Low-distortion planar embedding of rod-based structures

2026-02-08

AI Summary

This work addresses the inefficiencies in designing and fabricating three-dimensional rod-based structures, which often stem from geometric complexity and the lack of effective two-dimensional representations. To overcome this challenge, the authors propose a low-distortion planar embedding algorithm that optimizes geometric constraints to preserve critical lengths and angles while guaranteeing overlap-free layouts. The method establishes, for the first time, a unified mapping framework applicable to both pure rod networks and hybrid rod-surface structures, balancing geometric fidelity with manufacturability. Experimental validation demonstrates that the approach consistently produces high-fidelity, self-intersection-free 2D unfoldings across a variety of complex 3D rod-based geometries, significantly enhancing both design flexibility and fabrication efficiency.

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Abstract

Rod-based structures are commonly used in practical applications in science and engineering. However, in many design, analysis, and manufacturing tasks, handling the rod-based structures in three dimensions directly is generally challenging. To simplify the tasks, it is usually more desirable to achieve a two-dimensional representation of the rod-based structures via some suitable geometric mappings. In this work, we develop a novel method for computing a low-distortion planar embedding of rod-based structures. Specifically, we identify geometrical constraints that aim to preserve key length and angle quantities of the 3D rod-based structures and prevent the occurrence of overlapping rods in the planar embedding. Experimental results with a variety of rod-based structures are presented to demonstrate the effectiveness of our approach. Moreover, our method can be naturally extended to the design and mapping of hybrid structures consisting of both rods and surface elements. Altogether, our approach paves a new way for the efficient design and fabrication of novel three-dimensional geometric structures for practical applications.

Problem

• rod-based structures
• planar embedding
• low-distortion
• geometric mapping
• 3D-to-2D representation

Innovation

• planar embedding
• rod-based structures
• low-distortion mapping
• geometric constraints
• hybrid structures