Computer Engineering & Science >
A Class of QuasiQuartic Trigonometric Polynomial Bézier Curves with a Shape Parameter
Received date: 2010-04-16
Revised date: 2010-08-07
Online published: 2011-03-25
A class of quasiquartic trigonometric polynomial Bézier curves with a shape
parameter is presented. The curve is controlled by five points, and it has a lot of similar
characteristics with the traditional quartic Bézier curve, and its shape can be adjusted by a
parameter, which makes the curve feature more powerful expression ability. The shape
parameter affects the property of geometry, the larger is the parameter, and the more of the
curve approaches the control polygon, therefore, the trigonometric polynomial curve with the
shape parameter can be close to the given control polygon than the quartic Bézier curve. The
new curve can represent exactly the arc of circle, arc of ellipse, arc of parabola and other
quadratic curves without using a rational form. For designing free curves, the G2 and C3
continuity condition of twopiece curves are also discussed. The modeling examples illustrate
that the new curve has a high application value for computer aided geometric design.
YANG Lian,LI Juncheng . A Class of QuasiQuartic Trigonometric Polynomial Bézier Curves with a Shape Parameter[J]. Computer Engineering & Science, 2011 , 33(3) : 77 -81 . DOI: 10.3969/j.issn.1007130X.2011.
［1］施法中.计算机辅助几何设计与非均匀有理B样条［M］.北京:高等教育出版社, 2001.
［2］王国瑾,汪国昭,郑建民.计算机辅助几何设计［M］.北京:高等教育出版社, 2001.
［3］Mainar E, Pea T M, SanchezReyes J. Shape Preserving Alternatives to the Rational Bézier
Model［J］.Computer Aided Geometric Design, 2001, 18(1):3796.
［4］Pieg L, Tiller W. The NURBS Book［M］.2nd ed.Berlin Heidelberg: Springer, 1997.
［5］Zhang Jiwen. Ccurves: An Extension of Cubic Curves［J］.Computer Aided Geometric
Design, 1996, 13(3):199217.
［6］Han Xuli. Quadratic Trigonometric Polynomial Curves with a Shape Parameter［J］.Computer
Aided Geometric Design, 2002, 19(7):503512.
［7］Han Xuli. Cubic Trigonometric Polynomial Curves with a Shape Parameter［J］. Computer
Aided Geometric Design, 2004, 21(6):535548.
［8］苏本跃,黄有度.一类Bézier型的三角多项式曲线［J］.高等学校计算数学学报, 2005, 27(3):202
208.
［9］唐运梅,吴晓勤,韩旭里.基于三点形状可调的二次三角Bézier曲线［J］.计算机工程与科学, 2010，
32(3):6668.
［10］李军成,宋来忠.一组基于三角函数的类三次参数曲线［J］.计算机工程与设计, 2009, 29(10):2702
2704.
［11］李军成,陈国华,杨笃庆.可调的类三次Bézier三角曲线［J］.计算机工程与科学，2010，32(3):69
71.
/
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