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

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.

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