带形状参数的三角曲线曲面

为了保留B样条曲线的优点,同时克服B样条曲线在控制顶点给定的情况下不具备形状可调性、不能精确表示椭圆(圆)的缺点,定义了一种带形状参数的三角样条曲线.新曲线具有与三次B样条曲线相同的结构与基本性质,但因为引入了形状参数,并采用三角函数作为基底,新曲线还具备了三次B样条曲线不具备的两个性质,即形状可调性和可以精确表示椭圆(圆).另外,新曲线还具有比三次B样条曲线更好的连续性和对控制多边形的逼近性.

Trigonometric Curves and Surfaces with Shape Parameter

The shape of B-spline curve is fixed to its control polygon,and it cannot describe the ellipse exactly.In order to preserve the merits of B-spline curve,and overcome the two defects mentioned above,we define a new triangular spline curve with shape parameter.The new curve has the same structure and basic properties of cubic B-spline curve.Due to the induction of shape parameter,and adoption triangular function as basis,the new curve not only has shape adjustability,but also describes the ellipse exactly.In addition,the new curve has better continuity and approximation than cubic B-spline curve.