基于法矢控制的B样条曲面逼近的PIA方法

提出了一种基于法矢控制的 B 样条曲面逼近的渐进迭代逼近(PIA)算法。一方面该方法将离散数据点的切失、曲率、法矢等几何特征充分应用到离散数据点的逼近问题上，利用数据点两个方向的切矢构造出数据点的法矢约束来控制逼近曲面形状，相比于无法矢控制的 B 样条曲面逼近的渐进迭代逼近(PIA)方法，逼近曲面更光顺，可获得更好的逼近效果。另一方面由于该算法选取主特征点作为控制顶点，所以允许在曲面拟合中控制顶点的数目小于数据点的数目。而且PIA算法的每次迭代过程中的各个步骤都是独立的，很容易被应用到并行计算上，可提高计算效率。本文还给出了一些实例来验证该算法的有效性。

PIA for B-spline Surface Approximation with Normal Constraint

In this paper, we propose a progressive iterative approximation (PIA) algorithm for B-spline surface approximation with normal constraint. On the one hand, the discrete data points of the tangent vector, normal vector, curvature and other geometric characteristics are fully applied to the approximation problem of discrete data points, using the two directions of the tangent vector to construct normal constraint can avoid unnecessary fluctuations, and obtain better approximation effect. On the other hand, the number of selecting feature points is less than the number of data points, so the PIA algorithm can be used for the approximation of the mass of discrete data points. The steps in the process of each iteration of the algorithm are independent, which is easy to be applied to the parallel computing, which greatly improve the computational efficiency. Some examples are given to show the validity of the algorithm.