$G^1$ continuity,Curvature continuity" /> $G^1$ continuity" /> $G^1$ continuity,Curvature continuity" />

A New Method to Design Cubic Pythagorean-Hodograph Spline Curves with Control Polygon

Hongmei Kang , Xin Li

Communications in Mathematics and Statistics ›› 2019, Vol. 7 ›› Issue (3) : 363 -381.

PDF
Communications in Mathematics and Statistics ›› 2019, Vol. 7 ›› Issue (3) : 363 -381. DOI: 10.1007/s40304-018-0158-5
Article

A New Method to Design Cubic Pythagorean-Hodograph Spline Curves with Control Polygon

Author information +
History +
PDF

Abstract

A new method to design a cubic Pythagorean-hodograph (PH) spline curve from any given control polygon is proposed. The key idea is to suitably choose a set of auxiliary points associated with the edges of the given control polygon to guarantee the constructed PH spline has $G^1$ continuity or curvature continuity. The method facilitates intuitive and efficient construction of open and closed cubic PH spline curves that typically agrees closely with the same friendly interface and properties as B-splines, for example, the convex hull and variation-diminishing properties.

Keywords

Cubic pythagorean-hodograph (PH) curve / Control polygon / Interactive design / $G^1$ continuity')">$G^1$ continuity / Curvature continuity

Cite this article

Download citation ▾
Hongmei Kang, Xin Li. A New Method to Design Cubic Pythagorean-Hodograph Spline Curves with Control Polygon. Communications in Mathematics and Statistics, 2019, 7(3): 363-381 DOI:10.1007/s40304-018-0158-5

登录浏览全文

4963

注册一个新账户 忘记密码

References

AI Summary AI Mindmap
PDF

128

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/