中文摘要：

将曲线的最小物理变形能量作为目标函数，提出了一种三次T-Bezier曲线曲面的光顺延拓算法。利用G2连续性作为约束条件，则延拓的曲线具有两个自由度，并取其中的一个自由度为零；基于延拓曲线的最小物理变形能量确定第二个自由度及延拓曲线的控制点，进而确定延拓曲线，重新参数化所延拓的曲线可以与原曲线在拼接点处9连续拼接；此外，将该方法应用于双三次T-Bezier曲面的延拓。实例表明，该方法构造的曲线曲面具有较好的光顺性。

英文摘要：

Based on the minimal physical deformation energy of the curve, a fairing extension algorithm for cubic T-Bezier curve and surface is presented. Firstly, G2 continuity is used to describe the smoothness of two curves at their joint point. The exten- sion cubic curve has two freedom degrees. Then, the control points of extension curve are chosen as the solution by setting a freedom degree to be zero and determining the second freedom degree by minimizing the physical deformation energy. The new cubic T-Bezier curve is constructed by these produced control points. The extension curve is reparameterized to achieve C^8 conti- nuity with the given curve. Additionally, this method is also applied to the extension of hi-cubic T-Bezier surface in this paper. Experimental examples are presented to show that the extension curves and surfaces have better fairness.