B样条曲面的形状修改——基于等参线的曲面缝合

Shape Modification of B-Spline Surface——Stitch of B-Spline Surfaces Based on Isoparametric Curve

参数曲面的形状修改在几何建模的过程中具有非常重要的作用。本文给出了两种方法:最小二乘法和能量法。这两种方法能修改B样条曲面,使得修改后曲面的等参线精确地通过指定的目标曲线并可在目标曲线处达到C1连续拼接。推导出明确的公式可以计算修改后的曲面的新控制顶点,该方法简单、快速。最后给出了基于等参线B样条形状修改和曲面曲面缝合在飞机和汽车外形逆向设计中的具体应用实例。

The shape modification of parametric surfaces plays an important role in geometric modeling. Two approaches, least square based method and energy minimization based method, are presented to modify the shape of B-spline surfaces. The isoparametric curve on the modified surface passes through the specified target curve exactly and retains Ca continuity simultaneously. Explicit formulae are derived to compute the new control vertices of the modified surface, thus the proposed methods are simple and rapid. Examples of the isoparametric B-spline curve based shape modification and surface stitch are also presented for the revere shape design of the aircraft and the car.