## Appendix A
\begin{table}
\begin{tabular}{c c c} \hline
**Stereotype** & **Extends to** & **Definitions and Constraints** \\ \hline \(\sim\)TTRS\({}_{\text{\tiny{\textbullet}}}\) & \(\sim\)Block\({}^{\text{\tiny{\textbullet}}}\) & Entity that represents a pair of related MGREs, defining constraints between them. A \(\sim\)TTRS\({}_{\text{\tiny{\textbullet}}}\) & Entity that represents a pair of related MGREs, defining constraints between them. A \(\sim\)TTRS\({}_{\text{\tiny{\textbullet}}}\) & Entity that owns two Ports typed by \(\sim\)MGRE\({}^{\text{\tiny{\textbullet}}}\) Blocks, two Properties typed by \(\sim\)MGRE\({}^{\text{\tiny{\textbullet}}}\) Blocks, and at least one \(\sim\)RGE Constraint\({}^{\text{\tiny{\textbullet}}}\) ConstraintBlock (C22). \\ \hline \(\sim\)RGE Constraint\({}^{\text{\tiny{\textbullet}}}\) & \(\sim\)ConstraintBlock\({}^{\text{\tiny{\textbullet}}}\) & Geometric constraint between two RGEs, corresponding to the 13 simple cases shown in Figure 2. These 13 constraints are defined at the library level. The \(\sim\)RGE Constraint\({}^{\text{\tiny{\textbullet}}}\) ConstraintBlock must own two Parameters typed by \(\sim\)RGE\({}^{\text{\tiny{\textbullet}}}\) Blocks (C23). \\ \hline \(\sim\)Representation\({}^{\text{\tiny{\textbullet}}}\) & \begin{tabular}{c} UML4 SYSML:: \\ *Property\({}^{\text{\tiny{\textbullet}}}\) \\ \end{tabular} & \begin{tabular}{c} Property that represents another element of the model from a different viewpoint. \\ The \(\sim\)Representation\({}^{\text{\tiny{\textbullet}}}\) stereotype has an Attribute (“representsTo”) to define the \\ element it represents. The owner of a \(\sim\)Representation\({}^{\text{\tiny{\textbullet}}}\) Property must also own \\ another Property whose name coincides with the value of the “representsTo” \\ Attribute (C24). \\ \hline \(\sim\)Assembly MGRE\({}^{\text{\tiny{\textbullet}}}\) & \begin{tabular}{c} UML4 SYSML:: \\ *Port\({}^{\text{\tiny{\textbullet}}}\) \\ \end{tabular} & \begin{tabular}{c} Port typed by a \(\sim\)F\({}_\_\)TTRS\({}_{\text{\tiny{\textbullet}}}\)Repr\({}^{\text{\tiny{\textbullet}}}\) block (C25) that represents a geometry offered by an Artifact to participate in assembly relationships.An \(\sim\)Assembly MGRE\({}^{\text{\tiny{\textbullet}}}\) Port must be owned by an \(\sim\)Artifact\({}^{\text{\tiny{\textbullet}}}\) (*Party\({}^{\text{\tiny{\textbullet}}}\) or \(\sim\)Assembly\({}^{\text{\tiny{\textbullet}}}\)) Block (C26). \\ \hline \(\sim\)TransformationMatrix\({}^{\text{\tiny{\textbullet}}}\) & \begin{tabular}{c} UML4 SYSML:: \\ *Property\({}^{\text{\tiny{\textbullet}}}\) \\ \end{tabular} & \begin{tabular}{c} Homogeneous matrix that supports the translation and rotation of geometry \\ definitions to change the reference system considered. It is a Property that \\ characterizes a Part, so every geometry owned by this Part must be transformed in the same way. For this reason, the owner \(\sim\)Part\({}^{\text{\tiny{\textbullet}}}\) Block must contain only one \(\sim\)TransformationMatrix\({}^{\text{\tiny{\textbullet}}}\) Property (C27). \\ \hline \(\sim\)TM\_Port\({}^{\text{\tiny{\textbullet}}}\) & \begin{tabular}{c} UML4 SYSML:: \\ *Port\({}^{\text{\tiny{\textbullet}}}\) \\ \end{tabular} & \begin{tabular}{c} Behavior Port owned by an \(\sim\)F\({}_\_\)TTRS\({}_{\text{\tiny{\textbullet}}}\)Block that is connected with the \\ *TransformationMatrix\({}^{\text{\tiny{\textbullet}}}\) Property of the *F\({}_{\_}\)TTRS\({}_{\text{\tiny{\textbullet}}}\)Repr\({}^{\text{\tiny{\textbullet}}}\) Block (C28). \\ \end{tabular} \\ \hline \(\sim\)GT\_TTRS\_definition\({}^{\text{\tiny{\textbullet}}}\) & \(\sim\)Block\({}^{\text{\tiny{\textbullet}}}\) & \begin{tabular}{c} Mathematical definition of a geometric tolerance between TTRS-based feature \\ representations. Any Property typed by a \(\sim\)GT\_TTRS\_definition\({}^{\text{\tiny{\textbullet}}}\) Block always has \\ the \(\sim\)Representation\({}^{\text{\tiny{\textbullet}}}\) stereotype applied (C29). A \(\sim\)GT\_TTRS\_definition\({}^{\text{\tiny{\textbullet}}}\) Block \\ must own a \(\sim\)TZ\_TTRS\_definition\({}^{\text{\tiny{\textbullet}}}\) Block, 2 to 4 \(\sim\)TTRS\_Repr\({}^{\text{\tiny{\textbullet}}}\)usage\({}^{\text{\tiny{\textbullet}}}\) Ports (C42), and the same quantity of Properties typed by \(\sim\)F\({}_{\_}\)TTRS\({}_{\text{\tiny{\textbullet}}}\)Repr\({}^{\text{\tiny{\textbullet}}}\) Blocks as \\ \(\sim\)TTRS\_Repr\({}^{\text{\tiny{\textbullet}}}\)usage\({}^{\text{\tiny{\textbullet}}}\) Ports (C30). Moreover, a \(\sim\)GT\_TTRS\_definition Block must \\ own the same or higher quantity of Properties typed by \(\sim\)TTRS\({}^{\text{\tiny{\textbullet}}}\) Blocks than the \\ double of the number of \(\sim\)TTRS\_Repr\({}_{\_}\)usage\({}^{\text{\tiny{\textbullet}}}\) Ports with the Attribute role = \\ datum (C31) to relate the tolerance zone with the considered nominal and \\ deviated data. A \(\sim\)GT\_TTRS\_definition\({}^{\text{\tiny{\textbullet}}}\) Block must own (direct or indirectly) two \\ Properties typed by \(\sim\)SpecifValidation\({}^{\text{\tiny{\textbullet}}}\) and \(\sim\)TargetConstruction\({}^{\text{\tiny{\textbullet}}}\) \\ ConstraintBlocks, respectively, that relate the tolerance zone with the target \\ geometry and a \(\sim\)TargetDeviation\({}^{\text{\tiny{\textbullet}}}\) Property in which deviations for the target \\ constructions are defined (C32). \\ \hline \(\sim\)SpecifValidation\({}^{\text{\tiny{\textbullet}}}\) & \(\sim\)ConstraintBlock\({}^{\text{\tiny{\textbullet}}}\) & \begin{tabular}{c} Validation of the specification consistency, checking that the nominal MGRE of the \\ target coincides or is included in the nominal MGRE of the tolerance zone \\ (constructed from the nominal MGRE of the datum). A \(\sim\)SpecifValidation\({}^{\text{\tiny{\textbullet}}}\) \\ ConstraintBlock includes a Boolean Parameter (C33) to transfer the result of the validation. \\ \hline \(\sim\)TargetConstruction\({}^{\text{\tiny{\textbullet}}}\) & \(\sim\)ConstraintBlock\({}^{\text{\tiny{\textbullet}}}\) & \
\begin{tabular}{c} Construction of the deviated MGRE for the target geometry, using a \\ \(\sim\)DeviationVector\({}^{\text{\tiny{\textbullet}}}\) Parameter (C34) according to the limits imposed by the \\ tolerance zone MGRE and its size. \\ \hline \(\sim\)TZ\_TTRS\_definition\({}^{\text{\tiny{\textbullet}}}\) & \(\sim\)Block\({}^{\text{\tiny{\textbullet}}}\) \\ \end{tabular} &
\begin{tabular}{c} A geometrical space used to control/define the position/orientation of a target geometry. This geometrical space is characterized by a size, specified in a geometric tolerance specification, so a \(\sim\)TZ\_TTRS\_definition\({}^{\text{\tiny{\textbullet}}}\) Block owns an \\ AdjunctProperty that points to the \(\sim\)ToleranceSize\({}^{\text{\tiny{\textbullet}}}\) Property of a Property typed \\ by a \(\sim\)GT\_Specification\({}^{\text{\tiny{\textbullet}}}\) Block (35). A \(\sim\)TZ\_definition\({}^{\text{\tiny{\textbullet}}}\) Block also owns two \(\sim\)MGRE\({}^{\text{\tiny{\textbullet}}}\) Blocks, one of them with the Attribute “isNominal = true” and another \\ with the Attribute “isNominal = false” (C36). \\ \hline \end{tabular}
\end{table}