Axonometric Research Articles

OVERCOMING CAD DISADVANTAGES IN THE CONSTRUCTION OF DETAIL DRAWINGS IN ACCORDANCE WITH THE REQUIREMENTS OF CURRENT STANDARDS

The paper proposes a method for improving the construction of parametric three-dimensional models of parts and the execution of drawings to solve the problems of compliance with the requirements of current standards, in particular, the depiction of sections of parts in drawings in the Autodesk Inventor package. To solve this problem, it was proposed to use an additional parametric three-dimensional hollow element that uses the geometric information of thin walls, lugs, etc. and is tied to the sectional plane. Using the functionality of the Autodesk Inventor package, a parametric three-dimensional hollow element is built, which along the transverse plane has a size proportional and comparable to the size of thin walls, ears, etc., differing in infinitesimal value. The size of a parametric three-dimensional hollow element perpendicular to the direction of the cross-sectional plane, on the contrary, is incomparable to the size of thin walls, ears, etc. For the convenience of using a hollow three-dimensional element, it is proposed to place it in such a way that the transverse plane is the plane of symmetry for it. Such a position facilitates the use of a hollow three-dimensional element when depicting thin walls, ears, etc. on orthogonal projections in accordance with the requirements of current standards. In order to meet the requirements of current standards for axonometric projections, the sectional plane is shifted relative to the axis of symmetry beyond the hollow element of thin walls, lugs, etc. that fall into the section. Since the width of the hollow element was set as an infinitesimal value, when the sectional plane is shifted relative to the symmetry axis, the hollow element of walls, lugs, etc. is hatching. Under these conditions, by performing an axonometric projection with a longitudinal section, we obtain a minimum error in the location of the sectional plane relative to the symmetry axis of the part. The conditions for building the element(s) allow you to hide it if necessary. The construction of an additional three-dimensional hollow element(s) does not require knowledge of the built-in VBA programming language and the use of iLogic tools. Keywords: conventions and simplifications of images, projection views, axonometric, parametric hollow area, toolset, Autodesk Inventor package

Sketch2PQ: Freeform Planar Quadrilateral Mesh Design via a Single Sketch.

The freeform architectural modeling process often involves two important stages: concept design and digital modeling. In the first stage, architects usually sketch the overall 3D shape and the panel layout on a physical or digital paper briefly. In the second stage, a digital 3D model is created using the sketch as a reference. The digital model needs to incorporate geometric requirements for its components, such as the planarity of panels due to consideration of construction costs, which can make the modeling process more challenging. In this work, we present a novel sketch-based system to bridge the concept design and digital modeling of freeform roof-like shapes represented as planar quadrilateral (PQ) meshes. Our system allows the user to sketch the surface boundary and contour lines under axonometric projection and supports the sketching of occluded regions. In addition, the user can sketch feature lines to provide directional guidance to the PQ mesh layout. Given the 2D sketch input, we propose a deep neural network to infer in real-time the underlying surface shape along with a dense conjugate direction field, both of which are used to extract the final PQ mesh. To train and validate our network, we generate a large synthetic dataset that mimics architect sketching of freeform quadrilateral patches. The effectiveness and usability of our system are demonstrated with quantitative and qualitative evaluation as well as user studies.

GRAPHIC CULTURE OF CONSTRUCTIVE MODELING OF FIGURES IN METRIC STEREOMETRY

Two approaches for drawing of stereometric objects by a constructive method are presented using algorithms designed to help solve problems in the construction of correct, visual and easy-to-draw drawings. The first approach is based on operations borrowed from engineer drawing, where standardized axonometric projections guarantee the quality of drawings. The second one is based on the experience of many generations of teachers and practitioners. A list of methodological advice has been proposed. The analytical method of reasoning in computational problems is promoted, the method of combining with the image plane is established, which visualizes the way to the result, adds empiricism to the discipline. The presented statistical survey among mathematics teachers demonstrates their attitude to the constructive solution of stereometric problems. The advantages and disadvantages of teaching constructivism methods are highlighted. It has been established that the skills of qualitative drawings contribute to the formation of life competencies of pupils.

