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Symmetry
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Challenges and Trends in the Application of Descriptive Geometry Field...
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Challenges and Trends in the Application of Descriptive Geometry Field under the Current Paradigm of Computer – Assisted Design (CAD)

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Engineering and Materials".

Deadline for manuscript submissions: closed (30 April 2024) | Viewed by 8955

Special Issue Editors

Prof. Dr. Manuel Prado-Velasco

E-Mail Website
Guest Editor
Department of Engineering Graphics, University of Seville, 41092 Seville, Spain
Interests: descriptive geometry; computational geometric modeling; multilevel dynamic modeling and simulation; physiological modeling; cyborgs modeling; wearable sensors; bioengineering
Prof. Dr. Laura García-Ruesgas

E-Mail Website
Guest Editor
Department of Engineering Graphics, University of Seville, 41092 Seville, Spain
Interests: descriptive geometry; computational geometric modeling; multilevel dynamic modeling and simulation; physiological modeling; cyborgs modeling; wearable sensors; bioengineering

Special Issue Information

Dear Colleagues,

The evolution of modern computer-aided design (CAD) software tools has driven a change in the paradigm relating to the study, analysis, and representation of engineering and architectural technical systems, demonstrated by the removal of descriptive geometry as the foundation of the methods involved.

The ability of descriptive geometry (DG) as a scientific field to provide mathematic methods for the special analysis of three-dimensional (3D) geometric systems, through their plane projections loses relevance when the expert can address the 3D space using the 3D homologous computation in CAD.

However, DG also offers an abstract and well-defined mathematically formalism for the analysis and solution of 3D geometric systems. The removal of DG as the foundation of the methods involved in CAD models thus causes the loss of that well-defined formalism, what makes the analysis of non-direct 3D problems difficult.

This Special Issue explores the cutting-edge advances and trends in the application of DG for the technical drawing, analysis, and computational modelling of 3D geometric systems, under the current context of a wide diffusion of matured 3D CAD tools, providing novel solutions in academia, industry and research that overcome or complement those from CAD.

The Special Issue is not limited to classic engineering and architectural systems, but rather it addresses the computer implementations of DG mathematical procedures, including rotation and projection transformations, to explore the symmetry properties of 3D geometric systems, and to extend their applications to other scientific fields, such as bioengineering.

Potential topics include:

  • Descriptive geometry;
  • Technical drawing;
  • Engineering graphics;
  • Architectural graphics;
  • Computer modeling;
  • Computer simulation;
  • 3D systems modeling;
  • 3D systems analysis;
  • Geometry in bioengineering.

Prof. Dr. Manuel Prado-Velasco
Prof. Dr. Laura García-Ruesgas
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. Symmetry 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.

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Published Papers (4 papers)

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Research

21 pages, 11681 KiB  
Article
A 3D Descriptive Geometry Problem-Solving Methodology Using CAD and Orthographic Projection
by Eduardo Gutiérrez de Ravé and Francisco J. Jiménez-Hornero
Symmetry 2024, 16(4), 476; https://doi.org/10.3390/sym16040476 - 14 Apr 2024
Viewed by 1833
Abstract
In solving descriptive geometry (DG) problems, board (i.e., hand drawing) methods are frequently used, despite this discipline is still very important to enhance spatial vision. These methods are very different from CAD tools which are used in the field of design. CAD facilitates [...] Read more.
In solving descriptive geometry (DG) problems, board (i.e., hand drawing) methods are frequently used, despite this discipline is still very important to enhance spatial vision. These methods are very different from CAD tools which are used in the field of design. CAD facilitates the realization of geometric constructions and transformations (i.e., rotation, translation, copying, scaling, alignment, and symmetry, among others) are performed analytically. For this reason, a 3D DG problem-solving methodology using CAD and orthographic projection (CADOP) is introduced. Once the principles of DG, orthographic projection, and CAD fundamentals and tools are described, CADOP is applied to obtain (i) orthogonal views; (ii) principal lines of a plane; (iii) true-size view of a plane; (iv) parallelism, perpendicularity, and distance, and (v) angles. Considering the user coordinate system in CADOP allows one to place the horizontal plane in the suitable position to solve DG problems directly in one step. In the traditional methods, the use of auxiliary views must be carried out in several steps instead. The dynamic management of the 3D view of the scene is facilitated in CADOP, improving its understanding, and achieving the precision inherent in analytical calculations. Full article
(This article belongs to the Special Issue Challenges and Trends in the Application of Descriptive Geometry Field under the Current Paradigm of Computer – Assisted Design (CAD))
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38 pages, 7240 KiB  
Article
Challenges of Engineering Applications of Descriptive Geometry
by Zsuzsa Balajti
Symmetry 2024, 16(1), 50; https://doi.org/10.3390/sym16010050 - 29 Dec 2023
Cited by 3 | Viewed by 3198
Abstract
Descriptive geometry has indispensable applications in many engineering activities. A summary of these is provided in the first chapter of this paper, preceded by a brief introduction into the methods of representation and mathematical recognition related to our research area, such as projection [...] Read more.
Descriptive geometry has indispensable applications in many engineering activities. A summary of these is provided in the first chapter of this paper, preceded by a brief introduction into the methods of representation and mathematical recognition related to our research area, such as projection perpendicular to a single plane, projection images created by perpendicular projection onto two mutually perpendicular image planes, but placed on one plane, including the research of curves and movements, visual representation and perception relying on a mathematical approach, and studies on toothed driving pairs and tool geometry in order to place the development presented here among them. As a result of the continuous variability of the technological environment according to various optimization aspects, the engineering activities must also be continuously adapted to the changes, for which an appropriate approach and formulation are required from the practitioners of descriptive geometry, and can even lead to improvement in the field of descriptive geometry. The imaging procedures are always based on the methods and theorems of descriptive geometry. Our aim was to examine the spatial variation in the wear of the tool edge and the machining of the components of toothed drive pairs using two cameras. Resolving contradictions in spatial geometry reconstruction research is a constant challenge, to which a possible answer in many cases is the searching for the right projection direction, and positioning cameras appropriately. A special method of enumerating the possible infinite viewpoints for the reconstruction of tool surface edge curves is presented in the second part of this paper. In the case of the monitoring the shape geometry, taking into account the interchangeability of the projection directions, i.e., the property of symmetry, all images made from two perpendicular directions were taken into account. The procedure for determining the correct directions in a mathematically exact way is also presented through examples. A new criterion was formulated for the tested tooth edge of the hob to take into account the shading of the tooth next to it. The analysis and some of the results of the Monge mapping, suitable for the solution of a mechanical engineering task to be solved in a specific technical environment, namely defining the conditions for camera placements that ensure reconstructibility are also presented. Taking physical shadowing into account, conclusions can be drawn about the degree of distortion of the machined surface from the spatial deformation of the edge curve of the tool reconstructed with correctly positioned cameras. Full article
(This article belongs to the Special Issue Challenges and Trends in the Application of Descriptive Geometry Field under the Current Paradigm of Computer – Assisted Design (CAD))
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Graphical abstract

