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.

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