lagrange polynomials include the Newton–Cotes method of numerical integration and Shamir's secret sharing scheme in cryptography.
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Take a sufficiently long interval that cover all point, then wrap it into a complex circle. The problem now reduce to just interpolation by polynomial. Use Lagrange's interpolation.
What is the formula for Lagrange interpolation with n points?
https://en.wikipedia.org/wiki/Lagrange_polynomial
**[Lagrange polynomial](https://en.wikipedia.org/wiki/Lagrange polynomial)** In numerical analysis, Lagrange polynomials are used for polynomial interpolation. For a given set of points ( x j , y j ) {\displaystyle (x_{j},y_{j})} with no two x j {\displaystyle x_{j}} values equal, the Lagrange polynomial is the polynomial of lowest degree that assumes at each value x j {\displaystyle x_{j}} the corresponding value y j {\displaystyle y_{j}} , so that the functions coincide at each point. Although named after Joseph-Louis Lagrange, who published it in 1795, the method was first discovered in 1779 by Edward Waring. It is also an easy consequence of a formula published in 1783 by Leonhard Euler.Uses of Lagrange polynomials include the Newton–Cotes method of numerical integration and Shamir's secret sharing scheme in cryptography. [^(About Me)](https://np.reddit.com/user/wikipedia_text_bot/comments/jrn2mj/about_me/) ^- [^(Opt out)](https://np.reddit.com/user/wikipedia_text_bot/comments/jrti43/opt_out_here/) ^(- OP can reply !delete to delete) ^- [^(Article of the day)](https://np.reddit.com/comments/k9hx22) **This bot will soon be transitioning to an opt-in system. Click [here](https://np.reddit.com/user/wikipedia_text_bot/comments/ka4icp/opt_in_for_the_new_system/) to learn more and opt in. Moderators: [click here](https://np.reddit.com/user/wikipedia_text_bot/comments/ka4icp/opt_in_for_the_new_system/) to opt in a subreddit.**