Geometry & Graphics最新文献

{"title":"Building the Perspective of a Straight Line Along The Picture Trail and the Vanishing Point","authors":"N. Sal'kov","doi":"10.12737/2308-4898-2024-11-4-32-42","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-11-4-32-42","url":null,"abstract":"The article recalls the essence of academic subjects: descriptive geometry, drawing, engineering graphics, computer graphics and what each of these subjects is intended for. It is said about the compulsory study of geometry by students, especially those students who study in technical fields of study, about the role of descriptive geometry in the learning process and later in practical activities. Therefore, the existence of departments of geometric and graphic profile for each technical university is unconditionally necessary. It is explained that the modern disdainful attitude of the university leadership towards the departments of the geometric direction should not lead to the disappearance of these departments, since an engineer without knowledge of geometry is a fundamental underachiever, and at best an amateur. The reasons that led to the insufficiency of highly qualified specialists in the geometric and graphic profile in universities are given and, in this regard, some steps are proposed to improve the quality of engineering education. The situation of the educational process in the supposedly leading technical universities of the country, which have already got rid of the departments of the geometric direction or are on the road to this \"great\" achievement, is given as a negative example, as a result of which various information has been received for quite a long time about the not very favorable situation in these universities. Some measures are proposed to improve geometric education in Russian universities.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"166 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140249632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Area of correct space coordination by normal conic coordinates","authors":"Dmitriy Nesnov","doi":"10.12737/2308-4898-2023-11-3-3-11","DOIUrl":"https://doi.org/10.12737/2308-4898-2023-11-3-3-11","url":null,"abstract":"The field theory is widely represented in spherical and cylindrical coordinate systems, since the mathematical apparatus of these coordinate systems is well studied. Field sources with more complex structures require new approaches to their study. The purpose of this study is to determine the correct coordination of space by normal conic coordinates. This is necessary in subsequent studies, the task of which will be to simplify the expressions for the characteristics of the field by introducing a special coordination of space, which reflect the shape of the source and/or sink of the field. For example, a field with a rectilinear source is more convenient to refer to cylindrical coordinates, and a field with a point source - to spherical coordinates. Basically, the use of field theory in the study of physical processes by methods of applied geometry is limited to two classical curvilinear systems, although their presentation in arbitrary curvilinear coordinates is known. We will distinguish between global and local coordinate systems. The global system, as well as the coordinates of a point in this system, will be denoted by x, y, z. She is unchanging. The local system, as well as the coordinates of a point in this system, will be denoted by t, u, v. Local system variable. At each point in space belonging to the area of existence of the system, the local coordinate system is defined","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"30 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139156986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coursework on engineering graphics as the first design experience","authors":"Tat'yana Markova, Andrey Bochkov, M. Kokorin, T. Nikitina","doi":"10.12737/2308-4898-2023-11-3-26-38","DOIUrl":"https://doi.org/10.12737/2308-4898-2023-11-3-26-38","url":null,"abstract":"One of the priorities for higher education and the country as a whole today is serious engineering education. Geometric and graphic disciplines are the first ones directly related to the specialty in the curricula of any technical field of training. The extent of this stage cannot be underestimated: they carry out the required program work, students study the rules and modern means of developing design documents, and receive basic knowledge to continue mastering specialized courses. However, simply knowing the standards or being able to work with computer-aided design tools to solve engineering problems is not enough. A design engineer is a creator, an inventor. This means that one of the main tasks of teachers is to form a systematic technical, design thinking based on developed spatial imagination, the ability to think comprehensively, logically and creatively, and manifested in the ability to take specific actions to solve emerging problems and tasks, make decisions to achieve a specific result in the form of a technical product, a finished design based on the selected technology. This article explores the possibilities of including design