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

  title={Fair cubic transition between two circles with one circle inside or tangent to the other},
  author={Sarpono Dimulyo and Zulfiqar Habib and Manabu Sakai},
  journal={Numerical Algorithms},
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 G2 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. 
Smoothing Arc Splines by Cubic Curves
  • Z. Habib, M. Sakai
  • Mathematics, Computer Science
    2009 Sixth International Conference on Computer Graphics, Imaging and Visualization
  • 2009
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Arc splines are planar, tangent continuous, piecewise curves made of circular arcs and straight line segments. They are important in manufacturing industries because of their use in the cutting paths
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Smoothing an Arc Spline Using PH Quintic Spiral Transitions
This paper describes a method to smooth an arc spline. Arc splines are G continuous segments made of circular arcs and straight lines. We have proposed a smooth version of arc spline by replacing its
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It is first proved that there is no spiral arc solution with turning angle less than or equal to @p and then, that any convex solution admits at least two vertices.
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Planar G2 transition between two circles with a fair cubic Bézier curve
A planar cubic Be´zier spiral
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Inflection points and singularities on planar rational cubic curve segments
  • M. Sakai
  • Mathematics, Computer Science
    Comput. Aided Geom. Des.
  • 1999