Improving the method of controlling the search for surface and underwater objects by a hybrid robotic complex

One of the important scientific tasks of organising the control of searching for surface and underwater objects is to ensure the efficiency and trouble-free movement of a hybrid robotic complex in the modes of transition and search operation. An analysis of modern methods of controlling the search for surface and underwater objects by robotic vehicles in search operations, scientific and environmental research, monitoring, inspection and military underwater operations shows the need to use hybrid robotic systems. As part of the intellectualisation of the route planning process, it is relevant to solve the problem of synthesising an optimal trajectory to ensure that the search is carried out in all designated areas of the operation. The paper solves the problem of organising the management of searching for surface and underwater objects by a hybrid robotic complex, namely, building a route in the area of interest as an optimal spline trajectory of a moving object. The possibility of constructing a navigation function through the effective use of the curvature of the spline trajectory as a reproductive template for constructing an axonometric projection is determined. To accomplish this task, the paper improves the method of controlling the search for surface and underwater objects by a hybrid robotic complex by formalising the processes of planning the route of the hybrid robotic complex and the processes of information processing, forecasting the navigation situation and choosing a strategy for preventing dangerous situations by combining intelligent and numerical methods. The developed algorithm for constructing a search route for a hybrid robotic complex allows automated formation of spline trajectories in real time with synchronous submission of information about the parameters of the route to the control system of the hybrid robotic complex. This approach makes it possible to automate the search operation process and apply it in the CoCoRo and e-Navigation concepts

Аксонометрические проекции в России: вчера, сегодня, завтра

Purpose: The history of the development of axonometric projections is considered in this work. The contribution of Russian scientists to the theory of this method is established. The analysis of the current state of the regulatory framework has been carried out. The necessity of making changes to the current standard is justified. Archival and handwritten sources have been investigated. The article shows the way of the consistent emergence, development and improvement of the theory of axonometric projections. Examples of its use in different periods are shown. The contribution of Russian scientists to the improvement of the theory of the axonometry method and its application in construction and industry is established. The main advantages of axonometry are shown: visual clarity and the possibility to determine the parameters of a real object based on such images. The inaccuracies of the axonometry theory representation in modern regulatory documents are analyzed. The necessity to depict axonometric axes when creating images is indicated. Axonometric projections are considered as a method of geometric modeling in computer-aided design systems, which allows creating visual planar models of artificial structures and other objects. This also allows to create a unified information model of the object, to carry out joint work of various specialists at the design stages, to ensure the storage and editing of information throughout the entire life cycle of the object. Methods: To achieve results, various research methods have been applied: theoretical analysis of historical, scientific literature, normative and program-methodical documentation, study of the experience of graphic images of foreign and domestic specialists, generalization and systematization of scientific provisions on the research topic, analysis of the results of research work. Results: The necessity of making changes to the existing regulatory documents is justified. Practical significance: The correct display of axonometry in regulatory documents will improve its practical application and specialist training.

아트헤어의 다각적 표현을 위한 엑소노메트릭 연구

This study intends to explore masterpieces which are characteristic concerning ancient Greek and Roman mythologies and to analyze the underlying meanings behind the allergories of the Gods and Goddesses of Mount Olympus. With the help of computer graphics and 2D Axonometric projection, this study to realize the devised hair artwork by drawing inspiration form the assessed allegories. The significance of computer graphics id that they can be used to create pieces whose expression by hand is simply impossible and try different types of expressions with various new expressive techniques that may be employed in the Beauty sector. Digital beauty design utilizing Photo-shop may empower all specialists of the beauty industry to develop their work if the innumerable possibilities and benefits which may be represented through Photo- shop are employed.This demonstrates that manifold and also nuanced approaches in general may be applied to Art hair through employing different tools, making it simple to adapt and change patterns. Graphic approaches that surpass the boundaries of realistic types of expression. especially, can be used to produce visually creative works in the realm of Beauty Art, indicating their versatility.

