| 孙钊,张迪,刘华勇.一类带形状参数的代数三角融合样条的
构造及其应用[J].安徽建筑大学学报,2019,27(1):94-102 |
| 一类带形状参数的代数三角融合样条的
构造及其应用 |
| The Construction and Application of a Class of Algebraic-TrigonometricSpline with Shape Parameters |
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| DOI： |
| 中文关键词: 三角曲线曲面 几何连续性 局部 形状参数 融合 |
| 英文关键词: trigonometric curve and surface geometric continuity local shape parameter blending |
| 基金项目:安徽省高等学校自然科学研究项目(KJ2018A0518) |
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| 中文摘要: |
| 本文在原三角样条基函数加上和为零的多项式引入了局部形状参数，构造了具有两类形状参数的并
满足几何连续的AT-B-Spline 样条基函数. 基于此基函数定义了相应的AT-B-Spline 样条曲线，给出了曲线的
良好性质及证明，并讨论曲线的连续性、形状参数对曲线的影响规律. 同时还构造了旋转面并给出了形状参
数对旋转面外形修改的实例. 另外，AT-B-Spline 样条曲线可以精确地表示圆锥曲线. 这类曲线不仅具有三
角样条的一般性质，而且具有全局的和局部的调配性以及较灵活的连续性：当形状参数给定不同值时，AT-BSpline
样条曲线交互地控制曲线的连续性. 实例表明，AT-B-Spline 样条曲线克服了传统曲线曲面在形状调整方
面的局限性，该方法是有效且实用的。 |
| 英文摘要: |
| By adding extra polynomial in the original trigonometric spline ，two local shape parameters are introduced. So
the AT-B-Spline basic functions with two types of shape parameters and geometric continuity are proposed. Then，based
on the AT-B-Spline basis，the corresponding AT-B-Spline curve is defined. The continuity of the curves，the influence of
shape parameters on the curve are demonstrated. This paper also constructs rotating surfaces and answers examples to
modify the shape parameters of the rotating surfaces. In addition，AT-B-Spline curve can also accurately represent some
conic curve. This kind of curve not only has the general properties of triangular spline，both global and local deployment
and flexible continuity：when the shape parameters are taken different values，thus the continuity can interactively
control curve. Experimental results show that AT-B-Spline overcame the disadvantage of the traditional curve and surface
in shape adjustment，which is an effective and practical method. |
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