elements in educational tasks at the initial stage of training students of mechanical engineering specialties. A description of the course work carried out in the third semester as part of the engineering graphics course at Peter the Great St. Petersburg Polytechnic University is presented. According to the assignment, students develop design documentation for the product according to the diagram, description of the operating principle of the device and drawings of the main parts, make, if necessary, changes to the design to increase the manufacturability of parts and assembly and improve the technical and consumer properties of the product, and one of the parts, as directed teacher, is replaced by a welded assembly unit. The article sets the goals and objectives of the work, describes the stages of implementation and the role of the teacher, and also developed a training manual to ensure independent work of students. An assessment was made of the first experience of using the technique. Conclusions and recommendations are presented.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"9 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139156392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BUILDING THE PERSPECTIVE OF A STRAIGHT LINE ALONG THE PICTURE TRAIL AND THE VANISHING POINT","authors":"N. Sal'kov, N. Kadykova","doi":"10.12737/2308-4898-2023-11-3-19-25","DOIUrl":"https://doi.org/10.12737/2308-4898-2023-11-3-19-25","url":null,"abstract":"The article is exclusively applied and methodical in nature and is intended for the study of constructions in the section \"Perspective\". The paper considers the construction of the perspective of a straight line of the general position with the help of a picture trace and a vanishing point. In perspective, the traces of a straight line are the points of intersection with the picture and subject planes. Vanishing point – the perspective of an improper point of a straight line. The article discusses the picture trail, the vanishing point and the construction of a straight line segment by means of these perspective points. In textbooks for builders, such a task is not set at all and is not considered. Three authors have solutions in textbooks for architects: A.G. Klimukhin, Yu.I. Koroev and T.S. Timrot. However, they also have some disadvantages, which are discussed in this article. In the work proposed to the reader, such an arrangement of geometric components is performed that there is neither parallelism nor perpendicularity between them, that is, they are all located at acute angles to each other, which means that a general case of construction is proposed for consideration. So, we have a right angle only between the horizontal and frontal planes of projections, as well as between the picture and object (horizontal plane of projections) planes. The angles between the other geometric components are exceptionally sharp: a straight line of general position in the P1/P2 system is taken, it is also a straight line of general position in the P1/K system. Thus, the article considers, unlike other textbooks, the general case of a direct task.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"10 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139156337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SYNTHETIC REPRESENTATION OF THE \"OBLIQUE SYMMETRY\" TRANSFORMATION USING THE EXAMPLE OF AN ELLIPSE","authors":"V. Rustamyan, E. Bayanov, R. Slavin","doi":"10.12737/2308-4898-2023-11-3-12-18","DOIUrl":"https://doi.org/10.12737/2308-4898-2023-11-3-12-18","url":null,"abstract":"Geometric transformations play a pivotal role in computer graphics, determining the position and shape of objects. In machine learning, they are applied for processing and analyzing data, such as in images. In geometric surface modeling, they are utilized for the creation and transformation of three-dimensional forms. In physics, geometric transformations assist in describing the motion of objects in space and time. The aim of this work is to analyse and study the geometric transformation known as \"oblique symmetry.\" Primarily, the article seeks to elucidate a number of important properties of this transformation, expanding the field of knowledge in perspective-affine correspondence. Throughout the study, the principal directions of oblique symmetry are identified, and their relationship with the axis and direction of the transformation is established. It is crucial to emphasise that the analysis makes it evident that the axis and the direction of symmetry are equivalent and interchangeable. Additionally, the article addresses the challenge of transforming an arbitrary ellipse, defined by its semi-axes, into a circle of equal area. In this context, a method is proposed to determine the axis and direction of oblique symmetry for a given ellipse. Based on the results obtained and the analysis conducted, the authors propose a geometric algorithm that provides the capacity to resolve positional problems in the field of descriptive geometry. This algorithm also offers a novel method for constructing ellipses with given semi-axes, which holds practical significance in various engineering and geometric issues. In the