有理三角Bézier曲线曲面光滑融合的构造

为了使自由曲线曲面在较为简单的条件下能够达到相对高阶的光滑拼接，并在不改变控制顶点的情况下自由调整曲线曲面的形状，构造了含多个形状参数的有理三角函数.基于该组基函数，定义了含多个形状参数的有理三角曲线曲面，并讨论了曲线曲面的光滑拼接条件.根据拼接条件，分别定义了由含多个形状参数的有理三角曲线曲面构成的分段组合曲线、分片组合曲面.这种新的曲线曲面能够自动保证组合曲线、曲面的连续性.数值实例的结果显示了该方法的有效性.

Smooth blending of rational trigonometric Bézier curves and surfaces

In order to achieve high level of smooth blending between the free form curves and surfaces in relatively simple conditions and easy shape adjustment of the curves and surfaces without changing their control vertices, a set of rational trigonometric Bézier basis functions with multiple shape parameters are constructed. Based on these basis functions, the rational trigonometric Bézier curves and surfaces with multiple shape parameters are defined, and the conditions for smooth joining of these curves and surfaces are derived. Following the above conditions of blending, the piecewise composite rational curves and surfaces with multiple shape parameters are defined, which automatically meet with the higher order continuity. The results of numerical examples show the effectiveness of the method.