Research And Application Of Moving Surface Fitting On Modeling Of Complex Surface

The complexity of the complex surface mainly reflected in two aspects: Firstly, for products involved in surface modeling in many marginal disciplines and fields producing high-tech products, high accuracy must been retained to meet certain the high-precision of mathematical characteristis; secondly, modern people not only pay attention to actual functions of the product but higher demands in the appearance of products, in order to rechieve more wonderful aesthetic effect. To meet the algorithm requirements of high numerical precision and smoothness in the complex surface modeling, the paper firstly research the theoretical methods about the complex surface modeling, then mainly research important factors of moving surface fitting and their improvement, used in the modeling of a new type of large vision mirrors. Finally the better results of the numerical sense were retained to meet mandatory standards.This paper mainly consists of the theoretical methods of complex surface modeling, the research of improved moving surface fitting and analysis of example. They state as follow.In the first part, the theoretical methods about the complex surface modeling are introduced. We analyze and compare cubic spline interpolation, B-spline interpolation quadric surface fitting, non-uniform rational B-spline surface fitting and so on.In the second part, we mainly research and improve the moving surface fitting. Firstly, we state the basical theorem of moving surface fitting, the necessary and sufficient condition of reversibility of A matrix, and its geometric significance, then analyze explicitly influences of different selection about, basis function, radius of influencing domain and weighted function. Since sometime equations caused by moving least-square are sick and even irreversible, we present the moving least square by adopting weighted orthogonal basis and the selecting principle of expanding properly radius of influencing domain. Finally, in the light of shortcomings of the moving least square, we present a kind of improved algorithm furtherly, which is easy to obtain by programming and is more sufficient to advance the precision of the fitting surface in the premise of ensuring the surface smooth. In the third part, we give application of practical example and analysis of result. Firstly, we introduce related knowledges of rearview mirror and the basis theory of reverse engineer. Secondly, we apply moving surface fitting on practical example——surface fitting of automobile rearview mirror, establish corresponding mathematical models and programme to achieve algorithms by Matlab. According to analyzing and comparing results, we prove the effectiveness of selecting principles about radius of influencing domain and the improved algorithm. The improved algorithm is confirmed to improve the precision of the fitting surface.At last, we summary the research work of the paper and put forward the idea of the next step of work.