一种基于端点非插值性的NURBS曲面重构方法

A reconstruction method for NURBS surface by curve unclamping

为了解决多面片拼接曲面、多修饰特征曲面连续性差且难以延展的问题,提出了基于端点非插值性的NURBS曲面重构方法.首先根据位置和曲率的不同,将原始曲面离散为点云数据,根据离散点计算各个采样路径上的节点矢量;然后计算出曲面重构所需的端点非插值性的共同节点矢量及相应的控制点,并将共同节点矢量转化成标准的端点插值节点矢量,根据最新的端点插值节点矢量在无数据点区间插入新的型值点;最后将所有数据点重新拟合成单一曲面.重构结果表明,通过使用该方法重构所需的计算量降低,重构出的曲面精度较高.在曲率变化剧烈处,既保证了与原始曲面的贴合率,又保证了截面线的曲率连续性.该方法将原始曲面重构为单一曲面,提高了曲面重构精度,有效地解决了造型中易出现的曲面退化、曲面畸变等问题.

To solve the poor continuity and extension of surface with multipatch splicing and dress up features, a non-uniform rational B-spline （NURBS） surface reconstruction method based on the unclamping was proposed. First, the original surface was discretized into point-cloud according to the different locations and curvatures, the knot vectors of each sampling path were calculated based on discreted points. Then, the unclamping common knot vector and the control net required for surface-reconstruction were calculated, and the unclamping common vector needed to be changed into the clamping common vector. Based on the latest clamping vector, new data points were inserted in-to the rectangle without data. Finally, all data points were fitted to a single surface. The reconstruction results show that the amount of calculation is reduced and the reconstructed surface has high accuracy .It can guarantee the fitting ratio and the continuity of curvature where the curvature has sharp change. During modeling, the proposed method reconstructs the original surface to a single surface, improves the precision of the surface reconstruction and solves problems, such as surface degradation and surface distortion.