# How do you fill a composite Bézier curve composed of a list of cubic Bézier curves

bezier-curvedesmosspline

According to Wikipedia:

"A composite Bézier curve is a series of Bézier curves joined end to end where the last point of one curve coincides with the starting point of the next curve."

I've created my own composite Bézier curve (also called a Béziergon) by creating a list of points (number of points must be $$4+2n$$ $$($$when $$n\geq{2}$$ and $$n$$ is an integer)), then creating a list of cubic Bézier curves from these points and connecting them together. I put them in Desmos, displayed the splines and it was successful.

However, when I use Desmos's parametric fill function, this happens:

This happens because I used a list of cubic Bézier curves, and it fills each cubic Bézier curve instead of the shape. I tried making a polygon to connect the endpoints of each cubic Bézier curve so that the empty space was filled, but that didn't work.

I observe that if any of the control points (not endpoints) of the cubic Bézier curves is inside the polygon, the polygon will be exposed on the outside. However, I do not know how to fix this problem.

Does anybody have any hints or ideas how to solve this problem? Do I have to create my own custom fill function?

If you want, here is the Desmos graph link. If you know how to solve this problem, perhaps you can copy the Desmos graph, type in your own solution, and put the new link in your answer. Thank you!