Constrained Interpolation with Implicit Plane Cubic A-Splines

  • S. Behar-Jequín
  • J. Estrada-Sarlabous
  • V. Hernández-Mederos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5197)


In this work we focus on the following problem: given an ordered set of points in the plane lying on one side of a given boundary polygon, construct a smooth curve interpolating these points, such that the curve lies on the same side of the polygon as the data.

We have developed a G 2-continuous cubic A-spline scheme smoothing the polygon defined by the line segments joining consecutive data points, such that the spline curve lies completely on the same side of the boundary polygon as the data. The proposed A-spline scheme provides an efficient method for generating a smooth robot’s path that avoids corners or polygonal objects for a given planned path, for designing a smooth curve on a polygonal piece of material, etc.


Constrained interpolation G2-continuous cubic A-spline Shape preserving spline 

Mathematics Subject Classification

65D07 (splines) 65D05 (interpolation) 65D17 (Computer Aided Design) 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • S. Behar-Jequín
    • 1
  • J. Estrada-Sarlabous
    • 2
  • V. Hernández-Mederos
    • 2
  1. 1.Facultad de Matemática y ComputaciónUniversidad de la HabanaCuba
  2. 2.Instituto de Cibernética, Matemática y Física, CITMACuba

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