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

  • Hongmei KangEmail author
  • Xin Li


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.


Cubic pythagorean-hodograph (PH) curve Control polygon Interactive design \(G^1\) continuity Curvature continuity 

Mathematics Subject Classification

65D07 65D17 


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Copyright information

© School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Soochow UniversitySuzhouChina
  2. 2.University of Science and Technology of ChinaHefeiChina

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