Solution of the inverse problem of modified cyclographic model

Abstract

In cyclographic modeling of a line of three-dimensional space, direct and inverse problems are known. A sufficient
number of publications are devoted to the solution of these problems in the scientific literature. The authors of the
work, on the basis of studies of the well-known classical cyclographic model, obtained its modification, called the
modified cyclographic model. The need for this model caused by the solution of a number of practical problems of
geometric modeling, in particular in the field of developing surface forms of roads, where traditionally only the direct
problem of geometric modeling is considered, in which it is required to determine the surface shape of the latter
along the spatial axis of the road. The authors proposed a solution to the inverse problem of modeling for a modified
cyclographic projection, which makes it possible to restore a curved line of space from its cyclographic image. The
paper gives a justification and a solution to the inverse problem of cyclographic modeling, implemented on a numerical example. The results of the work can be used in computer-aided design systems that specialize in the
design of general and special roads.