摘要
论文研究傅里叶级数函数在防伪扭索曲线设计上的应用。采用实验的方法,在防伪版纹设计软件Cerber中,利用傅里叶级数公式,基于X轴方向、Y轴方向构建复合函数,生成相应的扭索曲线。复合函数的级数越多,曲线形状越复杂,超过4级时,曲线的防伪等级高,反向破解难度大;X轴、Y轴二维方向同时构建复合函数时,曲线防伪性能增强;构建复合函数时,正弦分量取0,对应的曲线具有对称性。利用傅里叶级数公式建立的复合函数,生成的扭索曲线防伪性能好,美观大方,在防伪版纹设计中具有较大的应用价值。
Research on the application of Fourier series function in the design of anti-counterfeiting curve.In the anti-counterfeiting curve design software Cerber,based on Fourier series function,generating the compound function about variable X and variable Y,then the curve drawn by the compound function.As the number of compound function harmonics increases,the curve shape is complicated.When the number is more than 4,it is difficult to draw the same curve by other means.When variable X and variable Y are available,the curve shape is complicated and difficult to be counterfeited.The curve is symmetrical when the sine harmonics of the compound function is not available.By changing the coefficients of the compound function harmonics,complicated and beautiful anti-counterfeiting curve can be drawn.
作者
夏自由
XIA Ziyou(Changsha Normal University,Changsha 410100)
出处
《计算机与数字工程》
2019年第11期2926-2929,2938,共5页
Computer & Digital Engineering
关键词
扭索曲线
防伪
傅里叶级数
guilloche curve
anti-counterfeiting
Fourier series function