Urban Journeys of the Rhizomatic Line

Using visual hierarchy, representational media often separate diverse urban experiences. Three categories of foreground, middle ground, and background are easily distinguished in photography and painting. Urban sketches separate buildings, figures, and natural features. In architectural working drawing, “poché, entourage, and mosaïque” forms a structural system for representing cut walls, environment, and texture respectively[1]. Recently, photogrammetry or Lidar scanning claim to break these hierarchies by creating “a uniform unbiased document of things in space as they exist.”[2] However, these tools fail to reveal the speculative imaginary experiences hidden behind surfaces.This series of my drawings that I named “rhizomatic line”, is the result of a non-hierarchical process inspired by French philosophers Gilles Deleuze and Felix Guattari's concept of rhizomes. Described as an array of attractions without beginning or end, a rhizome negotiates between things, “fosters connections between fields, the removal of blockages.”[3] Rather than producing fragmented abstract shapes, the rhizomatic line moves between the objects and intertwines them. Seemingly recording eye movement, rhizomatic, line does not construct complete outlines, but through loosing their completion, it connects them. As it explores the city, it does not differentiate between humans, pedestrian lines, high-rise building edges, urban skylines, stairways, leaves of a small plant hiding behind a window in a private room, entrances to residential units atop towers, or imaginative spaces.When looking at similar images, different people show different eye movements.[4] A designer sees the world in the process of construction, and from multiple perspectives at once. Architects use a specific language to draw rhizomatic lines. Axonometric projection takes advantage of both the visual aspect of perspective in photography, as well as the mathematical precision of orthographic projection in computer cartesian systems. Although I do not claim that my rhizomatic lines are true or close to the vision, I emphasize on " a continuous space in which elements are in constant motion."[5] The dotted texture suggests one understanding of the scene's porosity, among many others. Through the blurring of boundaries between poché, entourage, and mosaïque, only a portion of the image is displayed as a work under construction, inviting the viewer to complete it with their imagination. In this sense, a rhizomatic line is not a cartesian representation of space. This single “active line” ending in itself, is an exploratory journey fusing imaginations, speculations, desires, memories, and dreams about the city; “a walk for a walk's sake.”[6] [1] Michael Young, Reality Modeled After Images: Architecture and Aesthetics After the Digital Image. (New York: Routledge, 2021), 10. [2] Young, Reality Modeled After Images: Architecture and Aesthetics After the Digital Image. 53. [3] Gilles Deleuze and Felix Guattari, A Thousand Plateaus: Capitalism and Schizophrenia. Translated by Brian Massumi, (Minneapolis: University of Minnesota, 1987), 12. [4] Alfred Yarbus. "Eye Movements During Perception of Complex Objects." Eye Movements and Vision”, (Springer: Boston, MA, 1967) [5] Stan Allen. "Construction with Lines: On Projection", Practice: Architecture, Technique+ Representation. (New York: Routledge, 2009), 19. [6] Paul Klee. Pedagogical Sketchbook. Translated by Sybil Moholy-Nagy, (New York: Praeger Publisher,1953), 16.

Аxonometric transformations of a complex drawing

When drawing up technical drawings, it is sometimes necessary to have visual representations along with images of objects in the orthogonal projection system. For such images, the method of axonometric projection is used (axonometry is a Greek word, literally translated as measurement along the axes; axon means axis, metreo means measuring). The essence of the axonometric projection method: an object, together with the axes of rectangular coordinates to which it is assigned in space, is projected onto a certain plane so that none of its coordinate axes is projected onto it at a point. In this case, the object itself is projected onto this projection plane in three dimensions. In this case, the dimensions of the object in axonometric projections along all three axes are distorted. The change in linear dimensions along the axes is characterized by the distortion indices (coefficients) along the axes. The distortion index is the ratio of the length of a segment on the axonometric axis to the length of the same segment on the corresponding axis of the rectangular coordinate system in space. The purpose of this paper is to construct an axonometric projection of a circle located in the plane of general position using classical methods of descriptive geometry - methods of transforming a complex drawing. Axonometry stands alone in descriptive geometry, which is due to the theoretical multitude of approaches in which the coordinate system is a model of geometric space. Certain difficulties in mastering axonometry are related not only to this but also to its insufficient methodological support. Thus, in the definition of axonometric projection, the standards do not contain key phrases about the orientation of the object and the associated coordinate system relative to the projection direction, which should not be parallel to any coordinate axis. There is no clarity about axonometric planes, their location relative to the main planes in rectangular projection. The article describes a method for constructing an axonometric projection of a circle located in the plane of general position relative to the planes formed by axonometric axes. An example of constructing an ellipse - a projection of a circle for a projecting plane - is given, which can be extended to the conditions of the plane of general position without fundamental changes. The proposed article can be recommended for students who study descriptive geometry and engineering graphics courses in depth, and can also be useful for young teachers as a supportive material in working with students.

