  Recent years have witnessed the surge of learned representations that
directly build upon point clouds. Though becoming increasingly expressive, most
existing representations still struggle to generate ordered point sets.
Inspired by spherical multi-view scanners, we propose a novel sampling model
called Spotlights to represent a 3D shape as a compact 1D array of depth
values. It simulates the configuration of cameras evenly distributed on a
sphere, where each virtual camera casts light rays from its principal point
through sample points on a small concentric spherical cap to probe for the
possible intersections with the object surrounded by the sphere. The structured
point cloud is hence given implicitly as a function of depths. We provide a
detailed geometric analysis of this new sampling scheme and prove its
effectiveness in the context of the point cloud completion task. Experimental
results on both synthetic and real data demonstrate that our method achieves
competitive accuracy and consistency while having a significantly reduced
computational cost. Furthermore, we show superior performance on the downstream
point cloud registration task over state-of-the-art completion methods.
