Discrete isogonal nets with similar parallelograms

Wang, Hui, Li, Xinye, Li, Zhi and Wang, Cheng (2025) Discrete isogonal nets with similar parallelograms. Computer-Aided Design, 189. ISSN 0010-4485

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Abstract

High-quality surface designs are increasingly significant in industrial applications, such as architecture and product design, yet they pose challenges in balancing visual appeal and functional requirements. Isogonal nets (I-nets) stand out for their aesthetically pleasing patterns and engineering practicality. However, constructing such nets remains difficult due to their dependence on complex angle constraints or a narrow focus on orthogonal scenarios. We propose a novel representation and construction method for I-nets characterized by similar mid-edge subdivided parallelograms in the quad faces. This approach achieves a simple yet versatile representation that generalizes orthogonal nets and extends to the construction of isogonal 4-webs (I-webs). By focusing on constraining edge ratios, our method enables efficient integration into mesh optimization algorithms. We demonstrate the effectiveness of I-nets and I-webs in freeform shapes through conformal mapping and numerical optimization. Experiments on various surfaces validate our method, showcasing its potential for both theoretical advancements and practical applications.

Item Type:	Article
Additional Information:	Funding information: This work was supported by the Xi’an Jiaotong University Young Talent Support Program, China (No. 11303225010702). Zhi Li was supported by the Australian Research Council, Australia (No. FL190100014). Cheng Wang was supported by the University of East Anglia Internal Research Fund, United Kingdom (No. 60002351FA1).
Uncontrolled Keywords:	4* ,/dk/atira/pure/researchoutput/REFrank/4_
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Data Science and AI Faculty of Science > Research Groups > Visual Computing and Signal Processing
Depositing User:	LivePure Connector
Date Deposited:	29 Aug 2025 15:30
Last Modified:	31 Aug 2025 06:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/100250
DOI:	10.1016/j.cad.2025.103937

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