We propose the extended Bezier spiral in this paper. The spiral is useful for both design purposes and improved aesthetics. This is because the spiral is one of the Bezier curves, which play an important role in interactive curve design, and because the assessment of the curve is based on the human reception of the curve. For the latter purpose we utilize the logarithmic distribution graph that quantifies the designers' preferences. This paper contributes the unification of the two different curve design objectives (the interactive operation and so called "eye pleasing" result generation); which have been independently investigated so far.

Clothoid or cornu spiral segments were used as transition spirals forming C-and S-shaped curves between circles as well as straight lines in various situations of highway road design. These transitions are the center lines of rail, highway road design. The above C and S-shaped form curves consist one or more transition segments. We study the possibility of using the single transition spirals in the situations that use many transition spirals to form smooth transition spline between circles as well as straight lines. We also compute the bounds for the scaling of such single spirals using the practical equation. This paper is aimed to give a method avoiding non-linear equations by finding range for the scaling factor of the clothoids which can take initially an appropriate closer value from this range.