Geometric Simulation and Descriptive Geometry

N. Sal'kov

doi:10.12737/22841

GEOMETRIC SIMULATION AND DESCRIPTIVE GEOMETRY Geometric Simulation and Descriptive Geometry

АА Аа

Published in Geometry & Graphics · Volume 4, Issue 4 · Pages 31–40 · Rubric: Methodical questions of teaching

DOI: https://doi.org/10.12737/22841

Received: 24.11.2016 Accepted: 18.12.2016 Published: 18.12.2016 Language of publication: ru-RU

Authors

N. Sal'kov

Academic degree: candidate of technical sciences

Science rang: professor

MIREA – Russian technological university Russian Federation

ABSTRACT

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.

KEYWORDS

descriptive geometry, geometric simulation, mathematical simulation, graphical model

Text

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.

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Sal'kov N. A. Geometric Simulation and Descriptive Geometry // Geometry & Graphics. 2016. no. 4. pp. 31-40. DOI: https://doi.org/10.12737/22841. (Date of access 12.11.2026).

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N. Sal'kov. "Geometric Simulation and Descriptive Geometry." Geometry & Graphics 4.4 (2016): 31-40. DOI: https://doi.org/10.12737/22841.

APA

Sal'kov N. A. (2016). Geometric Simulation and Descriptive Geometry. Geometry & Graphics, 4(4), 31-40. https://doi.org/10.12737/22841

Chicago

N. Sal'kov. "Geometric Simulation and Descriptive Geometry." Geometry & Graphics 4, no. 4 (2016): 31-40. https://doi.org/10.12737/22841.

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{{cite journal | author = Sal'kov N. A. | title = Geometric Simulation and Descriptive Geometry | journal = Geometry & Graphics | year = 2016 | volume = 4 | issue = 4 | pages = 31-40 | doi = 10.12737/22841 }}

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