Geometry & Graphics最新文献

{"title":"Geometric and Graphic Training of Technical Students in Modern Conditions","authors":"Z.T. Nazarova","doi":"10.12737/2308-4898-2024-12-1-41-49","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-12-1-41-49","url":null,"abstract":"Geometric and graphic training is an integral part of the education of technical students. It is aimed at developing skills in working with geometric and graphic models, which allows students to successfully solve problems related to design and construction. This article discusses the directions of development of geometric-graphic training in modern conditions, as well as its influence on the formation of professional competencies among students. Describes a study conducted in the 2022–2023 academic year at the Ural State University of Transport (Ekaterinburg) in order to identify the shortcomings of the existing methodology for geometric-graphic training and develop proposals for its adjustment. \u0000 \u0000Modern pedagogical activities are based on information technologies, e-learning systems, and interactive teaching methods. Much is said about the requirements for students to successfully study the discipline (initial preparation, ability to work with information, quick acquisition of skills in specialized programs), but it is also worth highlighting the qualities necessary for a teacher to ensure a successful educational process: the ability to conduct an electronic training course , communication with students indirectly through special educational platforms, the ability to adapt to new challenges of the modern world (introduction of e-learning, the COVID-19 pandemic, presentation of material using examples understandable to modern students). \u0000 \u0000Modern demands on engineers and designers are high - they need to have a wide range of knowledge and skills to effectively carry out design work. Competent use of graphics programs and applications, as well as the ability to work with 3D models are just some of the key competencies in this area. The development of geometric-graphic training allows students to master these skills already at the training stage, which gives them an advantage when searching for work and increases their competitiveness in the labor market.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"9 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141804375","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 Quality of Graphic Training at the University: Desired, Actual, Action","authors":"D. Tikhonov-Bugrov, S. Abrosimov, E. Soloduhin","doi":"10.12737/2308-4898-2024-12-1-32-40","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-12-1-32-40","url":null,"abstract":"The concept of quality is considered in relation to graphic training in higher education. Among the wide variety of quality assurance issues, competent and result-oriented approaches to assessing the effectiveness (quality) of training are distinguished. It is noted that there are many questions for discussions, however, it is obvious that in the same case, the main role is played by monitoring and audit on the basis of a description of the expected learning outcomes. According to the Federal State Educational Standard, the graduate must be able to solve the “problems of design procedures” correctly, in accordance with the requirements of regulatory documents, to draw up design documentation, use computer and information technologies, and automated design tools. This is the basis of the notorious competency - based approach to training, in which the requirements of certain employers, and not the scientific justification of the existence of the necessary knowledge, skills that do not deny the possessions, are dominated. The situation is described in which the St. Petersburg professional community first encountered a similar approach to training. There is a contradiction between the principles of D.V. Manturov, declaring the need for wide and versatile training of modern engineers, and reality. \u0000 \u0000The comprehensive impact on the quality of preparation of the level of basic training of applicants, the transformations of the organizational structure of universities, attempts to reduce screening in the undergraduate and specialty through the introduction of specific rating systems and technological cards that allow students to certify students (not fulfilling the requirements of the Program) only by passing the minimum level of competence . On the example of an elite educational group, recruited under the Rostec Wings program, the problems of ensuring the quality of graphic training, a tendency to reduce the intellectual level of students due to total gadgetization are shown. It is noted that in this situation to ensure the possible quality of students' training, independent cathedral rating systems that stimulate the educational activities of students should be developed.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"84 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141802498","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":"K. Polke's Theorem in Computer Model Space in 2D Modeling","authors":"L. Sokolova","doi":"10.12737/2308-4898-2024-12-1-12-21","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-12-1-12-21","url":null,"abstract":"The application of Polke's theorem in the search for a coordinate system for an electronic geometric model in the model space of a computer in 2D geometric modeling is considered. \u0000 \u0000The possibility of creating an electronic geometric model in a system of axonometric axes in 2D modeling for scientific and educational purposes using a coordinate method is shown. \u0000 \u0000It is possible to solve problems on axonometric coordinate planes that do not provide solutions in a rectangular coordinate system. In the computer model space, it has become possible to solve classical problems of descriptive