摘要
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。
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 con- tinuity and approximation than cubic B-spline curve.
出处
《东华理工大学学报（自然科学版）》
CAS
2012年第2期197-200,共4页
Journal of East China University of Technology(Natural Science)
关键词
曲线曲面造型
B样条曲线
形状参数
三角基
curve and surface modeling
B-spline curve
shape parameter
trigonometric basis
