#### 8.7.3.6 IfcCartesianTransformationOperator

| Opérateur de transformation cartésienne
| Kartesische Transformation

An IfcCartesianTransformationOperator defines an abstract supertype of different kinds of geometric transformations.

> NOTE Definition according to ISO/CD 10303-42:1992
> A Cartesian transformation operator defines a geometric transformation 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, by the base axis function, from the direction attributes axis1, axis2 and, in Cartesian transformation operator 3d, axis3. If |T|= -1, the transformation includes mirroring. The local origin point A, the scale value S and the matrix T together define a transformation.
> The transformation for a point with position vector P is defined by

> > P -> A + STP

> The transformation for a direction d is defined by

> > d -> Td

> The transformation for a vector with orientation d and magnitude k is defined by

> > d -> Td, and
> > k -> Sk

> For those entities whose attributes include an axis2 placement, the transformation is applied, after the derivation, to the derived attributes p defining the placement coordinate directions. For a transformed surface, the direction of the surface normal at any point is obtained by transforming the normal, at the corresponding point, to the original surface. For geometric entities with attributes (such as the radius of a circle) which have the dimensionality of length, the values will be multiplied by S.

> For curves on surface the p curve.reference to curve will be unaffected by any transformation. The Cartesian transformation operator shall only be applied to geometry defined in a consistent system of units with the same units on each axis. With all optional attributes omitted, the transformation defaults to the identity transformation. The Cartesian transformation operator shall only be instantiated as one of its subtypes.

> NOTE Entity adapted from cartesian_transformation_operator defined in ISO10303-42.

> HISTORY New entity in IFC2x.

XSD Specification:

<xs:element name="IfcCartesianTransformationOperator" type="ifc:IfcCartesianTransformationOperator" abstract="true" substitutionGroup="ifc:IfcGeometricRepresentationItem" nillable="true"/>
<xs:complexType name="IfcCartesianTransformationOperator" abstract="true">
<xs:complexContent>
<xs:extension base="ifc:IfcGeometricRepresentationItem">
<xs:sequence>
<xs:element name="LocalOrigin" type="ifc:IfcCartesianPoint" nillable="true"/>
</xs:sequence>
</xs:extension>
</xs:complexContent>
</xs:complexType>

EXPRESS Specification:

ENTITY IfcCartesianTransformationOperator

| SUBTYPE OF (IfcGeometricRepresentationItem);

Axis1 | : | OPTIONAL IfcStrippedOptional;
Axis2 | : | OPTIONAL IfcStrippedOptional;
LocalOrigin | : | IfcCartesianPoint;
Scale | : | OPTIONAL IfcStrippedOptional;

| DERIVE

Scl | : | REAL := NVL(Scale, 1.0);
Dim | : | IfcDimensionCount := LocalOrigin.Dim;

| WHERE

ScaleGreaterZero | : | Scl > 0.0;

END_ENTITY;

Attribute Definitions:

Axis1 | : | The direction used to determine U[1], the derived X axis direction.
Axis2 | : | The direction used to determine U[2], the derived Y axis direction.
LocalOrigin | : | The required translation, specified as a cartesian point. The actual translation included in the transformation is from the geometric origin to the local origin.
Scale | : | The scaling value specified for the transformation.
Scl | : | The derived scale S of the transformation, equal to scale if that exists, or 1.0 otherwise.
Dim | : | The space dimensionality of this class, determined by the space dimensionality of the local origin.

Formal Propositions:

ScaleGreaterZero | : | The derived scaling Scl shall be greater than zero.

Inheritance Graph:

ENTITY IfcCartesianTransformationOperator

| ENTITY IfcRepresentationItem

| INVERSE

LayerAssignment | : | SET [0:1] OF IfcPresentationLayerAssignment FOR AssignedItems;
StyledByItem | : | SET [0:1] OF IfcStyledItem FOR Item;

| ENTITY IfcGeometricRepresentationItem

| ENTITY IfcCartesianTransformationOperator

Axis1 | : | OPTIONAL IfcStrippedOptional;
Axis2 | : | OPTIONAL IfcStrippedOptional;
LocalOrigin | : | IfcCartesianPoint;
Scale | : | OPTIONAL IfcStrippedOptional;

| DERIVE

Scl | : | REAL := NVL(Scale, 1.0);
Dim | : | IfcDimensionCount := LocalOrigin.Dim;

END_ENTITY;

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