I have a list of cubic bezier curves in 3D, such that the curves are connected to each other and closes a cycle.
I am looking for a way to create a surface from the bezier curves. Eventually i want to triangulate the surface and present it in a graphic application.
Is there an algorithm for surfacing a closes path of cubic bezier segments?
This might work provided the loop of curves is not too complex ...
Find a point to serve as a "center" point $P$ for the surface. For example, scatter a few dozen points along the loop of curves, and take $P$ to be the average of these points.
If you have $n$ Bezier curves $B_i$, then you can consider them to be a single composite curve parameterised over the interval $[0,n]$. The $i$-th curve $B_i$ corresponds to the parameter interval $[i,i+1]$. Let's denote this composite curve by $C(u)$, for $u \in [0,n]$. Then you can define a surface by $$ S(u,v) = (1-v)P + vC(u/n) \quad (0 \le u \le 1 \; ; \; 0 \le v \le 1) $$ This probably won't be a very beautiful surface, but if you're just going to triangulate it, then beauty maybe doesn't matter much.
If your loop of curves is highly convoluted, then this approach won't work very well. You will still get a surface, but it might be an unusable mess,