CC BY
9Oriental Renaissance: Innovative,
educational, natural and social sciences
Scientific Journal Impact Factor
VOLUME 1 | ISSUE 11
ISSN 2181-1784
SJIF 2021: 5.423
UDC. 22.151.3
PERSPECTIVE DETERMINATOR METHOD
Kodirov MurodjonYusupovich
Senior Lecturer,
Fergana Polytechnic Institute, Fergana, Uzbekistan ABSTRACT
The article is devoted to the method of determining the prospects on the subject of "Descriptive geometry" for university students in the classroom. The proposed method for studying descriptive geometry using an integrated approach makes it possible to reduce the amount of study time for solving promising graphic problems.
Keywords: object that gives the plane of the picture, creative approach, variability, teaching methodology, fundamental, perspective, building, perspective of a point, perspective of a straight line, perspective of a plane.
АННОТАЦИЯ
Статья посвящена методике определения перспективности по предмету «Начертательная геометрия» для студентов вузов на занятиях.
Предлагаемый метод изучения начертательной геометрии с использованием комплексного подхода позволяет сократить объем учебного времени для решения перспективных графических задач.
Ключевые слова: объект, задающий плоскость рисунка, творческий подход, вариативность, методика обучения, фундаментальный, перспектива, построение, перспектива точки, перспектива прямой линии, перспектива плоскости.
INTRODUCTION
Each projected building must be drawn in perspective. According to the perspective, one can correctly judge the external appearance, the proportions and the ratio of the volumes of individual elements, the expected visual perception of the designed object. For building the perspectives of the main volumes of the structure, you can use the method based on the use of the determinant of perspectives, which gives the plane of the picture the properties of an independent space.
Let us explain this definition. Each specific position of the point of view in space corresponds to a single perspective image of the object in the picture. The continuous movement of this point causes a continuous transformation of one perspective into another on the plane of the sky. Thus, the plane of the sky is the
395
December 2021
www.oriens.uz
Oriental Renaissance: Innovative,
educational, natural and social sciences
Scientific Journal Impact Factor
VOLUME 1 | ISSUE 11
ISSN 2181-1784
SJIF 2021: 5.423
bearer of an innumerable set of perspectives of a given object, corresponding to an innumerable set of positions of the point of view in space.
In order to select the desired perspective from this set, it is necessary to build those graphic elements on the plane of the picture, the position and appearance of which will not depend on the position of the point of view in space. Such elements are called graphic invariants of continuous transformations of one perspective into another. These invariants form on the plane of the picture graphic constructions common to the whole set of perspectives, called determinants of perspectives, i.e. form a determinant of images.
DISCUSSION AND RESULTS
Consider the construction of the perspectives of the main geometric figures -points, lines and planes - using the determinants of their perspectives.
Let's agree that the point of view moves along the main ray.
The frontal plane of projections will be taken as the plane of the picture, in front of which we will place the depicted figures.
Point perspective. If the point of view S moves away from the original point A (A1, A2) and the picture plane, occupying a number of successive positions S1, S2, S3 ... S<» on the main ray, then the perspective of point A moves along the plane of the sky, also occupying a number of sequential positions A1, A2, A3 ... A2 on a rectilinear trajectory a '(Fig. 1).
Fig. 1. Rectilinear trajectory.
Line a ' is a graphical invariant of transformation of perspectives of point A, because its position in the picture does not depend on the point of view. On the plane of the picture, it passes through two fixed points - the main point of the picture P and the frontal projection A2 as the perspective of point A from the infinitely distant
396
December 2021
www.oriens.uz
Oriental Renaissance: Innovative,
educational, natural and social sciences
Scientific Journal Impact Factor
VOLUME 1 | ISSUE 11
ISSN 2181-1784
SJIF 2021: 5.423
center. The same straight line is the determinant of the perspectives of point A, since any point of it can be taken as the perspective of point A.
The perspective is straight. The perspective of the line segment AB, parallel to the picture, can be viewed as a line connecting the perspectives A 'and B' of its ends. Therefore, we draw straight lines a 'and b' through the main point P and projections A2 and B2 as geometric places of all perspectives of the end points A and B (Fig. 2, a, b).
These straight lines constitute the perspective and limit the section of the plane of the sky as the area of existence of all the perspectives of the segment AB. Since the given segment is parallel to the picture, i.e. intersects with it at an infinitely distant point, then any segment drawn in the constructed compartment parallel to the A2 B2 projection is the desired perspective.
