THE IMPORTANCE OF SHADOWS IN HUMAN LIFE AND SOME RULES FOR DRAWING SHADOWS IN PERSPECTIVE IMAGES

ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 980 THE IMPORTANCE OF SHADOWS IN HUMAN LIFE AND SOME RULES FOR DRAWING SHADOWS IN PERSPECTIVE IMAGES Nigmоnov Bahrom Vossykovich¹ O‘rinova Shoxista Baxtiyor qizi ² Ermatova Arofat Bahramovna³ Tashkent University of Architecture and Civil Engineering, Tashkent, Uzbekistan Abstract: The purpose of this article is to introduce students to the fundamentals of shadow construction in perspective drawings, including determining the direction of light rays, methods for constructing cast and self-shadows, as well as developing spatial thinking skills and the ability to visualize lighting in graphic compositions. Special attention is given to the differences between shadows formed under natural and artificial lighting conditions. In natural lighting, the primary light source is typically the Sun, which results in a strict, nearly parallel direction of light rays. This simplifies the construction of shadows, as all shadows from objects are cast in the same direction. Additionally, the intensity of light and the length of shadows vary depending on the time of day and weather conditions, which must be taken into account when creating realistic compositions. In contrast, artificial lighting involves one or more point light sources (such as lamps or spotlights), which produce a radial, divergent direction of light rays. This requires different approaches to shadow construction: shadows may vary depending on the position of the light source relative to the object, may overlap, be duplicated, and form more complex shapes. Understanding these differences is essential for accurately and expressively depicting light and shadow relationships in architectural, design, and artistic graphics. Thus, the article examines both the theoretical aspects of lighting and the practical methods of shadow construction, enabling students to create convincing and technically sound perspective drawings with consideration of various light sources. Keywords: axonometry, own and cast shadows, orthogonality, geometric solids, multiplicity, student, method, specialists, laws of proportion, scientific research, didactics, theory, practical application, composition, skill. In the "National Program for Personnel Training," one of the main tasks is defined as the preparation of specialists who, along with deep theoretical and practical knowledge in their chosen field, are able to work independently, improve their level of knowledge and qualifications on their own, creatively approach problem-solving, correctly identify and analyze problematic situations, and quickly adapt to changing conditions. As is well known, in modern conditions where the sphere of information and knowledge is rapidly expanding, it is quite difficult to convey all the necessary information to students only during classes. Experience shows that a student can deeply assimilate knowledge only under the condition of independent work and constant improvement. The main knowledge, skills, and abilities of students ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 981 are formed precisely in the process of independent learning, developing the ability to work autonomously and fostering interest in creative work. Therefore, planning and organizing independent learning for students, creating all necessary conditions for this, as well as teaching students not only during lessons but also developing skills for independent knowledge seeking, indicating ways to obtain information, and providing recommendations for self-study, is one of the primary tasks of higher education institutions. Independent student work is a systematic activity aimed at mastering a certain part of knowledge, skills, and abilities outlined in the curriculum for a specific subject, which the student performs both under the guidance and advice of a teacher and independently, both inside and outside the classroom. The organization of independent work for students at the initial stages of learning is associated with a number of tasks. It is especially difficult for first-year students to adapt to the new requirements of higher education because they almost do not know how to organize their learning activities independently. They face major difficulties in finding the necessary information from various sources, analyzing it, highlighting the main points and systematizing them, making notes, clearly and vividly expressing their thoughts, properly managing their time, as well as correctly assessing their mental and physical capabilities. Most importantly, they are psychologically unprepared for independent learning. Therefore, every professor or teacher should first instill confidence in students about their abilities and intellectual capacities, patiently and gradually teaching them how to properly organize independent knowledge acquisition. Considering that the knowledge and skills mastered independently by students become more complex and extensive each year, it is necessary to increase their initiative and role in the learning process. A student beginning to get used to independent learning not only completes the tasks assigned by the teacher but also