Understanding human perception is critical to the design of effective visualizations. The relative benefits of using 2D versus 3D techniques for data visualization is a complex decision space, with varying levels of uncertainty and disagreement in both the literature and in practice. This study aims to add easily reproducible, empirical evidence on the role of depth cues in perceiving structures or patterns in 3D point clouds. We describe a method to synthesize a 3D point cloud that contains a 3D structure, where 2D projections of the data strongly resemble a Gaussian distribution. We performed a within-subjects structure identification study with 128 participants that compared scatterplot matrices (canonical 2D projections) and 3D scatterplots under three types of motion: rotation, xy-translation, and z-translation. We found that users could consistently identify three separate hidden structures under rotation, while those structures remained hidden in the scatterplot matrices and under translation. This work contributes a set of 3D point clouds that provide definitive examples of 3D patterns perceptible in 3D scatterplots under rotation but imperceptible in 2D scatterplots.