Affiliation:
1. Omsk State Technical University
Abstract
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.
Publisher
Keldysh Institute of Applied Mathematics
Reference14 articles.
1. E. V. Lyubchinov, K. L. Panchuk, Geometric modeling of solutions of the direct and inverse tasks of geometric optics on a plane, IOP Conf. Series: Journal of Physics: Conf. Series. Vol. 1210 (2019), P. 012087. doi: 10.1088/1742-6596/1210/1/012087.
2. T.M. Myasoedova, K.L. Panchuk, Formation of a family of contour-parallel cutting tool trajectories on the basis of cyclographic mapping, Scientists of Omsk – to the region: Proceedings of IV Regional Science and Technology Conference, Russia, 2019, pp. 142-146.
3. K.L. Panchuk, E.V. Lyubchinov, Cyclographic interpretation and computer-aided solution to a system of algebraic equations, Geometry and Graphics, Vol. 7(3) (2019), pp. 3-14. doi: 10.12737/article_5dce5e528e4301.77886978.
4. K. L. Panchuk, A. S. Niteyskiy, E. V. Lyubchinov, Cyclographic Modeling of Surface Forms of Highways, IOP Conference Series: Materials Science and Engineering, pp. 21–22 сентября 2017 года. – Chelyabinsk: Institute of Physics Publishing. Vol. 262 (2017), P.012108. doi: 10.1088/1757-899X/262/1/012108.
5. K. L. Panchuk, N. V. Kaygorodtseva, Cyclographic Descriptive Geometry, Omsk, OmGTU, 2017 (in Russian).