Research Of Some Curves With Multiple Parameters In CAGD

The curves and surfaces with multiple parameters have very important application in CAGD. This paper mainly introduces two kinds of cruves and surfaces with multiple parameters.(1) Quadratic non-uniform hyperbolic B-spline curves with multiple shape parametersWe present a class of quadratic non-uniform hyperbolic B-spline curves with multiple shape parameters based on three points. Taking different values of the shape parameters, one can totally or locally adjust the shapes and position of the curves. Without using multiple knots or solving system of equations, the curves can directly interpolate certain control points and control sides. The hyperbola can be also represented by them.(2) Extensions of Said-Bézier type generalized Ball curves and surfaces with multiple shape parametersExtensions of Said-Bézier type generalized Ball curves and surfaces over triangular domain with multiple shape parameters are presented in this paper. Their blending functions have explicit expressions and are easy to derivate and integrate. They include the common Ball curves and surfaces, Bézier curves and surfaces. The shape of the curves and surfaces can be adjusted entirely or locally by changing the values of the shape parameters.