刘旭敏, 黄厚宽, 王刘强, 马素静. 带形状参数样条曲线的研究[J]. 计算机研究与发展, 2007, 44(3).
 引用本文: 刘旭敏, 黄厚宽, 王刘强, 马素静. 带形状参数样条曲线的研究[J]. 计算机研究与发展, 2007, 44(3).
Liu Xumin, Huang Houkuan, Wang Liuqiang, Ma Sujing. Study of Spline-Curves with Shape Parameters[J]. Journal of Computer Research and Development, 2007, 44(3).
 Citation: Liu Xumin, Huang Houkuan, Wang Liuqiang, Ma Sujing. Study of Spline-Curves with Shape Parameters[J]. Journal of Computer Research and Development, 2007, 44(3).

## Study of Spline-Curves with Shape Parameters

• 摘要: 如何通过调整形状参数修改曲线形状是计算机辅助几何设计中一个有意义的研究课题.为了有效地利用形状参数来调整曲线的形状，增强修改曲线的灵活性，研究了5种带形状参数B样条曲线的表示方法及性质，这些曲线模型都可以通过改变形状参数的取值，调整曲线接近控制多边形的程度，从而得到不同位置的连续曲线.分析了每种造型方法的形状参数对曲线形状的影响，给出了形状参数的适用范围，比较了5种造型方法的特点.通过大量的公式推导和实验，提出了利用形状参数不同取值来表示一些自由曲线的新方法，并用实例进行了说明.实验证明，C-B样条曲线、带形状参数的均匀B样条曲线、带形状参数双曲多项式的均匀B样条曲线、带形状参数三角多项式的均匀B样条曲线都可利用形状参数的特定取值表示一些工业领域常用的自由曲线，这比起用控制顶点表示同样的自由曲线更为简单.

Abstract: To modify the curve shapes by means of adjusting the shape parameter is a topic of great significance in computer-aided geometric design. In order to adjust effectively the shape of a curve by using shape parameters and boost up its flexibility, the representations and properties of five types of B-spline curves with shape parameters are studied. For these curves, the approaching degree to their control polygon can be adjusted through the change of the value of shape parameters, and the curves with different continuity can be gained. The effects of the shape parameters on the curve shapes are analyzed, the range of shape parameters is presented, and the characteristics of each modeling means are compared. Through formula evolvements, experiments and illustrations with examples, some new approaches to present free-curves by means of different shape parameter values are also worked out. Experiments show that C-B spline curve, uniform B-spline with shape parameter, hyperbolic polynomial uniform B-spline with shape parameter and trigonometric polynomial uniform B-spline with shape parameter can be used to produce some frequently used free form curves in the industrial field when the shape parameter is assigned with some specific values. This process is simpler than producing these free form curves by using controlling vertex.

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