Trigonometric Polynomial Uniform B-spline Curves and Surfaces with Multiple Shape Parameters

In geometric modelling,the demand of local control ability of curves and surfaces is increasing.To provide more alternative approaches for designers,based on the piecewise integral,a class of trigonometric polynomial uniform B-spline curves and surfaces with multiple shape parameters is presented and the important properties of these curves and surfaces are discussed.The shape of such curves and surfaces can be adjusted totally or locally by changing the values of the shape parameters,and feasible range of the shape parameter values can be extended with the elevation of the order.The accurate expressions of straight lines,ellipses,parabolas and spirals are worked out by means of the presented trigonometric polynomial uniform B-spline curves,and some geometrical modelling examples of the curves are given to show that this kind of curves are of significant practical applications in computer aided geometric design.