Geometry & Graphics最新文献

{"title":"Algorithmic Complex for Solving of Problems with Quadrics Using Imaginary Geometric Images","authors":"D. Voloshinov","doi":"10.12737/2308-4898-2020-3-32","DOIUrl":"https://doi.org/10.12737/2308-4898-2020-3-32","url":null,"abstract":"The paper is devoted to the consideration of a number of issues related to the creation of an algorithmic complex designed to solve positional and metric problems with quadrics on a projection model . A feature of the complex is the active use of geometric schemes and algorithms involving imaginary geometric images. In the paper has been presented a detailed description of constructive geometric algorithms for constructing of conics, quadrics and associated geometric images in a system of constructive geometric modeling – Simplex. All the discussed algorithms are available for independent repetition by the reader. In the paper have been presented and implemented algorithms for constructing conic from a point, a polar, and three points; constructing conic from two pairs of complex conjugate points and one real point; determination of a point on a quadric’s surface; setting a quadric by nine points in three-dimensional space. A new alternative frame of the quadric has been considered, based on which have been solved problems of constructing a tangent and a normal to the quadric, finding an intersection line of an arbitrary plane with the quadric, and performing polar and inverse transformations with respect to the quadric. Have been proposed algorithms for constructing an autopolar tetrahedron with respect to the quadric, and for constructing a conic from an autopolar triangle and two points. Have been considered problems of determining a collinear transformation in three-dimensional space and control the quadric through it. The implementation of the algorithms considered in the paper allowed conclude that there is an urgent need to develop tools for modeling imaginary conics, without which the complex of solving problems with quadrics cannot be taken for the complete one.","PeriodicalId":12604,"journal":{"name":"Geometry & Graphics","volume":"1 1","pages":"3-32"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83148081","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":"Augmented Reality Technologies in Students Project Activities","authors":"S. Ignat'ev, Z. Tret'yakova, M. Voronina","doi":"10.12737/2308-4898-2020-51-57","DOIUrl":"https://doi.org/10.12737/2308-4898-2020-51-57","url":null,"abstract":"This study’s relevance is determined by the absence of serious research, science-based, tested and verified programs and training materials related to the use of Augmented Reality (AR) technologies when getting students education in Engineering and Computer Graphics (ECG). The study’s aim was the introduction of AR-technologies in the project activities of first-year students. The study was conducted on the base of St. Petersburg Mining University. 48 first-year students of the Civil Engineering Faculty, pursuing a specialist's degree in “Construction of Unique Buildings and Structures”, participated in the project activity. The students' project activities results showed that at present, AR-technologies have gained popularity not only among designers and planners, but also among schoolteachers, as well as among lecturers and students of technical universities. A student team of St. Petersburg Mining University solved the design problem using AR-technology and created an informational 3-D model of the building structure. The existing methods related to students training have been completed and updated with the method of graphical presentation for the students' project activities results with the help of AR-technologies. As a result of the students’ project activities study, has been revealed the thoroughly obvious need for teaching a new generation of students to use AR-technologies. The aim is implementation of AR-technologies by students in the perspective, with continuous and subsequent self-education, as well as teaching future designers of rational use of AR-technologies to solve educational and practical problems, including areas of engineering and computer graphics. The study had showed that currently there is not enough of scientifically based learning materials for the organization of students' project activities using AR-technologies. Has been revealed the need for further scientific research in the field of AR-technologies implementation in the students’ project activities within the framework of ECG academic discipline. The paper materials can be useful for lecturers of all levels.","PeriodicalId":12604,"journal":{"name":"Geometry & Graphics","volume":"232 1","pages":"51-57"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76290303","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":"Augmented Reality in Descriptive Geometry","authors":"S. Ignat'ev, Z. Tret'yakova, M. Voronina","doi":"10.12737/2308-4898-2020-41-50","DOIUrl":"https://doi.org/10.12737/2308-4898-2020-41-50","url":null,"abstract":"In this paper is investigated the possibility of Augmented Reality (AR) technologies contextualizing in teaching methods for “Descriptive Geometry” (DG) student course. The aim of the investigation was the study of the current state of knowledge and practice in the field of DG students teaching with the help of AR-technologies, and identification of key issues affecting the adoption by users (teachers and students) of AR-technologies as a modern educational tool in the. Conducted an analysis of existing researches in the field of modern educational tool in the field of DG. Has been carried out the analysis of current investigations in the field of DG students teaching based on AR-technology. The key problems affecting the adoption by users of AR-technologies as an educational tool in the field of DG have been determined. Existing methods of DG students teaching using AR-technologies in