geometry, the solution of which is associated only with the method of projecting space onto the projection plane. \u0000 \u0000Secondary axonometry in the system of axonometric coordinate axes in 2D modeling has allowed us to solve a number of problems that do not have a solution in a rectangular coordinate system: \u0000 \u0000• simulate the parallel (oblique) direction of the correspondence of two related shapes; \u0000 \u0000• move the shape in space by rotating around the axonometric coordinate axes; \u0000 \u0000• the construction of an arbitrary relationship of two affine corresponding figures with mutual perpendicularity of the axis of kinship and the direction of kinship; \u0000 \u0000• switch to the coordinate solution method instead of projecting on the projection plane; \u0000 \u0000• vased on the numerical equality of isometric coordinates with natural ones, it is possible to switch from one coordinate system to another right in the process of solving problems. \u0000 \u0000A new reading of Polke's theorem expands the possibilities of the model space of personal computers for solving scientific and educational problems. However, a necessary condition for the implementation of these capabilities is the availability of isometric constructions by software. \u0000 \u0000The possibility of learning how to create an electronic drawing from a full-scale part in the educational process is shown. In this case, it is advisable to use an isometric image as an electronic model, as it has visibility in a single-picture view and simplicity of drawing in a coordinate way. \u0000 \u0000According to the constructed axonometric view, rectangular views are programmatically obtained using rectangular coordinates. A rectangular electronic drawing is formed from these types. If the purpose of its creation is to build a 3D geometric model of an object, then the construction can be continued, considering the created electronic drawing as the initial conditions for building a 3D model of the object","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"31 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141803537","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 Study of Geometry as the Most Important Way to Develop Heuristic Thinking","authors":"N. Sal'kov","doi":"10.12737/2308-4898-2024-12-1-22-31","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-12-1-22-31","url":null,"abstract":"Geometry by its nature is the most visual science of all that takes place in the life of mankind, and therefore the most visual for those who study at school or university – any book, \u0000 \u0000even the most non-technical, contains drawings, and drawings, in turn, are directly related to geometry in general and descriptive geometry in general in particular. After all, geometry studies points, lines and surfaces, but if you look closely, any drawing consists of points, lines and surfaces. It is not difficult to notice, so it is difficult to refute. The clarity of the drawings for beginners to learn something is the most important help for understanding the text. From the clarity of the school with its drawings in textbooks, the first step is taken to abstraction: the study of exclusively points and flat geometric shapes that are included in planimetry. After studying the names of geometric shapes, the student begins to study the laws of construction, to study various theorems, to prove them, to apply these proofs to other, more complex theorems. Here comes into play a phenomenon that can be called heuristic thinking based on logical constructions. The article also shows the use of Olympiads – urban and All-Russian – to further improve the development of heuristic thinking among students in order to replenish the departments of geometric profiles of universities as a result, as well as replenish our country with scientists in the direction 2.5.1 — \"Descriptive geometry and computer graphics. Digital product lifecycle support.\" And in other areas, too.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"59 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141805865","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":"Expansion of Formation Options Linear Surfaces","authors":"N. Sal'kov","doi":"10.12737/2308-4898-2024-12-1-3-11","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-12-1-3-11","url":null,"abstract":"When solving large geometric problems, in some cases there is a need to solve smaller auxiliary problems. So, when expanding the options for forming ruled surfaces, a solution arose for constructing a plane or a straight line at certain angles of inclination to the planes of projections or to some given plane of general position. The article presents this related task of constructing a plane, as well as building a straight line using a sphere. The basis for constructing a plane and a straight line at certain angles to the projection planes is the application of a contiguous cone of rotation to an arbitrarily specified sphere. The same method is already used to construct a straight line and a plane to a given plane of general position, taking into account that this plane is tangent to some given surface. All constructions of linear surfaces are based on the principle of specifying three guides and three conditions limiting each of the generators in relation to the specified guides. The condition of passing the guide at certain angles to the surfaces expands the possibilities of designing ruled surfaces almost indefinitely.