The shell is represented by a collection of faces. The domain of the shell, if present, contains all those faces, together with their bounds. Associated with each face in the shell is a logical value which indicates whether the face normal agrees with (TRUE) or is opposed to (FALSE) the shell normal. The logical value can be applied directly as a BOOLEAN attribute of an oriented face, or be defaulted to TRUE if the shell boundary attribute member is a face without the orientation attribute.
The combinatorial restrictions on closed shells and geometrical restrictions on their domains are designed to ensure that any domain associated with a closed shell is a closed, orientable manifold. The domain of a closed shell, if present, is a connected, closed, oriented 2-manifold. It is always topologically equivalent to an H-fold torus for some H ≥ 0. The number H is referred to as the surface genus of the shell. If a shell of genus H has a domain within coordinate space R^3^, then the finite region of space inside it is topologically equivalent to a solid ball with H tunnels drilled through it.
The Euler equation applies with B=0, because in this case there are no holes. As in the case of open shells, the surface genus H may not be known a priori, but shall be an integer ≥ 0. Thus a necessary, but not sufficient, condition for a well-formed closed shell is the following:
- Every edge shall be referenced exactly twice by the loops of the face.
- Each oriented edge shall be unique.
- No edge shall be referenced by more than two faces.
- Distinct faces of the shell do not intersect, but may share edges or vertices.
- Distinct edges do not intersect but may share vertices.
- Each face reference shall be unique.
- The loops of the shell shall not be a mixture of poly loop and other loop types. Note: this is given, since only poly loop is defined as face bound definition.
- The closed shell shall be an oriented arcwise connected 2-manifold.
- The Euler equation shall be satisfied. Note: Please refer to ISO 10303-42 for the equation.
|SET [0:1] OF IfcPresentationLayerAssignment FOR AssignedItems
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.
|SET [0:1] OF IfcStyledItem FOR Item
Reference to the IfcStyledItem that provides presentation information to the representation, e.g. a curve style, including colour and thickness to a geometric curve.
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|SET [1:?] OF IfcFace
The set of faces arcwise connected along common edges or vertices.
SUBTYPE OF (IfcConnectedFaceSet);