In cyclographic modeling of lines of space R3 direct and inverse problems and their solutions are known. In addition to the classic cyclographic projection, there is modified cyclographic projection of a line of space, developed on the basis of the classic one. The modified cyclographic projection has practical relevance in design of general purpose road surface forms. For this projection, the solution of the direct problem, i.e. to determine modified cyclographic projection given a curve of space (road axis), is known. In this paper, we propose a solution to the inverse problem - to restore the initial space curve given its modified cyclographic projection. The paper provides justification for solution to the inverse problem and considers on example an analytic solution to the inverse problem given second-order curves. The results of this study can be applied as the basis for development of computer-aided design systems for road surface forms, both in creation of new working surface forms, and in restoration the existing ones.