21 pages, 6054 KiB  
Article
The Place of Descriptive Geometry in the Face of Industry 4.0 Challenges
by M. Carmen Ladrón-de-Guevara-Muñoz, María Alonso-García, Óscar D. de-Cózar-Macías and E. Beatriz Blázquez-Parra
Symmetry 2023, 15(12), 2190; https://doi.org/10.3390/sym15122190 - 12 Dec 2023
Viewed by 1143
Abstract
Industrial process automation has long been the main goal in production lines that seek to decrease human involvement. However, it is broadly agreed that a collaboration between humans and technologies must still exist as human capital is required to provide certain skills and [...] Read more.
Industrial process automation has long been the main goal in production lines that seek to decrease human involvement. However, it is broadly agreed that a collaboration between humans and technologies must still exist as human capital is required to provide certain skills and abilities that machines cannot offer yet. For instance, in the context of design and simulation, CAD, CAM, and CAE professionals must count not only on a deep knowledge of the technology employed but also on specific skills that make the human factor an integral piece of the transition. These abilities are considered fundamental to achieving sustainable development in the industrial sector. This work focuses on analyzing through four study cases where whether specular o bilateral symmetry, a.k.a. planar symmetry is present, the weaknesses found in the human factor related to CAD training of future industrial engineers. The most common mistakes found when developing the different symmetric pieces proposed are thoroughly examined in order to define their origin, which mainly lies in students’ lack of descriptive geometry (DG) understanding. This is aggravated in some cases by the lack of spatial visualization abilities. The unstoppable and fast advances in design and simulation tools and technologies require humans to update their capabilities almost in real time. However, results show that this should not threaten the need for the human mind to spatially understand the changes being made on the screen. Otherwise, humans are at risk of ending up at the service of machines and technologies instead of the opposite. Full article
(This article belongs to the Special Issue Challenges and Trends in the Application of Descriptive Geometry Field under the Current Paradigm of Computer – Assisted Design (CAD))
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21 pages, 2707 KiB  
Article
Intersection and Flattening of Surfaces in 3D Models through Computer-Extended Descriptive Geometry (CeDG)
by Manuel Prado-Velasco and Laura García-Ruesgas
Symmetry 2023, 15(5), 984; https://doi.org/10.3390/sym15050984 - 26 Apr 2023
Cited by 1 | Viewed by 1903
Abstract
Computer-extended Descriptive Geometry (CeDG) is a new approach to solving and building computer models of three-dimensional (3D) geometrical systems through descriptive geometry procedures (thus inheriting invariant-symmetry properties from projective geometry) that have demonstrated reliability and accuracy. CeDG may calculate [...] Read more.
Computer-extended Descriptive Geometry (CeDG) is a new approach to solving and building computer models of three-dimensional (3D) geometrical systems through descriptive geometry procedures (thus inheriting invariant-symmetry properties from projective geometry) that have demonstrated reliability and accuracy. CeDG may calculate a parametric implicit functional form for the spatial curves generated in the intersection of two surfaces, as well as of the flattened pattern of any developable surface involved in those encounters. This study first presents the theoretical foundations and methodology to calculate those curves. Secondly, a compound hopper is defined and modeled through CeDG (implemented in GeoGebra) and CAD (Solid Edge© 2023) approaches to evaluate the advantages of CeDG against CAD. The results demonstrate the robustness and accuracy of the CeDG technique for he intersection and flattening of surfaces and the advantages of CeDG against Solid Edge 2023 in solving the hopper case study. Full article
(This article belongs to the Special Issue Challenges and Trends in the Application of Descriptive Geometry Field under the Current Paradigm of Computer – Assisted Design (CAD))
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