On the smoothness of compound of the lines and surfaces in cyclographic modeling of surface forms of roads

The automated road design systems allowed us to substitute the two-stage design of the axis of the road (in plan and profile) with the spatial curve in the form of parametric splines or Bezier curves. However, the smoothness of compound, both segments of curves and compartments of the road surfaces, is still an open matter. The authors continue to develop the method of surface forms construction for automobile roads based on cyclographic mapping. The possible options for surface forms construction are presented; their advantages and disadvantages are shown. The matters of smoothness of compound of segments of the curves during the shaping of the road and the carriageway edge axis, as well as the shaping of the compartments of the surfaces of the carriageway formed on these segments are considered. Symbolic and numerical calculations are made, which show the direct correlation between the smoothness order of the compound of the road axis segments, presented in the form of a polynomial spline, the edges of the carriageway and surface compartments. At the stage of designing the automobile road axis and subsequent construction of its surface forms, the results of the work allow to preselect the smoothness order of the compound of segments of the lines and compartments of the road surfaces, which can be used in the development of CAD systems for roads.