How to find the equation of a curve describing a figure?

Question

Mathematics

Actually, that's the whole question, except that it can be slightly clarified: how to find the equation of the curve describing the figure, if the coordinates of the points on which the figure is built are known?
For example, what equation can describe a figure consisting of points with such coordinates:
( 40, 20 )
( 140, 120 )
( 120, 140 )
( 20, 40 )

Answer 1

Apparently, you need to somehow interpolate. For example, the easiest way, Lagrange interpolation polynomial . It has the property that it will definitely pass through all points, but between them it will behave unpredictably (read - fly to heaven or to the plinth). Well, all other interpolations exist.

Answer 2

First, we need to clarify what kind of curve we are looking for - y = f (x) or parametric, of what order.
On a vskidka, something like a distorted ellipse or some kind of sine fits into your points, if the order of the points is given incorrectly.

Answer 3

Bizier curves are the foundation of vector graphics.
The starting point is 100% they are.