The article discusses the Martin attractor (hopalong), which is a type of computational algorithm that allows generating visual structures that can have applications in graphic design or generative art. The available sources (the earliest references to Martin attractors in foreign and russian literature, modern ones - software systems for construction, web-pages of mathematical systems Maple and Wolfram), the mathematical model of the generalized Martin attractor and its special case – hopalong are analyzed. The influence of parameters on the image of hopalong is briefly considered, the irregular nature of the relationship between the image of hopalong and its parameters is shown, a number of hypotheses are put forward that require further verification. Known methods of hopalong coloring are considered and new ones are proposed. A new fractal approach to constructing hopalongs and studying hopalong as a hyperfractal is proposed. The essence of the fractal approach is briefly described, in which iterative calculations are performed for individual points of the image, with each such point corresponding to a strictly defined combination of parameter values. The construction of hopalong images based on the fractal approach is shown. The influence of the choice of statistical criterion on the hopalong image is shown. Two such criteria are shown - the average value of the jump length (the length of the trajectory divided by the number of iterations) and the area of the overall rectangle of the figure. Examples of hopalong images as sections of a hyperfractal object are shown. The methodology for further research of hopalongs for graphic design and generative art problems is outlined in general terms. Examples of problems that can be set for a student research work are given.
Polyhedrons, as one of the types of spatial forms, are of considerable practical interest and, due to this, are widely reflected in various fundamental and applied sciences, in engineering, architecture and design. Polyhedrons can be found in the designs of machine parts, machines and tools. They are also used in the design of complex technical structures, industrial and residential buildings, industrial design objects and jewelry. Convex polyhedrons are of the greatest practical interest. This study substantiates the need for a more in-depth study of the topic «Polyhedra» in the course «Engineering Graphics» for undergraduate students of some areas of Peter the Great St. Petersburg Polytechnic University (SPbPU) due to the specifics of their area of training and further use in practical activities. The article provides an analysis of the degree of disclosure of the topic of polyhedra in the course of stereometry in high school and in the discipline "Engineering graphics" studied at the university. The article shows the results of a statistical study conducted by the authors to control residual knowledge on the topic of «Polyhedra» in the school course of stereometry based on a survey of students from various areas of SPbPU. The purpose of the survey is to identify issues that require clarification and additions when studying the section «Descriptive Geometry» of the discipline «Engineering Graphics». The assessment of knowledge was carried out according to three selected criteria: knowledge of the main types of polyhedra, understanding the topology of regular polyhedra, previously acquired skills in constructing sections of polyhedra (cube) with a plane in an axonometric projection. An attempt was made to systematize convex polyhedra by their degree of regularity in a single classification, combining some provisions of the school course of stereometry and the section «Descriptive Geometry» of the discipline «Engineering Graphics» studied in higher educational institutions. A classification is presented with a detailed description of the designs of various polyhedral shapes and their main characteristics. The classification does not pretend to be a final version, and can be supplemented with polyhedra with other classification features, for example, by the shape of the faces or their inscribeability in a sphere. Separately considered are various types of prisms, pyramids and prismatoids, which are of the greatest practical interest and are studied in detail in the school course of stereometry and the section «Descriptive Geometry» of the discipline «Engineering Graphics» mastered at the University.
The article is devoted to the discussion of some aspects of computer graphics. The relevance of the research topic is due to the constant growth in demand for high-quality and efficient graphical visualization of data. In this regard, there is a need to understand how graphical systems work. The results of the research can be useful in creating various applications for scientific computing, computational modeling, and educational purposes. The purpose of the study is to implement an original algorithm for graphical construction of an ellipse and analyze the effectiveness of the proposed solution using standard graphical primitives in Python. The study attempts to propose original approaches to implementing individual basic elements of computer graphics and to investigate the effectiveness of the proposed algorithms in comparison with standard (library) solutions based on a specific programming language. Indeed, the quality of a graphical application's visualization directly depends on the algorithms chosen for manipulating graphical primitives. Different methods have their own advantages and disadvantages in terms of accuracy, performance, and application areas. This provides a fertile ground for exploring new ideas in the implementation of graphical objects and conducting a comparative analysis of such algorithms with standard solutions based on a specific programming language. The article focuses on two aspects of the research: the mathematical foundation of the proposed method and its computer implementation. It is well-known that ellipses offer greater flexibility in creating visual elements in gaming software. In particular, elliptic curves are used in image compression algorithms. Traditional compression methods based on rectangular blocks often produce imperfect results. Due to their anisotropy, ellipses allow for more accurate approximation of complex shapes in images. The proposed algorithm relies on the unique property of anisotropy, which allows for easy deformation of ellipses in the desired direction, enabling them to adapt more effectively to the specific features of the image being generated. The research described in the article clearly demonstrated that the ellipse drawing method proposed by the authors consistently outperforms the basic Python method on any number of curves in terms of runtime. The difference in the performance of the program runs allows us to make an assumption about the effectiveness of the original method in experiments with high computational load.
A number of topical problems related to geometric and graphic training of students of chemical directions of training a technical university in the study of the discipline "Engineering and computer graphics" are considered. Among these problems, one of the important is the weak basic graphic training of students, including due to the lack of manual drawing in secondary schools and professional educational organizations in the era of global digitalization and the active use of computer-aided design systems in the educational process. Key words: quality of education, engineering graphics, computer graphics, drawing, three-dimensional modeling, KOMPAS-3D, end-to-end graphic preparation. A study conducted in 2024 at the Federal State Budgetary Educational Institution of Higher Education "Yaroslavl State Technical University" (Yaroslavl) at the Department of Descriptive Geometry and Engineering Graphics among students of the Institute of Chemistry and Chemical Technology is described in order to determine the impact of manual drawing on the quality of graphic training of students in conjunction "sketching-manual drawing-computer graphics and three-dimensional modeling" and determine the place and role of manual drawing at present. As a result of the study, students are faced with difficulties when performing practical work both when sketching and manual mechanical engineering, and when using only software products for three-dimensional modeling and creating associative drawings and specifications. Methods have been developed to enhance the effectiveness of this discipline's educational process by harmoniously combining traditional manual drawing techniques with the creation of graphic documents in the KOMPAS-3D CAD system. Justifications are given for the need to form a regional model of end-to-end geometric and graphic training "School College - University”, which makes it possible to optimally approach the process of forming the content of educational disciplines at all levels of education and, thereby, improve the quality of training of university graduates.
The article highlights the problem of using situational tasks in the educational process, along with classical problems of descriptive geometry, taking into account the specifics of future professional activities. At the initial stage of studying descriptive geometry, it is important to acquire theoretical knowledge related to professional activities. Solving any graphical problem establishes interdisciplinary connections, which helps students develop a holistic perception of many practical problems from various fields of science and technology. When studying the topic «Straight Line and Point» it is suggested to use graphical models of engineering practice. Typical and control tasks are presented. Typical tasks are used to prepare for solving problems in practical classes after a specific lecture and after studying the corresponding section in the textbook. Control tasks are the main tasks that students must solve in their workbooks after completing a topic. Some of these tasks can be solved independently or with the help of a teacher in practical classes. The use of graphical generalizations of real objects in engineering practice allows future engineers to acquire theoretical knowledge and the fundamentals of professional practice. The results of this work are successfully used in the performance of calculation and graphic tasks, both in groups and individually. The results of the study lead to the conclusion that in order to acquire the competencies necessary to create and implement engineering solutions, a future specialist must have a solid theoretical foundation based on real-life professional experience.
