A fast and fully automatic design of 3D printed patient-specific cranial implants is highly desired in cranioplasty - the process to restore a defect on the skull. We formulate skull defect restoration as a 3D volumetric shape completion task, where a partial skull volume is completed automatically. The difference between the completed skull and the partial skull is the restored defect; in other words, the implant that can be used in cranioplasty. To fulfill the task of volumetric shape completion, a fully data-driven approach is proposed. Supervised skull shape learning is performed on a database containing 167 high-resolution healthy skulls. In these skulls, synthetic defects are injected to create training and evaluation data pairs. We propose a patch-based training scheme tailored for dealing with high-resolution and spatially sparse data, which overcomes the disadvantages of conventional patch-based training methods in high-resolution volumetric shape completion tasks. In particular, the conventional patch-based training is applied to images of high resolution and proves to be effective in tasks such as segmentation. However, we demonstrate the limitations of conventional patch-based training for shape completion tasks, where the overall shape distribution of the target has to be learnt, since it cannot be captured efficiently by a sub-volume cropped from the target. Additionally, the standard dense implementation of a convolutional neural network tends to perform poorly on sparse data, such as the skull, which has a low voxel occupancy rate. Our proposed training scheme encourages a convolutional neural network to learn from the high-resolution and spatially sparse data. In our study, we show that our deep learning models, trained on healthy skulls with synthetic defects, can be transferred directly to craniotomy skulls with real defects of greater irregularity, and the results show promise for clinical use. Project page: https://github.com/Jianningli/MIA.