arXiv subjects

Rushan Ziatdinov

Publications and source records attributed to Rushan Ziatdinov.

At least 19 recordsLinked to original sources

arXiv2025

Generating Digital Models Using Text-to-3D and Image-to-3D Prompts: Critical Case Study

In the world of technology and AI, digital models play an important role in our lives and are an essential part of the digital twins of real-world objects. They can be created by designers, artists, or game developers using spline curves and surfaces, meshes, and voxels, but making such models is too time-consuming. With the growth of AI tools, there is interest in the automated generation of 3D models, such as generative design approaches, which can save creators valuable time. This paper reviews several online 3D model generators and critically analyses the results, hoping to see higher-quality results from different prompts.

cs.GR↗

arXiv2025

Bernstein polynomials: a bibliometric data analysis since the year 1949 based on the Scopus database

It's hard to imagine human life in the digital and AI age without polynomials because they are everywhere but mostly invisible to ordinary people: in data trends, on computer screens, in the shapes around us, and in the very fabric of technology. One of these, the simple but elegant Bernstein polynomials, was discovered by a scientist from the Russian Empire, Sergei Bernstein, in 1912 and plays a central role in mathematical analysis, computational and applied mathematics, geometric modelling, computer-aided geometric design, computer graphics and other areas of science and engineering. They have been the sub-ject of much research for over a hundred years. However, no work has carried out database-derived research analysis, such as bibliometric, keyword or network analysis, or more generally, data analysis of manuscript data related to Bernstein polynomials extracted from digital academic databases. This work, which appears to be the first-ever attempt at the bibliometric data analysis of Bernstein polynomials, aims to fill this gap and open researchers' eyes to potentially new or underexplored areas of mathematics and engineering where Bernstein polynomials may one day be used to make discoveries. The results may be helpful to academics researching Bernstein polynomials and looking for potential applications, collaborators, supervisors, funding or journals to publish in.

math.HO↗

arXiv2025

Network visualisations related to special functions based on the Scopus data since 1940

Special functions are essential in theoretical and applied mathematics and have various applications in the applied sciences. Mathematicians have studied them for centuries, but there is still no bibliometric analysis that summarises the datasets of publications showing different network visualisations, such as co-author and keyword visualisations, basic keyword statistics and other data analyses. This work appears to be the first attempt to fill this gap by presenting different network visualisations based on 4025 documents with the keyword "special function" in their title, abstract or keywords belonging to the field of mathematics in the Scopus database. We also show that special functions are rarely used in geometric modelling, a mathematical foundation for CAD, industrial design, architecture, and other applied fields, and we discuss how different visualisations for special functions can be generated in the Julia programming language. The generated image and video visualisations can be helpful to academics to see the impact of different authors, to define their new research topics, to see connections or lack thereof between various topics, to find the most popular special functions, or for teaching purposes to show the importance of special functions and links to other topics in modern pure and applied mathematics and other sciences.

cs.DL↗

arXiv2025

Developable Ruled Surfaces Generated by the Curvature Axis of a Curve

Ruled surfaces play an important role in various types of design, architecture, manufacturing, art, and sculpture. They can be created in a variety of ways, which is a topic that has been the subject of much discussion in mathematics and engineering journals. In geometric modelling, ideas are successful if they are not too complex for engineers and practitioners to understand and not too difficult to implement, because these specialists put mathematical theories into practice by implementing them in CAD/CAM systems. Some of these popular systems such as AutoCAD, Solidworks, CATIA, Rhinoceros 3D, and others are based on simple polynomial or rational splines and many other beautiful mathematical theories that have not yet been implemented due to their complexity. Based on this philosophy, in the present work, we investigate a simple way to generate ruled surfaces whose generators are the curvature axes of curves. We show that this type of ruled surface is a developable surface and that there is at least one curve whose curvature axis is a line on the given developable surface. In addition, we discuss the classifications of developable surfaces corresponding to space curves with singularities, while these curves and surfaces are most often avoided in practical design. Our research also contributes to the understanding of the singularities of developable surfaces and, in their visualisation, proposes the use of environmental maps with a circular pattern that creates flower-like structures around the singularities.

math.DG↗

arXiv2025

Visual Perception, Quantity of Information Function and the Concept of the Quantity of Information Continuous Splines

