IfcBSplineCurveWithKnots

Item	Change	Description
IFC2x3 to IFC4
IfcBSplineCurveWithKnots	ADDED
IFC4 Addendum 1
IfcBSplineCurveWithKnots
Degree	MODIFIED	Type changed from INTEGER to IfcInteger.
ClosedCurve	MODIFIED	Type changed from LOGICAL to IfcLogical.
SelfIntersect	MODIFIED	Type changed from LOGICAL to IfcLogical.
KnotMultiplicities	MODIFIED	Type changed from INTEGER to IfcInteger.

Semantic definitions at the entity

Entity definition

The IfcBSplineCurveWithKnots is a spline curve parameterized by spline functions for which the knot values are explicitly given.

NOTE Definition according to ISO/CD 10303-42:1992
This is the type of b-spline curve for which the knot values are explicitly given. This subtype shall be used to represent non-uniform B-spline curves and may be used for other knot types.
Let L denote the number of distinct values amongst the d+k+2 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. 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.

NOTE Entity adapted from b_spline_curve_with_knots defined in ISO10303-42.

HISTORY New entity in IFC4.

Attribute definitions

#	Attribute	Type	Cardinality	Description	G
6	KnotMultiplicities	IfcInteger	L[2:?]	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.	X
7	Knots	IfcParameterValue	L[2:?]	The list of distinct knots used to define the B-spline basis functions.	X
8	KnotSpec	IfcKnotType		The description of the knot type. This is for information only.	X
	UpperIndexOnKnots :=SIZEOF(Knots)	IfcInteger		The upper index on the knot arrays; the lower index is 1.	X

Formal Propositions

Rule	Description
ConsistentBSpline	The function IfcConstraintsParamBSpline returns TRUE if no inconsistencies in the parametrisation of the B-spline are found.
CorrespondingKnotLists	The number of elements in the knot multiplicities list shall be equal to the number of elements in the knots list.

Inherited definitions from supertypes

Entity inheritance

Attribute inheritance

#	Attribute	Type	Cardinality	Description	G
IfcRepresentationItem
	LayerAssignment	IfcPresentationLayerAssignment @AssignedItems	S[0:1]	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. IFC2x3 CHANGE The inverse attribute LayerAssignments has been added. IFC4 CHANGE The inverse attribute LayerAssignment has been restricted to max 1. Upward compatibility for file based exchange is guaranteed.	X
	StyledByItem	IfcStyledItem @Item	S[0:1]	Reference to the IfcStyledItem that provides presentation information to the representation, e.g. a curve style, including colour and thickness to a geometric curve. IFC2x3 CHANGE The inverse attribute StyledByItem has been added.	X
IfcGeometricRepresentationItem
IfcCurve
	Dim :=IfcCurveDim(SELF)	IfcDimensionCount		The space dimensionality of this abstract class, defined differently for all subtypes, i.e. for IfcLine, IfcConic and IfcBoundedCurve.	X
IfcBoundedCurve
IfcBSplineCurve
1	Degree	IfcInteger		The algebraic degree of the basis functions.	X
2	ControlPointsList	IfcCartesianPoint	L[2:?]	The list of control points for the curve.	X
3	CurveForm	IfcBSplineCurveForm		Used to identify particular types of curve; it is for information only.	X
4	ClosedCurve	IfcLogical		Indication of whether the curve is closed; it is for information only.	X
5	SelfIntersect	IfcLogical		Indication whether the curve self-intersects or not; it is for information only.	X
	UpperIndexOnControlPoints :=(SIZEOF(ControlPointsList) - 1)	IfcInteger		The upper index on the array of control points; the lower index is 0. This value is derived from the control points list.	X
	ControlPoints :=IfcListToArray(ControlPointsList,0,UpperIndexOnControlPoints)	IfcCartesianPoint	A[0:UpperIndexOnControlPoints]	The array of control points used to define the geometry of the curve. This is derived from the list of control points.	X
IfcBSplineCurveWithKnots
6	KnotMultiplicities	IfcInteger	L[2:?]	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.	X
7	Knots	IfcParameterValue	L[2:?]	The list of distinct knots used to define the B-spline basis functions.	X
8	KnotSpec	IfcKnotType		The description of the knot type. This is for information only.	X
	UpperIndexOnKnots :=SIZEOF(Knots)	IfcInteger		The upper index on the knot arrays; the lower index is 1.	X

Formal representations

XML Specification

 <xs:element name="IfcBSplineCurveWithKnots" type="ifc:IfcBSplineCurveWithKnots" substitutionGroup="ifc:IfcBSplineCurve" nillable="true"/>

 <xs:complexType name="IfcBSplineCurveWithKnots">

  <xs:complexContent>

   <xs:extension base="ifc:IfcBSplineCurve">

    <xs:attribute name="KnotMultiplicities" use="optional">

     <xs:simpleType>

      <xs:restriction>

       <xs:simpleType>

        <xs:list itemType="ifc:IfcInteger"/>

       </xs:simpleType>

       <xs:minLength value="2"/>

      </xs:restriction>

     </xs:simpleType>

    </xs:attribute>

    <xs:attribute name="Knots" use="optional">

     <xs:simpleType>

      <xs:restriction>

       <xs:simpleType>

        <xs:list itemType="ifc:IfcParameterValue"/>

       </xs:simpleType>

       <xs:minLength value="2"/>

      </xs:restriction>

     </xs:simpleType>

    </xs:attribute>

    <xs:attribute name="KnotSpec" type="ifc:IfcKnotType" use="optional"/>

   </xs:extension>

  </xs:complexContent>

 </xs:complexType>

EXPRESS Specification


ENTITY IfcBSplineCurveWithKnots

 SUPERTYPE OF(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;

 EXPRESS-G diagram

	B茅zier-Spline-Kurve mit (gegebenen) Kontrollpunkten
	BSpline Curve With Knots