Manufactured aero-engine blades are normally inspected in sections. Given discrete sectionspecific data points, the related geometric error evaluation task for three-dimensional tolerances of the blades is challenging and not yet well studied by researchers. Particularly, the existing method shows limited effectiveness in detecting position error and difficulty in accurate estimation of orientation error of airfoil sections. Moreover, touch-probes on a coordinate measuring machine are traditionally used to collect sectional coordinate data, which is a lengthy process as the data is collected through probe contact with the blade surface. Blade manufacturers would rather use 3D laser scanning that can complete data acquisition much faster. However, this poses a new challenge to data analysis. The collected set of points, referred to as point cloud, is all over the surface rather than at the desired, pre-specified sections. Thus, generating reliable section-specific data from the massive, unorganized scanned data points remains a problem to be solved.

This thesis first presents a new methodology for evaluating three-dimensional tolerances of airfoil sections based on reconstructing the airfoil profiles from section-specific data points. According to a given measurement uncertainty, a progressive curve fitting scheme is proposed to generate the airfoil profile that meets the uncertainty constraint. Subsequently, the profile is utilized in related feature extraction of the proposed error evaluation approach. The second part of the thesis focuses on generating the reliable section-specific data points from the complete surface scan. An adaptive surface projection of data points onto the pre-specified section plane is proposed. A localized surface-fitting scheme is devised for this purpose. The main challenge lies in the selection of local data points, referred to as local neighborhood, for surface fitting. In particular, with the non-uniform distribution of data points in a noisy point cloud, existing neighborhood selection methods lead to biased fitting results. To avoid bias, a method of establishing balanced local neighborhood for surface fitting is proposed. An automated technique is also presented for systematic identification of eligible points for projection. The proposed computational framework in this thesis enables fully automatic and accurate evaluation of geometric errors using the latest high-speed geometric inspection platform.