conclusion of the article, a specific example of applying the developed method is provided, clearly demonstrating its practical value and real capabilities in solving positional problems in the field of descriptive geometry. Moreover, directions for future research in the field of shape formation are suggested, utilising the \"oblique symmetry\" transformation in the spaces and .","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"49 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139155230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Frame-By-Frame Animation in Teaching Descriptive Geometry","authors":"N. Paliy","doi":"10.12737/2308-4898-2023-11-3-39-47","DOIUrl":"https://doi.org/10.12737/2308-4898-2023-11-3-39-47","url":null,"abstract":"The paper presents using of frame-by-frame animation of geometric constructions in the course \"Descriptive Geometry\" to present educational graphic material in a more accessible and visual form for students. Electronic support of descriptive geometry classes used at the Department of Engineering Graphics at Bauman Moscow State Technical University made in the technique of frame-by-frame animation in the format of presentations and electronic text publications is presented. The technique of creating frame-by-frame animation is described. Geometric constructions are performed using computer graphics systems, in layers; each layer contains one step of construction. When layers are showed on alternately, a number of graphic files are created, which are inserted in a certain sequence on presentation slides or on the pages of an electronic text publication. During the demonstration, a visualization of the course of geometric constructions is created on the screen. Teachers when giving lectures and practical classes use electronic support of classes, made in the format of presentations to demonstrate the course material on the screen in the classroom. The presentations contain graphic material in the technique of frame-by-frame animation and minimal text material; the teacher gives the necessary explanations. Electronic support of classes, made in the form of an electronic educational visual aid, is used for independent work of students. Unlike classroom presentations, in an electronic educational visual aid, the animation of geometric constructions is accompanied by a text step-by-step description of the sequence of solving geometric problems. The main advantage of using electronic training software made in frame-by-frame animation technology compared to traditional software is the visibility and the ability to consistently, step by step, understanding the course of graphic constructions, with the ability to go back and repeat the sequence at any stage.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"77 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139156849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"About the Sequence of Mentioning Authors in the Works","authors":"N. Sal'kov, N. Kadykova","doi":"10.12737/2308-4898-2023-11-2-3-6","DOIUrl":"https://doi.org/10.12737/2308-4898-2023-11-2-3-6","url":null,"abstract":"It is said about the unjustified distribution of the authors' places in the title of the article. The most practical and rational approach to creating a list of authors is proposed. The newfangled principle of the structure of articles is criticized.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116041525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Use of Descriptive Geometry Methods for Graphical Study of the Parameters of the Cutting Part of a Spiral Drill","authors":"N. Paliy","doi":"10.12737/2308-4898-2023-11-2-39-46","DOIUrl":"https://doi.org/10.12737/2308-4898-2023-11-2-39-46","url":null,"abstract":"The article presents examples of practical application of descriptive geometry methods for solving engineering problems of determining and studying the parameters of the cutting part of a spiral drill. The necessity of graphical constructions is noted, which is due to the fact that it is impossible to measure the rear angle by a direct measurement method using a universal measuring instrument due to the complex geometric shape of the measuring object. The analysis of the geometric shape of the working part of the spiral drill, which includes the main rear conical surface of the drill tooth, the front screw surface of the drill groove, the cylindrical surface of the tooth back, the main and transverse cutting edges are presented. Using the double contact theorem, a projection of the tooth profile of a spiral drill is constructed on a plane parallel to the drill axis with a given profile projection on a plane perpendicular to the drill axis. The tooth profile is determined by the lines of intersection of the conical surface with the cylindrical surface and with the helical surface of the drill groove. The shape of the drill groove is considered to be set. Projections of the transverse cutting edge of the drill are constructed as lines of intersection of two conical surfaces with intersecting axes. The problem is solved using a bundle of auxiliary planes. The tendency of an increase in the angle of inclination of the transverse cutting edge to the drill axis with a decrease in the distance between the intersecting axes of conical surfaces is shown. Graphically, at an arbitrary point of the drill blade, the value of one of the main geometric parameters of the drill - the rear angle is determined. It is shown that the closer the point of the blade is to the center of the drill, the greater the value of the rear angle. The constructions are made in the 2D Compass-Graph design system. The paper used alternative methods for solving geometric problems, which, unlike traditional ones, provide a simpler and more visual graphical solution.