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

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.

Analytical Method of Modelling the Geometric System of Communication Route

“…However, it is easy to note that there is a distinct disproportion in taking interest in this problem. A search for new solutions is going on this sphere on vehicular roads (e.g., [4][5][6][7][8][9][10][11][12]). As regards the railway lines, the situation is entirely different.…”

Fairing Arc Spline and Designing by Using Cubic Bézier Spiral Segments

“…However, their method does not provide any solution for transition curves when circular arcs on both sides are tangent to each other. Such cases are discussed in [3] but without any analysis of number of curvature extrema in a C-or S-shaped transition curves. J-shaped case is presented in [33] but again there is no discussion on transition when straight line and circular arc are tangent to each other.…”