Methodological systems for the preparation and holding of Olympiads and the development of students' intellectual abilities RTU MIREA

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 .

Synthetic Representation of the "Oblique Symmetry" Transformation Using the Example of an Ellipse

Rustamyan,

Bayanov,

Slavin

2023

A Systematic Approach to Teaching Students the Capabilities of Modern Computer-Aided Design Systems

Paliy

2024

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. A 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". Examples 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. Examples of control tasks for editing created models and drawings are given, which are necessary for students to acquire skills important for engineering practice. It 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.

About Student Research Work

Boykov,

Efremov

2024

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.