Numerical Algorithms

, Volume 51, Issue 4, pp 461–476 | Cite as

Fair cubic transition between two circles with one circle inside or tangent to the other

  • Sarpono Dimulyo
  • Zulfiqar HabibEmail author
  • Manabu Sakai
Original Paper


This paper describes a method for joining two circles with a C-shaped and an S-shaped transition curve, composed of a cubic Bézier segment. As an extension of our previous work; we show that a single cubic curve can be used for blending or for a transition curve preserving G 2 continuity regardless of the distance of their centers and magnitudes of the radii which is an advantage. Our method with shape parameter provides freedom to modify the shape in a stable manner.


Path planning G2 transition Cubic Bézier Computer-aided design (CAD) Computer graphics Path planning Highway designing 


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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Department of Mathematics & Computer ScienceKagoshima UniversityKagoshimaJapan
  2. 2.Department of Computer ScienceNational University of Computer & Emerging SciencesLahorePakistan

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