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Methods of constructions of sections and shadows of four-dimensional objects are explained. We visualize images of an object and its section or shadow at the same time in a double orthogonal projection on two perpendicular three-dimensional spaces. Our techniques are similar to the methods used in Monge’s projection of the three-dimensional space. Constructions are created in the interactive 3D modeling software GeoGebra 5, in which the user can freely move some input elements. We focus on a synthetic approach to description of the four-dimensional space with the use of descriptive geometry tools.

This study presents the design and fabrication of a parametric physical model using additive manufacturing to visualize the double orthogonal projection of a line, enhancing engineering education through tangible geometric representation. The model consists of two articulated plates representing the principal projection planes and flexible cylindrical elements depicting a spatial line and its projections. Designed in SolidEdge, all parts were fabricated with FDM technology using a Creality Ender 3 printer and PLA filament. The plates include three articulation points enabling simulation of perpendicular and aligned positions. Flexible cylinders inserted into aligned holes create a kinematic mechanism that demonstrates the transformation from 3D line to 2D projections. A spotlight enhances spatial interpretation by marking projection points. Process parameters: layer height 0.2 mm, nozzle 0.4 mm, temperature 190–210°C, and speed 50–60 mm/s, ensured dimensional accuracy and a ±0.1 mm tolerance. The model proved stable, repeatable, and effective as a dynamic teaching tool in descriptive geometry and STEM (Science, Technology, Engineering, and Mathematics) education.

In the stages of understanding and study, by students, of descriptive geometry, the treble orthogonal projection of a point, creates problems in the situations in that one or more descriptive coordinates are zero. Starting from these considerations the authors have created an original computer program which offers to the students the possibility to easily understanding of the way in which a point is represented, in draught, in the treble orthogonal projection whatever which are its values of the descriptive coordinates.

A method of visualization of four-dimensional objects using a double orthogonal parallel projection onto two orthogonal three-dimensional spaces is proposed. A synthetic approach, with the use of basic descriptive geometry tools of Monge’s projection in interactive 3D graphical software, is taken. Descriptive constructions of projections of points, lines, planes and three-dimensional spaces are shown. Methods of measuring true lengths of segments and rotating projections of objects into the modeling space are described. The focus lies on improving the spatial ability and understanding of the four-dimensional space. An example of a construction is carried out on a model of tesseract. All the constructions are analogies of constructions in Monge’s projection of a three-dimensional space. With advantages of interactive computer graphics, the constructions are easy to perform, and objects are easy to manipulate with.

When capturing a QR code on a cylinder, there may be geometric distortions due to the angle of the camera and the cylindrical deformation, which makes the QR code difficult to recognize. To solve this problem, a correction algorithm for QR codes is proposed in this paper. First, the boundary of the QR code on the cylinder is extracted by a morphological algorithm and geometry calculations. Then, the feature points on the image are accurately located. Next, the standard size of the QR code is determined by using the cross-ratio method in descriptive geometry. Finally, the image is corrected by perspective projection. It is proven that the algorithm can correct the distortion of the cylinder image effectively, and it has the ability to properly identify cylindrical QR codes.

The article presents a new method of developing individual tasks (IHA) for solving positional-metric problems of descriptive geometry based on 3 D models, taking into account intensive control. The technique of effective self-study of methods of changing complex drawing with the use of visual 3D models is considered.

The research analytically investigates the measurement problem associated with coasts. Through the use of fractal geometry, the coast is broken down into a parametrized curve, subsequently unfolded along a horizontal axis “normalized” by rays whose fulcrum is traced back to the lighthouses located along the coastline.

Architecture connects science and art. Thus, the student from the Faculty of Architecture and Urbanism manifests himself as a creative being, capable of accumulating new information from various fields related to architecture, processing them, capitalizing on them and finally, through the result of creation, enriching the built environment. In their projects, technical thinking and various constructive systems are used, which are based on the training of three-dimensional thinking through descriptive geometry. This paper presents how geometric knowledge is applied in various projects within the disciplines studied at the Faculty of Architecture and Urbanism, Cluj-Napoca.

Descriptive Geometry is a fundamental aspect of technical drawing, critical in engineering, architecture, and design disciplines. This article explores the application of TikZ Euclide, a versatile tool for LaTeX writing language, in simplifying the understanding and implementation of Descriptive Geometry. Through simple examples, this article aims to demonstrate the potential and power of TikZ Euclide in visualizing and constructing geometric figures, fostering a clearer comprehension of Descriptive Geometry principles.

The paper presents applications developed for teaching descriptive geometry. The purpose of the applications is represented by the understanding of the basic elements of the descriptive geometry - the lines and the planes and their relative positions in space. The applications are focused on the line contained in a plane, this item being very important for the other relative positions of a line and a plane - the line concurrent with a plane and the line parallel to a plane.