Geometric Modeling by Blending Hermite Interpolation

A family of generalized Hermite-like interpolation polynomials is considered for geometric modeling. The generalized Hermite-like interpolation polynomials provide bias and tension control facilities for constructing continuous interpolating curves and surfaces. Geometric and algebraic forms of the generalized Hermite-like interpolation model are established and the representations of some conic segments based on the generalized trigonometric Hermite-like interpolation model are discussed. Moreover, a variable degree C2 continuous interpolation spline with the Hermite-like interpolation polynomials is established in this paper. The new interpolation spline, which need not solve m-system of equations, provides higher approximation order than normal cubic Hermite interpolation spline for proper parameters. The idea is extended to produce Coons-like surfaces.