To construct the perspective of a segment not parallel to the picture, it is necessary, as before, to draw straight lines a 'and b' and determine its picture trace (Fig. 2, c). Point 1 'coincides with its perspective, and its position in the picture does not depend on the position of the point of view in space. The determinant of the perspectives of a given segment is composed of lines a 'and b' and its picture trace 1 '. Any line segment drawn through point 1 'within the limits of the compartment limited by them will be the perspective of the specified segment.
Perspective plane. In most cases, the image is subject to flat figures, which can be considered as closed broken lines. The links of these broken lines are line segments, the construction of the perspectives of which was discussed above.
The picture traces of all the displayed planes will be located on one straight line - the picture trail 1 ' 2 ' of this plane. The position of this line in the picture does not depend on the position of the point of view in space, and therefore, together with the
397
December 2021
www.oriens.uz
Oriental Renaissance: Innovative,
educational, natural and social sciences
Scientific Journal Impact Factor
VOLUME 1 | ISSUE 11
ISSN 2181-1784
SJIF 2021: 5.423
straight lines a b', c d', it forms a determinant of the perspectives of a given plane (Fig. 3).
So, the determinant of perspectives allows you to build any perspective of a given object without resorting to the operation of central projection of this object onto the plane of the picture.
Let's consider an example of constructing a building perspective using the perspective determiner method (Fig. 4).
Preliminary operations are performed on the plan and facade. The direction of the main ray is chosen in the plan, the base of the picture K is drawn perpendicular to it (the further K is from the object and point of view, the larger the perspective will be). Then the planes of the depicted faces are extended until they intersect with the picture and the bases 10 = 20, 30 = 40, 50 = 60 of the picture traces of these planes are marked.
December 2021
www.oriens.uz
Oriental Renaissance: Innovative,
educational, natural and social sciences
Scientific Journal Impact Factor
VOLUME 1 | ISSUE 11
ISSN 2181-1784
SJIF 2021: 5.423
Preliminary constructions on the picture are performed - to create an independent plane model of space, it is necessary to attach a perspective determinant to the picture plane.
Without changing the relative position of the building plan and the base K, by plane-parallel movement, the latter is located horizontally in a free space of the drawing and the moved building plan is drawn. Continuing the main ray S to the intersection with the horizon line h1 h2, the main point of the picture P is constructed.
The main point P and the constructed orthogonal projections A11, B11, C11 of the original points will determine the straight lines a ', b', c '..., which, together with the picture traces of the face planes, will form the desired determinant of perspectives.
Further, the perspective of the main volumes is built. Drawing a straight line through point 1 ' under the desired angle, the perspective of the straight line AB is set. Further constructions are performed as building a closed polyline perspective, using the previously constructed perspective determiner.
Then, on the perspective of the main volumes, using graphical constructions, the perspectives of the parts are built (or completed).
CONCLUSION
The use of this method for an architect working on the creation of an object will allow at any stage of design to create a model of an object that clearly shows its shape, size and proportions, to identify and eliminate compositional imperfections.
REFERENCES
1. Valiev A.N. «RERSPEKTIVA» „VORIS-NASHRIYOT11, Toshkent — 2012
2. Муродов Ш. ва бошкалар. «Чизма геометрия»: дарслик,Иктисод-молия, 2006 йил.-267 бет.
3. Хорунов Р.Х.Чизма геометрия курси,Тошкент,”Ук;итувчи”Д997 йил.-432 бет.
4. Zulfiya, B., Rakhmonali, S., & Murodjon, K. (2021). A BRIEF HISTORY OF THE DEVELOPMENT AND TEACHING OF DRAWING SCIENCE IN UZBEKISTAN.
5. Karimov, R. (2021). PLANNING OF BELT BRIDGE FOR UNSYMMETRICAL PROGRESSIVE STAMPING. Scientific progress, 2(2), 616623.
399
December 2021
www.oriens.uz
Oriental Renaissance: Innovative,
educational, natural and social sciences
Scientific Journal Impact Factor
VOLUME 1 | ISSUE 11
ISSN 2181-1784
SJIF 2021: 5.423
6. Karimov, R. J. O. G. L., & Toxtasinov, R. D. O. (2021). FEATURES OF CHIP FORMATION DURING PROCESSING OF POLYMER COMPOSITE MATERIALS. Scientific progress, 2(6), 1481-1487.
