## 5 Conclusions
### Abbreviations  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} CMM & Coordinate Measurement Machine. \\ ANOVA & ANalysis Of VAriance. \\ R\&R & Repeatability and Reproducibility. \\ FACE & A connected region on a parametric surface in \(\mathbb{R}^{3}\). \\ \(\mathcal{C}\) & Boundary representation (CAD model) of the reference geometry. \(\mathcal{C}\subset\mathbb{R}^{3}\) is a 2-manifold, represented as set of BODY, LUMPSs, FACEs, LOOPs, EDGEs, and VERTICES. \\ \(M\) & Triangular mesh \(M=(X,T)\) of the scanned workpiece. \(X=\{x_{0},x_{1},\ldots,n\}\) and \(T=\{t_{0},t_{1},\ldots,n\}\) are the points (geometry) and triangles (topology) of the mesh, respectively. \(M\subset\mathbb{R}^{3}\) is a 2-manifold. \\ \(A\) & Revolution (datum) axis \(A=(\vec{v},a_{0})\) of the workpiece \(M\). The vector \(\vec{v}\in\mathbb{R}^{3}\) defines the direction of the axis and \(a_{0}\in\mathbb{R}^{3}\) is a point lying on the axis. \\ \(\Delta\Phi\) & Circular runout (mm) of the scanned workpiece \(M\). \(\Delta\Phi\geq 0\) measures how much a cylindrical feature oscillates when rotated around the revolution axis \(A\). \\ \(h\) & Height \(h>0\) (mm) where the circular runout \(\Delta\Phi\) is measured in the workpiece. This height is measured from \(a_{0}\), in the direction of \(\vec{v}\). \\ \(W\) & Reference coordinate system \(W=\{w_{x},w_{y},w_{z};p_{w}\}\). \(W\) is the coordinate system of \(\mathcal{C}\) and the coordinate system of \(M\) after mesh registration. \\ \(W_{M}\) & Coordinate system of \(M\) before mesh registration. \\ \(SE(3)\) & Special Euclidean group. Group of all rigid transformations in \(\mathbb{R}^{3}\). \(SE(3)\) is composed by all the possible rotation matrices and all possible translations in \(\mathbb{R}^{3}\), i.e., \(SE(3)=SO(3)\times\mathbb{R}^{3}\). \\ \(T_{0}\) & Initial rigid transformation \(T_{0}\in SE(3)\) that approximately maps \(W_{M}\) to \(W\). \\ \(T_{icp}\) & Rigid transformation \(T_{icp}\in SE(3)\) that maps \(T_{0}(W_{M})\) to \(W\). \(T_{icp}\) is the result of registering the mesh \\ \(M\) to the reference \(\mathcal{C}\). \\ \(T_{f}\) & Rigid transformation \(T_{f}\in SE(3)\) that maps \(W_{M}\) to \(W\). \(T_{f}=T_{icp}\circ T_{0}\). \\ \(M_{bore}\) & Cylindrical surface \(M_{cylinder}\subset M\) whose axis vector is the revolution axis vector of the workpiece \(\vec{v}\). \\ \(M_{come}\) & Conical surface \(M_{cone}\subset M\) used to compute the axis reference point \(a_{0}\). \\ \(\mathcal{C}_{bore}\) & Subset of FACES \(\mathcal{C}_{bore}\subset\mathcal{C}\) which define a cylindrical surface in the CAD reference. These set of faces are used to extract \(M_{bore}\) from \(M\). \\ \(\mathcal{C}_{cone}\) & Subset of FACES \(\mathcal{C}_{cone}\subset\mathcal{C}\) which define a conical surface in the CAD reference. These set of faces are used to extract \(M_{cone}\) from \(M\). \\ \(\varepsilon\) & Distance threshold (mm) used to extract the mesh features \(M_{bore}\), \(M_{cone}\). \\ \(d\) & Datum diameter \(d>0\) (mm). The point \(a_{0}\) is located on the plane where the conical surface \(M_{cone}\) attains the diameter \(d\). \\ \(P\) & Circular feature \(P\subset M\) where the circular runout \(\Delta\Phi\) is measured with respect to \(A\). \(P\) defines a polyline perpendicular to the axis \(A\) (\(P\perp A\)). \\ \(T_{h}\) & Plane \(T_{h}\subset\mathbb{R}^{3}\) used to extract \(P\) from \(M\). The plane \(T_{h}\) has normal \(\vec{v}\) and pivot point \(a_{0}+h\vec{v}\). \\ \(T\) & Temperature of the workpiece (\({}^{\circ}\mathcal{C}\)). \\ \(a\) & Number of workpieces for the ANOVA test. \\ \(b\) & Number of operators for the ANOVA test. \\ \(m\) & Number of measurements for the ANOVA test. \\ \end{tabular}