Fairing Extension of Quadratic TC-Bezier Curves with Shape Parameter

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 curve as the objective function. The control points of the extension curve are determined by minimizing 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 be used in the modeling of complex curve and surface engineering.