【作者】 朱安风；

【导师】 黄有度；

【作者基本信息】 合肥工业大学 ， 计算数学， 2007， 硕士

【摘要】 本文一共包含五章内容。第一章简单的介绍了研究背景以及主要研究内容。第二章在空间T_n=span{1，t，t²，…，t^n-4，sinht，cosht，tsinht，tcosht}中提出一组名为H-Bézier的基，讨论了该基的性质。并用该组基定义了H-Bézier曲线，同时证明有许多实际应用价值的曲线（如代数曲线和超越曲线）可以用H-Bézier曲线的形式精确表示。第三章在第二章的基础上在空间T_n=span{1，t，t²，…，t^n-4，sinht，cosht，sinh2t，cosh2t}中也提出一组名为H-Bézier的基，讨论了该基的性质。并用该组基定义了H-Bézier曲线，同时证明有许多实际应用价值的曲线（如代数曲线和超越曲线），可以用H-Bézier曲线的形式精确表示。第四章介绍三次样条函数的定义，给出用型值点处的一阶导数、二阶导数表示插值三次样条曲线的关系式，最后给出求解插值三次样条曲线的步骤。第五章从双曲函数出发，构造了一类插值于首、末端点及其切矢的参数样条曲线，称为H-Ferguson曲线，并研究了合成H-Ferguson曲线的算法。引入了参数α可调整整条曲线。H-Ferguson曲线丰富了参数样条曲线，是一种可行的算法。更多还原

【Abstract】 This thesis is composed of five chapters.In the first chapter, the author briefly introduces the background and the maincontent of this thesis.The second chapter, a basis called H-Bezier basis, is constructed for thespace T_n=span{1,t,t²,…,t^n-4,sinh t, cosh t, t sinh t, t cosh t}. Properties of this basis areanalyzed and H-Bezier curves are defined based on it. Then it is demonstrated thatmany valuable curves, such as algebraic curves and transcendental curves, can beexpressed by H-Bezier curves.Basis on the second chapter, in the third chapter a basis called H-Bezier basis, isconstructed for the space T_n=span{1,t,t²,…,t^n-4,sinh t, cosh t, sinh 2t, cosh 2t}.Properties of this basis are analyzed and H-Bezier curves are defined based on it.Then it is demonstrated that many valuable curves, such as algebraic curves andtranscendental curves, can be expressed by H-Bezier curves.The fourth chapter, the definition of cubic spline function is introduced. By firstderivative of given data points、second derivative of given data points, therelational expression of interpolation cubic spline curve is given. Finally, the stepsof solving the interpolation cubic spline curve is given.The fifth chapter, a kind of parameter spline curve is constructed based onalgebra and hyperbola function, which is named H-Ferguson curve. TheH-Ferguson curve interpolates start point and end point, and also interpolatestangent vectors of start point and end point. Then the arithmetic of composedH-Ferguson curve is studied. H-Ferguson curve enriches the theory of parameterspline curves, which is a feasible method of constructing interpolation curve.更多还原