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Geometric simulation is creation of a geometric model, whose properties and characteristics in a varying degree determine the subject of investigation’s properties and characteristics. The geometric model is a special case of the mathematical model. The feature of the geometric model is that it will always be a geometric figure, and therefore, by its very nature, is visual. If the mathematical model is a set of equations, which says little to an ordinary engineer, the geometric model as representation of the mathematical model and as the geometric figure itself, enables to "see" this set. Any geometric model can be represented graphically. Graphical model of an object is a mapping of its geometric model onto a plane (or other surface). Therefore, the graphical model can be considered as a special case of the geometric model. Graphical models are very various – these are graphics, and graphical structures of immense complexity, reflecting spatial geometric figures. These are drawings of geometric figures, simulating processes of all kinds. The simulation goes on as follows. According to known geometric and differential criteria the geometric model is executed. Then a mathematical model is composed based on the geometric model, finally a computer program is compiled on the mathematical model. As a result of consideration in this paper the process of obtaining the geometric models of surface and linear forms for auto-roads it is possible to make a following conclusion. For geometric simulation and the consequent mathematical one the descriptive geometry involvement is vital. Just the descriptive geometry is used both on the initial and final stages of design.
descriptive geometry, geometric simulation, mathematical simulation, graphical model
Предварительно напомним, что такое геометрическое моделирование и геометрическая модель в частности.
Геометрическое моделирование — это создание геометрической модели, свойства и характеристики которой в той или иной степени определяют свойства и характеристики объекта исследования. То есть объект или его свойства и характеристики должны иметь такое же математическое описание, что и геометрическая модель. При геометрическом моделировании следует использовать все имеющиеся ветви геометрии, а также другие разделы математики.
Геометрическая модель является частным случаем математической модели. Особенностью геометрической модели является то, что она всегда будет геометрической фигурой, а поэтому в силу своей природы, в отличие от математической модели, является наглядной [20].
Математическая модель [13] — приближенное описание какого-либо класса явлений внешнего мира, выраженное с помощью математической символики.
Если математическая модель — это набор уравнений, мало что говорящий простому инженеру, то геометрическая модель, будучи выражением математической модели и являющаяся геометрической фигурой, позволяет «увидеть» этот набор.
Использование исключительно аналитических методов не всегда приводит к желаемому результату. Поэтому логическим продолжением моделирования, математического или геометрического, является переход к компьютерной графике, когда на компьютер возлагается работа по воспроизведению динамики модели и по проведению экспериментов с ней.
После получения геометрической модели идет изучение объекта по созданной геометрической модели, которое состоит в исследовании модели на предмет выявления ее свойств и характеристик, их связей и преобразований.
Любую геометрическую модель можно представить графически. Геометрическая модель, как и любая другая, имеет определенный уровень адекватности объекту исследования, и этот уровень должен быть достаточным для достижения цели.
1. Voloshinov D.V. O perspektivakh razvitiya geometrii i ee instrumentariyakh [On the prospects of the development of geometry and its instruments]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 2, pp. 37-47. DOI:https://doi.org/10.12737/3844.
2. Gryaznov Ya.A. Otsek kanalovoy poverkhnosti kak obraz tsilindra v rassloyaemom obrazovanii [Compartment as the image of the surface of a canal in the cylinder Stratifiable education]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 1, pp. 17-19. DOI:https://doi.org/10.12737/2077.
3. Zhikharev L.A. Obobshchenie na trekhmernoe prostranstvo fraktalov Pifagora i Kokha [The generalization to three-dimensional space fractal Pythagoras and Koch]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 3, pp. 24-37. DOI:https://doi.org/10.12737/14417.
4. Ivanov G.S. Konstruktivnyy sposob issledovaniya svoystv parametricheski zadannykh krivykh [A constructive way to study the properties of parametrically defined curves]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 2, I. 3, pp. 3-6. DOI:https://doi.org/10.12737/6518.
5. Ivanov G.S. Konstruirovanie tekhnicheskikh poverkhnostey. (matematicheskoe modelirovanie na osnove nelineynykh preobrazovaniy) [Construction of technical surfaces (the mathematical modeling based on nonlinear transformations)]. Moscow, Mashinostroenie Publ., 1987.
