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Mathematics and Computer Programming in 2D and 3D Open Source...
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Mathematics and Computer Programming in 2D and 3D Open Source Software

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 9971

Special Issue Editor

Dr. Tihomir Dovramadjiev

E-Mail Website
Guest Editor
Faculty of Shipbuilding, Technical University of Varna, 9010 Varna, Bulgaria
Interests: PLM; CAD; CAE; CAM; graphs in computer science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematics is strongly related to computer programming. The application of maximum accuracy based on mathematical principles and functions is a guarantee of reliability and quality in the development of applications in 2D and 3D open-source computer software. The application in science and practice of open-source computer software is especially relevant. This is based not only on free and easy access to these resources, but mostly on the extremely fast development of these systems, which is largely due to the human factor and the periodic receipt of improvements to the respective applications. Open-source systems play an important role in 2D and 3D computer software. These software exist individually but can sometimes be correlated, used interconnectedly, and built as hybrid variants. Given the massive digitalization, open-source systems attract academics and researchers, leading companies, private users, students interested in computer programming and activities, as well as all stakeholders. Looking for opportunities for maximum quality of development, the application of mathematical functions in coding to create entirely new or to upgrade existing software is of great importance.

This section invites researchers who use the mathematical functions and computer codes in practice to present, at a high level, their activities related to:

  • Applications in 2D and 3D open-source computer software;
  • Creation of new 2D and 3D open-source computer software;
  • Upgrading of existing 2D and 3D open-source computer software;
  • Development of extensions as add-ons, add-ins, and plug-ins;
  • Creating scripts;
  • Creation of two-dimensional and three-dimensional finished models;
  • Creating parametric applications for generating 2D and 3D models based on mathematical values;
  • Application of mathematical functions and writing scripts directly in three-dimensional software (e.g., Blender, FreeCAD and others);
  • Оthers relevant to the topic.

Dr. Tihomir Dovramadjiev
Guest Editor

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • mathematics
  • programming
  • coding
  • application
  • 2D
  • 3D
  • open source
  • software
  • extensions
  • add-ons

Published Papers (5 papers)

