8.9.3.6 IfcBSplineCurveWithKnots

Definition according to ISO/CD 10303-42:1992 This is the type of b-spline curve for which the knot values are explicitly given. This subtype shall be used to represent non-uniform B-spline curves and may be used for other knot types. Let L denote the number of distinct values amongst the d+k+2 knots in the knot list; L will be referred to as the ‘upper index on knots’. Let m~j~ denote the multiplicity (i.e., number of repetitions) of the _j_th distinct knot. Then: Entity adapted from b_spline_curve_with_knots defined in ISO10303-42. New entity in IFC4.

Figure 8.9.3.6.A

All knot multiplicities except the first and the last shall be in the range 1,...,d; the first and last may have a maximum value of d + 1. In evaluating the basis functions, a knot u of, e.g., multiplicity 3 is interpreted as a sequence u, u, u,; in the knot array.

8.9.3.6.2 Entity inheritance

8.9.3.6.3 Attributes

#	Attribute	Type	Description
IfcRepresentationItem (2)
	LayerAssignment	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. IFC2x3-CHANGE The inverse attribute LayerAssignments has been added. IFC4-CHANGE The inverse attribute LayerAssignment has been restricted to max 1. Upward compatibility for file based exchange is guaranteed.
	StyledByItem	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. IFC2x3-CHANGE The inverse attribute StyledByItem has been added.
IfcCurve (1)
*	Dim	IfcDimensionCount	This attribute is formally derived. `IfcCurveDim(SELF)` The space dimensionality of this abstract class, defined differently for all subtypes, i.e. for IfcLine, IfcConic and IfcBoundedCurve.
IfcBSplineCurve (7)
1	Degree	IfcInteger	The algebraic degree of the basis functions.
2	ControlPointsList	LIST [2:?] OF IfcCartesianPoint	The list of control points for the curve.
3	CurveForm	IfcBSplineCurveForm	Used to identify particular types of curve; it is for information only.
4	ClosedCurve	IfcLogical	Indication of whether the curve is closed; it is for information only.
5	SelfIntersect	IfcLogical	Indication whether the curve self-intersects or not; it is for information only.
*	UpperIndexOnControlPoints	IfcInteger	This attribute is formally derived. `(SIZEOF(ControlPointsList) - 1)` The upper index on the array of control points; the lower index is 0. This value is derived from the control points list.
*	ControlPoints	ARRAY [0:UpperIndexOnControlPoints] OF IfcCartesianPoint	This attribute is formally derived. `IfcListToArray(ControlPointsList,0,UpperIndexOnControlPoints)` The array of control points used to define the geometry of the curve. This is derived from the list of control points.
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IfcBSplineCurveWithKnots (4)
6	KnotMultiplicities	LIST [2:?] OF IfcInteger	The multiplicities of the knots. This list defines the number of times each knot in the knots list is to be repeated in constructing the knot array.
7	Knots	LIST [2:?] OF IfcParameterValue	The list of distinct knots used to define the B-spline basis functions.
8	KnotSpec	IfcKnotType	The description of the knot type. This is for information only.
*	UpperIndexOnKnots	IfcInteger	This attribute is formally derived. `SIZEOF(Knots)` The upper index on the knot arrays; the lower index is 1.

Table 8.9.3.6.C

8.9.3.6.4 Formal propositions

Name	Description
ConsistentBSpline	The function IfcConstraintsParamBSpline returns TRUE if no inconsistencies in the parametrisation of the B-spline are found.
`IfcConstraintsParamBSpline(Degree, UpperIndexOnKnots, UpperIndexOnControlPoints, KnotMultiplicities, Knots)`
CorrespondingKnotLists	The number of elements in the knot multiplicities list shall be equal to the number of elements in the knots list.
`SIZEOF(KnotMultiplicities) = UpperIndexOnKnots`

Table 8.9.3.6.D

8.9.3.6.5 Examples

Figure 8.9.3.6.B

Basin Advanced Brep

8.9.3.6.6 Formal representation

ENTITY IfcBSplineCurveWithKnots
 SUPERTYPE OF (ONEOF
	(IfcRationalBSplineCurveWithKnots))
 SUBTYPE OF (IfcBSplineCurve);
	KnotMultiplicities : LIST [2:?] OF IfcInteger;
	Knots : LIST [2:?] OF IfcParameterValue;
	KnotSpec : IfcKnotType;
 DERIVE
	 UpperIndexOnKnots : IfcInteger := SIZEOF(Knots);
 WHERE
	ConsistentBSpline : IfcConstraintsParamBSpline(Degree, UpperIndexOnKnots,
UpperIndexOnControlPoints, KnotMultiplicities, Knots);
	CorrespondingKnotLists : SIZEOF(KnotMultiplicities) = UpperIndexOnKnots;
END_ENTITY;

8.9.3.6 IfcBSplineCurveWithKnots

8.9.3.6.1 Semantic definition

8.9.3.6.2 Entity inheritance

8.9.3.6.3 Attributes

8.9.3.6.4 Formal propositions

8.9.3.6.5 Examples

8.9.3.6.6 Formal representation

8.9.3.6.7 References

8.9.3.6.8 Changelog

8.9.3.6.8.1 IFC4