IfcCartesianTransformationOperator
Definition from ISO/CD 1030342:1992: A cartesian transformation operator defines a geometric transformation composed of translation, rotation, mirroring and uniform scaling. The list of normalised 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: Corresponding STEP entity : cartesian_transformation_operator, please refer to ISO/IS 1030342:1994, p. 32 for the final definition of the formal standard.
HISTORY New class in IFC Release 2.x.
ISSUE: See issue log for changes made in IFC Release 2.x
EXPRESS specification:

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. 
WR1  :  The derived scaling Scl shall be greater than zero. 
Name  Type  Referred through  ExpressG 
IfcCartesianTransformationOperator2D  Entity 

Diagram 4 
IfcCartesianTransformationOperator3D  Entity 

Diagram 4 
IfcGeometricRepresentationItem  Entity 

Diagram 1 
IfcMappedItem  Entity 

Diagram 2 
