文章摘要
G2连续条件下圆域B样条曲线的延拓与拼接
Extension and splicing of disk B-Spline curve with G2 constraint
投稿时间:2022-04-04  修订日期:2022-04-20
DOI:
中文关键词: 圆域曲线  延拓  G2连续  能量函数  拼接
英文关键词: disk curve  curve extension  G2 continuity  energy function  curve matching
基金项目:安徽省高等学校自然科学研究资助项目;安徽省级质量工程资助项目;安徽建筑大学质量工程资助项目
作者单位邮编
徐虎 安徽建筑大学 230601
刘华勇 安徽建筑大学 230601
李亚男 安徽建筑大学 
王曾珍 安徽建筑大学 
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中文摘要:
      为克服圆域B样条曲线在C2连续条件下延拓到目标圆盘时的形状不可调整性,提出利用圆域Bézier曲线在G2连续条件下延拓圆域B样条曲线的算法。首先通过极小化能量目标函数确定延拓部分即圆域Bézier曲线自由度,使得到的圆域曲线形状达到最优状态。然后将节点向量重新参数化,延拓后的组合圆域曲线转化为圆域B样条曲线,重复利用该算法可以将圆域B样条曲线延拓至多个目标圆盘。随后提出利用六次圆域Bézier曲线作为过渡曲线延拓、拼接任意两条圆域B样条曲线的算法,最后给定数值实例验证本文所提方法的普适性和有效性。
英文摘要:
      In order to overcome the shape irregularity of disk B-spline curve extended to target disk under C2 continuous condition, an algorithm of disk B-spline curve extended by disk Bézier curve under G2 continuous condition was proposed. Firstly, The energy objective function is minimized to determine the parameters and obtain the curve with optimal shape. Then the knot vector are re-parameterized ,and the combined disk curve after extension was transformed into disk B-spline curve to meet the C2 continuity requirement at the connecting disk, and the algorithm can be reused to extend disk B-spline to multiple target disks. In addition, a six-degree disk Bézier curve is given as a splicing transition curve, and an algorithm for matching any two disk B-spline curves is proposed. Finally, experimental results show that the algorithm has good universality and effectiveness.
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