The geometry of projective blending surfaces
The main point of the article is the completeness theorem: Let G and H be irreducible quadrics. Let \(G'\) and \(H'\) be two quadrics such that \(G\cap H'=g\) and \(H\cap G'=h\) are irreducible, and assume that \(G\cap H\) is irreducible and coincides neither with g nor with h. Then every degree-4 surface F tangent to G in the curve g and tangent to H in the curve h has the equation \(K^ 2-\mu GH=0,\) where \(\mu\) is a constant and K is a quadric containing both g and h. The authors summarize foregoing investigations (affine version), explore new aspects (projective version), and discuss other methods and the prospects for deriving blending surfaces automatically.
scientific article; zbMATH DE number 4100057