7. Karimov, R. J. O. G. L., O’G’Li, S. S. D., & Oxunjonov, Z. N. (2021). CUTTING HARD POLYMER COMPOSITE MATERIALS. Scientific progress, 2(6), 1488-1493.
8. Jaxongir o’g’li, R. K., & Sobirovna, N. S. IMPROVING THE QUALITY OF LASER CUTTING OF METALS BY OPTIMIZING THE TECHNOLOGICAL PARAMETERS OF THE PROCESS.
9. Rustam Karimov Jaxongir ugli, & Karimov Ravshan Xikmatullaevich. (2021). DESIGN OF DIES WITH SPLIT DIES. EURASIAN JOURNAL OF SOCIAL SCIENCES, PHILOSOPHY AND CULTURE, 1(3), 35-39.
10. Rustam Karimov Jaxongir o'g'li, Abullayeva Dona Toshmatovna, Rustamova Muxlisa Muxtoraliyevna, & Toxirov Islom Xakimjon o'g'li. (2021). PROGRESSIVE CONSTRUCTIONS OF ADJUSTABLE SHEET PUNCHING STAMPS. EURASIAN JOURNAL OF SOCIAL SCIENCES, PHILOSOPHY AND CULTURE, 1(2), 46-53.
11. I. O. Ergashev, R. J. Karimov, A. M. Turg’unbekov, & S. S. Nurmatova (2021). Arrali jin mashinasidagi kolosnik panjarasi bo’yicha olib borilgan ilmiy tadqiqotlar tahlili. Scientific progress, 2(3), 78-82
12. Ilhom Olimjonovich Ergashev, Rustam Jaxongir o’g’li Karimov, Ravshan Xikmatullayevich Karimov, & Salimaxon Sobirovna Nurmatova (2021). Kolosnik almashinuvchi mashinasi elementi egilishining nazariy tadqiqotlari. Scientific progress, 2(3), 83-87
13. Rustam Karimov Jaxongir ugli, & Polotov Karimjon Quranboevich. (2021). IMPROVE THE EFFICIENCY OF TURNING LIGHT ALLOYS. EURASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 1(3), 26-30.
14. Rustam Karimov Jaxongir ugli, & Jumaev Nizomiddin Kenjaboy ugli. (2021). COMBINED METHOD OF TURNING BILLS FROM POLYMER MATERIALS. EURASIAN JOURNAL OF MEDICAL AND NATURAL SCIENCES, 1(3), 1-6.
15. Rustam Karimov Jaxongir o'g'li, & Polotov Karimjon Quranbaevich. (2021). PROGRESSIV SHTAMPLASH KONSTRUKSIYALARINI REJALASHTIRISH. PLANNING OF PROGRESSIVE STAMPING CONSTRUCTIONS. EURASIAN JOURNAL OF LAW, FINANCE AND APPLIED SCIENCES, 1(3), 10-18.
400
December 2021
www.oriens.uz
Oriental Renaissance: Innovative,
educational, natural and social sciences
Scientific Journal Impact Factor
VOLUME 1 | ISSUE 11
ISSN 2181-1784
SJIF 2021: 5.423
16. No'monov Nodirjon Farxodjon ugli, & Karimov Rustam Jaxongir ugli. (2021). DESIGN OF A MODERN FASTENING AND LOOSENING DEVICE FOR MACHINING OF PLATE-TYPE PARTS ON A MILLING MACHINE. EURASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 1(4), 1-5. https://doi.org/10.5281/zenodo.5766304
17. No'monov Nodirjon Farxodjon ugli, & Karimov Rustam Jaxongir ugli. (2021). DESIGN OF A MODERN FASTENING AND LOOSENING DEVICE FOR MACHINING OF PLATE-TYPE PARTS ON A MILLING MACHINE. EURASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 1(4), 1-5. https://doi.org/10.5281/zenodo.5766304
18. Ахунбабаев, О. А. (2016). ОПТИМИЗАЦИЯ СООТНОШЕНИЯ ДЛИНЫ НИТИ ОСНОВЫ И ТКАНИ НА ТКАЦКИХ СТАНКАХ СТБУ2-180-1ШН. In Дизайн, технологии и инновации в текстильной и легкой промышленности (Инновации-2016) (pp. 13-16).
