Subdivision of point-normal pairs with application to smoothing feasible robot path

Evgeny Lipovetsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In a previous paper (Lipovetsky and Dyn in Comput Aided Geom Des 48:36–48, 2016), we introduced a weighted binary average of two 2D point-normal pairs, termed circle average, and investigated subdivision schemes based on it. These schemes refine point-normal pairs in 2D and converge to limit curves and limit normals. Such a scheme has the disadvantage that the limit normals are not the normals of the limit curve. In this paper, we address this problem by proposing a new averaging method and obtaining a new family of algorithms based on it. We demonstrate their new editing capabilities and apply this subdivision technique to smooth a precomputed feasible polygonal point robot path.

Original languageEnglish
Pages (from-to)2271-2284
Number of pages14
JournalVisual Computer
Issue number7
StatePublished - Jul 2022


  • 2D curve design
  • Bezier quasi-average
  • Modified 4-point scheme
  • Modified Lane–Riesenfeld algorithm
  • Robot path smoothing
  • Subdivision in the environment with obstacles
  • Subdivision of 2D point-normal pairs


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