Shape analysis of cubic trigonometric Bezier curves with a shape parameter

被引：31
作者：
Han, Xi-An [1 ,2 ]
Huang, XiLi [3 ]
Ma, YiChen [2 ]
机构：
[1] Acad Equipment Command & Technol, Dept Basic Theories, Beijing 101416, Peoples R China
[2] Xi An Jiao Tong Univ, Sch Sci, Xian 710049, Shaanxi, Peoples R China
[3] Acad Equipment Command & Technol, Dept Expt Command, Beijing 101416, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 06期
关键词：
Trigonometric Bezier curve; Shape parameter; Shape diagram; Inflection point; Singularity; POLYNOMIAL CURVES; GEOMETRIC CHARACTERIZATION; INFLECTION POINTS; SINGULARITIES; SEGMENTS; SPLINES;
D O I：
10.1016/j.amc.2010.07.065
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For the cubic trigonometric polynomial curves with a shape parameter (TB curves, for short), the effects of the shape parameter on the TB curve are made clear, the shape features of the TB curve are analyzed. The necessary and sufficient conditions are derived for these curves having single or double inflection points, a loop or a cusp, or be locally or globally convex. The results are summarized in a shape diagram of TB curves, which is useful when using TB curves for curve and surface modeling. Furthermore the influences of shape parameter on the shape diagram and the ability for adjusting the shape of the curve are shown by graph examples, respectively. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.
引用
收藏
页码：2527 / 2533
页数：7
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