Based On The Fusion Curve And Surface Modeling Technology Research And Applications

This thesis is focused on the curve and surface modeling problem in CAGD and CAM field. Based on a blending-based viewpoint, we roundly summarize our theoretical research work and experimental application in this thesis. The contents includes the blending-based curve modeling methods, conic blending scheme, several generalized blending-based interpolation schemes, the fairness and convexity-preserving analysis, and blending-based surface research, etc.We first review the research history, classification, characteristic and significance of the free-form curve and shape modeling. We then present a survey of the several key technologies in the recent CAGD field. This is the base motivation of our research topics. Due to the significance of the blending-based modeling method, we detailedly analysis the existing three types of blending-based circular interpolation schemes, summarize the process of the blending-based method, and thoroughly expound the research motivation and main research contents of this method, which will be viewed as the theoretical framework for our research topics in the following chapters.In order to construct blending schemes with better modeling ability, we introduce the rational bezier curve into our blending process, and then propose three types of the nonlinear conic blending schemes, two of which are proved to be C~2 continuous. The advantages of the proposed scheme lie in that it can simutaniously meet the requirements like fairness, C~2 continuity, local adjustability, etc. We also demonstrate the compatibility between the blending scheme and the NURBS system.Act as a powerful supplementary for the field of concrete data interpolation, we abstract the main idea of the blending scheme, organically combine the blending vector and the type of the participanting curves, and then propose the bi-circular blending scheme. We also generalize the parametrical blending equations into the matrix form, obtaining the C~1 continuous rational first-order blending vector, the C~1 continuous rational quadratic blending vector, and the C~3 continuous cubic blending vector. With the help of our abstraction of the blending process, we are able to achieve more valuable blending schemes.According to the convexity theory of the discrete data, we present the convexity-preserving condition for the conic blending scheme from the geometry point of view, which can avoid directly computing the parametrical expression for the first-order, second-order, or even high order blending equations. Using the generalized C~1 continuous rational first-order blending vector in the Chapter 4, we verify the convexity-preserving property for the proposed condition.Due to the modeling power of the proposed blending methods, we then propose a novel recursion approach, which can arbitrarily build C~n continuous interpolatory curves. This approach can largely strengthen the modeling ability of the blending-based schemes, and is valuable for constructing high-order interpolatory curves.Being inspired by the Bezier spline and patch theory, we formulate the three- dimentional blending-based patch equation, and make comparison with the Bezier patch properties. As a matter of fact, the blending-based surface patch has many advantages that the Bezier patch do not have, that is, our blending-based surface patch does not need to handle the mesh smoothing connect problem and the patch automatically achieve C~n continuous according to the selected blending vector.We finally incooperate the blending-based idea into the digital image interpolation field, and then propose a conic blending based adaptive nonlinear image interpolation algorithm. The formulated kernel interpolation function, comparing to the traditional methods, excels in efficiency and interpolation ability. Experimental results also demonstrate that our algorithm can not only preserve the high-frequency information within the image, but it also reconstructs the low-frequency information as well.