拟合是计算机图形学的基础算法之一，在逆向工程、几何建模等方面有着重要的应用。作为以骨架为基础的参数化实体表示，盘B样条曲线和球B样条曲线有严格的数学定义，能够显式表示骨架，容易操控。在已有的盘B样条曲线和球B样条曲线理论研究中，有关盘B样条曲线和球B样条曲线的延拓算法、求交算法以及表面拟合算法等都已经展开了研究，并取得了一定的成果，对实体拟合的研究还未开展。因此本文就有关盘B样条曲线和球B样条曲线实体拟合方面的内容进行研究。主要研究内容和创新如下： （1）本文提出了二维盘B样条曲线实体拟合算法，可精确地表示原始二维区域。此工作的创新点为：首先，率先提出了盘B样条曲线实体拟合算法流程，并且将近似逼近问题转化成非线性优化问题；其次，通过对盘B样条曲线上下边界公式进行了准确的计算和求解，提出了通过计算散乱点到盘B样条曲线的单向Hausdorff距离来确定优化目标函数；最后采用PSO（Particle Swarm Optimization）算法对数据点的参数值、初始的节点向量和控制盘进行优化，最终得到优化后的盘B样条曲线。以汉字的二维笔画为实验对象，对优化过程中的拟合曲线的控制盘个数、拟合误差、算法时间复杂度与算法鲁棒性进行了详细分析，实验结果充分验证算法有效性。 （2）本文提出了三维球B样条曲线实体拟合算法实现对原始三维实体数据形状的有效表示。此部分的创新性工作为：首先，将近似逼近问题转换为非线性优化问题。在精确分析球B样条表面公式的基础上，构建了球B样条曲线与拟合散乱点的单向Hausdorff距离的离散解法和连续解法，并将其作为拟合的优化目标函数；其次，应用PSO算法解决拟合过程中的高维不可微函数优化问题，统一对数据点的参数值、初始的节点矢量和控制球进行迭代优化，最终得到优化的球B样条曲线。本部分以三维血管的体数据为实验对象，对优化过程中的拟合曲线控制点个数、误差分析、算法时间复杂度与算法鲁棒性进行了详细分析，实验结果充分验证算法有效性。 本文在表面拟合算法的基础上，进一步对盘B样条曲线和球B样条曲线实体拟合算法展开研究。本研究为二维和三维实体的造型提供了理论基础，同时为模式识别、物体建模、二维动画和三维动画的制作等方面的应用提供了算法支持，具有重要的理论研究意义与实际应用价值。

Fitting is one of the basic algorithms of computer graphics, and it has important applications in reverse engineering and geometric modeling. As a parameterized region representation based on skeleton, disk B-spline curves and ball B-spline curves have rigorous mathematical definition, and are flexible for modeling and manipulation. And it can explicitly represent the skeleton. In the previous theoretical study of disk B-spline curves and ball B-spline curves, extension algorithm, intersection algorithm, fitting scattered points on the surface algorithm, etc. have been investigated yet. But region fitting has not been investigated yet. In this paper, we study the problem of fitting scattered points in 2D/3D region to generate disk B-spline curves and ball B-spline curves. （1）A region fitting algorithm for two-dimension disk B-spline curves is proposed in this paper. And it can accurately represent the original two-dimension region. The innovation of this work is as follows: firstly, the region fitting algorithm of disk B-spline curves is first proposed., and in the fitting algorithm, we convert the approximation problem to a nonlinear optimization problem. Secondly, by calculating and solving the upper and lower boundary of disk B-spline curves, the optimization objective fuction is determined by calculating the one-way Hausdorff distance from the scattered points to the disk B-spline curves. Finally, we use PSO(Particle Swarm Optimization) algorithm to solve the above optimization problem. The procedure includes initialization of DBSC, parameterization of scattered points, knot vector determination and computing control disks. The two-dimension strokes of Chinese characters are used as experimental objects. The number of control disks, the fitting error, the time complexity of the algorithm and the robustness of the algorithm are analyzed in detail in the optimization process. The experimental results fully verify the effectiveness of the algorithm. （2）A region fitting algorithm for three-dimension ball B-spline curves is presented in this paper. And it can effectively represent the shape of original three-dimension solid data. The innovative work of this part is as follows: firstly, we convert the approximation problem to a nonlinear optimization problem. On the basis of exact analysis of the surface formula of the ball B-spline curves, the discrete solution and continuous solution of the one-way Haudorff distance between the ball B-spline curves and the scattered points are constructed, and it is used as the optimization objective function of the fitting. Secondly, the PSO algorithm is used to solve the optimization problem of high-dimensional undifferentiable function in the fitting process, and the parameters of the data points, the initial knot vector and the control balls are iteratively optimized, finally the optimized ball B-spline curve is obtained. In this part, the volume data of the three-dimension blood vessel is taken as the experimental object, and the number of control points, the error analysis, the time complexity of the algorithm and the robustness of the algorithm are analyzed in detail. Finally, the experimental results fully vertify the effectiveness of the algorithm. Based on the surface fitting algorithm, we further study the region fitting algorithms of disk B-spline curves and ball B-spline curves. This study provides a theoretical basis for the modeling of two-dimensional and three-dimensional solid, and it can provide algorithm support for the application of pattern recognition, object modeling, two-dimensional animation and three-dimensional animation production. This research has important theoretical significance and practical application value.