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Axioms
Special Issues
Innovations in Geometric Modelling and CAD: Exploring Boundaries and Beyond
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Innovations in Geometric Modelling and CAD: Exploring Boundaries and Beyond

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Geometry and Topology".

Deadline for manuscript submissions: 1 September 2024 | Viewed by 2431

Special Issue Editors

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
Prof. Dr. Kenjiro T. Miura

E-Mail Website1 Website2
Guest Editor
Department of Mechanical Engineering, Shizuoka University, Hamamatsu, Japan
Interests: geometric modeling; aesthetic curves and surfaces; image processing; intelligent optical measurement; computing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent decades, geometric modelling has become an interesting and powerful branch of modern science and engineering, driven by innovations and breakthroughs in computer-aided design (CAD) and visualisation technologies. Its theories are mainly rooted in mathematics and computer science, enabling applications in diverse fields such as industrial design, computer graphics, visualisation and animation, CAD/CAM, virtual reality (VR), architecture, biomedical engineering and others. However, we believe that the field of geometric modelling needs continuous exploration and innovation to reach new frontiers and to penetrate into areas where it is less used than in other fields, such as biology, space science, nanoengineering, chemical engineering, quality engineering, environmental engineering, robotics, solar engineering, etc.  In this context, we aim to focus this Special Issue on the intersection and synthesis of geometric modelling, CAD and innovative technologies. We are looking for groundbreaking research on curve and surface modelling, visual perception, geometric aesthetics, and the integration of novel mathematical methods and innovative technologies such as artificial intelligence and virtual, augmented and mixed reality into future CAD systems. In addition, we are particularly interested in innovative technologies for CAD and the integration of fundamentally new mathematical approaches and paradigms, as well as in AI-based tools that have the potential to revolutionise CAD and geometric modelling. The scope of this Special Issue includes original research in the field of geometric modelling and CAD and its applications in various domains, including innovations, engineering, art, physics, medical engineering, computer graphics and architecture. We also encourage submissions that explore theoretical mathematics and geometry that can be applied to address challenges and create innovative approaches to geometric modelling and CAD. We hope that this Special Issue will serve as a platform for researchers and practitioners to share their knowledge and insights, paving the way for exciting advances and innovative approaches in geometric modelling and CAD. We look forward to receiving your contributions and together driving innovation in the field forward.

Prof. Dr. Rushan Ziatdinov
Prof. Dr. Kenjiro T. Miura
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

  • applied, discrete and computational geometry and topology
  • computer-aided design (CAD)
  • digital twins
  • curve, surface and solid modelling
  • geometric modelling in arts
  • high-quality shapes
  • industrial and scientific applications
  • isogeometric analysis
  • mathematical design
  • mesh generation
  • non-polynomial curves and surfaces (spirals, log-aesthetic curves, GLACS, superspirals, quaternion curves, etc.)
  • optical illusions
  • special functions in geometric modelling

Published Papers (1 paper)

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Research

14 pages, 5584 KiB  
Article
Developable Ruled Surfaces Generated by the Curvature Axis of a Curve
by Ferhat Taş and Rushan Ziatdinov
Axioms 2023, 12(12), 1090; https://doi.org/10.3390/axioms12121090 - 28 Nov 2023
Cited by 1 | Viewed by 1341
Abstract
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 a lot of discussion in mathematics and engineering [...] Read more.
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 a lot of 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 method of generating 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, as 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. Full article
(This article belongs to the Special Issue Innovations in Geometric Modelling and CAD: Exploring Boundaries and Beyond)
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