We propose a novel method for 3D object reconstruction from a sparse set of views captured from a 360-degree calibrated camera rig. We represent the object surface through a hybrid model that uses both an MLP-based neural representation and a triangle mesh. A key contribution in our work is a novel object-centric sampling scheme of the neural representation, where rays are shared among all views. This efficiently concentrates and reduces the number of samples used to update the neural model at each iteration. This sampling scheme relies on the mesh representation to ensure also that samples are well-distributed along its normals. The rendering is then performed efficiently by a differentiable renderer. We demonstrate that this sampling scheme results in a more effective training of the neural representation, does not require the additional supervision of segmentation masks, yields state of the art 3D reconstructions, and works with sparse views on the Google's Scanned Objects, Tank and Temples and MVMC Car datasets.