OPTIMAL SPLINE TRAJECTORY OF THE SHIP INFORMATIVE ROUTE IN THE MAP-AIDED NAVIGATION

The task of organizing an informative route as an optimal spline trajectory of a moving object with an assessment of the informativeness of the map-aided navigation standard is completed. From the perspective of the planning approach, an optimal geometric path, passing through pre-determined iconic intermediate points, taking into account the avoidance of navigational hazards as “obstacle spots” has been formed. Within the framework of the strategy of informative planning of the spline path, the actuality of solving the problem of synthesizing the optimal trajectory in two variants is noted: by the methods of B-splines and classical polynomial interpolations as the implementation of the tactics of a mobile object movement in a conflict environment. A comparative characteristic of two alternative algorithms for solving the problem, specifying the advantages and disadvantages of each option, is given. As a demonstration of the practical applicability of the interpolation approach, the spline trajectory of an illustrative example in route of map-aided navigation is designed against the background of a contour map of isolines. Emphasis is placed on the possibility of forming the shape of the navigation isosurface due to the effective use of the curvature of the spline trajectory as a reproductive template for constructing an axonometric projection. A forecast about the trends of the possible use of a separate optimal trajectory of the object movement directly for the construction of the informative field profile of any degree of complexity is made. A hypothesis about the feasibility of practical use of chaotic architecture of spline gradients for effective planning of the optimal trajectory is put forward. The fan of spline gradient vectors with a personal orientation in the direction of the maximum change in the navigation function on each segment of the piecewise polyline of the path in the vessel routing procedure is considered. The issue of ensuring the possibility of making a coordinated decision on the vessel management by personnel due to the automated formation of spline trajectories in real time with synchronous representation of geometric computer support to the watch assistant, which allows us to offer integration of the tasks under consideration into the cloud-based intelligent technology of “augmented reality” is formulated.

Determination of coordinates of unmanned aircrafts by means of kinematic projection

A methodology for determining the mechanical trajectory and spatial coordinates of unmanned aircrafts by means of kinematic projection is described. The suggested methodology consists in the formation of two moving independent centers of kinematic projection by launching intercepting drones into space. Electromagnetic radio waves emitted by unmanned aircrafts pierce an unknown flying object and generate two independent projecting rays intersecting at the place of searching a flying object. At that, the instantaneous (at a certain moment) projection of the point of spatial location of the searched object will be located in an imaginary `picture plane' on the line connecting the projections of the points created by projecting rays of the intercepting drones. Since all the objects of projection are mobile in this case, the whole projection of the trajectory of the searched object will be displayed on the operator's monitor. The formation of a `more picture-like plan' perpendicular to the main one will allow us to build an axonometric view not only for the projection, but directly for the aircraft spatial movement trajectory. Every point of this trajectory gives us information about `instant' coordinates of the location of the aircraft in space. Velocity is calculated as the ratio of spatial displacement of a flying object to the duration of movement. The scientific novelty of the method of determining the trajectories, velocities, and coordinates of an unmanned aircraft consists in the combination of radar detection of a moving object with kinematic design used for its implementation in order to calculate instantaneous coordinates of the object. This methodology solves the problem of determining more accurately the coordinates of flying objects that are not clearly and qualitatively displayed on radar monitors due to small size, mass, and specific materials used in manufacture. At the same time, the influence on the accuracy of determining the coordinates of unmanned aircrafts reflected from the fixed obstacles placed on the relief surface of earth was established. The results of this study can be used in practice in military science, for example, during the anti-terrorist operation in the occupied territories of Ukraine, with the aim to detect and neutralize enemy reconnaissance unmanned aircrafts. The use of this method in aerial photography for clear fixation of drone coordinates during aerial surveys for terrain topography is also promising.

