Embodiments provide systems, methods, and computer storage media for fitting 3D primitives to a 3D point cloud. In an example embodiment, 3D primitives are fit to a 3D point cloud using a global primitive fitting network that evaluates the entire 3D point cloud and a local primitive fitting network that evaluates local patches of the 3D point cloud. The global primitive fitting network regresses a representation of larger (global) primitives that fit the global structure. To identify smaller 3D primitives for regions with fine detail, local patches are constructed by sampling from a pool of points likely to contain fine detail, and the local primitive fitting network regresses a representation of smaller (local) primitives that fit the local structure of each of the local patches. The global and local primitives are merged into a combined, multi-scale set of fitted primitives, and representative primitive parameters are computed for each fitted primitive.