# 8.8.3.26 IfcPolygonalBoundedHalfSpace

## 8.8.3.26.1 Semantic definition

The polygonal bounded half space is a special subtype of a half space solid, where the material of the half space used in Boolean expressions is bounded by a two-dimensional boundary. The base surface of the half space is positioned by its normal relative to the object coordinate system (as defined at the supertype IfcHalfSpaceSolid), and its boundary (with straight and arc segments) is defined in the XY plane of the position coordinate system established by the Position attribute, the subtraction body is extruded perpendicular to the XY plane of the position coordinate system, that is, into the direction of the positive Z axis defined by the Position attribute.

The boundary is defined by a 2 dimensional polyline (or 2 dimensional composite curve, consisting of straight segments and circular arc segments, or indexed poly curve) within the XY plane of the position coordinate system. The side of the surface which is in the half space is determined by the surface normal and the agreement flag. If the agreement flag is TRUE, then the subset is the one the normal points away from. If the agreement flag is FALSE, then the subset is the one the normal points into.

Figure 8.8.3.26.A illustrates a polygonal bounded half space.

• Black coordinates indicate the object coordinate system (usually provided by IfcLocalPlacement).
• Green coordinates indicate the position coordinate system; the PolygonalBoundary is given within this coordinate system. It is provided by IfcPolygonalBoundedHalfSpace.Position. This coordinate system is relative to the object coordinate system. The extrusion direction of the subtraction body is the positive Z axis.
• Red coordinates indicate the normal of the plane. It is provided by the BaseSurface (IfcSurface.Position). This normal is also relative to the object coordinate system.

The polygonal bounded half space is used to limit the volume of the half space in Boolean difference expressions. Only the part that is defined by a theoretical intersection between the half space solid and an extruded area solid, defined by extruding the polygonal boundary, is used for Boolean expressions.

The PolygonalBoundary defines the 2D polyline which bounds the effectiveness of the half space in Boolean expressions. The BaseSurface is defined by a plane, and the normal of the plane together with the AgreementFlag defines the side of the material of the half space.

Informal Propositions:

1. The IfcPolyline or the IfcCompositeCurve providing the PolygonalBoundary shall be closed.
2. If the PolygonalBoundary is given by an IfcCompositeCurve, it shall only have IfcCompositeCurveSegment's of type IfcPolyline, or IfcTrimmedCurve (having a BasisCurve of type IfcLine, or IfcCircle)
3. The BaseSurface defined at supertype IfcHalfSpaceSolid shall be of type IfcPlane
4. The normal of the plane, being the BaseSurface, shall not be perpendicular to the z-axis of the position coordinate system

## 8.8.3.26.5 Formal representation

ENTITY IfcPolygonalBoundedHalfSpace
SUBTYPE OF (IfcHalfSpaceSolid);
Position : IfcAxis2Placement3D;
PolygonalBoundary : IfcBoundedCurve;
WHERE
BoundaryDim : PolygonalBoundary.Dim = 2;
BoundaryType : SIZEOF(TYPEOF(PolygonalBoundary) * [
'IFC4X3_DEV_9f90c1f0.IfcPolyline',
'IFC4X3_DEV_9f90c1f0.IfcCompositeCurve',
'IFC4X3_DEV_9f90c1f0.IfcIndexedPolyCurve'
]) = 1;
END_ENTITY;