8.9.3.7 IfcBSplineSurface
ABSTRACT This definition may not be instantiated
8.9.3.7.1 Semantic definition
The IfcBSplineSurface is a general form of rational or polynomial parametric surface.
The symbology used here is:
Variable  Definition 

K1  upper_index_on_u_control_points 
K2  upper_index_on_v_control_points 
P_{ij}  control_points 
w_{ij}  weights 
d1  u_degree 
d2  v_degree 
The control points are ordered as: P_{00}, P_{01}, P_{02}, ..., P_{K1(K21)}, P_{K1K2}
The weights, in the case of the rational subtype, are ordered similarly.
For each parameter, s = u or v, if k is the upper
index on the control points and d is the degree for s, the knot array is an array of (k +
d + 2) real numbers [s_{d}, ...., s_{k+1}], such that for all indices j in
[d, k]; s_{j} ≤ s_{j+1}. This array is
obtained from the appropriate u_knots or v_knots list by repeating each multiple knot according to the
multiplicity.
N_{i}^{d}, the ith normalised Bspline basis function of degree d,
is defined on the subset [s_{id}, ...., s_{i+1}] of this
array.
Let L denote the number of distinct values amongst the 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 jth distinct knot value. Then:
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.
The surface form is used to identify specific quadric surface types (which shall have degree two), ruled surfaces and surfaces of revolution. As with the bspline curve, the surface form is informational only and the spline data takes precedence.
The surface is to be interpreted as follows: In the polynomial case the surface is given by the equation:
In the rational case the surface equation is:
8.9.3.7.2 Entity inheritance

 IfcSurface
 IfcAnnotationFillArea
 IfcBooleanResult
 IfcBoundingBox
 IfcCartesianPointList
 IfcCartesianTransformationOperator
 IfcCsgPrimitive3D
 IfcCurve
 IfcDirection
 IfcFaceBasedSurfaceModel
 IfcFillAreaStyleHatching
 IfcFillAreaStyleTiles
 IfcGeometricSet
 IfcHalfSpaceSolid
 IfcLightSource
 IfcPlacement
 IfcPlanarExtent
 IfcPoint
 IfcSectionedSpine
 IfcSegment
 IfcShellBasedSurfaceModel
 IfcSolidModel
 IfcTessellatedItem
 IfcTextLiteral
 IfcVector
8.9.3.7.3 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. 

IfcSurface (1)  
*  Dim  IfcDimensionCount 
This attribute is formally derived.
The space dimensionality of IfcSurface. It is always a threedimensional geometric representation item. 
Click to show 3 hidden inherited attributes Click to hide 3 inherited attributes  
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 selfintersecting; this is for information only. 
*  UUpper  IfcInteger 
This attribute is formally derived.
Upper index on control points in u direction. 
*  VUpper  IfcInteger 
This attribute is formally derived.
Upper index on control points in v direction. 
*  ControlPoints  ARRAY [0:UUpper] OF ARRAY [0:VUpper] OF IfcCartesianPoint 
This attribute is formally derived.
Array (twodimensional) of control points defining surface geometry. This array is constructed from the control points list. 
8.9.3.7.4 Formal representation
ENTITY IfcBSplineSurface
ABSTRACT SUPERTYPE OF (ONEOF
(IfcBSplineSurfaceWithKnots))
SUBTYPE OF (IfcBoundedSurface);
UDegree : IfcInteger;
VDegree : IfcInteger;
ControlPointsList : LIST [2:?] OF LIST [2:?] OF IfcCartesianPoint;
SurfaceForm : IfcBSplineSurfaceForm;
UClosed : IfcLogical;
VClosed : IfcLogical;
SelfIntersect : IfcLogical;
DERIVE
UUpper : IfcInteger := SIZEOF(ControlPointsList)  1;
VUpper : IfcInteger := SIZEOF(ControlPointsList[1])  1;
ControlPoints : ARRAY [0:UUpper] OF ARRAY [0:VUpper] OF IfcCartesianPoint := IfcMakeArrayOfArray(ControlPointsList,
0,UUpper,0,VUpper);
END_ENTITY;