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Axioms
Special Issues
Mathematics, Computer Graphics and Computational Visualizations
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Mathematics, Computer Graphics and Computational Visualizations

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 31 March 2025 | Viewed by 3845

Special Issue Editors

Prof. Dr. Vesna Velickovic

E-Mail Website
Guest Editor
Department of Computer Science, Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
Interests: visualization in mathematics; computer graphics; software development; image processing
Prof. Dr. Rushan Ziatdinov

E-Mail Website1 Website2
Guest Editor
Department of Industrial Engineering, Keimyung University, Daegu 704-701, Republic of Korea
Interests: geometric modeling; high-quality shapes; computer-aided geometric design; computer-aided design; scientific visualization; computing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematics and computer graphics are mutually beneficial. Computational mathematics methods permeate computer graphics and provide the theoretical support and background for various computer graphics algorithms. On the other hand, computer graphics provides tools for visualizing abstract and complex mathematical concepts, which contributes significantly to their understanding.

The advent of computer graphics has played a pivotal and transformative role in the evolution of computational visualization and has had a significant impact on all levels of science, technology, engineering, arts, and mathematics (STEAM). Computational visualization, as a field that combines mathematics and computer graphics through visual imagery, has proven to be a highly effective medium for communicating abstract and tangible concepts.

The goal of this Special Issue is to explore computational visualization from different angles: to develop new mathematical methods that support the creation of computational visualizations; to use creative mathematical techniques in the development of software for visualization; to graphically represent complex mathematical objects and concepts and the relationships between them, but also illustrations and simulations of scientific, technological, engineering, and artistic (STEAM) content; to use programming languages and their extensions for 2D and 3D graphical applications and popular tools for 2D and 3D modeling, computer-aided design, rendering, and animation, for interactive geometry, algebra, and calculus, and for symbolic evaluation, and other software for developing scientific computational visualizations.

Please click on the video for details: https://www.youtube.com/watch?v=OedQDuEdgo8.

Prof. Dr. Vesna Velickovic
Prof. Dr. Rushan Ziatdinov
Guest Editors 

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • visualization of abstract and complex concepts
  • computational methods
  • computational visualization
  • computer graphics
  • computer-aided design
  • computer-aided geometric design
  • curve, surface, and solid modeling
  • data visualization
  • geometric modeling
  • graphical representation
  • information visualization
  • mathematics in computer graphics
  • scientific visualization
  • simulation
  • visualization methods

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Published Papers (3 papers)

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20 pages, 10798 KiB  
Article
Visualization of Isometric Deformations of Helicoidal CMC Surfaces
by Filip Vukojević and Miroslava Antić
Axioms 2024, 13(7), 457; https://doi.org/10.3390/axioms13070457 - 6 Jul 2024
Viewed by 789
Abstract
Helicoidal surfaces of constant mean curvature were fully described by do Carmo and Dajczer. However, the obtained parameterizations are given in terms of somewhat complicated integrals, and as a consequence, not many examples of such surfaces are visualized. In this paper, by using [...] Read more.
Helicoidal surfaces of constant mean curvature were fully described by do Carmo and Dajczer. However, the obtained parameterizations are given in terms of somewhat complicated integrals, and as a consequence, not many examples of such surfaces are visualized. In this paper, by using these methods in some particular cases, we provide several interesting visualizations involving these surfaces, mostly as an isometric deformation of a rotational surface. We also give interpretations of some older results involving helicoidal surfaces, motivated by the work carried out by Malkowsky and Veličković. All of the graphics in this paper were created in Wolfram Mathematica. Full article
(This article belongs to the Special Issue Mathematics, Computer Graphics and Computational Visualizations)
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7 pages, 595 KiB  
Article
Volume-Preserving Shear Transformation of an Elliptical Slant Cone to a Right Cone
by Marco Frego and Cristian Consonni
Axioms 2024, 13(4), 245; https://doi.org/10.3390/axioms13040245 - 9 Apr 2024
Viewed by 852
Abstract
One nappe of a right circular cone, cut by a transverse plane, splits the cone into an infinite frustum and a cone with an elliptical section of finite volume. There is a standard way of computing this finite volume, which involves finding the [...] Read more.
One nappe of a right circular cone, cut by a transverse plane, splits the cone into an infinite frustum and a cone with an elliptical section of finite volume. There is a standard way of computing this finite volume, which involves finding the parameters of the so-called shadow ellipse, the characteristics of the oblique ellipse (the cut) and, finally, the projection of the vertex of the cone onto the oblique ellipse. This paper shows that it is possible to compute that volume just by using the information of the shadow ellipse and the height of the cone. Indeed, the finite slant cone has the same volume of an elliptic right cone, with the base being the shadow ellipse of the cut portion and with the height being the distance between the vertex of the cone and the intersection of the height of the original cone with the cutting plane. This is proved by introducing a volume-preserving shear transformation of the elliptical slant cone to a right cone, so that the standard volume formula for a cone can be straightforwardly applied. This implies a simplification in the procedure for computing the volume, since the oblique ellipse—i.e., the difficult part—can be neglected because only the shadow ellipse needs to be determined. Full article
(This article belongs to the Special Issue Mathematics, Computer Graphics and Computational Visualizations)
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12 pages, 1758 KiB  
Article
Kantorovich Version of Vector-Valued Shepard Operators
by Oktay Duman, Biancamaria Della Vecchia and Esra Erkus-Duman
Axioms 2024, 13(3), 181; https://doi.org/10.3390/axioms13030181 - 9 Mar 2024
Viewed by 1064
Abstract
In the present work, in order to approximate integrable vector-valued functions, we study the Kantorovich version of vector-valued Shepard operators. We also display some applications supporting our results by using parametric plots of a surface and a space curve. Finally, we also investigate [...] Read more.
In the present work, in order to approximate integrable vector-valued functions, we study the Kantorovich version of vector-valued Shepard operators. We also display some applications supporting our results by using parametric plots of a surface and a space curve. Finally, we also investigate how nonnegative regular (matrix) summability methods affect the approximation. Full article
(This article belongs to the Special Issue Mathematics, Computer Graphics and Computational Visualizations)
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