independently selects and master’s additional knowledge according to their needs, interests, and abilities. Depending on the specifics of the subject, students may be given various types of assignments for independent work. The decision on which assignments to give is made by the department. Assignments should be carefully thought out and aimed at strengthening, deepening, expanding, and supplementing the knowledge acquired by students during lessons. One of the main factors for a complete, deep, and comprehensive mastery of a subject is independent work. The reason is that the hours allocated to the curriculum are limited, and it is impossible to fully absorb the material during classes. For independent work, students need methodological materials. These methodological materials should be designed so that when solving problems and completing exercises, students refer to various information sources and educational literature. This article aims to address this very problem. Knowledge of descriptive geometry serves as the foundation for mastering engineering graphics. The human eye perceives surrounding objects thanks to their illumination by some source of light. In perspective, shadows often play a primary compositional role in revealing the content of works of visual art. Observing objects around us, one can notice that the degree of their illumination varies. Planes located close to the light source and illuminated at a 90° angle are strongly lit, while illumination decreases at other positions. Surfaces on which light rays do not fall remain dark. Different illumination of an object or surface relief helps to represent their spatial form. Artists depict light and shadow using hatching, shading, toning, and color intensity. When composing or depicting ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 982 an object, it is necessary to know the rules of light and shadow distribution and their construction. To make a drawing correct and realistic, it is important to understand these patterns well. The personal and cast shadows of objects are formed as follows. Light rays emanating from the point light source S illuminate the plane K (Figure 1). If an object stands in the path of these rays, the rays are blocked, and an unlit area forms on the plane. This area is called the cast shadow of the object. The object itself is partially lit and partially in shadow. The unlit part of the object is called its own shadow. The line dividing the illuminated and unilluminated parts is called the contour of the object's own shadow or the line of light and shadow separation. The construction of cast and own shadows depends on lighting conditions. There are two types of light sources: artificial and natural. An artificial light source is located close to the object. Examples include electric lamps, kerosene lamps, candles, or matches. In this case, light rays emanate from a single point and spread differently — this is called central illumination (Figure 1). Natural light sources include the Sun and the Moon. Light rays from the Sun and Moon are considered parallel because they are very far away, and the rays reaching the Earth appear as parallel lines. Such lighting is called parallel illumination (Figure 2). Figure 1 Figure 2 The intensity of cast and own shadows depends on several factors. These include the distance of the light source, the strength of illumination, the color and brightness of objects, air clarity, time of day, and others. In real conditions, own shadows are never completely black. This is explained by the fact that such surfaces are illuminated by light rays reflected from other objects. Additionally, the surface of the own shadow is influenced by light rays scattered by dust particles suspended in the air. The illuminated part of the shadow caused by reflected rays is called the reflex. In practice, it is impossible to fully take into account all phenomena affecting the intensity of light and shadow. Therefore, when drawing from memory or life, as well as when composing, it is necessary to highlight a number of rules for depicting light and shadow. Own shadows of objects are depicted lighter than cast shadows because they are affected by reflex. For the same reason, the upper part of the own shadow is lighter than the lower part. If the object is polyhedral, the boundary transition from light to shadow is clearly marked by an edge (Figure 3, a). For objects with curved shapes, the transition from light to shadow is smooth and gradual (Figure 3, b). ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 983 Figure 3 The most illuminated areas of objects with shiny surfaces sparkle and are called highlights. Cast shadows, as they move away from the object and the light source, become more blurred and weaker. If the shadow is large, its edges farther from the object also become less distinct. Figure 4 In practice, it is often necessary to construct shadows cast by an object when there are two light sources. In this case, the shadows may partially overlap (Figure 4). Overlapping shadows are called ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 984 full shadows, while those that do not overlap are called penumbras. Penumbras are lighter than full shadows because light rays from one source illuminate the shadow cast by the other source. Full shadows and penumbras also form from light scattered on surfaces with soft lighting (for example, from a ceiling lamp). Construction of Shadows from an Artificial Light Source To construct the shadow of an object, it is necessary to know the projections of the light source. Constructing shadows in perspective is a task of determining positions. In this case, the points or lines of intersection of light rays emanating from the source or the planes of light with the surfaces on which the shadow falls are found. The construction of a shadow from an artificial light source proceeds as follows. In Figure 5, a vertically oriented segment AB, a light source S, and its base S' are shown. To determine the shadow on the plane of the objects, rays are drawn from point S through all points of the segment. These rays form a light plane. The light plane intersects the plane of the objects and forms the shadow of the segment. Thus, it is sufficient to determine the shadow of point A — this is the line AS — and connect it with point B ≡ BS (since point B lies on the plane of the objects, its shadow coincides with the point itself). To determine the contours of shadows cast by objects, the shadows of characteristic points are found and connected. Suppose there is a vertically positioned rectangular plane standing on the plane of the objects and a light source — it is necessary to construct the shadow of the rectangle (Figure 6). First, the shadows of the vertical sides are determined, and their endpoints are connected. Side AB of the rectangle is parallel to the plane of the objects. Therefore, AB // ASBS. Hence, they intersect at point F. The intersection of parallel lines at one point simplifies the construction of shadows and allows verifying the correctness of the construction. Figure 5 Figure 6 ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 985 In the figure, a vertical plane and a segment AB are given. It is necessary to determine the shadows of segment AB on the objects and on the vertical planes (Figure 7). To do this, the lines of intersection of the light plane passing through line AB with the objects and the vertical planes are found. The bases of the vertical plane intersect the light plane at point 1. The vertical line passing through point 1 is the line of intersection of the planes. The light ray passing through point A intersects this line at point AS. The broken line B1AS is the shadow of segment AB. Figure 7 In the figure, a vertical plane and a segment AB resting on it are given (Figure 8). It is necessary to construct the shadows of the plane and the segment. The shadow of the vertical plane is constructed in the same way as in Figure 6. To construct the shadow of the segment, its projection on the plane of the objects is first determined. For this, the projection of point E, which touches the plane and is denoted as E', is found and connected with point B. Then, the projection of point A, denoted as A', is found, and its shadow on the plane of the objects — the line AS — is determined. Points AS and BS are connected, forming the shadow ASBS. The shadow of the segment on the vertical plane will be the line of intersection of the vertical plane with the light plane, denoted as E1. ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 986 Figure 8 The figure shows a matchbox and a match resting on it. It is necessary to construct the shadows of these objects (Figure 9). First, the shadow of the box is constructed (the method of constructing this shadow is known from previous examples and figures). To construct the shadow of the match, its projection on the plane of the objects is determined using point E, which touches the box. The projection is denoted as A'B (see Figure 8). Then, the shadows of the match on the plane of the objects and on the vertical side of the box are constructed, as shown in the previous example. To construct the shadow of the match on the upper horizontal side of the box, two points touching the shadow are determined. One of these is point E, and the other is point DS (point DS is located on the opposite side of the intersection of the shadows of the box and the match at point D1S, which is determined by drawing a ray). Since the shadows of the match on the plane of the objects and on the box are parallel, they share one common intersection point. ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 987 The figure shows a triangular prism lying on the plane of the objects and a vertically positioned cone (Figure 10). It is necessary to construct the shadows of these objects. The construction of the shadow of the prism is known to us (see Figure 9). To construct the shadow of the cone, first the shadow of the apex T on the plane of the objects is determined — the line TS. Then, projections are drawn from point TS onto the base of the cone. To construct the shadow of the cone on the face of the prism, two pairs of points touching the shadow are determined (1, 2 and 3, 4). Points 1 and 2 are found according to the known scheme (see figure). To determine points 3 and 4, the shadow of the cone is constructed on the vertical plane passing through the upper edge of the prism. Figure 10 A lamp is suspended in the corner of a room, and it is necessary to determine the boundary of the light cast from it (Figure 11). ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 988 This problem is solved by determining the line of intersection of the light cone with the floor and the wall. The light cone intersects the floor in a circle, and the wall in a hyperbola (since the wall is parallel to two generators of the cone). The light falling on the floor is actually a circle, which in perspective appears as an ellipse. The center of the light is point S. Using a horizontal projecting plane passing through point S, point S′ is determined, as well as the major diameter of the ellipse A1SBS (the construction of the diameter is shown in the drawing). The ellipse on the floor is constructed using a square drawn outside the circle with diameter A1SBS (the ellipse construction is not shown in the drawing). The points where the ellipse intersects the baseboard correspond to the tangent points of the hyperbola on the wall, which form the boundary of the light on the wall. Point DS is the vertex of the hyperbola and lies on the line of intersection of the wall with the horizontal projecting plane, passing perpendicularly through the light source. Other points touching the hyperbola are determined similarly to point DS. Figure 11 The perspective shows a corner of a room illuminated by a lamp, as well as furniture (Figure 12). It is necessary to construct the shadows cast by the furniture. Since the shadows fall on the floor and on two walls, the projections of the light source S on these surfaces are determined — points S', S'', and S'''. ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 995 Figures 26 Construction of the shadow of a cylindrical arch (Figure 27). To construct the shadow of the arch edge AE, a vertical light plane is drawn through it. This plane intersects the ground at point E1 — this is the shadow of the edge on the ground, and it intersects the inner wall of the arch at the vertical shadow 1AS (the shadow AS is formed by connecting point A with the light source S). To construct the shadow of the curved edge of the arch, the light rays are projected onto the plane of the front wall. For this, point F1 is connected with the light source S and extended until it intersects the vertical line passing through point F2. The intersection point SF is the point where the rays meet on the wall. From point SF, a perpendicular is drawn to the arch, defining point D — the upper boundary of the shadow. The shadow of the arch segment AD falls on the inner wall. To find the shadow of an arbitrary point B, a light plane is also drawn through it. This plane intersects the arch along the line B1F1. Point B is connected with the light source S. The ray SB and the line B1F1 lie in the same plane, so they intersect at point BS. Point BS is the shadow of point B. Using this method, any number of points belonging to the contour of the cast shadow can be found. ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 996 Figures 27 Construction of the self-shadow of a sphere (Figure 28). The self-shadow of a sphere has the shape of a circle, which appears as an ellipse in perspective. The radius of the self-shadow (circle) is equal to the radius of the sphere. The plane P, on which the selfshadow lies, passes through the center of the sphere and is perpendicular to the direction of the light rays. The line of intersection of plane P with the infinite plane P∞P_{\nifty} P∞ is determined by drawing a plane perpendicular to the line P∞P_{\nifty} P∞. From the center of the sphere O, a frontal line f is drawn and the diameter of the sphere is measured by marking points M and N. The segment MN is the diameter of the self-shadow. Point F is the intersection point of diameter MN and the diameter EG perpendicular to it. Points E and G are determined using point F1 (where OF=FF1OF = FF_1OF=FF1). At point F1 on the plane of the selfshadow, lines intersect at an angle of 45° to diameters MN and EG. Therefore, by connecting points M and N with point F1, points E and G are obtained, which belong to the common diagonal corresponding to the self-shadow. Points A and B are obtained by projecting from point S to the perspective of the sphere. Intermediate points belonging to the self-shadow can be found by establishing a homological correspondence between the frontal section of the sphere and the contour of the self-shadow. The axis of correspondence is the diameter MN, and the center of homology is point F2 (the intersection point of the axes of rotation). The drawing shows how to find points D and K. ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 997 Figures 28 Construction of the shadow in a cylindrical mihrab with a spherical upper part (Figure 29). The shadow of the vertical edge of the mihrab AA1AA_1AA1, falling on the ground and the inner wall of the mihrab, is determined using a light plane passing through the edge and point S. The boundary of the shadow is point AS. From point AS begins the shadow cast by the curved edge of the mihrab. Shadows from arbitrary points D and B on the curved edge fall on the cylindrical wall of the mihrab as DS and B1SB_1SB1S respectively (B1SB_1SB1S is the shadow running along the cylindrical wall). By connecting points AS, DS, and B1SB_1SB1S, point DS on the boundary line separating the cylindrical and spherical parts of the mihrab is determined (the randomly chosen shadow of point D falls on the boundary line). The shadow falling on the spherical part of the mihrab can be constructed using homology. The homology is established between the circular edge of the mihrab and the contour of the cast shadow. The line OK is the axis of homology, and point S is the center of homology (O is the center of the mihrab, K is the projection point, the method of determining which is shown in Figure 27). Points relating to the contour of the cast shadow are determined in pairs of corresponding points. These are points D and DS. The drawing shows the construction of shadows ES and BS from points E and B. In this example, the construction of the self-shadow of the sphere is not shown (the construction of the self-shadow of the sphere is given in Figure 28). ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 998 Figures 29 Figure 30 shows the construction of the shadow in the perspective of the object. The sun is located to the left of the observer. Using the example of finding the shadow of point D — the shadow DS cast by the object onto the ground — the construction is demonstrated. The shadow on the stairs is constructed according to the drawing. To construct the shadow cast from the roof onto the front facade, the lower plane of the roof is used as the plan. Figures 30 ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 999 Construction of the shadow of a building For constructing the shadow, it is advisable to use the plan projected downward, since a plan drawn on site is “compressed” and can lead to significant errors and difficulties when building shadows. The light source (the Sun) is located to the left and behind the observer. Points S and S1 are outside the boundaries of the drawing, so their positions are determined on an additional sheet of paper attached to the drawing. To determine the shadow AS, cast from point A of the main roof onto the auxiliary roof, a light plane N (Nn) is drawn through point A (A1). This plane intersects line 12 of the auxiliary roof. The ray passing through point A intersects line 12, creating point AS. Point BS is determined similarly. By connecting AS and BS, the shadow of the edge AB on the auxiliary roof—ASBS—is obtained. Connecting point BS with point 4 constructs the shadow BS4. Shadows cast from the front edge of the building D (D1) onto the ground, the wall of the auxiliary room, and the roof are determined using the light plane N1 (N1H) passing through the edge. This plane intersects the ground along line DS1, the wall along line 56S, and the roof along line 67 (point 6S is found by projecting a light ray from point 6). These lines (part of line 67) represent the shadows of the building edge on the ground, wall, and roof. By connecting point 6S with the intersection point of the horizontal edges of the auxiliary roof, the shadow of the edge on the wall is obtained (since the edge is parallel to the wall, the shadow will also be parallel). The shadow on the door is found by drawing a light plane through point G (G1). The shadow cast from the inclined edge of the main roof onto the building wall is constructed through the shadows of two points belonging to this edge (the drawing shows the construction of the shadow of point E—ES). The shadow cast from the chimney onto the roof is found by drawing vertical light planes through the edges of the chimney and their intersections with the roof slope. Figures 31 References: 1. Saidaliyev S.S. Descriptive Geometry and Engineering Graphics. Publishing House of Tashkent State Technical University. – 335 pages, 2022. ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-11 1000 2. Ramazonova G.S. Descriptive Geometry and Engineering Graphics, textbook, part 1, TSTU2024. 3. Ramazonova G.S. Topographic Drawing, textbook, TSTU-2024. 4. Saidaliyev S.S. Descriptive Geometry and Engineering Graphics, textbook, part 2, TSTU2024. 5. Ramazonova G., Saidaliyev S. (2022). A Brief Historical Overview of the Development of Descriptive Geometry and Engineering Graphics. International Journal of Philosophical Research and Social Sciences, pp. 144–151. Retrieved from [source]. http://www.ijpsss.iscience.uz/index.php/ijpsss/article/view/284. 6.Рамазонова Г., Сайдалиев С. (2024)“ЗНАЧЕНИЕ ЗАКОНОДАТЕЛЬНЫЕ ПЕРСПЕКТИВЫ ДЛЯ БУДУЩИХ АРХИТЕКТОРОВ” Miasto Przysztosci Kielce ISSN-L: 2544-980X Volume 47. 16.04.2024. (675-682 betlar). https://miastoprzyszlosci.com.pl/index.php/mp/article/view/2934/2699. 7. Рамазонова Г., Сайдалиев С. (2024) “THE ROLE OF THE LAWS OF PERSPECTIVE IN THE ACTIVITIES OF FUTURE ARCHITECTS” European Journal of Innovation in Nonformal Education (EJINE) Vol:4 Issue 5. ISSN: 2795-8612. 13.04.2024. (50-57 betlar). https://inovatus.es/index.php/ejine/article/view/3104/2949. 8. Ramazonova G.S. (2024) “THE IMPORTANCE OF ENGINEERING GRAPHICS FOR PRODUCTION PHARMACY STUDENTS” Miasto Przysztosci Kielce ISSN-L: 2544-980X Volume 47. 16.04.2024.Miasto Przysztosci Kielce ISSN-L: 2544-980X Volume 47. 16.04.2024. (885-890 betlar). https://miastoprzyszlosci.com.pl/index.php/mp/article/view/3262/3021.