B-Spline for any number of control points

I am currently working on a soft body system using numeric spring physics and I have finally got that working. My issue is that everything is currently in straight lines.

I am aiming to replicate something similar to the game “The floor is Jelly” and everything work except the smooth corners and deformation which currently are straight and angular.

I have tried using Cubic Bezier equations but that just means every 3 nodes I have a new curve. Is there an equation for Bezier splines that take in n number of control points that will work with loop of vec2’s (so node[0] is the first and last control point).

Sorry I don’t any code to show for this but i’m completely stumped and googling is bringing up nothing.