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Interactive Design of Cubic IPH Spline Curves

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Abstract

Indirect Pythagorean hodographs (IPH) spline curves are a set of curves which have rational Pythagorean hodographs after reparameterization by a fractional quadratic transformation. In this paper, the authors provide an algorithm to interactively design a cubic IPH spline curve from any given control polygon. The method has the same friendly interface and properties as those for B-splines, meanwhile facilitates intuitive and efficient construction of open and closed IPH spline curves. The key idea is to solve the ratios of a set of auxiliary points associated with the edges and then construct a piecewise cubic IPH spline curve which has as high as possible continuity, i.e., the absolute curvature value of the adjacent curve segments are the same. A very interesting observation is that for any open control polygon, a quadratic B-spline curve can have continuous absolute curvature by carefully choosing the knots as the function of the control points.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230026, China

    Jingjing Zhang

  2. University of Science and Technology of China, Hefei, 230026, China

    Xin Li

Authors
  1. Jingjing Zhang
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  2. Xin Li
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Correspondence to Jingjing Zhang or Xin Li.

Additional information

This research was supported by the National Science Foundation of China under Grant No. 11801126.

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Zhang, J., Li, X. Interactive Design of Cubic IPH Spline Curves. J Syst Sci Complex 36, 1302–1318 (2023). https://doi.org/10.1007/s11424-023-1286-x

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  • DOI: https://doi.org/10.1007/s11424-023-1286-x

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