According to the particular characteristics of cad modeling in reverse engineering and the practical demands from customers , the author made an elaborate and in - depth study on b - spline surface reconstruction in three aspects , including b - spline surface fairing , local b - spline surface designing and b - spline surface approximating based on complicated boundary constraints 本文结合反求工程cad建模自身的特点和用户的实际需要，主要对b样条曲面造型三个方面的工作做了较为细致和深入的研究和探讨： b样条曲面光顺、 b样条曲面局部设计和基于复杂边界约束的b样条曲面逼近。
3 ) b - spline surface fitting to contour data is studied . a fitting method of using uniform knot vector is given . using this method , the resulted b - spline s urface not only satisfy the requirements of precision , but also possess fewer c ontrol vertices and good fairness , the computation speed is greatly improved t oo 3 )研究了逐层扫描数据的曲面拟合问题，给出了一种是利用统一的节点矢量进行拟合的算法，用该法得到的b样条曲面不仅可以满足精度要求，而且具有较少的控制顶点和较好的光顺性，计算速度也有较大的提高。
So as to deal with this problem , local b - spline surface designing method with complicated trimmed boundary constraints is advanced . for two neighboring surfaces , we first trim a belt along the common boundary and then bridge a b - spline surface between these two trimmed surfaces with a smooth blending . with respect to the comer area comprised of several adjoining surfaces , a rectangular region covering the comer area is obtained by trimming operations at first , and later a local b - spline for filling the rectangular region is completed through interpolation or approximation 在两张相邻的曲面之间，先在其公共边界处裁剪出一个带状区域，然后再采用曲面搭接的方式实现曲面之间的光滑过渡；而在邻接曲面的公共角点处，先在该角点附近区域裁剪出一个矩形拓扑域，然后运用插值或逼近的方法，设计出一张既满足于该区域的边界条件同时又插值或逼近内部采样点的b样条曲面。
Chapter 4 discusses the usage of two basic geometric reconstruction method ( bezier and b - spline surfaces reconstruction ) in virtual cad system based on the milti - hierarchical mesh model . bezier reconstruction method introduces li lixin ' s new c - t algorithms which adopts bezier patches on rectangles . b - spline reconstruction follows floater ' s shape - preserving parametric method using double cubic b - spline surface and extends it into non - four - side areas by inducing corner vertices and optimizing the sheer - shape boundary which amends the boundary distortion of the reconstructed surfaces 通过引入单边退化概念，进行四边域上的bezier曲面重建；通过引入保形参数化映射，讨论双三次b样条曲面重建方法；在网格曲面四边拓扑分析的基础上，给出了基于深度搜索的角点求取方法，拓展了floater双三次b样条曲面重建的应用范围。
Nurbs surfaces with single interior knots are simple and used widely . the thesis main aims at biuquartic , biquintic , k x fc - degree b - spline surfaces and bicubic nurbs with single interior knots . one of the contributions is to apply knot refinement and the geometric continuous conditions of bezier surfaces to deduce the geometric continuous constraints of nurbs patches and obtain the intrinsic equations of common boundary curves , where the intrinsic equations are the special phenomena of nurbs surfaces 节点向量是内部单节点的nurbs曲面是最简单也是最常用的，本文重点针对单节点的双四次、双五次和双k次b样条曲面及双三次nurbs曲面，运用节点插入技术和b zier曲面的几何连续理论成果，导出了它们之间的几何光滑拼接条件，同时得到了公共边界曲线所必须满足的本征方程，其中本征方程是nurbs曲面所独有的现象。
The parts reverseeng ineering deals with mostly have freeform surfaces . the regeneration of the free form surfaces is the main task of reverse engineering . in this paper some key techniques for nurbs surface reconstruction in reverse engineering such as b - spline curve fitting , b - spline surface fitting to scattered data , b - spline surfa ce fitting to contour data and b - spline curve fairing are studied 本文研究了逆向工程中b样条曲面重构的关键技术，包括b样条曲线的拟合、散乱数据的b样条曲面拟合、逐层扫描数据的b样条曲面拟合以及b样条曲线的光顺。
So , the research of cad model reconstruction from scattered point cloud should be carried out urgently . the main key techniques contents of surfaces reconstruction from scattered point cloud data include data pre - processing , such as denoising data 、 filling holes and simplifying data , segmenting data , producing quadrilateral domains , and fitting b - spline surfaces 本文直接以测量获得的散乱点云数据为对象,研究了点云数据的几何特性计算、平滑处理、孔洞修补、数据简化等,在此基础上,进一步研究了点云数据分块、四边界区域划分及曲面拟合。
Secondly , on the basis of the discrete data and smooth feature of the surface of the radome , the inner surface is reconstructed by the bicubic uniform b - spline surface approximating means with least square method . finally , a tool - path planning method is presented , which is a combination of the constant scallop - height method with the isoparametric method 在分析目前最为成熟的结构化和面向对象软件工程方法的基础上，应用结构化和面向对象方法相结合的思想，实现了天线罩测量和磨削的软件系统的分析、设计和开发。
Aiming at the lack of traditional ploting method in the areas of three dimension graphics , the b - spline surface is adopted . in order to more easily build the b - spline surface the control points are replaced with one center point during the storage , and make it clear to simulate the curve of branches 在三维图形的绘制方面，针对传统绘制方法的不足，采用b样条曲面来构造三维几何模型，在曲面的生成及存储过程中用一个中心点代替多个控制顶点，将对曲面的控制转为对曲线的控制，使得对枝条形状的模拟更加方便直观，并且减少了存储空间。
Here two different methods of reconstructing b - spline surfaces from arbitrary topological triangle meshes are proposed , namely one method based on catmull - clark subdivision and the other based on partitioning and resampling . if smaller patches are required , the method based on catmull - clark subdivision is presented 在本文中，主要基于两种不同的应用角度探讨了如何将任意拓扑的三角网格数据转换为b样条曲面表示：基于catmull - clark子剖分的曲面生成与基于分割与重采样的大片b样条曲面生成。
