Research On Controllable High-Order Smoothing Convex And Non-convex Bodies Based On KS Functions

Over the past decades, smoothing rough convex and non-convex bodies has been developed quickly in the world and found many applications in industry, it falls into the discipline of Computer Aided Geometric Design (CAGD), and it possesses important values of both applications and theoretical researches, as a result it is widely used in aviation, aerospace, automobile, shipbuilding and molding industry.This thesis has discussed the research history and current development of surface modeling and smoothing the appearance of 3-D geometric bodies both at home and abroad, and has analyzed the characteristics of all kinds of smoothing methods. Based on the characteristics of KS function (also called Maximum Entropy Function, or Condensing Function), a newsmoothing method has been presented —— Interior Radius Vector Sweeping (IRVS), someresearches have been done such as mathematic foundations of this method, characteristics and its applications, in addition, some application examples have been given.The main work in the thesis is as follows:1. Based on the characteristics of KS function, a more adoptable, more robust, high-orderdifferentiable function —— (?) function has been set up under the system of polar coordinate,and a new smoothing method —— Interior Radius Vector Sweeping has been set up.2. By using the Interior Radius Vector Sweeping method, the 3-D convex body defined by multiple functions has been smoothed.3. Referring the multi-stage substructure technology used in finite element method, anotherhigh-order smoothing method for non-convex bodies ——the high-order sequential smoothingmethod has been set up.4. "The virtual control function " has been defined to describe the smoothing and controlling plane, achieving another active controlling strategy beyond controlling smoothing process by interior parameter p of KS function.5. By extending Interior Radius Vector Sweeping and combining with Boolean operations, smoothing the convex cavities in the multiply connected domain has been studied.6. How to smooth the convex and non-convex bodies defined by discrete points has been described.The important conclusions are as follows:The K(?) function created in the polar coordinate system has same characteristics, high-order differentiation and precision controlling easily, as in Cartesian coordinate system. While the pole of polar coordinate is defined within the convex body, the minimum function in its enveloped set will be always selected by (?) function, so that it could be scanned and smoothed conveniently. The relevant theoretical research and typical examples in the thesis have proved the important role (?) function has played in the field.The important new developments in this thesis are as follows:1. Based on creating a new smoothing function ——(?) that is not only more general,but also robust and high-order differentiable while used, a new smoothing method has been introduced, i.e. the Interior Radius Vector Sweeping (IRVS), and its characteristics has been analyzed based on its mathematics background.2. Based on adding the "virtual control function", the derivative probability in the smoothed function set has been redistributed so that a new active controlling strategy has been achieved as well beyond using the parameter p .3.Based on the strategy of piece wisely smoothing, i.e. dividing the smoothed function set into some subset, therefore it is possible for smoothing the same category of complex non-convex bodies.This thesis has got financial support by National" 863 " high-tech research project: "Research of virtual prototype in complicated products based on coordination design and parallel engineering" (Serial number of the project: 2002AA411320).