Algorithms are presented for constructing G' continuous meshes of degree two (quadric) and degree
three (cubic) implicitly defined, piecewise algebraic surfaces, which exactly fit any given collection of
points and algebraic space curves, of arbitrary degree. A combination of techniques are used from
computational algebraic geometry and numerical approximation theory which reduces the problem to
solving coupled systems of linear equations and low degree, polynomial equations.
Chandrajit L. Bajaj,
"G1 interpolation using piecewise quadric and cubic surfaces", Proc. SPIE 1251, Curves and Surfaces in Computer Vision and Graphics, (1 August 1990); doi: 10.1117/12.19736; https://doi.org/10.1117/12.19736