The Ways to Create Geometric Patterns Automated Layout

Leonid V. Markin

doi:10.12737/10460

THE WAYS TO CREATE GEOMETRIC PATTERNS AUTOMATED LAYOUT The Ways to Create Geometric Patterns Automated Layout

АА Аа

Published in Geometry & Graphics · Volume 3, Issue 1 · Pages 64–69 · Rubric: Computer graphics

DOI: https://doi.org/10.12737/10460

Received: 31.03.2015 Accepted: 17.04.2015 Published: 17.04.2015 Language of publication: RUS

Authors

Leonid V. Markin

Academic degree: candidate of technical sciences

Science rang: professor

Moscow Aviation Institute (National Research University) Professor · Russian Federation

ABSTRACT

Improving the quality of products associated with improving the quality of their design, which is achieved by using modern information technologies. Considering the high density layout of a modern transport technology, is an urgent development of mathematical software and automated layout system. The basis for the creation of mathematical development and software development need the steps to geometric modeling as placed objects, and the allocating process. The article discusses the layout automation products with a high density layout (especially means of transport). Since the problem of accommodation is a classical geometrical problem, then it is necessary to develop solutions appropriate geometric models. The article describes the main types of geometric models describing the shape of composable objects, their classification and application. We describe an automated layout problem as a problem of placement of a certain group of objects of specified sizes and shapes in a confined space. The paper shows that with an abundance of models used in modern applied geometry, allowing to describe the geometric shape of objects of any complexity, their use in computer-aided layout does not provide a solution to the problem of automated layout. The article shows the possibilities of modern software and reasons that do not allow its direct use in tasks of automated layout. The mathematical formulation of the problem as a layout optimization problem, indicating its objective function, constraints and performance criteria. An approach (unit normal equations), which allows the creation of geometric models of automated layout, move from exhaustive search of accommodation options composable objects to intelligent automated placement algorithms.

KEYWORDS

geometric models, placement, automated layout, dense deployment conditions of mutual non-intersection, normal equation objects.

Text

При автоматизации проектирования любой техники на результат проектирования оказывает существенное влияние качество компоновки. Развитие современной транспортной и особенно авиационно-космической техники, рост требований к ней и повышение плотности компоновки заставляют конструкторов постоянно совершенствовать методы автоматизации проектирования. Даже первые опыты компьютеризации процесса проектирования при решении отдельных частных задач показали их высокую эффективность. Работы по автоматизации размещения не составляли исключения. Первые публикации, посвященные автоматизации решения задач размещения, относятся к 60-м гг. прошлого века и связаны с именами Л.В. Канторовича и В.А. Залгаллера по раскрою материалов методами линейного программирования. Однако переход от 2D-объектов к 3D-объектам и усложнение формы размещаемых объектов от линейных полос до реальных объектов современной техники вызвало лавинообразное усложнение математического описания процесса размещения. Несмотря на то что исследованию этого вопроса посвящены труды многих замечательных ученых, эта задача далека от своего разрешения.

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Zamestitel' glavnogo redaktora, chlen redsoveta

Vladimir Vyshnyepolskiy

Glavnyy redaktor

A. A. Ishchenko

Vypuskayuschiy redaktor

Dar'ya Sklyankina

501@infra-m.ru

Deputy editor-in-chief, member of the editorial Board

N. Sal'kov

nikolaysalkov@mail.ru

GOST

Markin L. V. The Ways to Create Geometric Patterns Automated Layout // Geometry & Graphics. 2015. no. 1. pp. 64-69. DOI: https://doi.org/10.12737/10460. (Date of access 23.09.2026).

MLA

Leonid V. Markin. "The Ways to Create Geometric Patterns Automated Layout." Geometry & Graphics 3.1 (2015): 64-69. DOI: https://doi.org/10.12737/10460.

APA

Markin L. V. (2015). The Ways to Create Geometric Patterns Automated Layout. Geometry & Graphics, 3(1), 64-69. https://doi.org/10.12737/10460

Chicago

Leonid V. Markin. "The Ways to Create Geometric Patterns Automated Layout." Geometry & Graphics 3, no. 1 (2015): 64-69. https://doi.org/10.12737/10460.

WIKI

{{cite journal | author = Markin L. V. | title = The Ways to Create Geometric Patterns Automated Layout | journal = Geometry & Graphics | year = 2015 | volume = 3 | issue = 1 | pages = 64-69 | doi = 10.12737/10460 }}

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