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Mathematics
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Mathematical Applications in Computer Graphics
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Mathematical Applications in Computer Graphics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 August 2025 | Viewed by 2732

Special Issue Editors

Dr. Xiaoqiang Zhu

E-Mail Website
Guest Editor
School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China
Interests: computer graphics; computer vision; artificial intelligence; virtual/augmented reality
Prof. Dr. Lihua You

E-Mail Website
Guest Editor
National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK
Interests: geometric modeling; computer animation; computer graphics; image and point cloud-based shape reconstruction; machine learning; applications of ODEs and PDEs in geometric modeling and computer animation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematics serves as the foundation for many of the most significant advancements in computer graphics. From geometric modeling to rendering techniques, mathematical principles enable the development of sophisticated algorithms that drive the creation and manipulation of complex visual data. This Special Issue aims to bring together cutting-edge research that leverages mathematical methodologies to address challenges and innovate within the field of computer graphics.

The convergence of mathematics and computer graphics has led to transformative progress in various applications, including virtual and augmented reality, digital arts, animation, and scientific visualization. However, many challenges remain, particularly in the efficient processing and rendering of complex data structures, real-time interaction, and accurate simulation of physical phenomena. This Special Issue seeks to highlight novel mathematical approaches that push the boundaries of what is possible in computer graphics.

We invite prospective authors to submit original manuscripts that explore mathematical techniques and their applications in computer graphics. Topics of interest include, but are not limited to, the following:

  • Geometric and solid modeling;
  • Techniques for geometric and solid modeling;
  • Curve and surface reconstruction;
  • Shape and surface modeling;
  • Rendering techniques;
  • Physically based rendering;
  • Global illumination;
  • Image-based rendering;
  • Simulation and animation;
  • Physically based animation;
  • Simulation of natural phenomena;
  • Computational photography and video processing;
  • Virtual and augmented reality;
  • VR/AR rendering techniques;
  • Interaction models in virtual environments;
  • Real-time graphics for VR/AR applications;
  • Data visualization and analysis;
  • Scientific visualization;
  • Visual analytics;
  • Information visualization;
  • Mathematical foundations;
  • Computational geometry;
  • Data compression for graphics;
  • Numerical methods in graphics;
  • Machine learning and AI in graphics;
  • Geometry-based machine learning models;
  • Deep learning for surface reconstruction and optimization;
  • Graph convolutional networks for graphics;
  • Applications in various domains;
  • Medical imaging and visualization;
  • Digital cultural heritage;
  • Computational fabrication.

Dr. Xiaoqiang Zhu
Prof. Dr. Lihua You
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. 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

  • geometric and solid modeling
  • visual analytics
  • computational geometry
  • numerical methods in graphics
  • machine learning and AI in graphics
  • geometry-based machine learning models
  • deep learning for surface reconstruction and optimization
  • graph convolutional networks for graphics