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"47 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141805292","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":"Descriptive Geometry Today: Problems and Prospects","authors":"Yuliya Semagina, E. Kozik, M. Vanchinova","doi":"10.12737/2308-4898-2024-11-4-43-51","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-11-4-43-51","url":null,"abstract":"Against the background of constant reduction of the time allocated for contact work with students in curricula, there are discussions on the necessity of teaching some disciplines in universities, and their list is constantly changing. In the current case, the current round of discussion is connected with the signing of the decree on the reform by the President of Russia V.V. Putin. Putin signed a decree on the reform of higher education. Now it is a pilot project, which will be tested in several universities for three years. It is about the transition of engineering training from bachelor's degree to specialization. The reform will require considerable efforts to develop new curricula, adjust the list of academic disciplines included in them. Simultaneously with the inclusion of modern disciplines into this list, the process of excluding obsolete and irrelevant disciplines is underway. \u0000 \u0000According to the experience of the past years, disciplines of the general engineering cycle are constantly subjected to \"reforms\". In the case of technical specialties, descriptive geometry is a permanent outsider [8, 28]. The developers of the Federal State Educational Standards of Higher Education (FSES HE), who announced a competency-based approach to the learning process and assessment of knowledge of university graduates, probably also hold the opinion that descriptive geometry is a \"dying\" discipline. \u0000 \u0000The purpose of the authors of the article is an attempt to look at the problem not from the point of view of the age of descriptive geometry, but only guided by the frequency and efficiency of its methods in engineering practice and modeling of geometric objects of spaces of dimension 2+ and more. \u0000 \u0000The set goal required the solution of several problems. One of them is to clarify the question of what exactly the reformers are trying to do. Is it to remove an academic discipline or a section of mathematics, which is, in fact, descriptive geometry, from the course of engineers' training? It is also necessary to find out for which specialties or directions the descriptive geometry course is superfluous or obsolete.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"40 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140248137","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 Geometric Basis of Designing a Technical Object","authors":"M. Leparov","doi":"10.12737/2308-4898-2024-11-4-3-14","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-11-4-3-14","url":null,"abstract":"The purpose of the article is to propose basic statements (a conditional general name for law, regularity, principle and rule) about the geometry of technical objects and about the process of their design, which, together with existing and future statements, form the geometric foundations of design. 26 statements are presented and a classification, functions and properties of geometry are proposed from the point of view of distribution and the importance of the latter for the technical object and the design process.In their entirety, the presented statements are proof of the importance and influence of geometry in the design process. The work substantiates the possibility of obtaining partially or completely the geometry of any other part or assembled unit, conditionally called a recipient, from any part or assembled unit, conditionally called a donor. It is shown that any “item” (a term for naming anything, regardless of type, structures and characteristics) can be used to change the geometry of any technical object. The impact of the geometry on the flowing through and passing through the substance, the influence of the flows on the geometry, as well as the influence of the geometry on the properties of the substance are noted. It is emphasized that geometry is a fundamental „building block“ of both the technical object and the design process. The well-deserved placement of geometry at the center of the design activity gives a new perspective on the design process, which expands the possibilities and tools for its realization.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"274 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140250020","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":"Integration of Three-Dimensional Reflections from Curved Mirrors Using Computer Algebra Tools","authors":"O. Suncov, L. Zhikharev, A. Efremov","doi":"10.12737/2308-4898-2024-11-4-15-31","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-11-4-15-31","url":null,"abstract":"This article is a continuation of the study of the process of reflection of various objects from curved mirrors. So, earlier in the works [18; 20], a geometric method of constructing the results of reflections was described, which was implemented mathematically in the article [38] using the principles of analytical geometry [6; 11–14; 30]. The obtained analytical equations of the reflection results were visualized in the Wolfram Mathematica [24] program with the ability to dynamically change the parameters of the mirror and the reflected object. However, in the listed works, only cases of reflection on the plane were considered. In this study, attention is paid to a more complex case — reflection in three-dimensional space. \u0000 \u0000The article considered the reflection of a point from surfaces of the second order: a cylinder, a cone, a single-cavity and double-cavity hyperboloids, a sphere, elliptical and hyperbolic paraboloids, and from a torus — a surface of the fourth order. As before, the reflection result obtained in each of the cases is accompanied by a program code for Wolfram Mathematica, which allows the reader to independently simulate the reflection process with different initial parameters. \u0000 \u0000In addition, the relationships between the results obtained were analyzed — both the relationships between the results of various three-dimensional reflections, and the relationship of the results of three-dimensional reflections with the results of similar plane reflections. In particular, on the basis of this, a hypothesis was formulated about the relationship between the curvature of the Gaussian mirror and the dimension of the object obtained as a result of reflection. \u0000 \u0000Based on the results of the work, conclusions were drawn and prospects for further research were outlined. One of them is to obtain an analytical mechanism for describing complex geometric surfaces using a set of simpler objects. This feature will increase the efficiency of specialists when working with reflections from complex surfaces in areas such as aircraft construction (for creating aerodynamic surfaces and air ducts), medicine [40], shipbuilding [7; 31; 42], etc.