Constrained Interpolation with Implicit Plane Cubic A-Splines

  • Authors:
  • S. Behar-Jequín;J. Estrada-Sarlabous;V. Hernández-Mederos

  • Affiliations:
  • Facultad de Matemática y Computación, Universidad de la Habana, Cuba;Instituto de Cibernética, Matemática y Física, CITMA, Cuba;Instituto de Cibernética, Matemática y Física, CITMA, Cuba

  • Venue:
  • CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
  • Year:
  • 2008

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Abstract

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 G2-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.