Constructing Convexity-Preserving Interpolation Curves of Hyperbolic Polynomial B-Splines Using a Shape Parameter

Using a blending factor, a parametrized singular polyline is blended with the hyperbolic polynomial B-spline curve to automatically generate a C\+2 (or G\+1) continuous hyperbolic polynomial B-spline with a shape parameter, which interpolates the given planar data points. By converting the curvature sign function of the interpolating curve into Bernstein polynomial, the nonnegativity conditions of Bernstein polynomial can be used to obtain the appropriate value of the shape parameter satisfying the convexity-preserving property of the constructed curve. The method is simple and convenient and need not to solve a system of equations or recur to a complicated iterative process, and the resulting interpolating curves possess smooth distribution of curvature. Several numerical examples are given to illustrate the correctness and validity of the algorithm.