IfcAxis2Placement3D IFC构件的位置和方向

IfcAxis2Placement3D定义了三维空间中物体的位置和方向，由三部分组成：

The attribute Axis defines the Z direction, RefDirection the X direction. The Y direction is derived.

注：Y轴方向由X轴和Z轴方向通过外积计算获得。

当Axis和RefDirection未定义时，X轴为P[1] ，默认值 [1.,0.,0.]。Y轴为P[2]，默认值为[0.,1.,0.]。Z轴为P[3] ，默认值为[0.,0.,1.]。

属性定义

#	Attribute	Type	Cardinality	Description	C
2	Axis	IfcDirection	[0:1]	The exact direction of the local Z Axis.	X
3	RefDirection	IfcDirection	[0:1]	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.	X
	P :=IfcBuildAxes(Axis, RefDirection)	IfcDirection	L[3:3]	The normalized directions of the placement X Axis (P[1]) and the placement Y Axis (P[2]) and the placement Z Axis (P[3]).	X

Rule	Description
LocationIs3D	The dimensionality of the placement location shall be 3.
AxisIs3D	The Axis when given should only reference a three-dimensional IfcDirection.
RefDirIs3D	The RefDirection when given should only reference a three-dimensional IfcDirection.
AxisToRefDirPosition	The Axis and RefDirection shall not be parallel or anti-parallel.
AxisAndRefDirProvision	Either both, Axis and RefDirection are not given and therefore defaulted, or both shall be given.

继承关系：

属性

#	Attribute	Type	Cardinality	Description	C
IfcRepresentationItem
	LayerAssignment	IfcPresentationLayerAssignment @AssignedItems	S[0:1]	Assignment of the representation item to a single or multiple layer(s). The LayerAssignments can override a LayerAssignments of the IfcRepresentation it is used within the list of Items.	X
	StyledByItem	IfcStyledItem @Item	S[0:1]	Reference to the IfcStyledItem that provides presentation information to the representation, e.g. a curve style, including colour and thickness to a geometric curve.	X
IfcGeometricRepresentationItem
IfcPlacement
1	Location	IfcCartesianPoint	[1:1]	The geometric position of a reference point, such as the center of a circle, of the item to be located.	X
	Dim :=Location.Dim	IfcDimensionCount	[1:1]	The space dimensionality of this class, derived from the dimensionality of the location.	X
IfcAxis2Placement3D
2	Axis	IfcDirection	[0:1]	The exact direction of the local Z Axis.	X
3	RefDirection	IfcDirection	[0:1]	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.	X
	P :=IfcBuildAxes(Axis, RefDirection)	IfcDirection	L[3:3]	The normalized directions of the placement X Axis (P[1]) and the placement Y Axis (P[2]) and the placement Z Axis (P[3]).	X

ENTITY IfcAxis2Placement3D
 SUBTYPE OF (IfcPlacement);
  Axis : OPTIONAL IfcDirection;
  RefDirection : OPTIONAL IfcDirection;
 DERIVE
  P : LIST [:] OF IfcDirection := IfcBuildAxes(Axis, RefDirection);
 WHERE
  LocationIs3D : SELF\IfcPlacement.Location.Dim = ;
  AxisIs3D : (NOT (EXISTS (Axis))) OR (Axis.Dim = );
  RefDirIs3D : (NOT (EXISTS (RefDirection))) OR (RefDirection.Dim = );
  AxisToRefDirPosition : (NOT (EXISTS (Axis))) OR (NOT (EXISTS (RefDirection))) OR (IfcCrossProduct(Axis,RefDirection).Magnitude > 0.0);
  AxisAndRefDirProvision : NOT ((EXISTS (Axis)) XOR (EXISTS (RefDirection)));
END_ENTITY;

