Geometric Modeling of Complex Shaped Bodies Using R-Functions

DOI

10.2991/978-94-6239-666-1_7How to use a DOI?

Keywords

R-functions; Geometric Modeling; Implicit Surfaces; Complex Shapes; CAD; CAGD (Computer-Aided Geometric Design); Solid Modeling; Shape Representation; Boolean Operations; Computer Graphics

Abstract

The accurate and efficient representation of complex geometric shapes is a critical challenge in various fields, including computer-aided design (CAD), computer graphics, simulation, and manufacturing. Traditional methods often struggle to handle intricate and organic shapes, necessitating the development of more versatile and robust modeling techniques. This paper explores the application of R-functions for geometric modeling of complex shaped bodies. R-functions, with their ability to define implicit surfaces, offer a powerful alternative to conventional explicit representations. This study delves into the theoretical foundations of R-functions, demonstrating their ability to combine multiple geometric primitives and perform complex Boolean operations seamlessly. We present several examples showcasing the effectiveness of R-functions in modeling a variety of intricate shapes, including both man-made and organic forms. Furthermore, we discuss the advantages and limitations of this approach, along with potential avenues for further research, such as optimization techniques and integration with other geometric modeling tools. The results demonstrate the promise of R-functions as a robust and efficient tool for geometric modeling of complex shapes, contributing to the advancement of shape representation and analysis techniques.

Copyright

© 2026 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Download article (PDF)

TY  - CONF
AU  - Alisher Azimov
AU  - Nafisa Tairova
AU  - Dildora Sabirova
AU  - Anvar M. Rahimov
PY  - 2026
DA  - 2026/05/07
TI  - Geometric Modeling of Complex Shaped Bodies Using R-Functions
BT  - Proceedings of the 5th International Conference on Research of Agricultural and Food Technologies (I-CRAFT 2025)
PB  - Atlantis Press
SP  - 55
EP  - 62
SN  - 3005-155X
UR  - https://doi.org/10.2991/978-94-6239-666-1_7
DO  - 10.2991/978-94-6239-666-1_7
ID  - Azimov2026
ER  -