519.6 Computer construction of an equidistant network of complex non-smooth curves on the terrain
Valishin A. A. (Bauman Moscow State Technical University), Tumanov I. A. (Bauman Moscow State Technical University), Akhund-zade M. R. (Bauman Moscow State Technical University)
EQUIDISTANT, NOT SMOOTH CURVES ON THE GROUND
doi: 10.18698/2309-3684-2020-2-95106
The paper considers the problem of constructing a network of equidistant surveys of coastal waters during the design of marine terminals, as well as for landing amphibious assaults on the coast. A computer algorithm is proposed for constructing equidistant complex irregular curves on the ground. The algorithm is implemented as a computer program. The program is tested on an example of a curve of a real coastal strip.
[1] Dubrovin B.A., Novikov S.P., Fomenko A.T. Sovremennaia geometria. Metodi I prilojenia [Modern geometry. Methods and applications.] Moscow, Nauka Publ., 1986, 750 p.
[2] Artobolevsky I. I. Teoria mehanizmov i mashin [Theory of mechanisms and machines]. Moscow, Nauka Publ., 1988, 636 p.
[3] Gray A. Modern Differential Geometry of Curves and Surfaces with Mathematica. London, CRC Press, 1997, 1056.
[4] Lawrence J.D. A catalog of Special Plane Curves. New York, Dover, 1972, 218 p.
[5] Yates R.C. A Handbook on Curves and their Properties. USA, Literary Licensing, 2012, 256 p.
[6] Kazakevich M. I., Lyubin A. E. Proektirovanie metallicheskih konstrukcii promishlennih tryboprovodov [Design of metal structures of industrial pipelines. 2nd ed. rev. and more]. Kiev, Budivelnik Publ., 1989, 169 p.
[7] Kozlovsky E.A. Gornaya enciklopediya. T.4. Ortin – Sociosfera [Mountain encyclopedia. Vol. 4. Ortin – Sociosphere]. Moscow, Soviet Encyclopedia Publ., 1989, 623 p.
[8] Kuznetsov A.L., Kirichenko A.V., Pogodin V.A., Shcherbakova-Slyusarenko V.N. Importance of simulation modelling for technological design and evaluating parameters of cargo terminals. Vestnik of Astrakhan State Technical University, 2017, №2, с. 93–100.
[9] Shirokova E.A., Tyuleneva O.N. Kurs lekcij po matematike dlya napravleniya 020700 – geologiya: uchebnoe posobie [Course of lectures on mathematics for the direction 020700 – geology: textbook]. Kazan, Kazan University Publ., 2012, 168 p.
[10] Shibaev O.V., Gnevasheva A.A. Razrabotka upravlyayushchej programmy dlya ob-rabotki detalej na tokarnyh stankah s CHPU [Development of a control program for processing parts on CNC lathes]. Moscow, MSTU MAMI Publ., 2001, 110 p.
[11] Valuev A.M., Minnakhmetov K. M. Vychisleniya v racional'nyh chislah pri reshenii tipichnyh zadach vychislitel'noj geometrii v sistemah avtoma-tizirovannogo proektirovaniya [Computations in rational numbers in solving typical problems of computational geometry in automated design systems]. Gornyj informacionno-analiticheskij byulleten' (nauchno-tekhnicheskij zhurnal) [Mining Information and Analytical Bulletin (Scientific and Technical Journal)], 2011, no. 12, pp. 133–138.
[12] Myasoedova T.M., Panchuk K.L. Geometric model of generation of the family of the contour-parallel trajectories (equidistant family) of the machine tool. Dynamics of Systems, Mechanisms and Machines (Dynamics), 2018, vol. 6, no. 2, pp. 262–269.
[13] Kurosh A.G. Kurs vysshej algebry [Course of higher algebra]. Moscow, Nauka Publ., 1965, 430 p.
[14] Samigullina A.R. The mathematical modelling of objects of linear algebra and analytic geometry in the computer mathematical system Maple. Vestnik Tatarskogo gosudarstvennogo gumanitarno-pedagogicheskogo universiteta, 2010, no. 3 (21), pp. 107–114.
[15] Dolya P.G. Modeling of piecewise smooth continuous functions and curves. Bulletin of V.N. Karazin Kharkiv National University. Ser. Mathematical modeling. Information technology. Automated control systems, 2005, no. 661 (4), pp. 97–103.
[16] T-FLEX CAD User Manual. Three-dimensional modeling [Electronic resource]: URL: https://tflexcad.ru/download/documentation/
[17] Razumovskij A.I. Sozdanie algoritma ekvidistanty s primeneniem me-todov kontekstnoj sredy [Creating an equidistant algorithm using contextual environment methods]. Sistemy proektirovaniya, tekhnologiche-skoj podgotovki proizvodstva i upravleniya etapami zhiznennogo cikla promyshlennogo produkta (CAD/CAM/PDM – 2009) [Systems of design, technological preparation of production and management of stages of the life cycle of an industrial product (CAD/CAM/PDM – 2009)], 2009, pp. 208–212.
Валишин А.А., Туманов И.А., Ахунд-заде М.Р. Компьютерное построение сети эквидистант сложных негладких кривых на местности. Математическое моделирование и численные методы. 2020. № 2. с. 95–106.
Download article
Количество скачиваний: 812