Bézier-Spline-Kurve | |

BSpline Curve | |

Courbe Bspline |

The IfcBSplineCurve is a spline curve parameterized by spline functions.

Figure 367 illustrates a B-spline curve.

NOTE Figure quoted from ISO 10303-42.

Figure 367 — B-spline curve |

NOTE Definition according to ISO/CD 10303-42:1992

A B-spline curve is a piecewise parametric polynomial or rational curve described in terms of control points and basis functions. The B-spline curve has been selected as the most stable format to represent all types of polynomial or rational parametric curves. With appropriate attribute values it is capable of representing single span or spline curves of explicit polynomial, rational, Bezier or B-spline type.

Interpretation of the data is as follows:

All weights shall be positive and the curve is given by

k+1= number of control points P _{i}= control points w_{i}= weights d= degree The knot array is an array of (

k+d+2) real numbers [u_{-d}...u_{k+1}], such that for all indices j in [-d,k],u_{j}<=u_{j+1}. This array is obtained from the knot data list by repeating each multiple knot according to the multiplicity.N, the^{d}_{i}ith normalized B-spline basis function of degreed, is defined on the subset [u, ... ,_{i-d}u] of this array._{i+1}Let

Ldenote the number of distinct values among thed+k+2 knots in the knot array;Lwill be referred to as the 'upper index on knots'. Letmdenote the multiplicity (number of repetitions) of the_{j}jth distinct knot. ThenAll knot multiplicities except the first and the last shall be in the range 1 ... degree; the first and last may have a maximum value of degree + 1. In evaluating the basis functions, a knot

uof e.g. multiplicity 3 is interpreted as a stringu, u, u,in the knot array. The B-spline curve has 3 special subtypes (Note: only 1, Bezier curve, included in this IFC release) where the knots and knot multiplicities are derived to provide simple default capabilities.- Logical flag is provided to indicate whether the curve self intersects or not.

NOTE Entity adapted fromb_spline_curvedefined in ISO10303-42.

HISTORY New entity in IFC2x2.

# | Attribute | Type | Cardinality | Description | G |
---|---|---|---|---|---|

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 |

Rule | Description |
---|---|

SameDim | All control points shall have the same dimensionality. |

# | 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 IFC4 CHANGE The inverse attribute | 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 | 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 | |||||

PositioningElement | IfcLinearPositioningElement @Axis | ? | X | ||

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 |

` <xs:element name="IfcBSplineCurve" type="ifc:IfcBSplineCurve" abstract="true" substitutionGroup="ifc:IfcBoundedCurve" nillable="true"/>`

<xs:complexType name="IfcBSplineCurve" abstract="true">

<xs:complexContent>

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

<xs:sequence>

<xs:element name="ControlPointsList">

<xs:complexType>

<xs:sequence>

<xs:element ref="ifc:IfcCartesianPoint" minOccurs="2" maxOccurs="unbounded"/>

</xs:sequence>

<xs:attribute ref="ifc:itemType" fixed="ifc:IfcCartesianPoint"/>

<xs:attribute ref="ifc:cType" fixed="list"/>

<xs:attribute ref="ifc:arraySize" use="optional"/>

</xs:complexType>

</xs:element>

</xs:sequence>

<xs:attribute name="Degree" type="ifc:IfcInteger" use="optional"/>

<xs:attribute name="CurveForm" type="ifc:IfcBSplineCurveForm" use="optional"/>

<xs:attribute name="ClosedCurve" type="ifc:IfcLogical" use="optional"/>

<xs:attribute name="SelfIntersect" type="ifc:IfcLogical" use="optional"/>

</xs:extension>

</xs:complexContent>

</xs:complexType>

```
ENTITY IfcBSplineCurve
```

ABSTRACT SUPERTYPE OF(IfcBSplineCurveWithKnots)

SUBTYPE OF (IfcBoundedCurve)**;**

Degree : IfcInteger;

ControlPointsList : LIST [2:?] OF IfcCartesianPoint;

CurveForm : IfcBSplineCurveForm;

ClosedCurve : IfcLogical;

SelfIntersect : IfcLogical;

DERIVE

UpperIndexOnControlPoints : IfcInteger := (SIZEOF(ControlPointsList) - 1);

ControlPoints : ARRAY [0:UpperIndexOnControlPoints] OF IfcCartesianPoint := IfcListToArray(ControlPointsList,0,UpperIndexOnControlPoints);

WHERE

SameDim : SIZEOF(QUERY(Temp <* ControlPointsList |

Temp.Dim <> ControlPointsList[1].Dim))

= 0;

END_ENTITY;