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Mathematics
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Research on Computational Geometry and Computer Graphics
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Research on Computational Geometry and 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: 25 November 2025 | Viewed by 3529

Special Issue Editor

Dr. Shiqing Xin

E-Mail Website
Guest Editor
School of Computer Science and Technology, Shandong University, Qingdao 266237, China
Interests: digital geometry processing; geometric optimization; 3D reconstruction; computational geometry

Special Issue Information

Dear Colleagues,

Computational geometry focuses on solving geometric problems and optimizing spatial algorithms, while computer graphics is concerned with creating, rendering, and interacting with visual content. Both fields have practical applications in a wide range of industries, from video games and movies to scientific simulations and engineering design.

This Special Issue will focus on recent theoretical and computational studies in the areas of computational geometry and computer graphics. Topics include (but are not limited to) the following:

  • Geometric algorithms;
  • Geometric data structures;
  • Geometric optimization;
  • Geometric modeling;
  • Robotics and motion planning;
  • Geometry processing;
  • Continuous/discrete representation of curves and surfaces;
  • Shape analyses;
  • Discrete differential geometry;
  • Shape optimization;
  • Geometric feature modeling and recognition;
  • Geometric learning/data-driven approaches.

Geometric deep learning techniques for 3D modeling are highly encouraged in this Special Issue.

Dr. Shiqing Xin
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

  • computational geometry
  • computer graphics
  • geometric algorithms
  • shape optimization
  • geometric deep learning

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

Published Papers (2 papers)

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Research

16 pages, 6694 KiB  
Article
The Various Radii Circle Packing Problem in a Triangle
by Ching-Shoei Chiang and Yi-Ting Chiang
Mathematics 2024, 12(17), 2733; https://doi.org/10.3390/math12172733 - 31 Aug 2024
Cited by 1 | Viewed by 1396
Abstract
Malfatti’s problem is the problem of fitting three circles into a triangle such that they are tangent to each other and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to include Tn = [...] Read more.
Malfatti’s problem is the problem of fitting three circles into a triangle such that they are tangent to each other and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to include Tn = 1 + 2 + … + n circles inside the triangle with special tangency properties among the circles and triangle sides; this problem is referred to as the extended Malfatti problem or the Tri(Tn) problem. In the extended Malfatti problem, the number of circles in the triangle is a triangle number because the tangency properties between the internal circles and the three sides of the triangle have a special type of structure; that is, the corner circle is tangent to two sides of the triangle and two other circles, the boundary circles are tangent to one side of the triangle and four other circles, and the inner circles are always tangent to six other circles. The circles we find in the extended Malfatti problem have the following property: the smallest and largest radii of the circles differ to a great extent. In the study presented herein, we propose algorithms to solve the problem that the tangency properties between the circles and the sides of the triangle are not fixed, so that the number of circles in the triangle is not necessarily a triangle number. The purpose of this change is to attempt to establish the radii of the circles in the triangle within a small range. Full article
(This article belongs to the Special Issue Research on Computational Geometry and Computer Graphics)
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19 pages, 12147 KiB  
Article
Convex Quadratic Programming for Computing Geodesic Distances on Triangle Meshes
by Shuangmin Chen, Nailei Hei, Shun Hu, Zijia Yue and Ying He
Mathematics 2024, 12(7), 993; https://doi.org/10.3390/math12070993 - 27 Mar 2024
Viewed by 1415
Abstract
Querying the geodesic distance field on a given smooth surface is a fundamental research pursuit in computer graphics. Both accuracy and smoothness serve as common indicators for evaluating geodesic algorithms. In this study, we argue that ensuring that the norm of the triangle-wise [...] Read more.
Querying the geodesic distance field on a given smooth surface is a fundamental research pursuit in computer graphics. Both accuracy and smoothness serve as common indicators for evaluating geodesic algorithms. In this study, we argue that ensuring that the norm of the triangle-wise estimated gradients is not larger than 1 is preferable compared to the widely used eikonal condition. Inspired by this, we formulate the geodesic distance field problem as a Quadratically Constrained Linear Programming (QCLP) problem. This formulation can be further adapted into a Quadratically Constrained Quadratic Programming (QCQP) problem by incorporating considerations for smoothness requirements. Specifically, when enforcing a Hessian-energy-based smoothing term, our formulation, named QCQP-Hessian, effectively mitigates the cusps in the geodesic isolines within the near-ridge area while maintaining accuracy in the off-ridge area. We conducted extensive experiments to demonstrate the accuracy and smoothness advantages of QCQP-Hessian. Full article
(This article belongs to the Special Issue Research on Computational Geometry and Computer Graphics)
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