MESH ALGORITHMS AND THEIR RELATIONSHIP WITH SPLINES: THEORY, COMPUTATION, AND PRACTICAL APPLICATIONS

Authors

  • Behruz Ulug‘bek ugli Kuvvatov Asia International University, Faculty of Social Sciences and Engineering, Bukhara, Uzbekistan

DOI:

https://doi.org/10.55640/

Keywords:

Mesh algorithms, triangle mesh, quad mesh, mixed mesh, triangulation, remeshing, subdivision, Catmull–Clark, Loop subdivision, B-spline, NURBS, parametric surfaces, tessellation, CAD/CAM, 3D modeling, surface reconstruction, spline-mesh conversion, computer graphics.

Abstract

The accurate representation of complex surfaces is central to computer graphics, CAD/CAM systems, 3D modeling, and scientific visualization. This study examines the mathematical foundations, algorithmic strategies, and computational methods underlying mesh generation and processing, emphasizing triangle, quad, and mixed meshes. It also explores the relationship between meshes and spline surfaces, including B-splines and NURBS, with practical examples illustrating how subdivision, remeshing, and spline fitting can be quantified and validated. Experiments demonstrate how discrete and parametric models can be integrated efficiently, maintaining geometric fidelity while optimizing computational resources.

Downloads

Download data is not yet available.

References

1.Babaev, S., Olimov, N., Imomova, S., & Kuvvatov, B. (2024). Construction of natural L spline in W2, σ (2, 1) space. AIP Conference Proceedings, 3004(1).

2.Behruz Ulug‘bek o‘g‘li Q. (2023). Use of artificial nervous systems in modeling. Multidisciplinary Journal of Science and Technology, 3(5), 269–273.

3.Behruz Ulug‘bek o‘g‘li Q. (2024). Eyler integrallari va Mittag-Leffler funksiyasining zamonaviy fizika va matematikadagi roli. Международный журнал научных исследователей, 9(1), 96–100.

4.Behruz Ulug‘bek o‘g‘li Q. (2025). Chiziqli algebra va splaynlar: chiziqli tenglamalar tizimlari va matritsalar asosida splayn hosil qilish. ИКРО журнал, 15(1), 773–776.

5.Behruz Ulugbek o‘g‘li Q. (2024). Informatika fanini o‘qitishda interfaol metodlardan foydalanish. PEDAGOG, 7(6), 52–62.

6.Behruz Ulugbek o‘g‘li Q. (2023). Mobil ilovalar yaratish va ularni bajarish jarayoni. International Journal of Scientific Researchers, 2(2).

7.Behruz Ulugbek o‘g‘li Q., & Quvvatov. (2024). Adobe Photoshop CC dasturida ishlash. PEDAGOG, 7(4), 390–396.

8.Behruz Ulugbek o‘g‘li Q., & Quvvatov. (2024). Fundamentals of algorithm and programming in MathCAD software. Multidisciplinary Journal of Science and Technology, 4(3), 410–418.

Downloads

Published

2025-12-08

Issue

Vol. 4 No. 11 (2025): Journal of Multidisciplinary Sciences and Innovations

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors retain the copyright of their manuscripts, and all Open Access articles are disseminated under the terms of the Creative Commons Attribution License 4.0 (CC-BY), which licenses unrestricted use, distribution, and reproduction in any medium, provided that the original work is appropriately cited. The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations.

How to Cite

MESH ALGORITHMS AND THEIR RELATIONSHIP WITH SPLINES: THEORY, COMPUTATION, AND PRACTICAL APPLICATIONS. (2025). Journal of Multidisciplinary Sciences and Innovations, 4(11), 663-666. https://doi.org/10.55640/

Similar Articles

1-10 of 332

You may also start an advanced similarity search for this article.