具有两类形状参数的代数三角混合样条曲线的构造和调配

doi:10.3969/j.issn.0255-8297.2017.03.012

应用科学学报 ›› 2017, Vol. 35 ›› Issue (3): 383-393.doi: 10.3969/j.issn.0255-8297.2017.03.012

具有两类形状参数的代数三角混合样条曲线的构造和调配

刘华勇, 李璐, 张大明, 王焕宝

安徽建筑大学数理学院, 合肥 230601

收稿日期:2016-11-08 修回日期:2016-12-14 出版日期:2017-05-30 发布日期:2017-05-30
作者简介:刘华勇，副教授，研究方向：计算机辅助几何设计和图形学，E-mail：aiaiwj@126.com
基金资助:
国家自然科学基金（No.61402010）；安徽省高等学校自然科学研究项目基金（No.KJ2015A328;No.KJ2016A151）资助

Construction and Blending of Algebraic-Trigonometric Spline Curves with Two Kinds of Shape Parameters

LIU Hua-yong, LI Lu, ZHANG Da-ming, WANG Huan-bao

School of Sciences and Physics, Anhui Jianzhu University, Hefei 230601, China

Received:2016-11-08 Revised:2016-12-14 Online:2017-05-30 Published:2017-05-30

摘要/Abstract

摘要：

带形状参数的样条曲线曲面是外形设计的重要方法，形状参数不是全局性的就是局部的，大多数仅考虑参数连续性。为了更好地修改和调配曲线曲面，构造了满足几何连续的带两类形状参数的代数三角样条曲线，简称为ATB-spline。这种曲线不仅具有普通三角多项式函数的性质，还具有全局和局部的可调性。两类形状参数在给定的范围内取值时，带两类形状参数的ATB-spline曲线满足一阶的几何连续；当两个相邻曲线中的形状参数取特殊值时，带两类形状参数的ATB-spline曲线满足不同性质的连续。利用曲线的性质构造了旋转面，讨论了两类形状参数对旋转面外形的调配并给出了实例。该曲线还可精确表示椭圆曲线。上述结果表明该方法构造的曲线是有效而实用的，并具有交互性。

关键词: 三角曲线曲面, 调配, 插值拟合, 几何连续性, 形状参数

Abstract:

A spline curve with shape parameters is an important method in design. In existing methods, however, shapes parameters are either global or local, and only parameter continuity are considered. To modify and blending the curves, an algebraic-trigonometric spline curve, called ATB-spline, is constructed with two kinds of shape parameters satisfying geometric continuity. This curve not only has the properties of ordinary trigonometric polynomials, but also has global and local properties. When the two kinds of shape parameters are taken in a given range, the ATB-spline curves with two kinds of shape parameters satisfy geometric continuity of the frst order; when the shape parameter of the two adjacent curves is given a special value, the ATB-spline curve with two kinds of shape parameters can satisfy continuity of the different properties. The rotation surface is constructed based on the property of the curve. Blending of the two kinds of shape parameters on the surface of the rotating surface is given together with an example. In addition, this curve can accurately represent conic curves. The above results indicate that curves constructed with this method are practical and effective.

Key words: geometric continuity, shape parameters, trigonometric curve and surface, interpolation and approximation, blending

中图分类号:

TP391

刘华勇, 李璐, 张大明, 王焕宝. 具有两类形状参数的代数三角混合样条曲线的构造和调配[J]. 应用科学学报, 2017, 35(3): 383-393.

LIU Hua-yong, LI Lu, ZHANG Da-ming, WANG Huan-bao. Construction and Blending of Algebraic-Trigonometric Spline Curves with Two Kinds of Shape Parameters[J]. Journal of Applied Sciences, 2017, 35(3): 383-393.

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具有两类形状参数的代数三角混合样条曲线的构造和调配

Construction and Blending of Algebraic-Trigonometric Spline Curves with Two Kinds of Shape Parameters

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