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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics & Computer Science, Kagoshima University, Koorimoto 1-21-35, 890-0065, Kagoshima, Japan

    Sarpono Dimulyo & Manabu Sakai

  2. Department of Computer Science, National University of Computer & Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan

    Zulfiqar Habib

Authors
  1. Sarpono Dimulyo
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  2. Zulfiqar Habib
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  3. Manabu Sakai
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Correspondence to Zulfiqar Habib.

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Dimulyo, S., Habib, Z. & Sakai, M. Fair cubic transition between two circles with one circle inside or tangent to the other. Numer Algor 51, 461–476 (2009). https://doi.org/10.1007/s11075-008-9252-1

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  • DOI: https://doi.org/10.1007/s11075-008-9252-1

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