In contrast to 2D scatterplots, the existing 3D variants have the advantage of showing one additional data dimension, but suffer from inadequate spatial and shape perception and therefore are not well suited to display structures of the underlying data. We improve shape perception by applying a new illumination technique to the pointcloud representation of 3D scatterplots. Points are classified as locally linear, planar, and volumetric structuresœôòôaccording to the eigenvalues of the inverse distance-weighted covariance matrix at each data element. Based on this classification, different lighting models are applied: codimension-2 illumination, surface illumination, and emissive volumetric illumination. Our technique lends itself to efficient GPU point rendering and can be combined with existing methods like semi-transparent rendering, halos, and depth or attribute based color coding. The user can interactively navigate in the dataset and manipulate the classification and other visualization parameters. We demonstrate our visualization technique by showing examples of multi-dimensional data and of generic pointcloud data.