Industry 4.0 comprises a wide spectrum of developmental processes within the management of manufacturing and chain production. Presently, there is a huge effort to automate manufacturing and have automatic control of the production. This intention leads to the increased need for high-quality methods for digitization and object reconstruction, especially in the area of reverse engineering. Commonly used scanning software based on well-known algorithms can correctly process smooth objects. Nevertheless, they are usually not applicable for complex-shaped models with sharp features. The number of the points on the edges is extremely limited due to the principle of laser scanning and sometimes also low scanning resolution. Therefore, a correct edge reconstruction problem occurs. The same problem appears in many other laser scanning applications, i.e., in the representation of the buildings from airborne laser scans for 3D city models. We focus on a method for preservation and reconstruction of sharp features. We provide a detailed description of all three key steps: point cloud segmentation, edge detection, and correct B-spline edge representation. The feature detection algorithm is based on the conventional region-growing method and we derive the optimal input value of curvature threshold using logarithmic least square regression. Subsequent edge representation stands on the iterative algorithm of B-spline approximation where we compute the weighted asymmetric error using the golden ratio. The series of examples indicates that our method gives better or comparable results to other methods.