Blending algebraic surfaces

A new definition of geometric continuity for implicitly defined surfaces is introduced. Under this definition, it is shown that algebraic blending surfaces (surfaces that smoothly join two or more surfaces) have a very specific form. In particular, any polynomial whose zero set blends the zero sets of several other polynomials is always expressible as a simple combination of these polynomials. Using this result, new methods for blending several algebraic surfaces simultaneously are derived.