I'm thinking about a way of generating a 2d surface from a region defined by 4 splines, each spline being a simple parametric 1d cubic curve.

Ideally I maybe can do something similar to the Tensor product surface, that uses only two curves, however, I want the points to be generated smoothly inside the boundary of 4 curves. Thinking about a map from the unity square to the surface, the edges $(0,t)$ and $(1,t)$ would correspond to two of the boundary curves. As same thing for $(t,0)$ and $(t,1)$ in the parameter space.

Is there a way to use the four curves in same way (maybe an extension of the tensor product) to generate the surface?

I know there is probably infinitely many ways of generating the surface, I just want one that is some kind of manifold (smooth and don't overlap).



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