New Extension of Uniform Cubic B-Spline Curve with Multiple Local Shape Parameters

胡钢 1; 2; 刘哲 1; 秦新强 2; 戴芳 2

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New Extension of Uniform Cubic B-Spline Curve with Multiple Local Shape Parameters

更新时间：2025-12-08

- New Extension of Uniform Cubic B-Spline Curve with Multiple Local Shape Parameters
- Vol. 42, Issue 10, Pages: 1245-1249(2008)
- 作者机构：
  
  1. 西北工业大学理学院,西安,710072
  2. 西安理工大学理学院,西安,710054
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP391.4
- Online First：10 October 2008，
  
  Published：2008
- 稿件说明：
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胡钢 1, 2, 刘哲 1, et al. New Extension of Uniform Cubic B-Spline Curve with Multiple Local Shape Parameters[J]. 2008, 42(10): 1245-1249.
DOI：

胡钢 1, 2, 刘哲 1, et al. New Extension of Uniform Cubic B-Spline Curve with Multiple Local Shape Parameters[J]. 2008, 42(10): 1245-1249. DOI：

摘要

为了构造带局部形状控制参数的B样条曲线

给出了一组含有λ

、 μ

2个形状参数的四次多项式调配函数

它是三次均匀B样条基函数的新扩展. 同时

分析了这组调配函数的性质

并基于调配函数定义了一种新的带有λ

、μ

2个局部形状控制参数的分段多项式样条曲线

其以三次均匀B样条曲线为特殊情形.最后

讨论了新曲线在曲线造型中的应用

并给出了相应扩展曲面的定义. 造型实例表明

新曲线不仅具有灵活的局部形状可调性和更强的描述能力

而且可以在不改变曲线G

连续性和不影响曲线其他各段形状的同时

通过改变局部形状参数对曲线每段的形状进行多种方式的局部调整

为曲线和曲面的设计提供了一种有效的新方法.

Abstract

The construction of B-spline curves with shape control parameters is one of the most popular areas in computer aided geometric design. A class of new polynomial basis functions with two local shape parameters λ

is presented to construct B-spline curves with multiple local shape control parameters

which is an extension of the classical cubic uniform B-spline basis functions. The properties of the proposed basis functions are analyzed and the corresponding piecewise polynomial curve with two local shape control parameters λ

is constructed. The extension not only inherits the outstanding properties of the cubic uniform B-spline curves

but also has a good performance on adjusting their

local shapes by changing the two local shape control parameters. In particular

the G

continuous and the shapes of other segments on the curve can remain unchanged during manipulating the shape of one segment on the curve. Eventually

some applications in curve design are discussed and an extended application in surface design is also presented. The modeling examples illustrate that the new extension provides a valuable way for the design of curves and surfaces.

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references

JOE B. Multiple-knot and rational cubic beta-splines[J]. ACM Trans on Graphics, 1989, 8(2): 100-120.

HAN Xuli. Quadratic trigonometric polynomial curves with a shape parameter [J]. Computer Aided Geometric Design, 2002,19(7):503-512.

ZHANG Jiwen. C-curves: an extension of cubic curves [J]. Computer Aided Geometric Design, 1996, 13(3):199-217.

LU ¨ Yonggang, WANG Guozhao, YANG Xunnian. Uniform hyperbolic polynomial B-spline curves [J]. Computer Aided Geometric Design, 2002, 19(6):379-393.

韩旭里, 刘圣军. 三次均匀B样条曲线的扩展 [J]. 计算机辅助设计与图形学学报, 2003, 15(5):576-578.

HAN Xuli, LIU Shengjun. An extension of the cubic uniform B-spline curves [J]. Journal of Computer Aided Design Computer Graphics, 2003, 15(5):576-578.

王文涛, 汪国昭. 带形状参数的均匀B样条 [J]. 计算机辅助设计与图形学学报, 2004, 16(6):783-88.

WANG Wentao, WANG Guozhao. Uniform B-spline with shape parameter [J]. Journal of Computer Aided Design Computer Graphics, 2004, 16(6):783-788.

王文涛, 汪国昭. 带形状参数的三角多项式均匀B样条 [J]. 计算机学报, 2005, 28(7): 1192-1198.

WANG Wentao, WANG Guozhao. Trigonometric polynomial uniform B-spline with shape parameter [J]. Chinese Journal of Computers, 2005, 28(7):1192-1198.

刘旭敏, 黄厚宽. 带形状参数样条曲线的研究 [J]. 计算机研究与发展, 2007, 44(3):487-496.

LIU Xumin, HUANG Houkuan. Study of spline-curves with shape parameters [J]. Journal of Computer Research and Development, 2007, 44(3):487-496.

徐岗, 汪国昭. 带局部形状参数的三次均匀B样条曲线的扩展 [J]. 计算机研究与发展, 2007, 44(6): 1032-1037

XU Gang, WANG Guozhao. Extensions of uniform cubic B-spline curve with local shape parameters [J]. Journal of Computer Research and Development, 2007, 44(6): 1032-1037.

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