The geometric shapes of the outside world objects hide an undisclosed emotional, psychological, artistic, aesthetic and shape-generating potential; they may attract or cause fear as well as a variety of other emotions. This suggests that living beings with vision perceive geometric objects within an information-handling process. However, not many studies have been performed for a better understanding of visual perception from the view of information theory and mathematical modelling, but the evidence first found by Attneave (1954) suggests that the concepts and techniques of information theory may shed light on a better and deeper understanding of visual perception. The quantity of information function can theoretically explain the concentration of information on the visual contours, and, based on this, we first propose the concept of the quantity of information continuous splines for visualization of shapes from a given set of discrete data without adding any in-between points with curvature extreme. Additionally, we first discover planar curve with a constant quantity of information function and demonstrate one of the conditions when a monotonic curvature curve has a constant quantity of information function.

q-bio.NC↗

arXiv2022

Multi-Criteria Assessment of Shape Quality in CAD Systems of the Future

Unlike many other works, where authors are usually focused on one or two quality criteria, the current manuscript, which is a generalization of the article [35] published in Russian, offers a multi-criteria approach to the assessment of the shape quality of curves that constitute component parts of the surfaces used for the computer modelling of object shapes in various types of design. Based on the analysis of point particle motion along a curved path, requirements for the quality of functional curves are proposed: a high order of smoothness, a minimum number of curvature extrema, minimization of the maximum value of curvature and its variation rate, minimization of the potential energy of the curve, and aesthetic analysis from the standpoint of the laws of technical aesthetics. The authors do not set themselves the task of giving a simple and precise mathematical definition of such curves. On the contrary, this category can include various curves that meet certain quality criteria, the refinement and addition of which is possible in the near future. Engineering practice shows that quality criteria can change over time, which does not diminish the need to develop multi-criteria methods for assessing the quality of geometric shapes. Technical issues faced during edge rounding in 3D models that affect the quality of industrial design product shape have been reviewed as an example of the imperfection of existing CAD systems.

cs.GR↗

arXiv2022

Generation Alpha: Understanding the Next Cohort of University Students

Technology is changing at a blistering pace and is impacting on the way we consider knowledge as a free commodity, along with the ability to apply skills, concepts and understandings. Technology is aiding the way the world is evolving, and its contributions to education are not an exemption. While technology advances will play a crucial part in future teaching-learning approaches, educators will also be challenged by the next higher-education generation, the Alpha Generation. This entrepreneurial generation will embrace the innovation, progressiveness, and advancement with the expectation that one in two Generation Alphas will obtain a university degree. In anticipating the educational challenges and opportunities of the future higher education environment, this research reflected on Generation Alpha as the next cohort of university students, considering their preferred learning styles, perceptions and expectations relating to education. The research employed a theoretical analysis based on the characteristics and traits that distinguishes Generation Alpha, spearheaded by technology advances. The empirical investigation considered three independent studies that were previous conducted by authors from Slovakia, Hungary, Australia, and Turkey to understand the challenges and opportunities pertaining to Generation Alpha. The research identified the influence of social media, social connections, high levels of perceptions and the Generation Alpha's ability to interpret information as strengths to consider in future teaching-learning approaches in the higher education environment. This research concluded with recommendations on how universities could be transformed to ensure a better learning experience for Generation Alpha students, aligned with their characteristics, perceptions and expectations.

cs.CY↗

arXiv2022

Synthesis of Modeling, Visualization, and Programming in GeoGebra as an Effective Approach for Teaching and Learning STEM Topics

GeoGebra is an interactive geometry, algebra, statistics, and calculus application designed for teaching and learn-ing math, science, and engineering. Its dynamic interface allows its users to accurately and interactively visualize their work, models, and results. GeoGebra employs the synthesis of three key features: modeling, visualization, and programming (MVP). Many studies have shown the positive effects of GeoGebra on the efficiency and effectiveness of learning and teaching topics related to science, technology, engineering, and mathematics. In this study, we dis-cuss how GeoGebra provides an environment for learning that is very interactive and collaborative between the learner and the instructor. We also show how integrating GeoGebra into the learning scheme can help improve the skills and knowledge of school and university students in numerous advanced mathematical courses, such as calcu-lus, mathematical statistics, linear algebra, linear programming, computer-aided design, computer-aided geomet-ric design, analytic and projective geometry, and graphical representation. Therefore, this study shows the effec-tiveness of GeoGebra and its MVP key features in science and engineering, particularly in topics related to mathe-matics. Each key feature of GeoGebra is thoroughly analyzed, and further analyses, along with how GeoGebra can be helpful in different topics, are discussed.

