计算机科学 ›› 2023, Vol. 50 ›› Issue (7): 119-128.doi: 10.11896/jsjkx.220800024
李林1, 解滨2, 韩力文1,3,4
LI Lin1, XIE Bin2, HAN Liwen1,3,4
摘要: h-Bézier曲线(h>0)又被称为Pólya曲线,它具有与经典Bézier曲线(h=0)一致的诸多优良性质。为此,文中研究了二次h-Bézier曲线具有单调曲率的充要条件及其构造算法。首先,讨论二次h-Bézier曲线曲率极值的存在性,得到曲线具有单调曲率的充要条件;通过引入曲率临界圆,给出判断二次h-Bézier曲线曲率单调性的几何方法,即检查二次h-Bézier曲线的中间控制点是否在曲率临界圆上或圆内;并由此得到构造具有单调曲率的二次h-Bézier曲线的两种算法,通过调节形状参数h可保证曲线具有单调递减或单调递增的曲率。其次,研究两条二次h-Bézier曲线的光滑拼接,基于对二次h-Bézier曲线性质的分析,选择第二条曲线在肩点处与第一条曲线的端点实现拼接,得到G2拼接的充要条件;讨论参数对拼接曲线形状的影响。最后,构造出同时满足G2拼接、曲率单调递减(或单调递增)的组合二次h-Bézier曲线。数值实例显示了组合二次h-Bézier曲线的造型优势和灵活性。
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