Research On Wang-Ball-Type Curve And Surface With Shape Parameters

Ball curves and surfaces are one of the important tools for designing curvesand surfaces, as well as Bézier curves and surfaces. However, when the controlpolygon is given, the location of Ball curve and Bézier curve is determined. Toadjust the shape of the curves, we need to adjust the control polygon, which is notflexible enough in practical application. In this thesis, we use the method ofintroducing two parameters in the basis functions of the curves to adjust the shapeof the curves by changing the value of the parameters. The family of new curves isunified representation of two kinds of Ball curves and Bézier curves.A class of Wang-Ball type blending functions with two shape parameters α、βis presented in this thesis firstly. This is an extension of Wang-Ball blendingfunctions, and the properties of this basis function are analyzed. Then, theWang-Ball type curves and surfaces with two shape parameters are defined basedon them, the properties of the corresponding curves are analyzed. The analysisshow that the defined curves not only inherit the properties of quartic Ball curves,but also achieve the transition from quartic Wang-Ball curves to Said-Ball curves and thetransition from quartic Said-Ball curves to Bézier curves. And it contains many curveslocating between the quartic Wang-Ball and Bézier curve. The geometric meaningof the shape parameters are studied, and it can generate curves fit closely to thecontrol polygon along with the different values of parameters, and it also can adjustthe shape of curves locally or globally. Then theG0、G1、G2_continuity conditionof two-piece of Wang-Ball type curves is discussed. Finally, the simulation exampleof the petals and vase generated by the Wang-Ball type curves with two shapeparameters show that the proposed method in this thesis can provide an effectivemethod for designing curves and surfaces.