Abstract:

The shapes of the standard cubic parametric Hermite curve and surface are hard to be adjusted when the interpolation conditions are given. For solving this problem, a class of quartic Hermite basis functions is presented through increasing the degree of basis functions. And then, the corresponding quartic Hermite parametric curve and surface with shape parameters are presented. The proposed curve and surface are extensions of the corresponding standard cubic Hermite parametric curve and surface. They not only inherit the interpolation properties of the standard cubic Hermite parametric curve and surface, but also can be local or global adjusted by using the shape parameters when the interpolation conditions are fixed, which offers a new method for constructing interpolation curve and surface.

Key words: cubic Hermite curve and surface;shape parameter;interpolation curve and surface