Low-distortion planar embedding of rod-based structures

TL;DR

This paper introduces a novel method for creating low-distortion 2D representations of 3D rod-based structures, aiding design, analysis, and manufacturing tasks by preserving key geometric features.

Contribution

The work develops a new geometric mapping technique that maintains length and angle constraints while preventing overlaps in planar embeddings of rod structures.

Findings

Effective preservation of geometric features in embeddings

Reduction of overlaps in 2D representations

Extension to hybrid rod-surface structures

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.