8.9.3.55 IfcRationalBSplineSurfaceWithKnots

8.9.3.55.1 Semantic definition

A rational B-spline surface with knots is a piecewise parametric rational surface described in terms of control points, and associated weight values.

The surface is to be interpreted as follows:

8.9.3.55.2 Entity inheritance

8.9.3.55.3 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.
IfcSurface (1)
*	Dim	IfcDimensionCount	This attribute is formally derived. `3` The space dimensionality of IfcSurface. It is always a three-dimensional geometric representation item. IFC4-CHANGE Derived attribute promoted from subtypes.
IfcBSplineSurface (10)
1	UDegree	IfcInteger	Algebraic degree of basis functions in u.
2	VDegree	IfcInteger	Algebraic degree of basis functions in v.
3	ControlPointsList	LIST [2:?] OF LIST [2:?] OF IfcCartesianPoint	This is a list of lists of control points.
4	SurfaceForm	IfcBSplineSurfaceForm	Indicator of special surface types.
5	UClosed	IfcLogical	Indication of whether the surface is closed in the u direction; this is for information only.
6	VClosed	IfcLogical	Indication of whether the surface is closed in the v direction; this is for information only.
7	SelfIntersect	IfcLogical	Flag to indicate whether, or not, surface is self-intersecting; this is for information only.
*	UUpper	IfcInteger	This attribute is formally derived. `SIZEOF(ControlPointsList) - 1` Upper index on control points in u direction.
*	VUpper	IfcInteger	This attribute is formally derived. `SIZEOF(ControlPointsList[1]) - 1` Upper index on control points in v direction.
*	ControlPoints	ARRAY [0:UUpper] OF ARRAY [0:VUpper] OF IfcCartesianPoint	This attribute is formally derived. `IfcMakeArrayOfArray(ControlPointsList, 0,UUpper,0,VUpper)` Array (two-dimensional) of control points defining surface geometry. This array is constructed from the control points list.
IfcBSplineSurfaceWithKnots (7)
8	UMultiplicities	LIST [2:?] OF IfcInteger	The multiplicities of the knots in the u parameter direction.
9	VMultiplicities	LIST [2:?] OF IfcInteger	The multiplicities of the knots in the v parameter direction.
10	UKnots	LIST [2:?] OF IfcParameterValue	The list of the distinct knots in the u parameter direction.
11	VKnots	LIST [2:?] OF IfcParameterValue	The list of the distinct knots in the v parameter direction.
12	KnotSpec	IfcKnotType	The description of the knot type.
*	KnotVUpper	IfcInteger	This attribute is formally derived. `SIZEOF(VKnots)` The number of distinct knots in the v parameter direction.
*	KnotUUpper	IfcInteger	This attribute is formally derived. `SIZEOF(UKnots)` The number of distinct knots in the u parameter direction.
Click to show 20 hidden inherited attributes Click to hide 20 inherited attributes
IfcRationalBSplineSurfaceWithKnots (2)
13	WeightsData	LIST [2:?] OF LIST [2:?] OF IfcReal	The weights associated with the control points in the rational case.
*	Weights	ARRAY [0:UUpper] OF ARRAY [0:VUpper] OF IfcReal	This attribute is formally derived. `IfcMakeArrayOfArray(WeightsData,0,UUpper,0,VUpper)` Array (two-dimensional) of weight values constructed from the WeightsData.

Table 8.9.3.55.A

8.9.3.55.4 Formal propositions

Name	Description
CorrespondingWeightsDataLists	The array dimensions for the weights shall be consistent with the control points data.
`(SIZEOF(WeightsData) = SIZEOF(SELF\IfcBSplineSurface.ControlPointsList)) AND (SIZEOF(WeightsData[1]) = SIZEOF(SELF\IfcBSplineSurface.ControlPointsList[1]))`
WeightValuesGreaterZero	The weight value associated with each control point shall be greater than zero.
`IfcSurfaceWeightsPositive(SELF)`

Table 8.9.3.55.B

8.9.3.55.5 Formal representation

ENTITY IfcRationalBSplineSurfaceWithKnots
 SUBTYPE OF (IfcBSplineSurfaceWithKnots);
	WeightsData : LIST [2:?] OF LIST [2:?] OF IfcReal;
 DERIVE
	 Weights : ARRAY [0:UUpper] OF ARRAY [0:VUpper] OF IfcReal := IfcMakeArrayOfArray(WeightsData,0,UUpper,0,VUpper);
 WHERE
	CorrespondingWeightsDataLists : (SIZEOF(WeightsData) = SIZEOF(SELF\IfcBSplineSurface.ControlPointsList))
AND 
(SIZEOF(WeightsData[1]) = SIZEOF(SELF\IfcBSplineSurface.ControlPointsList[1]));
	WeightValuesGreaterZero : IfcSurfaceWeightsPositive(SELF);
END_ENTITY;