# On the Development of a Surrogate Modelling Toolbox for Virtual Assembly
## Appendix A  
\begin{tabular}{l l l l} \hline \hline \multicolumn{2}{c}{Sumpet/G Operation} & \multicolumn{2}{c}{Description} & \multicolumn{2}{c}{Reference} & \multicolumn{2}{c}{Level of Destination} \\ \hline
**Point set selection** & \multicolumn{2}{c}{**Detection of relevant subsets of points**} \\ \hline
**Course Matching** & \multicolumn{2}{c}{Determine initial position before assembly closely to the final position [35]} \\ \hline
**Unconstrained Best Fit** \({}^{\text{A}}\) & \multicolumn{2}{c}{Alignment as provided by Iterative Closest} & [71] & \\  & \multicolumn{2}{c}{Point-Algorithm (ICP)} & \\ \hline
**Constrained Regular Geometries** \({}^{\text{A}}\) & \multicolumn{2}{c}{Alignment as provided by the ISO System for Geometrical} & \\  & \multicolumn{2}{c}{Product Specification (GPS) datum definition in ISO 5459 [28]} & \\ \hline
**Segmentation of contact faces** \({}^{\text{A}}\) & \multicolumn{2}{c}{Determination of subsets \(\text{s}_{1}\subseteq\text{S}_{1}\) and \(\text{s}_{2}\subseteq\text{S}_{2}\) that are by mechanical design provided as} \\  & \multicolumn{2}{c}{contact faces} \\ \hline  & \multicolumn{2}{c}{Determination of hypothetically corresponding, salient key} & \\  & \multicolumn{2}{c}{features in S\({}_{1}\) and S\({}_{2}\), such as Principal Curvature or Harris} & [35,72] & \\  & \multicolumn{2}{c}{Algorithm [72]} & \\ \hline
**Semantic segmentation** \({}^{\text{A}}\) & \multicolumn{2}{c}{Determination of subsets corresponding to geometrical} & \\  & \multicolumn{2}{c}{primitives} & \\ \hline
**Patch Selection** (CAD based)** \({}^{\text{A}}\) & \multicolumn{2}{c}{Determination of subsets corresponding to a maximal distance} & \\  & \multicolumn{2}{c}{to a nominal geometry such as a CAD file} & \\ \hline
**Pointset morphology** & \multicolumn{2}{c}{Description and manipulation of the surface morphology} & \\  & \multicolumn{2}{c}{Definition of Orfset and Intersection** \({}^{\text{A}}\)} & \multicolumn{2}{c}{Definition of a certain offset between faces (e.g., to simulate} \\  & \multicolumn{2}{c}{adhesive gap) or of an intersection (virtual penetration) to} & \\  & \multicolumn{2}{c}{simulate surface flattening or material loss (e.g., due to melting} \\  & \multicolumn{2}{c}{welding bead)} & \\ \hline Morphological Filtering \({}^{\text{A}}\) & \multicolumn{2}{c}{[51,52]} & \\ \hline
**Hertarian Contact** & \multicolumn{2}{c}{Manipulate surfaces locally to simulate surface flattening due to mechanical load} & [41] & \\ \hline
**Method of Influence Coefficients (MIC)** \({}^{\text{A}}\) & \multicolumn{2}{c}{Linearized computation of elastic deformation due to} & [50,57] & \\  & \multicolumn{2}{c}{mechanical load} & \\ \hline Linear Finite Element Analysis (FEA) \({}^{\text{A}}\) & \multicolumn{2}{c}{Computation of elastic deformation due to mechanical load} & [75,76] & \\ \hline
**Nonlinear FEA** \({}^{\text{A}}\) & \multicolumn{2}{c}{Computation of elastic and plastic deformation due to} & \\  & \multicolumn{2}{c}{mechanical load} & [65,66] & \\
**Objective Function** & \multicolumn{2}{c}{Searching of correspondences and the assembly position} & \\ \hline
**Modalities for Distance** & \multicolumn{2}{c}{Approaches to compute distances between S\({}_{1}\) and S\({}_{2}\)} & \\  & \multicolumn{2}{c}{} & \\ \hline
**Point to Point** \({}^{\text{B}}\) & \multicolumn{2}{c}{Distance computation discretized on single points} & [71] & \\ \hline
**Point to Plane or Triangle** \({}^{\text{B}}\) & \multicolumn{2}{c}{Triangle-based algorithms for distance calculation that more} & \\  & \multicolumn{2}{c}{precisely represent the physical distance} & \\ \hline
**Point correspondence** & \multicolumn{2}{c}{Metric considered to determine corresponding points recreating the physical contact scenario [38]} & \\ \hline
**Euclidean distance** \({}^{\text{B}}\) & \multicolumn{2}{c}{Only sufficient, when point clouds are relatively dense} & [38] & \\ \hline \hline \end{tabular}