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Is it possible to use blender to create a curved surface based on an original formula instead of the one used to create NURBS?

The way curved surfaces are created by computers is, for each conceivable point on a rectilinear surface, a formula is applied which evaluates the position of control vertices to determine where in space that location on the surface should be. What I'm wondering is, if it's possible to use a unique formula to evaluate the vertices, there in producing a new form which could be drastically different than would be the NURBS surface produced by those same control vertices?

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