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.

翻译：杆状结构在科学与工程的实际应用中十分常见。然而，在许多设计、分析与制造任务中，直接在三维空间中处理杆状结构通常具有挑战性。为了简化这些任务，通常更希望通过合适的几何映射获得杆状结构的二维表示。本研究提出了一种计算杆状结构低失真平面嵌入的新方法。具体而言，我们确定了几何约束，旨在保持三维杆状结构的关键长度与角度量，并防止平面嵌入中杆件发生重叠。通过对多种杆状结构的实验结果，展示了本方法的有效性。此外，我们的方法可以自然地扩展到由杆件与表面单元组成的混合结构的设计与映射。总之，本方法为实际应用中新型三维几何结构的高效设计与制造开辟了新途径。