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127155959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Development of a System for Semi-Automatic Modeling of Three-Dimensional Images","authors":"R. Slavin, N. Kargin, B. Slavin","doi":"10.12737/2308-4898-2023-11-2-47-55","DOIUrl":"https://doi.org/10.12737/2308-4898-2023-11-2-47-55","url":null,"abstract":"Descriptive geometry is one of the main disciplines of the general engineering cycle. It presents methods of accurate representation of spatial objects on a plane, as well as the identification of geometric shapes of figures from given images. That is, this discipline is designed to give future engineers the knowledge and skills to build and read drawings. \u0000By causing the intensive work of students' spatial thinking, descriptive geometry contributes to the development of spatial representation. In descriptive geometry, a flat image of a spatial object is called a plot (drawing). \u0000Students studying descriptive geometry get acquainted with examples of practical use of the theoretical provisions of descriptive geometry in course and diploma design. \u0000However, it is much easier to perceive drawings in volume if they can be rotated and viewed from different sides. For these purposes, you can not do without third-party software. Visualization of objects in the presence of a three-dimensional model is provided by Unity. But to create a three–dimensional model according to the drawing, other software is required - for example, Blender. Therefore, the authors set a goal: to create a semi-automatic visualization system for two-dimensional drawings in space based on Blender software and to develop comprehensive and simple documentation that will allow even people far from programming to use the program. \u0000It is known that Blender is a powerful program for creating three-dimensional graphics that allows you to create various objects, scenes, animations, as well as edit them. Blender is a free and open source program available to anyone interested in three-dimensional modeling and computer graphics creation. \u0000Among the Blender tools for creating three-dimensional models are powerful tools for modeling, sculpting, animation and visualization of objects and scenes. In Blender, you can also draw textures and create 3D animations using animation tools such as key frames.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125296591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Review of the conclusion of a land surveyor expert as evidence in a lawsuit","authors":"I. Beglov","doi":"10.12737/2308-4898-2023-11-2-7-17","DOIUrl":"https://doi.org/10.12737/2308-4898-2023-11-2-7-17","url":null,"abstract":". This article presents the results of a study of the geometric properties of the Nicomed conchoid and the oblique conchoid. In this paper, the oblique conchoid is modeled in a new way, namely by quasi-symmetry with respect to the elliptic axis. The method used is a fourth-order transformation of the plane relative to the second-order curve. That is, a straight line with quasi-symmetry is mapped into a fourth-order curve. The image of a straight line in this case consists of two branches that tend to two asymptotes. Quasi–symmetry makes it possible to obtain an oblique conchoid, as a special case under certain conditions, and in the general case, many other conchoidal curves. The use of this method made it possible to discover new geometric properties of conchoidal curves, in particular, to find a previously undescribed constructive correspondence between points belonging to different branches of the oblique conchoid. The paper formulates and proves three statements, namely: 1) The image of a straight line with its quasi-symmetry with respect to a circle is a Nicomedes conchoid, 2) the image of a circle with its quasi-symmetry with respect to a circle is a curve of the sixth order, 3) the image of a straight parallel major semiaxis of an ellipse with its quasi-symmetry with respect to a given ellipse is two symmetrical oblique conchoids with respect to the minor semiaxis of an ellipse. Also, the equations of the curves under consideration and their asymptotes in the general case are derived. \u0000The results of the research carried out in this paper expand the possibilities of using conchoidal curves in solving problems of engineering geometry. For example, when modeling various physical phenomena and processes, as well as in engineering and architectural design.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134185107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}