8.9.3.6 IfcBSplineCurveWithKnots
8.9.3.6.1 Semantic definition
The IfcBSplineCurveWithKnots is a spline curve parameterized by spline functions for which the knot values are explicitly given.
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

 IfcCurve
 IfcAnnotationFillArea
 IfcBooleanResult
 IfcBoundingBox
 IfcCartesianPointList
 IfcCartesianTransformationOperator
 IfcCsgPrimitive3D
 IfcDirection
 IfcFaceBasedSurfaceModel
 IfcFillAreaStyleHatching
 IfcFillAreaStyleTiles
 IfcGeometricSet
 IfcHalfSpaceSolid
 IfcLightSource
 IfcPlacement
 IfcPlanarExtent
 IfcPoint
 IfcSectionedSpine
 IfcSegment
 IfcShellBasedSurfaceModel
 IfcSolidModel
 IfcSurface
 IfcTessellatedItem
 IfcTextLiteral
 IfcVector
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. 

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. 

IfcCurve (1)  
*  Dim  IfcDimensionCount 
This attribute is formally derived.
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 selfintersects or not; it is for information only. 
*  UpperIndexOnControlPoints  IfcInteger 
This attribute is formally derived.
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.
The array of control points used to define the geometry of the curve. This is derived from the list of control points. 
Click to show 10 hidden inherited attributes Click to hide 10 inherited attributes  
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 Bspline basis functions. 
8  KnotSpec  IfcKnotType 
The description of the knot type. This is for information only. 
*  UpperIndexOnKnots  IfcInteger 
This attribute is formally derived.
The upper index on the knot arrays; the lower index is 1. 
8.9.3.6.4 Formal propositions
Name  Description 

ConsistentBSpline 
The function IfcConstraintsParamBSpline returns TRUE if no inconsistencies in the parametrisation of the Bspline are found. 


CorrespondingKnotLists 
The number of elements in the knot multiplicities list shall be equal to the number of elements in the knots list. 

8.9.3.6.5 Examples
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;