The Modelling of joining route segments of different curvature

The paper presents a new general method of modelling route segments curvature using differential equations. The method enables joining of route segments of different curvature. Transitional curves of linear and nonlinear curvatures have been identified in the case of joining two circular arcs by S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph quantic Bezier curve using the Lateral Change of Acceleration diagram and the dynamic model. The analysis of dynamic properties has showed an advantage of the obtained transition curve of nonlinear curvature over Bezier curves.