19. Toshqo‘ziyev, M., Axunboboyev, O., Berdiyev, T., Ochilov, S., &
Muxammadrasulov, S. (2021, July). INFLUENCE OF THE APPLICATION OF NEW AGROTECHNOLOGY DURING THE CREATION OF TUTO PLANTS IN THE CONDITIONS OF THE FERGHANA REGION ON THE RECLAMATION STATE OF THE SOIL. In Конференции.
20. Axunbabaev, O. A. (2018). THE ANALYTICAL DEPENDENCE OF THE TOTAL NUMBER OF CYCLES OF ABRASION OF THE MAIN THREADS ON A LOOM DUE TO THE SURF. Scientific-technical journal, 1(2), 144-147.
21. Джураев, Б. Э., Хасанов, Б. К., Ахунбабаев, О. А., & Мирзахонов, М. М. (2017). ОПРЕДЕЛЕНИЕ ПАРАМЕТРОВ СТРОЕНИЯ И ТЕХНОЛОГИИ ПРОИЗВОДСТВА НОВЫХ СТРУКТУР КРЕПОВЫХ ТКАНЕЙ. Физика волокнистых материалов: структура, свойства, наукоемкие технологии и материалы (SMARTEX), (1), 370-374.
22. Ахунбабаев, О. А. (2016). МАТЕМАТИЧЕСКОЕ ОПИСАНИЕ НАПРЯЖЕННОСТИ ФОРМИРОВАНИЯ НОВОГО ЭЛЕМЕНТА ТКАНИ НА ТКАЦКИХ СТАНКАХ С ДОПОЛНИТЕЛЬНЫМ СКАЛОМ. Физика волокнистых материалов: структура, свойства, наукоемкие технологии и материалы (SMARTEX), (1-1), 248-253.
23. Мухамадрасулов, Ш. Х., & Ахунбабаев, О. А. (2016). НЕКОТОРЫЕ ПУТИ
ПОВЫШЕНИЯ ЭФФЕКТИВНОСТИ ТЕХНОЛОГИИ ПРОИЗВОДСТВА НАТУРАЛЬНОГО ШЁЛКА. Физика волокнистых материалов: структура,
свойства, наукоемкие технологии и материалы (SMARTEX), (1-1), 303-309.
401
December 2021
www.oriens.uz
Oriental Renaissance: Innovative,
educational, natural and social sciences
Scientific Journal Impact Factor
у R О
VOLUME 1 | ISSUE 11
ISSN 2181-1784
SJIF 2021: 5.423
24. Мирзахонов, М., & Ахунбабаев, О. А. (2015). ТЕХНОЛОГИЯ
ПРОИЗВОДСТВА НОВЫХ СТРУКТУР КРЕПОВЫХ ТКАНЕЙ. Физика волокнистых материалов: структура, свойства, наукоемкие технологии и материалы (SMARTEX), 1(1-1), 210-212.
25. Хусанбоев, А. М., Тошкузиева, З. Э., & Нурматова, С. С. (2020). Приём деления острого угла на три равные части. Проблемы современной науки и образования, (1 (146)).
26. Dostonbek, V., & Salimaxon, N. (2021). The effect of scraping and surface
cleaning on the scraping of scraping to be dressing in the cutting of polymer materials. ACADEMICIA: An International Multidisciplinary Research
Journal, 11(6), 717-721.
27. Khusanbaev, A. M., Madaminov, J. Z., & Oxunjonov, Z. N. (2020). EFFECT OF RADIATION ON PHYSICAL-MECHANICAL PROPERTIES OF SILK THREADS. Theoretical & Applied Science, (5), 209-212.
28. Xusanboev, A. M. Umarova., & Abdullayeva, DT (2020). The rectification of curve flat arch. ACADEMICIA: An International Multidisciplinary Research Journal, 10(5), 62-65.
29. Хусанбоев, А. М. (2020). Зулфия Эралиевна Тошкузиева, and Салима Собировна Нурматова.". ПРИЁМ ДЕЛЕНИЯ ОСТРОГО УГЛА НА ТРИ РАВНЫЕ ЧАСТИ." Проблемы современной науки и образования, 1, 146.
30. Mamajonovich, K. A., Eraliyevna, T. Z., & Mukhtaraliyevna, R. M. (2020). Box curve (curl) of fan casing. ACADEMICIA: An International Multidisciplinary Research Journal, 10(5), 604-607.
402
December 2021
www.oriens.uz
