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 |
Pij | control_points |
wij | weights |
d1 | u_degree |
d2 | v_degree |
The control points are ordered as: P00, P01, P02, ..., PK1(K2-1), PK1K2
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, ...., sk+1], such that for all indices j in
[-d, k]; sj ≤ sj+1. This array is
obtained from the appropriate u_knots or v_knots list by repeating each multiple knot according to the
multiplicity.
Nid, the ith normalised B-spline basis function of degree d,
is defined on the subset [si-d, ...., si+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 mj 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 b-spline 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 three-dimensional 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 self-intersecting; 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 (two-dimensional) 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;