Geometric simulation of surface forms of superelevation attainment of a highway based on cyclographic mapping

Theoretical studies on highway design consider the road axis as a basic element that defines spatial forms of other road elements: the roadway, the roadside verge, and the slopes. Based on this principle of shaping of the road elements, mathematical models of shaping based on the cyclographic method of simulation of space and its objects are proposed in this article. Shaping of surface forms of road elements on its transition segment and on a curve essentially differs from shaping on a straightway section by a number of specific features that impede and complicate the process of theoretical and practical shaping. The article describes the possibility to construct mathematical models of shaping a superelevation attainment segment on the basis of cyclographic mapping of the road axis. An example with detailed analysis and visualization of each stage of shaping is given. Results of the work can be used for development of modern specialized CAD of highways.