IfcAxis2Placement3D
Definition from ISO/CD 1030342:1992: The location and orientation in three dimensional space of three mutually perpendicular axes. An axis2_placement_3D (IfcAxis2Placement3D) is defined in terms of a point (inherited from IfcPlacement supertype) and two (ideally orthogonal) axes. It can be used to locate and originate an object in three dimensional space and to define a placement coordinate system. The entity includes a point which forms the origin of the placement coordinate system. Two direction vectors are required to complete the definition of the placement coordinate system. The axis is the placement Z axis direction and the ref_direction (RefDirection) is an approximation to the placement X axis direction.
Definition from IAI: If the attribute values for Axis and RefDirection are not given, the placement defaults to P[1] (xaxis) as [1.,0.,0.], P[2] (yaxis) as [0.,1.,0.] and P[3] (zaxis) as [0.,0.,1.]. The WR5 is added in IFC to ensure that either both attributes (Axis and RefDirection) are given, or omitted.
NOTE Corresponding STEP name: axis2_placement_3d, please refer to ISO/IS 1030342:1994 for the final definition of the formal standard.
HISTORY New class in IFC Release 1.5, the IFC Release 1.0 entity IfcPlacement_3D was using three normalized and orthogonal axes. This definition is replaced in IFC Release 1.5 by the STEP definition of axis placement.
ISSUE: See issue log for changes made in IFC Release 1.5.1
Illustration
Definition of the IfcAxis2Placement3D within the threedimensional coordinate system. 
EXPRESS specification:

Axis  :  The exact direction of the local Z Axis. 
RefDirection  :  The direction used to determine the direction of the local X Axis. If necessary an adjustment is made to maintain orthogonality to the Axis direction. If Axis and/or RefDirection is omitted, these directions are taken from the geometric coordinate system. 
P  :  The normalized directions of the placement X Axis (P[1]) and the placement Y Axis (P[2]) and the placement Z Axis (P[3]). 
WR1  :  The dimensionality of the placement location shall be 3. 
WR2  :  The Axis when given should only reference a threedimensional IfcDirection. 
WR3  :  The RefDirection when given should only reference a threedimensional IfcDirection. 
WR4  :  The Axis and RefDirection shall not be parallel or antiparallel. 
WR5  :  Either both (Axis and RefDirection) are not given and therefore defaulted, or both shall be given. This
is a further constraint in IFC Release 1.5. 
Name  Type  Referred through  ExpressG 
IfcAxis2Placement  Select 

Diagram 3 
IfcElementarySurface  Entity 

Diagram 7 
IfcPlacement  Entity 

Diagram 3 
IfcSweptSurface  Entity 

Diagram 8 
