#### IfcCartesianTransformationOperator2D

Natural language names

##### Semantic definitions at the entity

Entity definition

Definition from ISO/CD 10303-42:1992: A Cartesian transformation operator 2d defines a geometric transformation in two-dimensional space composed of translation, rotation, mirroring and uniform scaling. The list of normalized vectors u defines the columns of an orthogonal matrix T. These vectors are computed from the direction attributes axis1 and axis2 by the base axis function. If |T|= -1, the transformation includes mirroring.

> NOTE: Corresponding STEP entity : cartesian_transformation_operator_2d, please refer to ISO/IS 10303-42:1994, p. 36 for the final definition of the formal standard.

> HISTORY: New entity in IFC Release 2x.

Attribute definitions

# | Attribute | Type | Cardinality | Description | A
--- | --- | --- | --- | --- | ---
| U :=IfcBaseAxis(2,SELF\IfcCartesianTransformationOperator.Axis1, SELF\IfcCartesianTransformationOperator.Axis2,?) | IfcDirection | L[2:2] | The list of mutually orthogonal, normalized vectors defining the transformation matrix T. They are derived from the explicit attributes Axis1 and Axis2 in that order. | X

Formal Propositions

Rule | Description
--- | ---
WR1 | The coordinate space dimensionality of this entity shall be 2.
WR2 | The inherited Axis1 should have (if given) the dimensionality of 2.
WR3 | The inherited Axis2 should have (if given) the dimensionality of 2.

##### Inherited definitions from supertypes

Entity inheritance
Attribute inheritance

# | Attribute | Type | Cardinality | Description | A
--- | --- | --- | --- | --- | ---
IfcRepresentationItem
IfcGeometricRepresentationItem
IfcCartesianTransformationOperator
1 | Axis1 | - |  | This attribute is out of scope for this model view definition and shall not be set. |
2 | Axis2 | - |  | This attribute is out of scope for this model view definition and shall not be set. |
3 | LocalOrigin | IfcCartesianPoint | [1:1] | The required translation, specified as a cartesian point. The actual translation included in the transformation is from the geometric origin to the local origin. | X
4 | Scale | - |  | This attribute is out of scope for this model view definition and shall not be set. |
| Scl :=NVL(Scale, 1.0) | REAL | [1:1] | The derived scale S of the transformation, equal to scale if that exists, or 1.0 otherwise. | X
| Dim :=LocalOrigin.Dim | IfcDimensionCount | [1:1] | The space dimensionality of this class, determined by the space dimensionality of the local origin. | X
IfcCartesianTransformationOperator2D
| U :=IfcBaseAxis(2,SELF\IfcCartesianTransformationOperator.Axis1, SELF\IfcCartesianTransformationOperator.Axis2,?) | IfcDirection | L[2:2] | The list of mutually orthogonal, normalized vectors defining the transformation matrix T. They are derived from the explicit attributes Axis1 and Axis2 in that order. | X

##### Formal representations

XSD Specification
`<xs:element name="IfcCartesianTransformationOperator2D" type="ifc:IfcCartesianTransformationOperator2D" substitutionGroup="ifc:IfcCartesianTransformationOperator" nillable="true"/>
<xs:complexType name="IfcCartesianTransformationOperator2D">
<xs:complexContent>
<xs:extension base="ifc:IfcCartesianTransformationOperator"/>
</xs:complexContent>
</xs:complexType>
`
EXPRESS Specification
`ENTITY IfcCartesianTransformationOperator2D
SUBTYPE OF (IfcCartesianTransformationOperator);
DERIVE
U : LIST [2:2] OF IfcDirection := IfcBaseAxis(2,SELF\IfcCartesianTransformationOperator.Axis1, SELF\IfcCartesianTransformationOperator.Axis2,?);
WHERE
WR1 : SELF\IfcCartesianTransformationOperator.Dim = 2;
WR2 : NOT(EXISTS(SELF\IfcCartesianTransformationOperator.Axis1)) OR (SELF\IfcCartesianTransformationOperator.Axis1.Dim = 2);
WR3 : NOT(EXISTS(SELF\IfcCartesianTransformationOperator.Axis2)) OR (SELF\IfcCartesianTransformationOperator.Axis2.Dim = 2);
END_ENTITY;

EXPRESS-G diagram

`

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