两类形状可调五次广义Ball曲线

图学学报

两类形状可调五次广义Ball曲线

出版日期:2011-12-30 发布日期:2015-08-12

Two Classes of Quintic Generalized Ball Curves with Adustable Shape

Online:2011-12-30 Published:2015-08-12

摘要/Abstract

摘要： 定义了两种带形状参数的曲线。第一种曲线包含了五次Wang-Ball和Said-Ball曲线以及介于这两种曲线之间的无数曲线；第二种曲线包含了五次Said-Ball和Bézier曲线以及介于这两种曲线之间的无数曲线。通过分析这两种曲线与五次Bézier曲线之间的关系，得出了形状参数的几何意义，并给出了这两种曲线的几何作图法。

关键词: ：Wang-Ball基函数, Said-Ball基函数, Bernstein基函数, Ball曲线, 形状参数

Abstract: Two new classes of curves with shape parameters are defined. The first class of curve contains the quintic Wang-Ball and Said-Ball curves and the curves located between them. The second class of curve contains the quintic Said-Ball and Bézier curves and the curves located between them. By analyzing the relationship between the new curves and the quintic Bézier curve, the geometric meaning of shape parameters are obtained, and the geometrical drawing method of the new curves are given.

Key words: Wang-Ball basis function, Said-Ball basis function, Bernstein basis function, Ball curve, shape parameter

严兰兰，张文，温荣生. 两类形状可调五次广义Ball曲线[J]. 图学学报.

YAN Lan-lan, ZHANG Wen, WEN Rong-sheng. Two Classes of Quintic Generalized Ball Curves with Adustable Shape[J]. Journal of Graphics.

[1]	胡先智 , 梁艳 , 吕丹 , 胡钢 . 基于GIMT和弧长参数化的QG-Ball曲线近似合并[J]. 图学学报, 2021, 42(5): 790-800.
[2]	邹倩 1,2，韩旭里 2 . 带形状参数的 R-Coons 曲面[J]. 图学学报, 2019, 40(2): 388-394.
[3]	彭兴璇，潘晶，陈雪娇，蒋新昕. 切点可调的带形状参数的二阶三角Bézier 曲线[J]. 图学学报, 2017, 38(4): 463-468.
[4]	严兰兰1，韩旭里2，李水平1. G1 保形多项式插值曲线[J]. 图学学报, 2017, 38(2): 144-154.
[5]	严兰兰，韩旭里. 基于全正基的三次均匀B 样条曲线的扩展[J]. 图学学报, 2016, 37(3): 329-336.
[6]	刘成志，李军成，杨炼. 带形状参数曲线的最优参数取值问题研究[J]. 图学学报, 2015, 36(4): 532-536.
[7]	刘植，李晨，谢进，费腾. 一类双参数三次Bézier 曲线的形状分析[J]. 图学学报, 2015, 36(3): 356-362.
[8]	郭大勇，成佳颐. 基于二项式系数设计矩阵的Bézier曲线扩展[J]. 图学学报, 2014, 35(4): 511-517.
[9]	严兰兰，韩旭里，黄涛. 五阶与六阶三角样条曲线[J]. 图学学报, 2014, 35(2): 200-207.
[10]	张莉，刘静静，檀结庆. 多形状参数的指数均匀B样条曲线曲面[J]. 图学学报, 2013, 34(3): 29-35.
[11]	刘小琼，杨国英. 带两个形状参数的四次Bézier 曲线的扩展[J]. 图学学报, 2013, 34(1): 41-45.
[12]	胡钢，吉晓民，沈晓芹，宋伟杰. CE-Bézier 曲面光滑拼接的研究与实现[J]. 图学学报, 2012, 33(5): 62-67.
[13]	严兰兰，梁炯丰，黄涛. 两种带形状参数的三角曲线[J]. 图学学报, 2012, 33(1): 25-30.
[14]	杨炼，李军成. 一类带两个形状参数的类四次三角Bézier曲线[J]. 图学学报, 2011, 32(6): 9-7.
[15]	严兰兰，梁炯丰，饶智勇. 三次Ball曲线的两种新扩展[J]. 图学学报, 2011, 32(5): 20-24.