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

19 pages, 2793 KiB  
Article
Neuronal Mesh Reconstruction from Image Stacks Using Implicit Neural Representations
by Xiaoqiang Zhu, Yanhua Zhao and Lihua You
Mathematics 2025, 13(8), 1276; https://doi.org/10.3390/math13081276 - 12 Apr 2025
Viewed by 339
Abstract
Reconstructing neuronal morphology from microscopy image stacks is essential for understanding brain function and behavior. While existing methods are capable of tracking neuronal tree structures and creating membrane surface meshes, they often lack seamless processing pipelines and suffer from stitching artifacts and reconstruction [...] Read more.
Reconstructing neuronal morphology from microscopy image stacks is essential for understanding brain function and behavior. While existing methods are capable of tracking neuronal tree structures and creating membrane surface meshes, they often lack seamless processing pipelines and suffer from stitching artifacts and reconstruction inconsistencies. In this study, we propose a new approach utilizing implicit neural representation to directly extract neuronal isosurfaces from raw image stacks by modeling signed distance functions (SDFs) with multi-layer perceptrons (MLPs). Our method accurately reconstructs the tubular, tree-like topology of neurons in complex spatial configurations, yielding highly precise neuronal membrane surface meshes. Extensive quantitative and qualitative evaluations across multiple datasets demonstrate the superior reliability of our approach compared to existing methods. The proposed method achieves a volumetric reconstruction accuracy of up to 98.2% and a volumetric IoU of 0.90. Full article
(This article belongs to the Special Issue Mathematical Applications in Computer Graphics)
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24 pages, 2799 KiB  
Article
Efficiency Investigation of Langevin Monte Carlo Ray Tracing
by Sergey Ershov, Vladimir Frolov, Alexander Nikolaev, Vladimir Galaktionov and Alexey Voloboy
Mathematics 2024, 12(21), 3437; https://doi.org/10.3390/math12213437 - 3 Nov 2024
Viewed by 793
Abstract
The main computationally expensive task of realistic computer graphics is the calculation of global illumination. Currently, most of the lighting simulation methods are based on various types of Monte Carlo ray tracing. One of them, the Langevin Monte Carlo ray tracing, generates samples [...] Read more.
The main computationally expensive task of realistic computer graphics is the calculation of global illumination. Currently, most of the lighting simulation methods are based on various types of Monte Carlo ray tracing. One of them, the Langevin Monte Carlo ray tracing, generates samples using the time series of a system of the Langevin dynamics. The method seems to be very promising for calculating the global illumination. However, it remains poorly studied, while its analysis could significantly speed up the calculations without losing the quality of the result. In our work, we analyzed the most computationally expensive operations of this method and also conducted the computational experiments demonstrating the contribution of a particular operation to the convergence speed. One of our main conclusions is that the computationally expensive drift term can be dropped because it does not improve convergence. Another important conclution is that the preconditioning matrix makes the greatest contribution to the improvement of convergence. At the same time, calculation of this matrix is not so expensive, because it does not require calculating the gradient of the potential. The results of our study allow to significantly speed up the method. Full article
(This article belongs to the Special Issue Mathematical Applications in Computer Graphics)
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22 pages, 3944 KiB  
Article
Analytical C2 Continuous Surface Blending
by Xiangyu You, Feng Tian, Wen Tang, Jian Chang and Jianjun Zhang
Mathematics 2024, 12(19), 3096; https://doi.org/10.3390/math12193096 - 3 Oct 2024
Viewed by 955
Abstract
Surface blending is an important topic in geometric modelling and is widely applied in computer-aided design and creative industries to create smooth transition surfaces. Among various surface blending methods, partial differential equation (PDE)-based surface blending has the advantages of effective shape control and [...] Read more.
Surface blending is an important topic in geometric modelling and is widely applied in computer-aided design and creative industries to create smooth transition surfaces. Among various surface blending methods, partial differential equation (PDE)-based surface blending has the advantages of effective shape control and exact satisfaction of blending boundary constraints. However, it is not easy to solve partial differential equations subjected to blending boundary constraints. In this paper, we investigate how to solve PDEs analytically and develop an analytical PDE-based method to achieve surface blending with C2 continuity. Taking advantage of elementary functions identified from blending boundary constraints, our proposed method first changes blending boundary constraints into a linear combination of the identified elementary functions. Accordingly, the functions for blending surfaces are constructed from these elementary functions, which transform sixth-order partial differential equations for C2 surface blending into sixth-order ordinary differential equations (ODEs). We investigate the analytical solutions of the transformed sixth-order ordinary differential equations subjected to corresponding blending boundary constraints. With the developed analytical PDE-based method, we solve C2 continuous surface blending problems. The surface blending example presented in this paper indicates that the developed method is simple and easy to use. It can be used to effectively control the shape of blending surfaces and at the same time exactly satisfy C2 continuous blending boundary constraints. Full article
(This article belongs to the Special Issue Mathematical Applications in Computer Graphics)
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