8.9.3.53 IfcRationalBSplineCurveWithKnots

8.9.3.53.1 Semantic definition

A rational B-spline curve with knots is a B-spline curve described in terms of control points and basic functions. It describes weights in addition to the control points defined at the supertype IfcBSplineCurve.

All weights shall be positive and the curve is given by:

where:

Variable	Definition
k+1	number of control points
P_i	control points
w_i	weights
d	degree

Table 8.9.3.53.B

8.9.3.53.2 Entity inheritance

8.9.3.53.3 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.
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.
Click to show 14 hidden inherited attributes
IfcRationalBSplineCurveWithKnots (2)
9	WeightsData	LIST [2:?] OF IfcReal	The supplied values of the weights.
*	Weights	ARRAY [0:UpperIndexOnControlPoints] OF IfcReal	This attribute is formally derived. `IfcListToArray(WeightsData,0,SELF\IfcBSplineCurve.UpperIndexOnControlPoints)` The array of weights associated with the control points. This is derived from the weights data.

Table 8.9.3.53.C

8.9.3.53.4 Formal propositions

Name	Description
SameNumOfWeightsAndPoints	There shall be the same number of weights as control points.
`SIZEOF(WeightsData) = SIZEOF(SELF\IfcBSplineCurve.ControlPointsList)`
WeightsGreaterZero	All the weights shall have values greater than 0.0.
`IfcCurveWeightsPositive(SELF)`

Table 8.9.3.53.D

8.9.3.53.5 Formal representation

 ENTITY IfcRationalBSplineCurveWithKnots
 SUBTYPE OF (IfcBSplineCurveWithKnots);
	WeightsData : LIST [2:?] OF IfcReal;
 DERIVE
	 Weights : ARRAY [0:UpperIndexOnControlPoints] OF IfcReal := IfcListToArray(WeightsData,0,SELF\IfcBSplineCurve.UpperIndexOnControlPoints);
 WHERE
	SameNumOfWeightsAndPoints : SIZEOF(WeightsData) = SIZEOF(SELF\IfcBSplineCurve.ControlPointsList);
	WeightsGreaterZero : IfcCurveWeightsPositive(SELF);
END_ENTITY;