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"60 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140248378","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 Student Research Work","authors":"A. Boykov, A. Efremov","doi":"10.12737/2308-4898-2024-11-4-61-75","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-11-4-61-75","url":null,"abstract":"The article summarizes the experience of managing student scientific work at the Departments of graphics of IGEU and RTU MIREA. Examples of topics of scientific and applied interest, the development of which can be conducted by undergraduate students, are given, the current state of development on these topics is given. As a result of attracting students to research, the following scientific results were obtained: the concept of a hyperfractal was introduced, the construction of hyperfractal sections by arbitrarily oriented planes, spheres was considered, the construction of a hyperfractal by adding iterative formulas was considered; an algorithm for visualizing imaginary extensions of complex shapes using computer graphics technologies is proposed, a four-dimensional space is used to model the complex plane, which is displayed using a hyperepure in the form of two three-dimensional orthogonal projections; the use of ordinary Bezier curves of the third order to represent quadratic and cubic parabolas, rational Bezier curves to represent general conical curves and ordinary Bezier curves is shown, as well as the representation of cubic splines using Bezier curves; experimental and analytical methods for constructing trajectories of points rigidly connected to the analogue of the Reulot triangle rotated in a frame of a given shape are considered; the concept of quasi-monograniers is formulated and considered on numerous examples, geometric cells of quasi-monograniers are described, an approach to constructing geometric cells bounded by congruent sections of curved surfaces is formulated and demonstrated; software geometric algorithms for constructing a driven centroid, according to a given leading and location of the axes of rotation for non-circular meshes are developed and implemented. The topics were formulated and an information reserve was created for future promising areas of research work of students at the department.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"47 S221","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140394848","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":"A Systematic Approach to Teaching Students the Capabilities of Modern Computer-Aided Design Systems","authors":"N. Paliy","doi":"10.12737/2308-4898-2024-11-4-52-60","DOIUrl":"https://doi.org/10.12737/2308-4898-2024-11-4-52-60","url":null,"abstract":"The article describes a systematic approach that is used at the Department of Engineering Graphics at Bauman Moscow State Technical University to teach students the possibilities of modern computer-aided design systems. \u0000 \u0000A methodology for teaching the basics of creating solid-state geometric models of parts and drawings in the Compass-3D system based on a systematic approach is presented. The structure and content of classes are described. The educational materials are developed on the basis of the students' knowledge of stereometry acquired at school and the knowledge gained during the parallel study of the engineering graphics section \"Projection drawing\". \u0000 \u0000Examples of practical tasks for students' independent work are given. The training begins with the construction of a flat contour, which is used as basis of a three-dimensional model. When constructing a contour, students practice to create the basic primitives that make up the contour, and superimposing geometric and dimensional dependencies on the primitives. The construction of solid-state models begins with the modeling of simple geometric bodies: a prism, a pyramid, a body of rotation. This allows students to focus on practicing shaping operations, and to better navigate the toolbars. Then, students consolidate their knowledge and skills in building models of more complex shapes, similar in design to mechanical engineering parts of two classes: \"body of rotation\" and \"non-body of rotation\". Students create electronic drawings based on the constructed models. At the same time, the following is being worked out: creating images in the drawing – views, sections, sections; applying dimensions while maintaining an associative connection with the part model; using drawing design elements. \u0000 \u0000Examples of control tasks for editing created models and drawings are given, which are necessary for students to acquire skills important for engineering practice. \u0000 \u0000It is noted that the acquired knowledge and skills can be used by students in further education. The proposed methodology can be recommended for use in the system of secondary and secondary vocational education.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"66 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140250066","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}