为了使设计的曲线曲面能在相对简单的条件下满足较高的光滑融合,并且在不改变控制顶点的情况下可任意修改曲线曲面形状,构造了带形状参数的三角Bézier基函数.基于该组基函数定义了λC-Bézier曲线曲面,即分别有4个控制顶点定义的三角曲线和16个控制网格定义的三角曲面.讨论了曲线、曲面光滑融合需满足的条件,根据融合条件可构造分段光滑的组合曲线曲面.这样融合的曲线曲面能在一定条件下保证组合曲线、曲面的连续性.数值实例显示了该方法的有效性.
Trigonometric polynomial functions with shape parameters are proposed. The λC-Bézier curve and surface basis can achieve higher order smoothness by joining in relatively simple conditions. Meanwhile, their shape can be adjusted freely without changing control points. Based on the trigonometric Bézier polynomial functions, we define a new λC-Bézier curve determined by four control points and a new λC-Bézier surface determined by sixteen control net.The smooth blending conditions of the new curve and surface are discussed. Under the blending conditions, we define a piecewise combination curve and surface consisting of the λC-Bézier curve and surface. The method automatically ensures continuity of the curve and surface. Experimental results show effectiveness of the method.
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