On The Theory Of H-bezier Curves

The thesis is comprise of six chaptersIn the first chapter, the author briefly introduces the background and the main content of this thesis. In the second chapter based on the analysis of the proprieties of cubic H-Bezier curves, a middle subdivision and any point subdivision algorithm are proposed. The connection conditions between cubic H-Bezier curves and cubic H-Bezier curves,and cubic H-Bezier curves and Bezier curves are derived and the cubic H-Bezier curves in the surface modeling are given.In the third chapter based on the research of the proprieties quartic H-Bezier curves with all edges tangent to a given control polygon.In the fourth chapter an effective middle subdivision formula for quartic H-Bezier curves is presented. Furthermore, it is proved that the control polygons generated by the subdivision converge to the original quartic H-Bezier curves.Two important properties, the variation diminishing (V-D) and convexity preserving property are proved for quartic H-Bezier curves.In the fifth chapter, presents a class of Bezier-type curves with parameter in spaceF3={1,t,sinht,cosht}, and the conic curve such as hyperbola catenary are exact denoted by H-Bezier curves. And then, the surface modeling using shape parameter is discussed.In the end, the author summarizes full text and prospects the research work of aftertime.