Smoothness of Connection of Ruled Road Surface Form Segments

Abstract

Since the modern systems of automated road surface form design have allowed us to abandon the two stages road axis design – the map projection and the cross projection – in favor of defining the road axis as a spatial curve in the form of parametric splines, the smoothness of connection of curves and surfaces comprising the roadway remains an open question. The authors further develop the cyclographic method in road surface formation and study the problem of smoothness of connection of ruled surfaces segments generated through the cyclographic mapping of a spatial curve. The present paper considers the aspects of smooth connection of polynomial spline curve segments and the respective cyclographic projections, as well as ruled surface segments that are directed by these curves. The results of the study allow one to pre-define the desirable order of smoothness of the connected curve segments and ruled surface segments comprising the road surface forms on the stage of road axis design and subsequent road surface formation. This fact can serve as the basis for development of CAD systems for road surface forms of general and special purpose.