Geometric Modelling for 3D Point Clouds of Elbow Joints in Piping Systems

Pipe elbow joints exist in almost every piping system supporting many important applications such as clean water supply. However, spatial information of the elbow joints is rarely extracted and analyzed from observations such as point cloud data obtained from laser scanning due to lack of a complete geometric model that can be applied to different types of joints. In this paper, we proposed a novel geometric model and several model adaptions for typical elbow joints including the 90° and 45° types, which facilitates the use of 3D point clouds of the elbow joints collected from laser scanning. The model comprises translational, rotational, and dimensional parameters, which can be used not only for monitoring the joints' geometry but also other applications such as point cloud registrations. Both simulated and real datasets were used to verify the model, and two applications derived from the proposed model (point cloud registration and mounting bracket detection) were shown. The results of the geometric fitting of the simulated datasets suggest that the model can accurately recover the geometry of the joint with very low translational (0.3 mm) and rotational (0.064°) errors when ±0.02 m random errors were introduced to coordinates of a simulated 90° joint (with diameter equal to 0.2 m). The fitting of the real datasets suggests that the accuracy of the diameter estimate reaches 97.2%. The joint-based registration accuracy reaches sub-decimeter and sub-degree levels for the translational and rotational parameters, respectively.