DEVELOPMENT OF A SCIENTIFIC SCHOOL ON APPLIED GEOMETRY FOUNDED BY PROFESSOR OBUKHOVA VIOLETTA SERGEEVNA

The creation of a school on applied geometry at the National University of Bioresources and Nature Management of Ukraine is associated with the names of the so-called prof. Obukhova Violetta and prof. Rozov Seraphim. Thanks to these outstanding personalities, the Department of Drawing Geometry and Mechanical Engineering of the Ukrainian Agricultural Academy (the old name of the department and university) became widely known in the former Soviet Union. Members of the department annually honor the memory of prof. Obukhova V., hold a scientific and practical conference «Obukhov Readings». Now the conference has acquired international status and is held by order of the rector of the university. The conference is attended by teachers from Kiev universities, from universities in other cities, scientists who had to work with V.S. Obukhova or listen to her lectures, being students, doctoral students, graduate students. The development of the school is evidenced by the fact that over the past 15 years, 15 PhD theses have been defended by former graduate students of the department. Some of them are working on doctoral dissertations. Today, the scientific school was headed by Doctor of Technical Sciences, Professor of Pilipakа Sergey. Under his leadership, 17 master's theses and 3 doctoral dissertations were defended. It should be noted that the range of scientific research of the school representatives is quite wide. Many publications focus on bending surfaces based on the invariability of the expression of a linear surface element. The main area of research is geometric modeling of technical forms and automation of their design. In the field of view of scientists - the design of unfolding surfaces, as a bypass single-parameter set of planes, the location on the surfaces of geodetic lines and their design according to a given curve, which should be a geodetic line for the surface and interpolation of a point series in plane and space.

OPTIMIZATION OF PRODUCTION TECHNICAL SYSTEMS BY MEANS OF STRUCTURAL-PARAMETRIC MODELING

The modern life of people is characterized by constant interaction with various technical systems. These are various buildings (residential, industrial and social purposes), means of transport (cars, ships and planes), production equipment, household appliances (television sets, computers, telephones, washing machines, and refrigerators), etc. A significant number of requirements, often contradictory, both individual and general, are made to the above objects. The first take into account the specifics of these products, and the second are universal in nature. Relevant examples are the immobility of structures, good transport controllability, accuracy of equipment, high-quality images of TVs, computers, etc. This is on the one hand. On the other hand, high reliability, long service life, low cost, etc. The operation of technical facilities is based on processes of various natures. But they also have common properties. These include geometric parameters of shape, size, position and time. In other words, everything around us is located in a certain space and happens in time. Such an extensive theoretical foundation was made to confirm the basic generalizing role of geometric models, including dynamic ones, in the modern automated development of many types of industrial products. The material presented above shows that the search of optimal variants, which are compromise for the existing conflicting requirements, of various technical objects is now an urgent problem of social development. One of the progressive directions of computer geometric modeling, developed by the scientific school of the Igor Sikorsky Kyiv Polytechnic Institute, is structural-parametric shaping. This methodology is quite universal, it is productively applied in the aviation industry, it has been introduced into general mechanical engineering, the oil refining industry, in the manufacture of composite materials, and begins to adapt to the needs of construction. The main purpose of this publication is to expand the scope of this approach through the further development of some of its theoretical provisions.

THEORY OF OBJECTIVE FORMATION IN DESIGN PRODUCTS SEWING VIROBIV

Theory of objective shaping in the design of garments. Modern methods of designing garments are considered. It is determined that the current areas are: particular features of modeling, which take into account the dynamics of dimensional features; methods of two- and three-dimensional design with an attempt to take into account anthropometric features and features of sewing materials. The disadvantages of the subjective approach according to the methods of approximate design are pointed out The new scientific direction of objective shaping in clothing design with the corresponding theory with criterion complex dependences which allow to carry out objective controllability of process of shaping and the forecast of qualitative indicators is proved. An example of shells with pre-deformed and bent section and their criterion dependence is given.