cs.CY↗

arXiv2018

Techniques for modeling a high-quality B-spline curves by S-polygons in a float format

This article proposes a technique for the geometrically stable modeling of high-degree B-spline curves based on S-polygon in a float format, which will allow the accurate positioning of the end points of curves and the direction of the tangent vectors. The method of shape approximation is described with the purpose of providing geometrical proximity between the original and approximating curve. The content of the notion of a harmonious, regular form of B-spline curve's S-polygon in a float format is revealed as a factor in achieving a high-quality of fit for the generated curve. The expediency of the shape modeling method based on S-polygon in a float format at the end portions of the curve for quality control of curve modeling and editing is substantiated. The results of a comparative test are presented, demonstrating the superlative efficacy of using the Mineur-Farin configuration for constructing constant and monotone curvature curves based on an S-polygon in a float format. The findings presented in this article confirm that it is preferable to employ the principle of "constructing a control polygon of a harmonious form (or the Mineur-Farin configuration) of a parametric polynomial" to a B-spline curve's S-polygon in a float format, and not to a B-polygon of the Bezier curve. Recommendations are given for prospective studies in the field of applying the technique of constructing a high-quality B-spline curves to the approximation of log-aesthetic curves, Ziatdinov's superspirals, etc. The authors of the article developed a technique for constructing smooth connections of B-spline curves with ensuring a high order of smoothness of the composite curve. The proposed techniques are implemented in the FairCurveModeler program as a plug-in to engineering CAD systems.

cs.GR↗

arXiv2018

Universal software platform for visualizing class F curves, log-aesthetic curves and development of applied CAD systems

This article describes the capabilities of a universal software platform for visualizing class F curves and developing specialized applications for CAD systems based on Microsoft Excel VBA, the software complex FairCurveModeler, and computer algebra systems. Additionally, it demonstrates the use of a software platform for visualizing functional and log-aesthetic curves integrated with CAD Fusion360. The value of the curves is evident in visualizing the qualitative geometry of the product shape in industrial design. Moreover, the requirements for the characteristics of class F curves are emphasized to form a visual purity of shape in industrial design and to provide a positive emotional perception of the visual image of the product by a person.

cs.GR↗

arXiv2018

New Approaches and Trends in the Philosophy of Educational Technology for Learning and Teaching Environments

The purpose of this study is to discuss instructional design and technology (IDT) model strategies for developing learning and teaching environments, based on philosophical approaches to educational technology theory. The study begins with a discussion of IDT models to define the history of educational technology or instructional technology theories, based on instructional strategies and improvements. In the study, authors discuss the strategies and steps that a design team should follow when designing learning environments in industry, business and military scenarios, based on the philosophy of educational technology and latest technologies, which should give way to effective learning environments. The steps include recognising terminology in educational technology concepts, psychological and instructional foundations in instructional design (ID), as well as approaches to educational technology. To recap, our purpose is to combine necessary IDT model strategies for the pedagogical design of learning environments, with new technologies. We will also discuss powerful IDT models that aim to meet the very high expectations of digital and humanist education. To develop a high-quality learning environment, we will explain technology design steps and practice in order to improve the learning of tasks, complex cognitive skills, attitudes, motivations and competencies in the future trends of educational technology. At the end of the study, integrated technologies in e-learning were discussed and presented, based on foundations of IDT and the philosophy of educational technology.

cs.CY↗

arXiv2015

Server component installation and testing of the university information and educational environment on the Moodle LMS platform

The informational educational environment (IEE) of an institution is a complex multilevel system which, along with methodical, organizational and cultural resources, accumulates the intellectual and technical potential of a university, as well as the informative and activity components of the learners and teachers. In practice, the formation of IEE is actually based on the creation of information technologies and their integration into the existing educational environment of the institution. The management of this system is carried out using specialized equipment and software. For the successful formation and operation of IEE, in the present work we review software products that form the basis of the organization of interactive and web interactions between students, teachers and all participants of the educational process. We analyse the technical capabilities that have provided users with IEE services such as the Apache web server with connected modules PHP, MySQL, the Java virtual machine and the Red5 server. We demonstrate the possibility of obtaining results from the interaction of these products, and reports on users' work in webinars, video conferences and web conferences.

