带形状参数的QT-Bézier曲线曲面的构造和应用

J4 ›› 2016, Vol. 38 ›› Issue (02): 344-349.

带形状参数的QT-Bézier曲线曲面的构造和应用

刘华勇1,2,李璐1,张大明1

(1.安徽建筑大学数理学院,安徽合肥 230601;2.安徽建筑大学科学计算与软件实验室,安徽合肥 230601)

收稿日期:2015-02-10 修回日期:2015-09-06 出版日期:2016-02-25 发布日期:2016-02-25
基金资助:
安徽省高等学校自然科学研究项目(KJ2015A328,KJ2015JD16,KJ2014A041)

Construction and application of QTBézier
curves and surfaces with shape parameters

LIU Huayong1,2 ,LI Lu1,ZHANG Daming1

(1.School of Mathematics ＆ Physics,Anhui Jianzhu University,Hefei 230022;
2.Scientific Computing and Software Lab,Anhui Jianzhu University,Hefei 230022,China)

Received:2015-02-10 Revised:2015-09-06 Online:2016-02-25 Published:2016-02-25

摘要/Abstract

摘要：

为了更加方便地表示和修改曲线曲面,提出了带形状参数的四次三角Bézier曲线曲面QTBézier的构造方法和应用。首先仿照Bézier曲线性质,构造了带形状参数的基函数,定义了带形状参数的QTBézier曲线曲面并研究了他们的一些主要性质,并就参数的选取做了一些分析。这种带形状参数的QTBézier曲线曲面是已有的一些曲线曲面的一般表达方法,如果选取一些特殊的参数,可以表示特殊的和已知的曲线曲面,还可以构造不同形状的旋转面。带形状参数的QTBézier曲线曲面可以很好地通过形状参数来调整曲线曲面的外形,而且能构造不同的旋转面,由于有额外的形状参数,更便于交互。

关键词: 形状参数, QTBé, zier, 连续性, 拼接

Abstract:

In order to express and modify curves and surfaces, we design quadratic trigonometric Bézier curves and surfaces with shape parameters. Firstly, we present a class of quadratic trigonometric Bézier basis functions with multiple shape parameters according to the properties of Bézier curves, and define the concept of quadratic trigonometric Bézier curves and surface with shape parameters. The properties are studied. The shape of the curves can be adjusted by altering the values of shape parameters while the control polygon is kept unchanged. With some particular shape parameters, special curves and surfaces are expressed, and rotating surface is constructed with different shapes. Quadratic trigonometric curves and surfaces with shape parameters can be a good representation of conic curves and surfaces. Since shape parameters are additional, so the interaction is more convenient.

Key words: shape parameters;quadratic trigonometric Bézier;continuity;joining

刘华勇1,2,李璐1,张大明1. 带形状参数的QT-Bézier曲线曲面的构造和应用[J]. J4, 2016, 38(02): 344-349.

LIU Huayong1,2 ,LI Lu1,ZHANG Daming1. Construction and application of QTBézier
curves and surfaces with shape parameters [J]. J4, 2016, 38(02): 344-349.

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