Discrete isogonal nets with similar parallelograms

Authors: Hui Wang, Xinye Li, Zhi Li, Cheng Wang

Time: 2025/08/12

Journal: Computer-Aided Design

DOI: https://doi.org/10.1016/j.cad.2025.103937

Highlights

• Simple isogonal nets (I-nets) align with current net definitions.

• I-nets use two fixed edge ratios for rapid mesh optimization.

• We debut isogonal 4-webs (I-webs) as a new geometry.

• Conformal maps and optimizations showcase I-nets and I-webs.

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 charac- terized 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.

Keywords: isogonal nets, isogonal webs, checkboard pattern, discrete differential geometry, conformal parameterization, mesh optimization, computational design, high-quality quad mesh

Citation

H. Wang, X. Li, Z. Li, C. Wang, “Discrete isogonal nets with similar parallelograms,” Computer-Aided Design, vol. 189, 103937, 2025.

BibTeX

@article{Wang2025103937,
title = {Discrete isogonal nets with similar parallelograms},
journal = {Computer-Aided Design},
volume = {189},
pages = {103937},
year = {2025},
issn = {0010-4485},
doi = {https://doi.org/10.1016/j.cad.2025.103937},
url = {https://www.sciencedirect.com/science/article/pii/S0010448525000983},
author = {Hui Wang and Xinye Li and Zhi Li and Cheng Wang},
}