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IfcAxis2Placement3D

Definition from ISO/CD 10303-42:1992: The location and orientation in three dimensional space of three mutually perpendicular axes. An axis2_placement_3D is defined in terms of a point (inherited from placement 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 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] (x-axis) as [1.,0.,0.], P[2] (y-axis) as [0.,1.,0.] and P[3] (z-axis) as [0.,0.,1.]. 

NOTE  Corresponding STEP name: axis2_placement_3d, please refer to ISO/IS 10303-42:1994 for the final definition of the formal standard. The WR5 is added to ensure that either both attributes Axis and RefDirection are given, or both are omitted.

HISTORY  New entity in IFC Release 1.5.

Illustration

axis2 placement 2D Definition of the IfcAxis2Placement3D within the three-dimensional coordinate system.

EXPRESS specification:

ENTITY IfcAxis2Placement3D
SUBTYPE OF ( IfcPlacement);
Axis  :  OPTIONAL IfcDirection;
RefDirection  :  OPTIONAL IfcDirection;
DERIVE
P  :  LIST [3:3] OF IfcDirection :=  IfcBuildAxes(Axis, RefDirection);
WHERE
WR1  :  SELF\IfcPlacement.Location.Dim = 3;
WR2  :  (NOT (EXISTS (Axis))) OR (Axis.Dim = 3);
WR3  :  (NOT (EXISTS (RefDirection))) OR (RefDirection.Dim = 3);
WR4  :  (NOT (EXISTS (Axis))) OR (NOT (EXISTS (RefDirection))) OR (IfcCrossProduct(Axis,RefDirection).Magnitude > 0.0);
WR5  :  NOT ((EXISTS (Axis)) XOR (EXISTS (RefDirection)));
END_ENTITY;

Attribute definitions:

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]).

Formal Propositions:

WR1  :  The dimensionality of the placement location shall be 3.
WR2  :  The Axis when given should only reference a three-dimensional IfcDirection.
WR3  :  The RefDirection when given should only reference a three-dimensional IfcDirection.
WR4  :  The Axis and RefDirection shall not be parallel or anti-parallel.
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.

Inheritance graph

ENTITY IfcAxis2Placement3D;
ENTITY IfcRepresentationItem;
INVERSE
LayerAssignments  :  SET OF IfcPresentationLayerAssignment FOR AssignedItems;
StyledByItem  :  SET [0:1] OF IfcStyledItem FOR Item;
ENTITY IfcGeometricRepresentationItem;
ENTITY IfcPlacement;
Location  :  IfcCartesianPoint;
DERIVE
Dim  :  IfcDimensionCount :=  Location.Dim;
ENTITY IfcAxis2Placement3D;
Axis  :  OPTIONAL IfcDirection;
RefDirection  :  OPTIONAL IfcDirection;
DERIVE
P  :  LIST [3:3] OF IfcDirection :=  IfcBuildAxes(Axis, RefDirection);
END_ENTITY;