DATA;
#= IFCORGANIZATION($,'Autodesk Revit 2015 (CHS)',$,$,$);
#= IFCAPPLICATION(#,'','Autodesk Revit 2015 (CHS)','Revit');
#= IFCCARTESIANPOINT((.,.,.));
#= IFCCARTESIANPOINT((.,.));
#= IFCDIRECTION((.,.,.));
#= IFCDIRECTION((-.,.,.));
#= IFCDIRECTION((.,.,.));
#= IFCDIRECTION((.,-.,.));
#= IFCDIRECTION((.,.,.));
#= IFCDIRECTION((.,.,-.));
#= IFCDIRECTION((.,.));
#= IFCDIRECTION((-.,.));
#= IFCDIRECTION((.,.));
#= IFCDIRECTION((.,-.));

#= IFCAXIS2PLACEMENT3D(#,$,$);
#= IFCAXIS2PLACEMENT3D(#,$,$);
#= IFCLOCALPLACEMENT($,#);
#= IFCLOCALPLACEMENT(#,#);

#= IFCAXIS2PLACEMENT3D(#,$,$);
#= IFCLOCALPLACEMENT(#,#);

#= IFCCARTESIANTRANSFORMATIONOPERATOR3D($,$,#,.,$);
#= IFCSHAPEREPRESENTATION(#,'Body','SweptSolid',(#));
#= IFCAXIS2PLACEMENT3D(#,$,$);
#= IFCREPRESENTATIONMAP(#,#);

#= IFCMAPPEDITEM(#,#);
#= IFCSHAPEREPRESENTATION(#,'Body','MappedRepresentation',(#));
#= IFCPRODUCTDEFINITIONSHAPE($,$,(#));

#= IFCCARTESIANPOINT((1325.86888709244,31631.0676658748,.));
#= IFCAXIS2PLACEMENT3D(#,$,$);
#= IFCLOCALPLACEMENT(#,#);
#= IFCCOLUMN('2ILfSTle57UhpKxVJ8Mj7L',#,'\X2\7EFC5408697C\X0\-\X2\6DF751DD571F77E95F6267F1\X0\:450 x 600 mm:365232',$,'450 x 600 mm',#,#,'');

计算构件y轴方向

# = IfcDirection((0.,.,.));   //z轴
# = IfcDirection((.,.,.));    //x轴
# = IfcAxis2Placement3D($,#,#);   //叉积计算出y轴 (0 ,1, 0)
# = IfcLocalPlacement($,#);
# = IfcDirection((.,.,.));  //z轴
# = IfcDirection((.,.,.));   //x轴
# = IfcAxis2Placement3D($,#,#);  //叉积计算出y轴(1, 0, -1)
# = IfcLocalPlacement(#,#);   //矩阵相乘(注意顺序)结果：x轴（0,0,1）y轴（1,0,0）z轴（0，1，0）

向量叉积计算

#include <iostream>

using namespace std;

struct Vec {
    double x;
    double y;
    double z;
};

Vec ThreeCross(const Vec& a, const Vec& b)
{
    Vec C;
    C.x = a.y * b.z - a.z * b.y;
    C.y = a.z * b.x - a.x * b.z;
    C.z = a.x * b.y - a.y * b.x;
    return C;
}

int main()
{
    Vec v1;
    v1.x = ;
    v1.y = ;
    v1.z = ;

    Vec v2;
    v2.x = ;
    v2.y = ;
    v2.z = ;

    Vec v3 = ThreeCross(v1,v2);

    cout << v3.x << "  " << v3.y << "  " << v3.z << endl;

    system("pause");
    return ;
}

向量叉积计算公式：

a=(X1,Y1,Z1),b=(X2,Y2,Z2),
a×b=（Y1Z2 - Y2Z1,Z1X2 - Z2X1,X1Y2 - X2Y1）
V1(1,2,3)

V2(4,5,6)

V1 * V2=(12-15,12-6,5-8)=（-3,6,-3）

参考：https://blog.csdn.net/liyazhen2011/article/details/82347074