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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.

formula
Figure 8.9.3.6.A

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

8.9.3.6.3 Attributes

# Attribute Type Description
IfcRepresentationItem (2)
IfcCurve (1)
IfcBSplineCurve (7)
Click to show 10 hidden 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 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.

SIZEOF(Knots)

The upper index on the knot arrays; the lower index is 1.

Table 8.9.3.6.C

8.9.3.6.4 Formal propositions

Name Description
ConsistentBSpline

The function IfcConstraintsParamBSpline returns TRUE if no inconsistencies in the parametrisation of the B-spline are found.

IfcConstraintsParamBSpline(Degree, UpperIndexOnKnots,
UpperIndexOnControlPoints, KnotMultiplicities, Knots)
CorrespondingKnotLists

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

SIZEOF(KnotMultiplicities) = UpperIndexOnKnots
Table 8.9.3.6.D

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;

8.9.3.6.7 References

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8.9.3.6.8 Changelog

8.9.3.6.8.1 IFC4

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