EVM: An Educational Virtual Reality Modeling Tool; Evaluation Study with Freshman Engineering Students

Educational Virtual Modeling (EVM) is a novel VR-based application for sketching and modeling in an immersive environment designed to introduce freshman engineering students to modeling concepts and reinforce their understanding of the spatial connection between an object and its 2D projections. It was built on the Unity 3D game engine and Microsoft’s Mixed Reality Toolkit (MRTK). EVM was designed to support the creation of the typical parts used in exercises in basic engineering graphics courses with a special emphasis on a fast learning curve and a simple way to provide exercises and tutorials to students. To analyze the feasibility of using EVM for this purpose, a user study was conducted with 23 freshmen and sophomore engineering students that used both EVM and Trimble SketchUp to model six parts using an axonometric view as the input. Students had no previous experience in any of the two systems. Each participant went through a brief training session and was allowed to use each tool freely for 20 min. At the end of the modeling exercises with each system, the participants rated its usability by answering the System Usability Scale (SUS) questionnaire. Additionally, they filled out a questionnaire for assessment of the system functionality. The results demonstrated a very high SUS score for EVM (M = 92.93, SD = 6.15), whereas Trimble SketchUp obtained only a mean score of 76.30 (SD = 6.69). The completion time for the modeling tasks with EVM showed its suitability for regular class use, despite the fact that it usually takes longer to complete the exercises in the system than in Trimble SketchUp. There were no statistically significant differences regarding functionality assessment. At the end of the experimental session, participants were asked to express their opinion about the systems and provide suggestions for the improvement of EVM. All participants showed a preference for EVM as a potential tool to perform exercises in the engineering graphics course.

Prilog istraživanju arhitekture Dvorskog kompleksa na Terazijama - Knežev dvorac (Stari konak) i Dvorac za prestolonaslednika Mihaila

This paper presents research on the historical and urban development of the palace complex on Terazije during the 19th and early 20th centuries, placing a focus on the period from the 1840s to the 1880s, i.e. upon the architecture of the Prince's Court (Knežev dvorac, also known as the Stari konak) and the Court of Crown Prince Mihailo, which were both demolished in the early 20th century. The process of urban transformation of the complex and the design of buildings for the accommodation of the then-rulers is presented, based on the available historical material (old plans and photographs), as well as pre-existing interpretations of this topic available in published literature. Both the appearance of the court buildings and the complex itself in certain phases of development are reconstructed, facilitated by comparative situational representations and axonometric projections. A typological and stylistic analysis of the architectural characteristics of the Stari konak and the court, which are to be considered representative examples of the transition from the Classicist to the Romantic era of Serbian architecture in the middle of the 19th century, is given. The paper places a particular emphasis on the historical and cultural significance in the present of these now-demolished buildings for preserving the memory of an extremely important period in the history of the modern Serbian state.

«Совершенно темное пятно»: супрематическая пангеометрия и проблема (не)ви́дения

The article examines the religious and philosophical components of K. Male­vich’s Suprematist paintings and the origin of their revolutionariness in the wide context of theoretical works: N. Lobachevsky’s “pangeometry”, El Lissitsky’s axonometry, P. Ouspensky’s fourth dimension, P. Florensky’s reverse perspec­tive, Z. Freud’s attraction to death, J. Lacan’s the symbolic and the real, the ab­solute presence of God through invisibility in the religious philosophy of J.-L. Marion. The author traces the stages of conceptualization of K. Malevich’s Suprematism: from the sketch of stage sets in opera «Victory over the Sun» (1913), where the predecessor of “Black square” (1915) first appeared, to the Suprematist abstract paintings with three-dimensional axonometric views of geo­metric figures and, finally, to their complete destruction. The phenomenon of to­tal invisibility, being a method of negative theology, becomes a condition for the birth of the Suprematist icons “Black square” and “White on white” (1917‒1918), which should be taken not as a regression to the two-dimensionality of paintings, but as an absolute form of the axonometric projection, the invisibility as a total seeing. The complete negation of geometric forms – a dead end, «an ut­terly dark spot» – can be understood as a space for transition toward the sacred transcendental Being, the presence of an absolute artistic form, which is en­dowed with the highest sacred meaning. The revolutionariness of Suprematism in this sense does not lie in its utopian contents. On the contrary, it is present in the “zero degree of forms” that denies even itself and in the contemplation per se on this emptiness as fullness.

