H-Bézier And Ferguson Curves Based On Hyperbola Function

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.