ADAPTIVE ALGORITHM FOR DETERMINING THE PARAMETERS OF AN INACCESSIBLE POINT OF AN OBJECT

In the present research the optimizing approach to the determination of the parameters of an inaccessible point of an object is developed. The common issues are revealed and essential steps of their resolution are identified. The essence of the problem is an objective contradiction between a requirement for the location of points A and B of the centers of the sighting tubes of optical devices in the same horizontal plane P1 and the lack of a real possibility to perform such to achieve this an identical one-level arrangement without error. The aim of the study is to develop strategies for determining the position of an inaccessible point of an object in the minimum domain between intersecting sighting rays as well as an adaptive algorithm for determining the values of the parameters of an inaccessible point under the given absolute and relative errors. To achieve this aim, the following problems are formulated and solved in the paper: 1. Develop strategies for determining the position of the inaccessible point of the object in the minimum domain between the intersecting sighting rays. 2. Develop an adaptive algorithm for determining the values of the parameters of an inaccessible point based on the specified absolute and relative errors. In the proposed optimizing approach, the three-dimensional geometrical model with crossed directional rays for the determination of coordinates of the inaccessible point of an object is developed. It is discussed that points С and C', coordinated of which to be determined, locates in domain [CDM, CEM], [C'D'M, C'E'M] of the minimum distance ρmin between crossed directional rays. The optimizing problem of the determination of coordinates of an inaccessible point of an object in space is reduced to a problem of the determination of the minimum distance between two crossed directional rays. It’s known from the theory of function of multiple variables that function ρ = f (tC'D', tC'E') reaches its extremum ρmin when its partial derivatives by each variable are equal to zero. Three strategies for selecting the position of the inaccessible point C (xC, yC, zC) in the found minimum region [CDM, CEM] are proposed. The required point C' (xC', yC', zC') can be located, for example, in the middle of the minimum segment [C'D'M, C'E'M]. The essence of the adaptive algorithm is in optimizing the variation of the initial values of data α, α', β, γ, γ', AB, at which the absolute and relative errors of the coordinates of the inaccessible point satisfy the error values set by the customer (0.0001-1.2%) The proposed approach is verified using real experimental data.

MULTIPARAMETRIC OPTIMIZATION OF THE SHAPE AND THICKNESS OF INSULATED ENERGY EFFICIENT CONSTRUCTED BUILDING WITH A SPECIFIC NUMBER OF FACES

To calculate the optimal parameters of outbuildings, a mathematical model and method for optimizing the shape and resistance of heat transfer for opaque and transparent structures with a certain constant number of faces, building volume and amount of insulation to minimize the thermal balance of enclosing structures with the environment during the heating period In the course of calculations the geometrical parameters of translucent, opaque structures in the heat-insulating shell of buildings are determined taking into account heat losses, heat influx from solar radiation by the criterion of ensuring minimum heat losses through enclosing structures, rational parameters (buildings) The given technique and mathematical models should be used in the future in the design of energy efficient buildings in the reconstruction and thermal modernization of buildings. This will increase their energy efficiency and, accordingly, the energy efficiency class of buildings. For the research faceted attached building in the form of a triangular pyramid, the reduction in heat loss was 14.82 percent only due to the optimization of the shape and redistribution of the insulation. Similar results were obtained for other initial forms. For the first time, a computerized method was proposed, an algorithm and application package Optimparam for multiparameter shape optimization and insulation of translucent and opaque structures for outbuildings with a given number of arbitrarily arranged faces were developed.

FOUR-DIMENSIONAL BALL IN A GRAPHIC REPRESENTATION

The paper presents a method for geometric modelling of a four-dimensional ball. For this, the regularities of the change in the shape of the projections of simple geometric images of two-dimensional and three-dimensional spaces during rotation are considered. Rotations of a segment and a circle around an axis are considered; it is shown that during rotation the shape of their projections changes from the maximum value to the degenerate projection. It was found that the set of points of the degenerate projection belongs to the axis of rotation, and each n-dimensional geometric image during rotation forms a body of a higher dimension, that is, one that belongs to (n + 1) -dimensional space. Identified regularities are extended to the four-dimensional space in which the ball is placed. It is shown that the axis of rotation of the ball will be a degenerate projection in the form of a circle, and the ball, when rotating, changes its size from a volumetric object to a flat circle, then increases again, but in the other direction (that is, it turns out), and then in reverse order to its original position. This rotation is more like a deformation, and such a ball of four-dimensional space is a hypersphere. For geometric modelling of the hypersphere and the possibility of its projection image, the article uses the vector model proposed by P.V. Filippov. The coordinate system 0xyzt is defined. The algebraic equation of the hypersphere is given by analogy with the three-dimensional space along certain coordinates of the center a, b, c, d. A variant of hypersection at t = 0 is considered, which confirms by equations obtaining a two-dimensional ball of three-dimensional space, a point (a ball of zero radius), which coincides with the center of the ball, or an imaginary ball. For the variant t = d, the equation of a two-dimensional ball is obtained, in which the radius is equal to R and the coordinates of all points along the 0t axis are equal to d. The variant of hypersection t = k turned out to be interesting, in which the equation of a two-dimensional sphere was obtained, in which the coordinates of all points along the 0t axis are equal to k, and the radius is . Horizontal vector projections of hypersection are constructed for different values of k. It is concluded that the set of horizontal vector projections of hypersections at t = k defines an ellipse.

