带形状参数的二次TC-Bezier曲线光顺延拓

Fairing Extension of Quadratic TC-Bezier Curves with Shape Parameter

在计算机辅助几何设计中,曲线的延拓得到了广泛的研究,但很少触及带形状参数的TC-Bezier曲线延拓的问题。本研究用连续作为约束条件,将曲线的最小物理变形能量作为目标函数,再根据最小化延拓曲线的物理变形能量来确定该延拓曲线的控制点,进而确定延拓曲线,从而得出带形状参数的二次TC-Bezier曲线的光顺延拓算法。实例表明,通过合理选择参数来调整曲线的形状,可以将该延拓技术应用于较复杂的曲线曲面工程造型中。

The extension problems of curves have been widely studied in the Computer Aided Geometric Design （CAGD）. However, the extension of TC-Bezier curves with shape parameter hasn＇ t been studied yet. This paper usescontinuity as the constraint condition to describe the smoothness of two curves at their joint point and takes the minimal physical deformation energy of the eurve as the objective function. The control points of the extension curve are determined by minimizin$ the physical deformation energy to decide the extension curve. Thus, a fairing extension algorithm of quadratic TC-Bezier curves with shape parameter is obtained. Examples show that via selecting reasonable parameter to adjust the shape of the curve, the extension technology can he used in the modeling of complex curve and surface engineering.