🤖 AI Summary
为解决双曲几何在欧氏空间中难以直观展示的问题，本文通过将双曲表面离散化为网格，并优化变形能量以匹配双曲平面中的边长，从而在欧氏空间中嵌入双曲表面。
📝 Abstract
Hyperbolic geometry exhibits geometric phenomena, such as fast area growth, that are difficult to visualize faithfully in Euclidean space, and which standard models like the Poincar\'e disk can obscure. To bring hyperbolic geometry to life, we embed hyperbolic surfaces in Euclidean space by discretizing the surfaces into meshes, and minimizing a distortion energy so that the edge lengths in the embeddings match those in the hyperbolic plane. The resulting surfaces buckle and ruffle to accommodate the extra area, making visible what flat models hide. We present exemplary illustrations, such as embedded disks, equidistant strips, diverging geodesics, and also artistic organic-like renders. We discuss our use of these models, as renders and 3D prints, in research talks, public engagement, outreach, and education.