We develop and test machine learning methods for the prediction of coarse 3D protein structures, where a protein is represented by a set of rigid rods associated with its secondary structure elements (alpha-helices and beta-strands). First, we employ cascades of recursive neural networks derived from graphical models to predict the relative placements of segments. These are represented as discretized distance and angle maps, and the discretization levels are statistically inferred from a large and curated dataset. Coarse 3D folds of proteins are then assembled starting from topological information predicted in the first stage. Reconstruction is carried out by minimizing a cost function taking the form of a purely geometrical potential. We show that the proposed architecture outperforms simpler alternatives and can accurately predict binary and multiclass coarse maps. The reconstruction procedure proves to be fast and often leads to topologically correct coarse structures that could be exploited as a starting point for various protein modeling strategies. The fully integrated rod-shaped protein builder (predictor of contact maps + reconstruction algorithm) can be accessed at http://distill.ucd.ie/.