Peculiarities of the underground mining of high-grade iron ores in anomalous geological conditions

This paper is dedicated to research into the geological peculiarities, shape of the ore body and the occurrence of the host rocks in the hanging wall of the Pivdenno-Biloz- erske deposit , as well as their influence on the degrees and quality of high-grade iron ore extraction. It is noted that in the interval of 480 – 840 m depths, a decrease is observed in the stability of the natural and technogenic massif, which is caused by the increase in rock pressure with depth, the influence of blast- ing operations on the massif and the difference in geological conditions. This has led to the collapse of hanging wall rocks and backfill into the mined-out space of chambers in certain areas of the deposit, the dilution of the ore and deterioration of the operational state of the underground mine workings. Attention is focused on the causes and peculiarities of consequences of the collapse of the hanging wall rocks during ore mining, which reduce the technical and-economic indexes of the ore extraction from the chambers. A 3D-model of an ore deposit with complex structural framework has been developed, which makes it possible to visually observe in axonometric projection the geological peculiarities and the shape of the ore body. The parameters have been studied of mining chambers in the 640 – 740 m floor under different changing geological conditions of the ore deposit and hanging wall rocks occurrence – the northern, central and southern parts. The difference in the iron content in the mined ore relative to the initial iron content in the massif has been defined as an indicative criterion of the influence of changing conditions on the production quality. The reasons have been revealed which contribute to the collapse of the rocks and the subsequent decrease in the iron content of the mined ore in ore deposit areas dif- fering by their characteristics. It has been determined that within the central and half of the southern ore deposit parts with a length of 600 m, an anomalous geological zone is formed, the manifestation of which will be increased with the depth of mining. It was noted that within this zone, with the highest intensity and density of collapse of hanging wall rocks, the influence of decrease in the slope angle and change in the strike direction are of greatest priority, and such geological factors as a decrease in hardness, rock morphology, deposit thickness increase this influence significantly. To solve the problems of the hanging wall rocks’ stability, it is recommended to study the nature and direction of action of gravity forces on the stope chambers in the northern, central and southern parts, as well to search for scientific solutions in regard to changes in the geometric shapes of stope chambers and their spatial location, improving the order of reserves mining in terms of the ore deposit area, the rational order of breaking-out ore reserves in the chambers with changing mining and geological conditions of the fields’ development.

Kolegium pijarów w Chełmie. Historia – architektura – autorstwo

The building of the old College of Piarist in Chełm – located on Lubelska Street, near the late baroque Church of Holy Apostles the Messengers – is now the seat of the Wiktor Ambroziewicz Chełm Land Museum. Until now, it has not raised much interest among researchers and – appearing as a work of architecture devoid of expressive style features – has not been the subject of scientific reflection. This situation is changed by the disclosure of the preserved drawing from 1698, showing the building in a horizontal projection and axonometric view, stored in the Archivio Generale delle Scuole Pie in Rome. The information contained in written documents kept there allow to determine the time of construction of the building for the years 1698-1700. The project proves that the preserved edifice did not change substantially its one-story block, set on the plan of the letter H. The innovations concerned only the roof part over the main body, which was originally the Krakow roof, and the extension of one of the side wings in 1720-1724 (so that the college was connected to the church). Neither did the subsequent transformations significantly affect the internal divisions, be it in the two-and-a-half tract main corpus, with the cross-corridor communication system introduced therein, or in the single tract side wings. The shape of the building and the severity of the development of its facade, representing the baroque in its classicizing version, suggests the designer – Giuseppe Piola, an architect working in Warsaw at the turn of the 17th and 18th centuries, building, at the request of the Piarist order, also their church and monastery complex in Szczuczyn. However, the extension of the college wing made in the first half of the 18th century should probably be associated with the person of another capital architect – Carlo Antonio Bay, who at the same time, together with his son-in-law, Vincenzo Rachetti, also an architect, made calculations for the Piarist priests from Chełm for the profitability of their parcel located in the suburbs of the city of Lublin. The building in Chełm was a monastic college, and at certain times also a “profesorium”, in which Piarist clerics learned philosophy at a higher level of education. Contrary to some suggestions, there was never a public school run by the Piarists in this building. It was founded – as a Russian gymnasium – only after the January Uprising and the dissolution of the Scholarum Piarum community.

