The paper has been conditionally accepted for presentation at the Symposium on Solid and Physical Modeling (SPM 2025) scheduled to take place in Hangzhou, China, from October 29 to November 2, 2025.

Additionally, it will be presented as a poster paper with a 10-minute oral presentation at the International Conference on Geometric Modeling and Processing (GMP2025), which will be held at Washington University in St. Louis, US, from May 28 to 30, 2025.

Hui Wang* (corresponding author), Xinye Li, Zhi Li, and Cheng Wang

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.

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