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Research

13 pages, 1962 KiB  
Article
Do Statistics Show Differences between Distance Estimations of 3D Objects in the Traffic Environment Using Glances, Side View Mirrors, and Camera Display?
by Aleksandar Trifunović, Tijana Ivanišević, Svetlana Čičević, Sreten Simović, Vedran Vukšić and Živana Slović
Mathematics 2023, 11(5), 1258; https://doi.org/10.3390/math11051258 - 05 Mar 2023
Cited by 1 | Viewed by 1194
Abstract
The driver’s task in traffic is to evaluate traffic situations and act in accordance with the estimate. One of the most common causes of road crashes is “incorrect estimated of the traffic situation”. Correct perception of surroundings is one of the prerequisites for [...] Read more.
The driver’s task in traffic is to evaluate traffic situations and act in accordance with the estimate. One of the most common causes of road crashes is “incorrect estimated of the traffic situation”. Correct perception of surroundings is one of the prerequisites for safe and successful driving. To investigate the mentioned issue, the authors of this paper conducted an experimental study with the aim of determining what affects the estimation of the object distance. In contrast to previous studies known from the available literature, our study presents experimental research of the estimated distance of 3D stimuli in three environments by direct observation, a rear-view mirror, and a camera display in a vehicle. One-hundred-and-sixty-four participants participated in the experiment. The research results show statistically significant differences in the estimation of the distance of 3D objects for different colors. Participants, for the largest number of stimuli, best estimate the distance from direct observation than through the rear-view mirror, while they make the most mistakes when estimating the distance of 3D objects using the camera display in a vehicle. On the other hand, in all described conditions, the respondents estimated the distance to the blue and green objects with the most significant errors. Full article
(This article belongs to the Special Issue Mathematics and Computer Programming in 2D and 3D Open Source Software)
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14 pages, 8895 KiB  
Article
Perspective Transformer and MobileNets-Based 3D Lane Detection from Single 2D Image
by Mengyu Li, Phuong Minh Chu and Kyungeun Cho
Mathematics 2022, 10(19), 3697; https://doi.org/10.3390/math10193697 - 09 Oct 2022
Viewed by 1714
Abstract
Three-dimensional (3D) lane detection is widely used in image understanding, image analysis, 3D scene reconstruction, and autonomous driving. Recently, various methods for 3D lane detection from single two-dimensional (2D) images have been proposed to address inaccurate lane layouts in scenarios (e.g., uphill, downhill, [...] Read more.
Three-dimensional (3D) lane detection is widely used in image understanding, image analysis, 3D scene reconstruction, and autonomous driving. Recently, various methods for 3D lane detection from single two-dimensional (2D) images have been proposed to address inaccurate lane layouts in scenarios (e.g., uphill, downhill, and bumps). Many previous studies struggled in solving complex cases involving realistic datasets. In addition, these methods have low accuracy and high computational resource requirements. To solve these problems, we put forward a high-quality method to predict 3D lanes from a single 2D image captured by conventional cameras, which is also cost effective. The proposed method comprises the following three stages. First, a MobileNet model that requires low computational resources was employed to generate multiscale front-view features from a single RGB image. Then, a perspective transformer calculated bird’s eye view (BEV) features from the front-view features. Finally, two convolutional neural networks were used for predicting the 2D and 3D coordinates and respective lane types. The results of the high-reliability experiments verified that our method achieves fast convergence and provides high-quality 3D lanes from single 2D images. Moreover, the proposed method requires no exceptional computational resources, thereby reducing its implementation costs. Full article
(This article belongs to the Special Issue Mathematics and Computer Programming in 2D and 3D Open Source Software)
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18 pages, 2777 KiB  
Article
Improved Sliding Algorithm for Generating No-Fit Polygon in the 2D Irregular Packing Problem
by Qiang Luo and Yunqing Rao
Mathematics 2022, 10(16), 2941; https://doi.org/10.3390/math10162941 - 15 Aug 2022
Cited by 1 | Viewed by 2830
Abstract
This paper introduces an efficient and robust sliding algorithm for the creation of no-fit polygons. The improved algorithm can cope with complex cases and is given an implementation in detail. The proposed concept of a touching group can simplify the judging process when [...] Read more.
This paper introduces an efficient and robust sliding algorithm for the creation of no-fit polygons. The improved algorithm can cope with complex cases and is given an implementation in detail. The proposed concept of a touching group can simplify the judging process when recognizing the potential translation vector for an orbital polygon. In addition, the generation of the no-fit polygon only involves three main steps based on the proposed concept. The proposed algorithm has a mechanism that searches other start positions to generate a complete no-fit polygon for handling complex cases. To improve the efficiency, many acceleration strategies have been proposed, such as point exclusion strategy and point inclusion test. The robust and efficient performance of the algorithm is tested by well-known benchmark instances and degenerate and complex cases, such as holes, interlocking concavities and jigsaw-type pieces. Experimental results show that the proposed algorithm can produce complete no-fit polygons for complex cases, and acceleration strategies can reduce the creation time of no-fit polygon on benchmark instances by more than sixteen percent on average. Full article
(This article belongs to the Special Issue Mathematics and Computer Programming in 2D and 3D Open Source Software)
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20 pages, 6657 KiB  
Article
Prototype of 3D Reliability Assessment Tool Based on Deep Learning for Edge OSS Computing
by Yoshinobu Tamura and Shigeru Yamada
Mathematics 2022, 10(9), 1572; https://doi.org/10.3390/math10091572 - 06 May 2022
Cited by 2 | Viewed by 1160
Abstract
We focus on an estimation method based on deep learning in terms of fault correction time for the operation reliability assessment of open-source software (OSS) under the environment of an edge computing service. Then, we discuss fault severity levels in order to consider [...] Read more.
We focus on an estimation method based on deep learning in terms of fault correction time for the operation reliability assessment of open-source software (OSS) under the environment of an edge computing service. Then, we discuss fault severity levels in order to consider the difficulty of fault correction. We use a deep feedforward neural network in order to estimate fault correction times. In particular, we consider the characteristics of fault trends by using three-dimensional graphs. Therefore, we can increase the recognizability of the proposed method based on deep learning for large-scale fault data from the standpoint of fault severity levels under edge OSS operation. Full article
(This article belongs to the Special Issue Mathematics and Computer Programming in 2D and 3D Open Source Software)
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23 pages, 5846 KiB  
Article
Investigation of 2D Seismic DDA Method for Numerical Simulation of Shaking Table Test of Rock Mass Engineering
by Xiaodong Fu, Jingyu Kang, Qian Sheng, Lu Zheng, Wenjie Du and Haifeng Ding
Mathematics 2022, 10(8), 1330; https://doi.org/10.3390/math10081330 - 17 Apr 2022
Viewed by 1580
Abstract
Since the basic theory of the discontinue deformation analysis (DDA) method was proposed, the DDA open source has gone through a long development process. At present, different kinds of programs have been widely applied in rock mass engineering such as slope, dam, and [...] Read more.
Since the basic theory of the discontinue deformation analysis (DDA) method was proposed, the DDA open source has gone through a long development process. At present, different kinds of programs have been widely applied in rock mass engineering such as slope, dam, and tunnel. This paper introduces the solution principle of DDA motion equations in detail, as well as the development status of the 2D open-source program. Numerical simulation of shaking table test of rock mass engineering using 2D DDA program is highlighted, and investigations of seismic wave pre-processing and seismic input method are carried out. First, based on the Newmark integration scheme, the integration algorithms of synthetic or measured seismic wave time history, correction function of seismic wave, and DDA simulation are unified. Then, three seismic input methods are implanted in the DDA program, and the applicability of various seismic input methods is discussed. On this basis, using the improved seismic 2D DDA program, a shaking table test of typical rock mass engineering is simulated. Through the comparison between the theoretical/test data and simulation results, the reliability of the improved DDA program in seismic response analysis is verified; the large mass method and the large stiffness method are more suitable for rigid foundation, such as shaking table test; the propagation of the seismic wave presents a significant amplification effect due to the reflection, refraction, and diffraction in the tunnel. The research results provide DDA theory and an open-source program for analyzing the seismic response of rock mass engineering. Full article
(This article belongs to the Special Issue Mathematics and Computer Programming in 2D and 3D Open Source Software)
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