St. Petersburg Mining University are gradually completed and updated. The work results showed that students have a positive perception of educational classes on DG course based on AR-technologies. Students successfully solve DG problems using AR-technology based on Vuforia platform; create 3-D models of geometric entities in SketchUp, and labels for camera fixing based on AutoCAD. When creating the software, the compiled C ++ programming language is used, based on which scripts (markers) are written that lift 3-D models of objects to given planes. The study results will be useful for developers of AR-platforms, AR-applications in the field of DG students training. They will allow avoid projects that may cause problems with the convenience of AR-applications using, what, in turn, will lead to the rejection of users from the introduction of this technology when getting students education in DG.","PeriodicalId":12604,"journal":{"name":"Geometry & Graphics","volume":"34 1","pages":"41-50"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77904344","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":"In Favor of Imaginaries in Geometry","authors":"A. Girsh","doi":"10.12737/2308-4898-2020-33-40","DOIUrl":"https://doi.org/10.12737/2308-4898-2020-33-40","url":null,"abstract":"“Complex numbers are something complicated”, as they are perceived in most cases. The expression “real numbers are also complex numbers” sounds strange as well. And for all that complex numbers are good for many areas of knowledge, since they allow solve problems, that are not solved in the field of real numbers. First and most important is that in the field of complex numbers all algebraic equations are solved, including the equation x2 + a = 0, which has long been a challenge to human thought. In the field of complex numbers, the problem solutions remain free from listing special cases in the form of \"if ... then\", for example, solving the problem for the intersection of the line g with the circle (O, r) always gives two points. And in the field of real numbers, three cases have to be distinguished: \u0000| Og | r → there is no intersection; \u0000| Og | = r → there is one double point. \u0000The benefit of complex numbers also lies in the fact that with their help not only problems that previously had no solutions are solved, they not only greatly simplify the solution result, but they also hold shown in this text further amazing properties in geometric figures, and open door to the amazing and colorful world of fractals.","PeriodicalId":12604,"journal":{"name":"Geometry & Graphics","volume":"20 12","pages":"33-40"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91442255","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":"Computer Verification of Descriptive Geometry Task Solutions for Engineering and Graphic Education","authors":"A. Boykov","doi":"10.12737/2308-4898-2020-66-81","DOIUrl":"https://doi.org/10.12737/2308-4898-2020-66-81","url":null,"abstract":"In this paper is formulated the relevance of computer tools creation for verification of descriptive geometry task solutions. Are analyzed the shortcomings of available methods and systems for such verification. A new verification method is proposed – the mode of superposition based on overlaying a student’s solution with a template and formal evaluation the overlaying results. To create templates for a wide range of descriptive geometry tasks, it is proposed to use a formal grammar of the correct solution, which is constructed using special nonterminal symbols – “and”, “or”, “transform” and “instance”. As the grammar’s terminal symbols are used geometric figures. Thus, the template consists of a graphic part (a set of figures) and a structural description (grammar). An implementation of this verification method is demonstrated as a software system for verifying of descriptive geometry task solutions in the form of DXF-files. A functional model of the verification system is given. The automatic formation of a template from a graphical model, which is created in a vector graphics editor and does not require a symbolic description, is considered, as well as processing procedure for a student’s solution, during which the verifiable model goes through phases of normalization, filtration, and extracting of higher-level elements. An example of checking for two solutions (the correct one and containing errors) of the task for constructing a perpendicular to a plane of general position is given. The work of a subsystem for verification result visualization is demonstrated too. The created system can be implemented in Internet-libraries of tasks, or in distance learning systems, and can be used for remote support of geometric-graphic courses. Conclusions about feasibility of introducing the proposed method as a tool in CAD-systems are made.","PeriodicalId":12604,"journal":{"name":"Geometry & Graphics","volume":"61 1","pages":"66-81"},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87353945","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":"Images of Linear Conditions on a Manhattan Plane","authors":"V. Yurkov","doi":"10.12737/2308-4898-2020-3-14","DOIUrl":"https://doi.org/10.12737/2308-4898-2020-3-14","url":null,"abstract":"In this paper are considered planar point sets generated by linear conditions, which are realized in rectangular or Manhattan metric. Linear conditions are those expressed by the finite sum of the products of distances by numerical coefficients. Finite sets of points and lines are considered as figures defining linear conditions. It has been shown that linear conditions can be defined relative to other planar figures: lines, polygons, etc. The design solutions of the following general geometric problem are considered: for a finite set of figures (points, line segments, polygons...) specified on a plane with a rectangular metric, which are in a common position, it is necessary to construct sets that satisfy