The last two decades have witnessed how threedimensional (3D) point cloud scanning and registration algorithms have become increasingly popular in areas as diverse as cinematography, robotics, and medicine, among others. Despite their broad application range, such algorithms remain to be computationally demanding and difficult to implement. In particular, the task of choosing and implementing suitable registration-pipeline processes for specific applications continues to be challenging in most practical cases. This paper presents the implementation of a point cloud stitching system to produce 360° 3D images from individual, partial views of a solid model. Performance analyses and evaluations supporting the decisionmaking process allow for identifying factors leading to the best accuracy and computational speed of the iterative closest point (ICP) registration algorithms considered for the task at hand. The outcomes of our analysis lead to interesting findings related to two well-known ICP variants, while also providing useful implementation guidelines for developing a practical 360° 3D scanning system.