Extension of Quadratic Uniform B-Spline Curves Based on the Linear Combination of Basic Functions

摘要

Based on the linear combination of B-spline bask functions,the quadratic uniform B-spline curves is extended. The extended curves not only include the original ones but also show much better shape-control and position-adjusting capability than the given ones. And the extended curves keep the form of quadratic polynomials. Its expression is simpler than that of the traditional shape parametric curves. Moreover,some properties of the extended curves are discussed in details. It is easy to find that,by adjusting the value of the shape factor,the shape and position of the curves can be changed. Meanwhile,the representation of the closed curves becomes very simple. So the generalized curves have theoretical significance and applicable value in the design of free curves and surfaces.