There is no settled universal 3D representation for geometry with many alternatives such as point clouds, meshes, implicit functions, and voxels to name a few. In this work, we present a new, compelling alternative for representing shapes using a sequence of cross-sectional closed loops. The loops across all planes form an organizational hierarchy which we leverage for autoregressive shape synthesis and editing. Loops are a non-local description of the underlying shape, as simple loop manipulations (such as shifts) result in significant structural changes to the geometry. This is in contrast to manipulating local primitives such as points in a point cloud or a triangle in a triangle mesh. We further demonstrate that loops are intuitive and natural primitive for analyzing and editing shapes, both computationally and for users.

翻译：目前几何表示尚无统一的通用三维表示方法，存在点云、网格、隐式函数、体素等多种替代方案。本工作中，我们提出一种使用横截面闭合循环序列表示形状的新颖且具有竞争力的替代方案。所有平面上的循环构成一种层级组织结构，我们利用该结构实现自回归形状合成与编辑。循环是对底层形状的非局部描述，简单的循环操作（如平移）即可引发几何结构的显著变化。这与操作局部基元（如点云中的点或三角网格中的三角形）形成鲜明对比。我们进一步证明，无论在计算层面还是对用户而言，循环都是用于分析和编辑形状的直观且自然的基元。