摘要
以其在弧长计算与等距线表示上的优势,PH曲线成为近年来计算机辅助几何设计研究的焦点问题之一。为此讨论了六次PH曲线的G^2 Hermite插值问题。在指定自由参数下,对两类六次PH曲线分别进行复分析曲线求解,得到满足G^2插值条件的六次PH曲线和控制顶点。通过弧长、能量积分、绝对旋转数的衡量,选取较好的插值曲线。进一步,讨论了用六次PH曲线G^2 Hermite插值逼近90°和67°圆弧的问题。在同一个自由参数下,选择插值最好的曲线,可实现六次C1 Hermite插值逼近圆弧的效果,且逼近90°圆弧时,优于五次G^2 Hermite插值逼近的PH曲线,而逼近67°圆弧时,与最好的五次PH曲线达到的效果几乎相同。
By the advantages of computing arcs and representing offsets, study of phythagorean hodograph curves is one of the hot topics in recent years. In this paper, G^2 Hermite interpolation by sextic PH curves is studied. Sextic PH curves can be classified into two types and the interpolation problem can be resolved to get the control points with some free parameter in complex representation. With the analysis of arc-length, bending energy and absolute rotation number, the better interpolation curves are selected. Moreover, the sextic PH G^2 Hermite interpolation is applied to approximate the 90° and 67° arcs. The best approximating curves can solve C1 Hermite interpolation by the PH sextics. And the best curves＇ performance is better than the quintic G^2 Hermite interpolation curves when approximating the 90° arc, and is almost same as the latter＇s best curve when approximating the 67° arc.
出处
《图学学报》
CSCD
北大核心
2016年第2期155-165,共11页
Journal of Graphics
基金
国家自然科学基金项目(11271060
11290143
11401077)
民用飞机专项项目(MJ-F-2012-04)
中央基本科研业务费资助项目(DUT16LK38)
辽宁省高等学校优秀人才支持计划项目(LJQ2014010)
