Generalized Circle Spline Curves And Surfaces Modeling And Its Applications

This thesis is focused on the curve and surface modeling problem in CAGD and CAM field. Based on a blending approach, we discuss generalized circle spline curves and surfaces modeling and its applications, including the blending-based curve modeling methods, locally adjustable generalized circular interpolation spline blending schemes, furthermore, these schemes are generalized to circular surface, and its application to blending pip surface is given. Thesis framework as follows.We first review the research history, classification, and significance of the free-form curve and shape modeling. We then present some key technologies in the recent CAGD field in order to introduce our research topic, the blending-based modeling method. We summarize the general process of the blending-based method including curves and surfaces and the potential pitfalls in the existing methods, then expound our research contents and motivation.In the third chapter, by means of two points and a tangent with free parameters, we propose a few fairing locally adjustable generalized circular blending schemes which is different from the existing circular schemes depended on three points. The advantages of the proposed schemes lie in that it can simultaneously meet the requirements like fairness, G1/G2 continuity, local adjustability, shape-preserving and etc. We also demonstrate the compatibility between the blending scheme and the NURBS system.Finally, we extend the blending-based method to the surface case, and construct locally adjustable generalized Gn continuous circular interpolation spline surface schemes with free parameters. Furthermore, blending the pip surface by proposed spline surface is given. Experiments show the proposed methods are effective.