6. Ivanov G.S. Teoreticheskie osnovy nachertatel´noy geometrii [Theoretical foundations of descriptive geometry]. Moscow, Mashinostroenie Publ., 1998. 158 p.
7. Ivanov G.S. Fraktal´naya geometricheskaya model´ mikropoverkhnosti [Fractal geometry model microsurface]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 1, pp. 4-11. DOI:https://doi.org/10.12737/18053.
8. Korotkiy V.A. Komp´yuternoe modelirovanie kinematicheskikh poverkhnostey [Computer modeling of the kinematic surfaces]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 4, I. 4, pp. 19-26. DOI:https://doi.org/10.12737/17347.
9. Krylov N.N. Nachertatel´naya geometriya [Descriptive geometry]. Moscow, Vysshaya shkola Publ., 1963. 361 p.
10. Kuzin A.A. Kratkiy ocherk istorii razvitiya chertezha v Rossii [A brief sketch of the history of drawing in Russia]. Moscow, Uchpedgiz Publ., 1956. 112 p.
11. Chetverukhin N.F., Levitskiy V.S., Pryanishnikova Z.I., Tevlin A.M., Fedotov G.I. Kurs nachertatel´noy geometrii [The course of descriptive geometry]. Moscow, Gos. izd-vo tekhniko-teoreticheskoy literatury Publ., 1956.
12. Makashina E.V. Geometricheskoe modelirovanie vremennykh ryadov v mnogomernom prostranstve [Geometric modeling of time series in the multidimensional space]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 1, pp. 20-21. DOI:https://doi.org/10.12737/19832.
13. Matematicheskaya entsiklopediya [Mathematical encyclopedia]. Moscow, Sovetskaya entsiklopediya Publ., 1982.
14. Miloserdov E.P. Raschet parametrov konstruktsii i razrabotka algoritmov realizatsii analemmaticheskikh solnechnykh chasov [Calculation of the design parameters and the development of the implementation of algorithms analemmaticheskih sundial]. Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 3, pp. 14-16. DOI:https://doi.org/10.12737/2076.
15. Miloserdov E.P. Traektorii planetarnykh sputnikov v tsilindricheskikh proektsiyakh [Trajectories of planetary satellites in cylindrical projections]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 1, pp. 15-16. DOI:https://doi.org/10.12737/2076.
16. Obukhova V.S. Poetapnoe modelirovanie tekhnicheskikh poverkhnostey [Incremental modeling of technical surfaces]. Referativnaya informatsiya o zakonchennykh nauchno-issledovatel´skikh rabotakh v vuzakh Ukrainskoy SSR: Prikladnaya geometriya i inzhenernaya grafika [Abstracts information on completed research projects in the Ukrainian SSR universities: Applied geometry and engineering graphics]. Kiev, Vishcha shkola Publ., 1977, pp. 5-6.
17. Podgornyy A.L. Geometricheskoe modelirovanie prostranstvennykh konstruktsiy. Doct. Diss. [Geometric modeling of spatial structures. Doct. Diss]. Moscow, 1975.
18. Ryzhov N.N. Algoritmy perekhoda ot konstruktivno-kinematicheskogo zadaniya poverkhnosti k analiticheskomu [Algorithms transition from konstruktivno- kinematic surface to the analytical tasks]. Trudy UDN im. P. Lumumby [Proceedings UDN them. Lumumba]. Moscow, 1971, V. 53, pp. 17-25.
19. Ryzhov N.N. Matematicheskoe modelirovanie proezzhey chasti avtomobil´nykh dorog [Mathematical modeling carriageway roads]. Moscow, MADI Publ., 1988.
20. Ryzhov N.N. Nachertatel´naya geometriya (ponyatiya, ikh opredeleniya i poyasneniya) [Descriptive geometry (the concepts, their definitions and explanations)]. Moscow, MADI (TU) Publ., 1993. 60 p.
21. Sal´kov N.A. Grafo-analiticheskoe reshenie nekotorykh chastnykh zadach kvadratichnogo programmirovaniya [Graph-analytical solution of some special problems of quadratic programming]. Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 1, pp. 3-8. DOI:https://doi.org/10.12737/3842.