any linear condition. The problems in which the given sets are point and segment ones have been considered in detail, and linear conditions are represented as a sum or as relations of distances. It is proved that solution result can be isolated points, broken lines, and areas on the plane. Sets of broken lines satisfying the given conditions form families of isolines for the given condition. An algorithm for building isoline families is presented. The algorithm is based on the Hanan lattice construction and the isolines behavior in each node and each sub-region of the lattice. For isoline families defined by conditions for relation of distances, some of their properties allowing accelerate their construction process are proved. As an example for application of the described theory, the problem of plane partition into regions corresponding to a given set of points, lines and other figures is considered. The problem is generalized problem of Voronoi diagram construction, and considered in general formulation. It means the next: 1) the problem is considered in rectangular metric; 2) all given points may be integrated in various figures – separate points, line segments, triangles, quadrangles etc.; 3) the Voronoi diagram’s property of proximity is changed for property of proportionality. Have been represented examples for plane partition into regions, determined by two-point sets.","PeriodicalId":12604,"journal":{"name":"Geometry & Graphics","volume":"19 1","pages":"3-14"},"PeriodicalIF":0.0,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74441591","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":"Application of Information Technologies in Checking Procedure of Future Specialists’ Graphic Literacy","authors":"T. Turutina, D. Tret’yakov","doi":"10.12737/2308-4898-2020-45-56","DOIUrl":"https://doi.org/10.12737/2308-4898-2020-45-56","url":null,"abstract":"Topical issues related to improving the quality of higher education and solving teaching-learning problems, aimed at providing a checking procedure of future specialists’ graphic literacy in the process of teaching graphic design are considered in this paper. Among the national tasks of providing specialists for various arears of professional activity, the improvement of higher education’s quality and practical training of competent staff capable for professional self-education is considered as one of priorities. Education is interpreted as a process and result of acquiring the system of knowledge and personality development. Sufficiently frequent updating of requirements to future specialists’ training because of practical implementation of information technology in all professional spheres makes actual the search for more efficient methodologies aimed at changing of professional competences. The development of graphic literacy as future specialists' professional competence is defined by the learning activity process signification. The specificity of graphic disciplines as result of the introduction of information technologies requires the development of an effective methodology to ensure the content of the educational process, changing the nature of expertise, knowledge and skills; forming competence as a special ability necessary to perform a particular action in the object-graphic area. In the modern process for learning of graphic courses the KOMPAS graphic program is widely used, along with Autocad, Archicad, Revit, and others. Further is interpreted the KOMPAS practical use in the process of preparation of future specialists for learning of graphic courses. The KOMPAS jumps out as the program allowing using information technologies in checking procedure of future specialists' graphic literacy. The features of generation in the KOMPAS graphic program are revealed, as well as the software application “Generator”, including an educational-methodical complex aimed at forming of the necessary competence, development of self-learning activities, checking of expertise, knowledge and skills on graphic courses.","PeriodicalId":12604,"journal":{"name":"Geometry & Graphics","volume":"11 1","pages":"45-56"},"PeriodicalIF":0.0,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82287416","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":"“Applied Geometry” Discipline Adaptation to Undergraduate for Exploitative Specialities of an Aviation High Educational Institution","authors":"O. Nazarova","doi":"10.12737/2308-4898-2020-57-64","DOIUrl":"https://doi.org/10.12737/2308-4898-2020-57-64","url":null,"abstract":"The problem of teaching and formulating the tasks for the “Applied Geometry” discipline is considered in this paper. Currently, in aviation high educational institutions there is a tendency to reduce the number of hours allocated to graphic disciplines; in addition, “Descriptive Geometry” – the habitual name of the discipline – has been replaced by name “Applied Geometry”. This is certainly connected with the transition to learning on undergraduate programs, that implies a competency-based approach, i.e., training in accordance with the necessary knowledge and methods of activity in a particular area [4; 9; 23; 29; 30; 34]. The planned results of learning in “Applied Geometry” include knowledge of methods for solving applied engineering-geometric problems, as well as the ability to use the basic elements of applied geometry and engineering graphics in professional activities, and to solve specific applied problems of geometric modeling [4; 14; 20; 22; 32]. For these reasons arises the question of the need to adapt “Descriptive Geometry” to the requirements and programs for the training of bachelors, bringing it to conformity with the name “Applied Geometry” of the discipline. According to the results of “Applied Geometry” studying, students ought to gain experience and have the ability to independently solve cognitive, organizational and other problems related to their future professional activities [28–30]. In this paper is proposed a general approach to the formulation of “Applied Geometry” problems for cadets pursuing a bachelor's degree in “Air Navigation” (25.03.03) and “Operation of Airports and Flight Support of Aircraft” (25.03.04). Using rather simple examples, has been considered the possibility to formulate the problem in such a way that instead of the traditional formulation it could be applied for a specific bachelor's degree. As well has been considered a complex applied problem, which is suitable as a task for performing a computational and graphic work, since it integrates several topics of the discipline.","PeriodicalId":12604,"journal":{"name":"Geometry & Graphics","volume":"19 1","pages":"57-64"},"PeriodicalIF":0.0,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82710491","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":"Dual Problems with Conics","authors":"A. Girsh","doi":"10.12737/2308-4898-2020-15-24","DOIUrl":"https://doi.org/10.12737/2308-4898-2020-15-24","url":null,"abstract":"The problem for construction of straight lines, which are tangent to conics, is among the dual problems for constructing the common elements of two conics. For example, the problem for construction of a chordal straight line (a common chord for two conics) ~ the problem for construction of an intersection point for two conics’ common tangents. In this paper a new property of polar lines has been presented, constructive connection between polar lines and chordal straight lines has been indicated, and a new way for construction of two conics’ common chords has been given, taking into account the computer graphics possibilities. The construction of imaginary tangent lines to conic, traced from conic’s interior point, as well as the construction of common imaginary tangent lines to two conics, of which one lies inside another partially or thoroughly is considered. As you know, dual problems with two conics can be solved by converting them into two circles, followed by a reverse transition from the circles to the original conics. This method of solution provided some clarity in understanding the solution result. The procedure for transition from two conics to two circles then became itself the subject of research. As and when the methods for solving geometric problems is improved, the problems themselves are become more complex. When assuming the participation of imaginary images in complex geometry, it is necessary to abstract more and more. In this case, the perception of the obtained result’s geometric picture is exposed to difficulties. In this regard, the solution methods’ correctness and imaginary images’ visualization are becoming relevant. The paper’s main results have been illustrated by the example of the same pair of conics: a parabola and a circle. Other pairs of affine different conics (ellipse and hyperbola) have been considered in the paper as well in order to demonstrate the general properties of conics, appearing in investigated operations. Has been used a model of complex figures, incorporating two superimposed planes: the Euclidean plane for real figures, and the pseudo-Euclidean plane for imaginary algebraic figures and their imaginary complements.","PeriodicalId":12604,"journal":{"name":"Geometry & Graphics","volume":"73 1","pages":"15-24"},"PeriodicalIF":0.0,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78408751","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 Students’ Creative Potential in the Framework of Academic Olympics on Engineering and Computer Graphics","authors":"Yu.I. Mishukovskaya, T. Usataya, L. Deryabina","doi":"10.12737/2308-4898-2020-65-72","DOIUrl":"https://doi.org/10.12737/2308-4898-2020-65-72","url":null,"abstract":"Currently, they present design objects in the form of three-dimensional models and drawings. Accordingly, when training students at a technical university, it is necessary to pay attention to design and graphic disciplines. From the first course of study it is necessary show to students the relationship of the studied graphic disciplines with their future professional activities; stimulate their cognitive interest and motivation for learning and creativity with the help of Academic Olympics, that will help to achieve a high level of students' professional competence. So, one of the main tasks for higher education in the context of implementation of modern Federal State Educational Standards is the formation of the necessary professional competencies and improving the quality of students’ engineering training in technical high educational institutions [16; 25]. The use in the educational process of multilevel creative graphic tasks performed by means of three-dimensional computer graphics helps students to perfect themselves in further educational and professional activities. Creative tasks for Academic Olympics contribute to the development of students' creative potential through creative self-realization. Tasks for Academic Olympics are creative problems in engineering graphics with elements of project activities. For creative self-realization in graphic activities, it is important not only to be aware of graphic tasks, but also to find in them personally meaningful sense, which is manifested when a student implements his own ideas in situations that are significant for him and in a familiar, meaningful environment for him. For this, to students are offered Academic Olympics tasks of various types: propaedeutic (developing the students’ general readiness for graphic activity) and creative tasks with elements of project activity, i.e., creative project tasks. It is necessary also to develop Academic Olympics tasks taking into account the students' training program.","PeriodicalId":12604,"journal":{"name":"Geometry & Graphics","volume":"19 1","pages":"65-72"},"PeriodicalIF":0.0,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82265037","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}