基于场表示的平面无序点集曲线重建算法

由无序离散点集重建出曲线曲面模型，在反求工程与计算机视觉中都有着广泛的应用。针对平面无序带噪声的曲线重建问题，通过模拟带电粒子在空间中形成场分布的现象，构造了一个反映平面点集形状与分布稠密程度的场函数，以场函数曲面的脊线在平面上的投影作为平面无序点集的重建曲线。为求得重建曲线，可先在平面上选取一条适当初始曲线，由初始曲线沿着场函数的梯度方向运动，其极限位置便为重建曲线。大量实例证明，这种方法简单可行，可获得满意的重建曲线；同时，对于带插值约束条件以及分布不均匀的点集，也可以获得满意的结果。

Planar Curve Reconstruction from Unorganized Points through Field Representation

Curve reconstruction from a set of unorganized points plays an important role in the fields of reverse engineering and computer vision. In this paper, we assume that every point are charged, then the intensity of the electric field will reflect the distribution and shape of the point set. Projection of the main ridge curve of the field surface on plane can be taken as the reconstruction curve of the point set. To find the reconstruction curve, we can first choose an appropriate initial curve on the plane and move every point on this curve along the gradient direction of the field function. The limit position of this active curve is the reconstructed curve. This method is simple and easy to implement. Experiments show that the algorithm is an efficient way for curve reconstruction. It also does well when the data points are incomplete or a series of fixed points should be passed through by the reconstructed curve.