cs.OH↗

arXiv2015

Developing Educational Computer Animation Based on Human Personality Types

Computer animation in the past decade has become one of the most noticeable features of technology-based learning environments. With today's high educational demands as well as the lack of time provided for certain courses, classical educational methods have shown deficiencies in keeping up with the drastic changes observed in the digital era. Without taking into account various significant factors such as gender, age, level of interest and memory level, educational animation may turn out to be insufficient for learners or fail to meet their needs. However, we have noticed that the applications of animation for education have been given only inadequate attention, and students' personality types have never been taken into account. We suggest there is an interesting relationship here, and propose essential factors in creating educational animations based on students' personality types. Particularly, we investigate how information in computer animation may be presented in a preferable way based on the fundamental elements of computer animation. The present study believes that it is likely to have wide benefits in the field of education. Considering the personality types in designing educational computer animations with the aid of gathered empirical results might be a promising avenue to enhance the learning process.

cs.HC↗

arXiv2014

The potential of mobile exhibition as a form of implementation for social transformation and educational expo-design in addressing public social problems

The article analyzes the humanistic basis of expo-design in conjunction with the ideological problems of modern design and the causes of their occurrence. It reveals the potential of mobile exhibition for social transformation in terms of its structural and ideological aesthetic content. It substantiates the effectiveness of expo-design expression's artistic and aesthetic means in viewer personality moral education. It investigates the features of social problems design presentation in the unity of the formative and design material components features of mobile exhibition.

cs.CY↗

arXiv2014

A mathematical design and evaluation of Bernstein-Bezier curves' shape features using the laws of technical aesthetics

We present some notes on the definition of mathematical design as well as on the methods of mathematical modeling which are used in the process of the artistic design of the environment and its components. For the first time in the field of geometric modeling, we perform an aesthetic analysis of planar Bernstein-Bezier curves from the standpoint of the laws of technical aesthetics. The shape features of the curve segments' geometry were evaluated using the following criteria: conciseness-integrity, expressiveness, proportional consistency, compositional balance, structural organization, imagery, rationality, dynamism, scale, flexibility and harmony. In the non-Russian literature, Bernstein-Bezier curves using a monotonic curvature function (i.e., a class A Bezier curve) are considered to be fair (i.e., beautiful) curves, but their aesthetic analysis has never been performed. The aesthetic analysis performed by the authors of this work means that this is no longer the case. To confirm the conclusions of the authors' research, a survey of the "aesthetic appropriateness" of certain Bernstein-Bezier curve segments was conducted among 240 children, aged 14-17. The results of this survey have shown themselves to be in full accordance with the authors' results.

cs.GR↗

arXiv2013

Introduction to computer animation and its possible educational applications

Animation, which is basically a form of pictorial presentation, has become the most prominent feature of technology-based learning environments. It refers to simulated motion pictures showing movement of drawn objects. Recently, educational computer animation has turned out to be one of the most elegant tools for presenting multimedia materials for learners, and its significance in helping to understand and remember information has greatly increased since the advent of powerful graphics-oriented computers. In this book chapter we introduce and discuss the history of computer animation, its well-known fundamental principles and some educational applications. It is however still debatable if truly educational computer animations help in learning, as the research on whether animation aids learners' understanding of dynamic phenomena has come up with positive, negative and neutral results. We have tried to provide as much detailed information on computer animation as we could, and we hope that this book chapter will be useful for students who study computer science, computer-assisted education or some other courses connected with contemporary education, as well as researchers who conduct their research in the field of computer animation.

cs.GR↗

arXiv2013

Rapid mental computation system as a tool for algorithmic thinking of elementary school students development

In this paper, we describe the possibilities of using a rapid mental computation system in elementary education. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. These operations are actually simple algorithms which can develop or improve the algorithmic thinking of pupils. Using a rapid mental computation system allows forming the basis for the study of computer science in secondary school.

cs.CY↗

arXiv2013

The effects of computer assisted and distance learning of geometric modelling

The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools for teaching mathematical concepts of mentioned areas, and distance education technologies would be indispensable for consolidation of successfully passed topics.

cs.CY↗