## 1 Introduction and Literature Review  
Marine propeller blades have highly complex and variable curved surface geometries, and constructing accurate computer-aided design (CAD) models directly from physical prototypes is challenging. Moreover, machined blades often deviate considerably from their original CAD models, and this machining variation can directly affect propulsion efficiency and service life. Therefore, enhancing the capability and efficiency of blade inspection is essential for substantially improving product quality and performance. In inspections of propeller blades, the focus is on critical areas such as the leading edge, trailing edge, suction surface, and pressure surface. Because of the sharp curvature at the leading and trailing edges and the relatively thin profile of blades, issues such as twisting and poor bonding with the hub are common. By contrast, the suction and pressure surfaces are relatively flat. To ensure structural accuracy and performance stability, the three-dimensional surface model of a blade must be precisely measured and reconstructed. Furthermore, minor surface deviations or defects on propeller blades can trigger inertial cavitation during high-speed rotation, which can reduce propulsion efficiency and damage the blades' surfaces. Accordingly, high-precision and high-efficiency measurement technology needs to be developed to ensure the quality of marine propellers. Because of the twisted and intricate geometry of marine propellers, the design, machining, and performance analysis of their blades is difficult [1; 2]. To achieve precise surface geometry and high propulsion performance, blades are typically manufactured using precision casting techniques, particularly the lost-wax casting process. However, during the drying and cooling phases of this process, the wax models are prone to deformation, which can cause substantial geometric deviations between the final cast components and original CAD models. Casting-induced deformation not only complicates subsequent geometric inspection but also hinders the development of effective machining compensation strategies [3], thereby compromising overall manufacturing accuracy and the operational performance of propellers. Examining the geometric deviations generated in conventional manufacturing, [PERSON] et al. [4] proposed the use of three-dimensional scanning technology to generate point cloud data, which were then employed for manufacturing quality feedback, and the construction of digital twins. Their method provides a quantifiable basis on which deviations can be corrected in the design and manufacturing processes. In their study, a 3D scanner was employed to acquire point cloud data from propeller blades. The data were then processed using Voronoi partitioning and Delaunay triangulation algorithms to reconstruct the geometric features of the blades' cross sections, including key parameters such as the camber line, chord length, location of maximum thickness, and skew angle. Found to have both strong versatility and a high degree of potential for automation, this approach complies with the geometric tolerance standards specified in ISO 484 [5] and is applicable to complex blade geometries with high skew angles and large chord length variation. Marine propellers are the core component of underwater propulsion systems; their geometric configuration and material properties exert decisive influences on propulsion efficiency and cavitation resistance. [PERSON] et al. [6] noted that conventional manual machining processes are insufficient to meet the current stringent requirements of high precision and high manufacturing consistency. Consequently, the industry is increasingly adopting computer numerical control (CNC) techniques. These techniques offer high repeatability and machining accuracy, greatly reduce the need for manual refinement, and enhance both manufacturing efficiency and quality stability.