## 3 Functionality of Key Modules
### Curvature Computation  
The evaluation of curvature is a differential geometry task [93]. For each tessellated surface point, it can be computed based on the angles and normal vectors of each attached cell [94]. The mean curvature \(H\) and Gaussian curvature \(K\) are most commonly evaluated, but the principal values of the surface curvature may also be computed. As curvature assessment is extremely sensitive to triangulation [95], one may use regular grid spacings and smooth the obtained values subsequently. Otherwise, methods featuring non-regular tessellations, such as [96], can be invoked, although the size of the neighborhood evaluation sphere must be known a priori. To obtain the curvature of planar defects, the closed node loop of the defect circumference is defined as a VTK poly-line object, with points of the poly-line mapping the input nodes of the imperfection. As the defect contour often possesses non-regular grid spacing--as in the case of the mesh shown in Figure 5a--the original poly-line is sub-divided using spline interpolation. To minimize the effect of the interpolation window at the start and end of the line, the defect contour-related poly-line is extended as a spatial thread with three turns. The fine-spaced sub-divided poly-line segment of the second turn is projected back to the initial _xy_-plane. The fine-spaced poly-line is dragged normal to the _xy_-plane and the obtained poly-data surface is subsequently tessellated. The VTK toolbox can then be utilized to compute the curvature of the evenly tessellated surface representing the defect contour [97]. The mean curvature is calculated for each triangle of the generated surface. Finally, the curvature values are smoothed with different filter lengths in order to study its value change if more neighboring data points are included. The notch radius is evaluated as \(\rho=1/(2H)\), as the second principal curvature is zero. The curvature computation script normalizes the input defect contour first. Thus, the depicted poly-data in Figure 7a lead to a value of one in the curvature map for the circular hole. As the position of the defect contour nodes are unchanged in Methods 2 and 3--both using the initial defect mesh pattern--the curvature-related results were identical for the sub-case method and the superposition method. The curvature computation was conducted for the four planar defects shown in Figure 7, having different extent, shape, and mesh-seed values. The applied control radius \(R_{c}=0.19\) mm was kept constant for all geometries, and the number of sub-divisions for each defect contour poly-line and applied filter distances varied. The circular defect in Figure 7a has a maximum extent of two millimeters (respectively one-millimeter radius), and the defect circumference was defined using 42 points. The elliptical defects in Figure 7b,c are geometrically identical, but the latter was rotated by thirty degrees in order to demonstrate that the curvature calculation is independent of the center axis of the defect. The ellipse has a maximum extent of four millimeters and 100 points along the circumference. The elongated planar defect shown in Figure 7d represents an arbitrarily shaped imperfection with a maximum extent of about 22 millimeters, with its geometry defined by 178 points along the circumference. The applicable curvature for each point of the refined poly-line was determined by studying the effect of varying filter lengths. The Gaussian filter distance was stepwise increased, thus changing the computed curvature to lower values. This is clearly visible in the case of the elliptical hole-in-plate cases (see Figure 7b,c). The obtained curvature was evaluated as the mean value of the contiguous filter distance block with similar curvature values. For the circular hole-in-plate (Figure 7a), the thereby evaluated radius was quite close to one, as the obtained curvature map was nearly constant.