Smoothing of Polygonal Chains for 2D Shape Representation Using a G2-Continuous Cubic A-Spline

  • Sofía Behar
  • Jorge Estrada
  • Victoria Hernández
  • Dionne León
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3773)


We have developed a G 2-continuous cubic A-spline, suitable for smoothing polygonal chains used in 2D shape representation. The proposed A-spline scheme interpolates an ordered set of data points in the plane, as well as the direction and sense of tangent vectors associated to these points. We explicitly characterize curve families which are used to construct the A-spline sections, whose members have the required interpolating properties and possess a minimal number of inflection points. The A-spline considered here has many attractive features: it is very easy to construct, it provides us with convenient geometric control handles to locally modify the shape of the curve and the error of approximation is controllable. Furthermore, it can be rapidly displayed, even though its sections are implicitly defined algebraic curves.

Mathematics Subject Classification: 65D07(splines), 65D05 (interpolation), 65D17 (Computer Aided Design).


Algebraic cubic splines polygonal chain data interpolation and fitting 2D shape representation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sofía Behar
    • 1
  • Jorge Estrada
    • 2
  • Victoria Hernández
    • 2
  • Dionne León
    • 2
  1. 1.Faculty of Mathematics and Computer SciencesHavana UniversityCuba
  2. 2.Institute of Mathematics and Theoretical PhysicsCITMACuba

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