论文标题
B-Spline曲线与数据点拟合时降低和均匀的参数近似
An error reduced and uniform parameter approximation in fitting of B-spline curves to data points
论文作者
论文摘要
提出了基于立方B-Spline曲线的三个或更高维空间中的近似数据点。平面曲线的表示形式合并并扩展到更高的维度。曲线拟合到数据点的顺序，或者假定该点均匀的参数值。在数据点上假定切线，对应于基本花纹中使用的属性，以保持形状保存和视觉令人愉悦的拟合度。分段连续的立方体曲线的控制点，满足基本样条段的边界条件，用于相应的坐标平面中的b-Spline曲线。还提出了使用最小平方含义计算的误差（基于数据点的一小部分）近似。
Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or uniform parameter values are assumed for the points. Tangents are assumed at the data points, corresponding to the property used in cardinal splines, for shape preserving and visually pleasing fit. Control points of piecewise continuous cubic bezier curves, meeting the boundary conditions of cardinal spline segments, are used for b-spline curve in corresponding coordinate planes. Approximation using error computed in the least square sense, based on a fraction of data points, is also presented.
