Construction of G3 conic spline interpolation

Ma Long, Zhang Caiming, Zhang Xin, Fuhua Cheng

Research output: Contribution to journalArticlepeer-review


In this paper, a new method to interpolate a sequence of ordered points with conic splines is presented. The degree of continuity at the joints of the resulting splines can reach G3; and the splines are faired by decreasing curvature extrema. The construction is not based on parametrization, but based on basic geometric elements, such as the directions of tangents and chord lengths. The weight of Rational Quadratic Bézier Spline is translated into an equivalent form called chord-tangent ratio. The main idea of the new method is converting the geometric construction problem into a conditional extrema problem through representing the curvature and the curvature changing rate at joints with tangent arguments and chord-tangent ratios, and then deriving the unknowns by solving the conditional extremum problem. Experiments show that splines constructed by the new method perform well not only in terms of continuity, but also in smoothness.

Original languageEnglish
Pages (from-to)15-27
Number of pages13
JournalCAD Computer Aided Design
StatePublished - Feb 1 2016

Bibliographical note

Funding Information:
This research was supported by the National Natural Science Foundation of China ( 61020106001 , 61373078 , 61202148 ), NSFC Joint Fund with Guangdong ( U1201258 ), National Research Foundation for the Doctoral Program of Higher Education of China ( 20110131130004 ).

Publisher Copyright:
© 2015 Elsevier Ltd.


  • Chord-tangent ratio
  • Conics
  • Curvature extrema
  • Fairing
  • Interpolation
  • continuity

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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