8.9.3.5 IfcBSplineCurve
ABSTRACT This definition may not be instantiated
8.9.3.5.1 Semantic definition
The IfcBSplineCurve is a spline curve parameterized by spline functions.
Figure 8.9.3.5.A illustrates a Bspline curve.
A Bspline curve is a piecewise parametric polynomial or rational curve described in terms of control points and basis functions. The Bspline curve has been selected as the most stable format to represent all types of polynomial or rational parametric curves. With appropriate attribute values it is capable of representing single span or spline curves of explicit polynomial, rational, Bezier or Bspline type.
Variable  Definition 

k+1  Number of control points 
P_{i}  Control points 
w_{i}  Weights 
d  Degree 
Interpretation of the data is as follows:
 All weights shall be positive and the curve is given by Figure 8.9.3.5.B, with variables defined in Table 8.9.3.5.D. The knot array is an array of (k+d+2) real numbers [u_{d} ... u_{k+1}], such that for all indices j in [d,k], u_{j} <= u_{j+1}. This array is obtained from the knot data list by repeating each multiple knot according to the multiplicity. N ^{d}_{i}, the ith normalized Bspline basis function of degree d, is defined on the subset [u_{id}, ... , u_{i+1}] of this array.
 Let L denote the number of distinct values among the d+k+2 knots in the knot array; L will be referred to as the 'upper index on knots'. Let m_{j} denote the multiplicity (number of repetitions) of the jth distinct knot. Then see Figure 8.9.3.5.C. All knot multiplicities except the first and the last shall be in the range 1 ... degree; the first and last may have a maximum value of degree + 1. In evaluating the basis functions, a knot u of e.g. multiplicity 3 is interpreted as a string u, u, u, in the knot array. The Bspline curve has 3 special subtypes (Note: only 1, Bezier curve, included in this IFC release) where the knots and knot multiplicities are derived to provide simple default capabilities.
 Logical flag is provided to indicate whether the curve self intersects or not.
8.9.3.5.2 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
8.9.3.5.3 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. 
Click to show 3 hidden inherited attributes Click to hide 3 inherited attributes  
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. 
8.9.3.5.4 Formal propositions
Name  Description 

SameDim 
All control points shall have the same dimensionality. 

8.9.3.5.5 Formal representation
ENTITY IfcBSplineCurve
ABSTRACT SUPERTYPE OF (ONEOF
(IfcBSplineCurveWithKnots))
SUBTYPE OF (IfcBoundedCurve);
Degree : IfcInteger;
ControlPointsList : LIST [2:?] OF IfcCartesianPoint;
CurveForm : IfcBSplineCurveForm;
ClosedCurve : IfcLogical;
SelfIntersect : IfcLogical;
DERIVE
UpperIndexOnControlPoints : IfcInteger := (SIZEOF(ControlPointsList)  1);
ControlPoints : ARRAY [0:UpperIndexOnControlPoints] OF IfcCartesianPoint := IfcListToArray(ControlPointsList,0,UpperIndexOnControlPoints);
WHERE
SameDim : SIZEOF(QUERY(Temp <* ControlPointsList 
Temp.Dim <> ControlPointsList[1].Dim))
= 0;
END_ENTITY;