## 1 Introduction
Shape errors may significantly impact calculations, which is why CAD-based inputs should be recalculated as simpler mathematical representations. When tolerance boundaries are added, complex curvature changes can be collapsed and simplified within these boundaries and the overall inspection becomes easier. Researchers' interests focus on the whole surface as well, not only on the profile. Interesting examples can be found in the works of [PERSON] [13], [PERSON] [14], and [PERSON] [15]. Profile fluctuations can be referenced to manufacturing processes. It is possible to determine areas with the greatest deviations and re-write inspection processes to focus on them. Reverse engineering tools like Geomagic [16] are very helpful for managing data clouds and obtaining results in a short period of time. Complex shapes can be described by well-understood mathematics. [PERSON] [17] initiated a method of building simplified splines based on knots, whereas [PERSON] [18,19] followed a similar approach, extending it to surfaces. Even with noisy datasets it is always possible to simplify the overall shape and identify crucial knots to determine the shape curvature as simplified shape errors have a marginal impact on the original shape. Aero-related components with complex curvatures are still a valuable subject to develop more reliable and efficient approaches. [PERSON] [20] developed a sampling method for twisted blades to improve measurement efficiency. A very similar method was developed by [PERSON] [21] for a turbine guide vane. [PERSON] [22] focused his attention on the twist itself, to solve high-precision measurement problems with this phenomenon. Shape preserving knot removal from B-spline sections is a good starting point for defining a CMM path. Researchers have already developed some algorithms based on C1 and more sophisticated C2 connections, which are vital in modern car and aero industries. Yet, further algorithms are needed to simplify the overall math and shape efficiency. Simplification can decrease the number of defining points by up to 99%, still preserving good overall quality whilst helping to obtain the desired tolerance [23]. A good example of curve fitting for noisy data can be found in the work of [PERSON] [24] or [PERSON] [25]. There are two important handbooks for CAD based researchers: the Computer Aided Design handbook [26] and the NURBS Book [27]. [PERSON] [28] made fundamental contribution to practical aspects of knot removal that is still used in modern CAD software. Many researchers use automation and AI (artificial intelligence) in their studies [1; 7; 8; 15]. This approach is not a new trend in industry, and it is gaining more popularity every year. It really helps to improve both the time and quality of inspection, allowing fast CMM path creation, usually based on a CAD model. Automated tools also allow inspection of a given part based on the best fit position for each part in reference to the CAD ideal position, unlike conventional measurements, referring to one standardized position. Almost everything can be automated: path planning, probe adjustments and interchange, or the measuring protocol itself [29]. A smart CMM inspection lies under automation and simplification, which will be highlighted in this paper. Part development is very expensive, therefore modern engineers always provide a 3D stack-up for worst case scenario--the part calculated for all material conditions, and similarly for operating conditions. Modern tools can simulate thousands of possible scenarios according to part shape variations and help to address them all without impacting the desired part life and strength. Engineering simulation analysis should contain all adverse working environment (excessive pressure, unexpected temperature increases, unexpected shutdowns etc.). This paper describes a measurement algorithm for turbine guide vane airfoils with reference to manufacturing processes and tolerances.