8.9.3.53 IfcRationalBSplineCurveWithKnots
8.9.3.53.1 Semantic definition
A rational B-spline curve with knots is a B-spline curve described in terms of control points and basic functions. It describes weights in addition to the control points defined at the supertype IfcBSplineCurve.
All weights shall be positive and the curve is given by:
where:
Variable | Definition |
---|---|
k+1 | number of control points |
Pi | control points |
wi | weights |
d | degree |
8.9.3.53.2 Entity inheritance
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- 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
8.9.3.53.3 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 self-intersects 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. |
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 B-spline 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. |
Click to show 14 hidden inherited attributes Click to hide 14 inherited attributes | |||
IfcRationalBSplineCurveWithKnots (2) | |||
9 | WeightsData | LIST [2:?] OF IfcReal |
The supplied values of the weights. |
* | Weights | ARRAY [0:UpperIndexOnControlPoints] OF IfcReal |
This attribute is formally derived.
The array of weights associated with the control points. This is derived from the weights data. |
8.9.3.53.4 Formal propositions
Name | Description |
---|---|
SameNumOfWeightsAndPoints |
There shall be the same number of weights as control points. |
|
|
WeightsGreaterZero |
All the weights shall have values greater than 0.0. |
|
8.9.3.53.5 Formal representation
ENTITY IfcRationalBSplineCurveWithKnots
SUBTYPE OF (IfcBSplineCurveWithKnots);
WeightsData : LIST [2:?] OF IfcReal;
DERIVE
Weights : ARRAY [0:UpperIndexOnControlPoints] OF IfcReal := IfcListToArray(WeightsData,0,SELF\IfcBSplineCurve.UpperIndexOnControlPoints);
WHERE
SameNumOfWeightsAndPoints : SIZEOF(WeightsData) = SIZEOF(SELF\IfcBSplineCurve.ControlPointsList);
WeightsGreaterZero : IfcCurveWeightsPositive(SELF);
END_ENTITY;