SYSTEMATIC GRAPHICALLY-INTERPRETED MODELS OF CREATION OF ENERGY EFFICIENT BUILDINGS

The article considers the creation of systematic graphically-interpreted models for matrix analysis of energy saving measures in the design of residential energy efficient and passive buildings, reconstruction of residential and historical buildings and the creation of energy-active architectural objects using alternative energy sources. Energy-efficient design of new buildings and modernization of old ones remains an urgent task. Ukraine's construction organizations are increasingly interested in reducing energy consumption and introducing energy-saving technologies. Scientists are trying to make housing more energy efficient, namely, consuming less energy compared to ordinary buildings and not polluting the environment. Increasing the level of energy supply and reducing the individual costs of servicing the house will allow solving the problem of creating graphically interpreted models of energy efficiency of the building and energy costs. The analysis is based on a combination of active and passive energy conservation measures and takes into account possible limitations based on a system approach in the construction of an integrated model of an energy active building. The analysis is based on a combination of active and passive energy saving measures and takes into account possible limitations based on a systematic approach by creation a comprehensive model of an energy-active building.

STRUCTURAL-PARAMETRIC MODEL OF SECOND-ORDER SURFACES

One of the modern directions for the further development of the applied geometry scientific school of the Igor Sikorsky Kyiv Polytechnic Institute is the structural-parametric shaping of various technical objects. Currently, the general theoretical foundations of this methodology and specialized means of its practical implementation are being developed. The results obtained in the design, manufacture and operation of specific industrial products largely depend on their efficiency. The created mathematical models serve as the basis for software modules, which become components of the applied computer information systems. In these conditions, the issues of developing the necessary methodological support are also important. From the side of the theory of structural-parametric shaping, requirements are imposed on new geometric means in accordance with the principles of universality and unification, variability, openness and development, a system approach, etc. As can be seen from the title of the publication, in our case we are talking about second-order surfaces, which, due to their useful properties, are quite common in many technical objects. Note that the plane is considered a simplified version of these figures. The indicated universality and unification consist in solving a wide range of problems using the same type of methods, techniques, algorithms, etc. Variability is the need to implement for the geometric model of its flexible and productive use, the openness and the development – of easy updating, expansion and improvement its components. The systems approach requires considering the created mean not only as interconnected elements, but also as a part of systems of a higher hierarchical level. The submitted second-order surface model satisfies the rules described above. Its main peculiarity lies in the combination of the vector definition of these items with the structural-parametric methodology. The developed techniques of shaping are suitable for wide practical use during the automated design of various technical objects, the processes of their production and operation.

IMPLICATION THE CROSS-PLATFORM LOVE2D ENGINE FOR RENDERING AND ARTIFICIAL INTELLEGENCE DEVELOPMENT

Recently, the market for consoles and mobile games is growing, and therefore to find a game engine that meets the demanding requirements of users is not an easy task. Technology platforms have become clear favorites of many developers. However, the market is volatile, and therefore the question of choosing a game engine will not lose its relevance in the near future and is the first, main, relevant and important subject of choice in this work. The relevance of this article is to write an original algorithm for 2D computer game, taking into account the latest intelligent technologies, which will be different from previous versions by its uniqueness: a new procedural generation, improved artificial intelligence of characters, original game mechanics, which necessitated the creation of a key to unlock levels. To work on this task, the open cross-platform LOVE2D engine and the Lua programming language a powerful, efficient and easy to learn language were substantiated. The reason for choosing the LOVE2D game engine is that its technology is unique in itself. Simple text was used in the development of the game algorithm. A significant number of issues were resolved in unique way from scratch while developing. Original positions of game mechanics are created such as unlocking the end of the level, the infinity of the game and focusing on the maximum "Score", increasing the size of each subsequent level, compared to the previous one, improved artificial intelligence of characters are the main differences from existing approaches used to create previous Super Mario Bros projects. The reason that makes this project more advanced and a little more random than the original game: it's a procedural level generation. Since the game is infinite it's really important to keep levels random and different. The obtained results made it possible to say that the work done is a new step forward in comparison with previous developments of algorithms for this 2D game. The original algorithm and code for 2D computer game, using the capabilities of modern information technologies, can be useful not only for creating mobile games, but also for solving virtual reality, augmented reality, TV presentation, visualization effects of the hologram. The project presented in the paper is made exclusively for the purpose of implementation in the educational process.

USE OF DYNAMIC BLOCKS FOR CREATION OF ELECTRONIC IMAGE LIBRARIES OF TYPICAL FIXING ELEMENTS BY AUTO CAD RESOURCES

The use of electronic libraries of parameterized images of objects made in the form of dynamic blocks in the practice of design work refers to resource-saving technologies that are actively used in modern production. The article considers an example of creating parameterized simplified images of fasteners using dynamic blocks of the computer-aided design system AutoCAD. Dynamic blocks can be used to create electronic image libraries of technological, design, electrical and other elements. The algorithm considered in the article to create dynamic blocks of simplified images of fasteners is introduced into the educational process at the Kyiv Polytechnic Institute named after Igor Sikorsky in the course "Engineering and Computer Graphics" and can be used in design practice. The testing of this algorithm in the training process yielded a positive result. When using parameterized drawings, students understand more deeply the impact of each parameter on the design of the object.