【摘要】 利用三次非均匀有理B样条,给出了一种构造局部插值曲线的方法,生成的插值曲线是C2连续的.曲线表示式中带有一个局部形状参数,随着一个局部形状参数值的增大,所给曲线将局部地接近插值点构成的控制多边形.基于三次非均匀有理B样条函数的局部单调性和一种保单调性的准则,给出了所给插值曲线的保单调性的条件.更多还原

【Abstract】 A local interpolation method is presented by using the cubic non-uniform rational B-spline curves.The generated interpolation curves can be C2 continuous and have a local shape parameter.As the increase o the value of a shape parameter,the curves approach locally the control polygon constructed by the interpolation points.Based upon the local monotonicity of the cubic non-uniform rational B-spline curves and a criterion of mono-tonicity preserving,the condition for the monotonicity preserving of the given interpolation curves is given.更多还原