3D scanning as a technique to digitize objects in reality and create their 3D models, is used in many fields and areas. Though the quality of 3D scans depends on the technical characteristics of the 3D scanner, the common drawback is the smoothing of fine details, or the edges of an object. We introduce SepicNet, a novel deep network for the detection and parametrization of sharp edges in 3D shapes as primitive curves. To make the network end-to-end trainable, we formulate the curve fitting in a differentiable manner. We develop an adaptive point cloud sampling technique that captures the sharp features better than uniform sampling. The experiments were conducted on a newly introduced large-scale dataset of 50k 3D scans, where the sharp edge annotations were extracted from their parametric CAD models, and demonstrate significant improvement over state-of-the-art methods.