Is there a program that creates formulas for 2d closed lines?

Question

higher mathematics

For example, I have a channel (like the letter "p"). I draw it by points on a Cartesian coordinate system and some program creates a formula for this figure for me. Is there such a program? Thank you.

Answer 1

Fourier transform along the x and y axes.
Here is the video . The source code of the program is in the description of the video.

Answer 2

This is called interpolation. The interpolating function can be of various types. Most often, a polynomial in degrees is chosen. To do this, use Newton's formula: https://ru.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D...