Algebraic surface design with Hermite interpolation

Chanderjit L. Bajaj, Insung Ihm
1992 ACM Transactions on Graphics  
This paper presents an efficient algorithm for constructing the lowest degree algebraic surfaces, which contain with C 1 continuity, any given collection of points and algebraic space curves having derivative information. Positional as well as derivative constraints on interpolating implicitly defined algebraic surfaces are translated into a homogeneous linear system, where the unknowns are the coefficients of the polynomial defining the algebraic surface. The containment of given points and
more » ... ves with C 1 continuity, termed Hermite interpolation, yields tangent plane continuous surface fits. Computational details of the Hermite interpolation algorithm are also presented along with several illustrative applications of the interpolation technique to the construction of joining or blending surfaces for solid models as well as fleshing surfaces for curved wireframe models. A heuristic approach to interactive shape control of implicit algebraic surfaces is also given, and various open problems in algebraic surface design are discussed.
doi:10.1145/102377.120081 fatcat:5bgtbvygyffphlaiktn5nxhney