22. Sal´kov N.A. Kinematicheskoe sootvetstvie vrashchayushchikhsya prostranstv [Kinematic matching rotating spaces]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 1, pp. 4-10. DOI:https://doi.org/10.12737/2074. 23. Sal´kov N.A. Modelirovanie avtomobil´nykh dorog [Modeling roads]. Moscow, INFRA-M Publ., 2012, 120 p.
23.
24. Sal´kov N.A. Nachertatel´naya geometriya - baza dlya komp´yuternoy grafiki [Descriptive Geometry - the basis for computer graphics]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 2, pp. 37-47. DOI:https://doi.org/10.12737/19832.
25. Sal´kov N.A. Nachertatel´naya geometriya: Bazovyy kurs [Descriptive geometry: Basic course]. Moscow, INFRA-M Publ., 2013. 184 p.
26. Sal´kov N.A. Nachertatel´naya geometriya do 1917 goda [Descriptive geometry up to 1917]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 2, pp. 18-20. DOI:https://doi.org/10.12737/780.
27. Sal´kov N.A. Nachertatel´naya geometriya. Osnovnoy kurs [Descriptive geometry. Basic course]. Moscow, INFRA-M Publ., 2014. 235 p.
28. Sal´kov N.A. Parametricheskaya geometriya v geometricheskom modelirovanii [Parametric geometry in the geometric modeling]. Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 3, pp. 7-13. DOI:https://doi.org/10.12737/6519.
29. Sal´kov N.A. Svoystva tsiklid Dyupena i ikh primenenie [Properties Dupin Dupin and their application]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 1, pp. 16-25. DOI:https://doi.org/10.12737/10454.
30. Sal´kov N.A. Svoystva tsiklid Dyupena i ikh primenenie [Properties Dupin Dupin and their application]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 2, pp. 9-23. DOI:https://doi.org/10.12737/12164.
31. Sal´kov N.A. Svoystva tsiklid Dyupena i ikh primenenie: sopryazheniya [Properties Dupin Dupin and their application]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 4, pp. 3-14. DOI: DOI:https://doi.org/10.12737/17345.
32. Sal´kov N.A. Svoystva tsiklid Dyupena i ikh primenenie: prilozheniya [Properties Dupin Dupin and their application]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 1, pp. 21-32. DOI:https://doi.org/10.12737/17347.
33. Sal´kov N.A. Tsiklida Dyupena i ee prilozhenie [Dupin Dupin and its application]. Moscow, INFRA-M Publ., 2016. 142 p.
34. Sal´kov N.A. Tsiklida Dyupena i krivye vtorogo poryadka [Dupin Dupin and second-order curves]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 2, pp. 19-28. DOI:https://doi.org/10.12737/19829.
35. Sal´kov N.A. Ellips: kasatel´naya i normal´ [Ellipse: tangent and normal]. Geometriya i grafika [Geometry and Graphics]. 2013, I. 1, p. 28-31. DOI:https://doi.org/10.12737/2084.
36. Sokolova N.Yu. Parametrizatsiya figur i konstruirovanie ogibayushchey poverkhnosti [Parameterization of shapes and design envelope surface]. Trudy UDN im. P. Lumumby [Proceedings UDN them. Lumumba]. V. 73, Prikladnaya geometriya Publ., Moscow, 1975. pp. 29-39.
37. Teoreticheskie osnovy formirovaniya modeley poverkhnostey [Theoretical bases of formation of surface models]. Moscow, MAI Publ., 1985.
38. Umbetov N.S. Konstruirovanie ekvipotentsial´noy poverkhnosti [Construction equipotential surface]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 1, pp. 11-14. DOI:https://doi.org/10.12737/2075.
39. Frolov S.A. Nachertatel´naya geometriya [Descriptive geometry]. Moscow, Mashinostroenie Publ., 1978. 240 p.
40. Shal´ M. Istoricheskiy obzor proiskhozhdeniya i razvitiya geometricheskikh metodov [Historical overview of the origins and development of geometric methods]. Moscow, 1883.