Методика подготовки студентов технических вузов графическим дисциплинам

In connection with transition of the higher education system to the bachelor's degree, a number of difficulties has arisen e in the student’s educational schedule. The question is especially acute for disciplines of general education, and a rather large reduction in classroom time has happened. Taking into account the rather low level of students training in the area of drawing, and sometimes its complete absence, due to the abolition of the subject of drawing from the mandatory school program, teachers are faced with more and more tasks on the formation of educational and methodical complexes [3; 6; 15–17; 23]. In this paper has been considered the issue related to complex training in the area of graphic disciplines for students of technical high educational institutions. These disciplines, as is known, are the basis of many special engineering disciplines, such as machine parts, theory of mechanisms and machines and so on. The fundamental component is the design documentation, the possession of which is necessary for a future engineer. Studying the general course of descriptive geometry and engineering graphics is not enough, training should be carried out taking into account the professional orientation and relevant competencies. However, despite the global automation in all areas, it is not necessary to completely abandon the traditional methods of training, for example, in descriptive geometry’s section. This course allows develop students' spatial reasoning [12–14; 19]. Work on descriptive geometry’s tasks gives for a student the opportunity to more clearly understand the projection principles, methods of drawings transformation, formation of complex surfaces, obtaining of visual images by constructing of axonometric projections or performing of a technical drawing. Another question in our opinion is the order for studying the section of engineering graphics, which is more appropriate to study using modern graphics programs [10; 11].

Have You Ever Used Two Picture Planes to Draw a Single Perspective View?

Apparently, the use of two picture planes to draw a single view has not been attempted before. Most perspective methods, after Alberti, take for granted the use of a single picture plane, disregarding its likely use in dual positions. What if two picture planes are necessary to draw a single view—for example, given a lack of spatial references at ground level to estimate the distance between two objects? This article demonstrates that to draw the interior of a building from which another building can be seen about 190 m away, where the projection of such building on the first picture plane would be imprecise, it may be wise to use a second picture plane. This leads to consideration of how objects change shape as they move away from the viewer. For example, if a cube recedes from the observer up to 100 times its side length, it takes on an axonometric view. This raises a question: Could axonometric projection be a particular case of perspective?

THE REL THE RELATIVE REL TIVE RELATIONSHIP BE TIONSHIP BETWEEN THE DIST WEEN THE DISTORTION COEFFICIEN COEFFICIENTS IN OBLIQUE AX S IN OBLIQUE AXONOMETRIC PROJEC TRIC PROJECTIONS FOR TIONS FOR THE POSTURE OF THE ARCHED IMAGES

In this paper, the interrelatedness of the distortion coefficients in oblique axonometric projections along axonometric axes is considered. The design angle and distortion factors in axonometry will be set depending on the angle. Structure axonometry is used to show on a small scale the relative position of buildings, roads, airfields, etc. located on a very large construction site. Because in such axonometry buildings, roads, airfields are generally described without changing the plans of the figures.

Study of possibilities of editor NanoCAD for design of building elements

The paper studies the possibilities of using a new home-produced nanoCAD editor for the design of building elements. Any product design nowadays is based on the 3D-model – 2D-model – 2D-drawing advanced technology. The focus is on 3D modeling. It is shown that for 3D modeling in the nanoCAD editor, which replaces the well-known AutoCAD, there are various tools. These include numerous 3D commands and the corresponding dialog boxes. As an illustration, the procedure and step-by-step examples of building up the intersection lines for composite surfaces, views and axonometric projections are given. The transition to the nanoCAD editor is proved to be appropriate and relevant.

CONSTRUCTING AXONOMETRIC PROJECTIONS FOR THE CUTTING OF WOODEN STRUCTURES IN THE AUTOCAD SYSTEM

A technique for constructing axonometric projections for the cutting of wooden structures in the AutoCAD system is proposed.