Bézier-Spline-Fläche | |

BSpline Surface | |

Surface Bspline |

Item | SPF | XML | Change | Description |
---|---|---|---|---|

4.0.0.0 |
||||

IfcBSplineSurface | ADDED |

The IfcBSplineSurface is a general form of rational or polynomial parametric surface.

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

A b_spline_surface is a general form of rational or polynomial parametric surface which is represented by control points, basis functions, and possibly, weights. As with the corresponding curve entity it has some special subtypes where some of the data can be derived.

- The symbology used here is:

K1= upper_index_on_u_control_points K2= upper_index_on_v_control_points P_{ij}= control_points w _{ij}= weights d1= u_degree d2= v_degree - The control points are ordered as
PThe weights, in the case of the rational subtype, are ordered similarly._{00}, P_{01}, P_{02}, ......, P_{K1(K2-1)}, P_{K1K2}

- For each parameter,
s=uorv, ifkis the upper index on the control points anddis the degree fors, the knot array is an array of (k+d+ 2) real numbers [s_{-d}, ...., s_{k+1}], such that for all indices j in [-d,k];s_{j}≤s_{j+1}. This array is obtained from the appropriate u_knots or v_knots list by repeating each multiple knot according to the multiplicity.

N_{i}^{d}, theith normalised B-spline basis function of degreed, is defined on the subset [s_{i-d}, ....,s_{i+1}] of this array.

- Let
Ldenote the number of distinct values amongst the knots in the knot list;Lwill be referred to as the ‘upper index on knots’. Letm_{j}denote the multiplicity (i.e., number of repetitions) of thejth 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 ofd+1. In evaluating the basis functions, a knotuof, e.g., multiplicity 3 is interpreted as a sequenceu,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:

NOTE Entity adapted fromb_spline_surfacedefined in ISO10303-42.

HISTORY New entity in IFC4.

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

1 | UDegree | IfcInteger |
Algebraic degree of basis functions in u. | X | |

2 | VDegree | IfcInteger |
Algebraic degree of basis functions in v. | X | |

3 | ControlPointsList | IfcCartesianPoint | L[2:?] L[2:?] | This is a list of lists of control points. | X |

4 | SurfaceForm | IfcBSplineSurfaceForm | Indicator of special surface types. | X | |

5 | UClosed | IfcLogical |
Indication of whether the surface is closed in the u direction; this is for information only. | X | |

6 | VClosed | IfcLogical |
Indication of whether the surface is closed in the v direction; this is for information only. | X | |

7 | SelfIntersect | IfcLogical | Flag to indicate whether, or not, surface is self-intersecting; this is for information only. | X | |

UUpper :=SIZEOF(ControlPointsList) - 1 | IfcInteger | Upper index on control points in u direction. |
X | ||

VUpper :=SIZEOF(ControlPointsList[1]) - 1 | IfcInteger | Upper index on control points in v direction. |
X | ||

ControlPoints :=IfcMakeArrayOfArray(ControlPointsList, 0,UUpper,0,VUpper) | IfcCartesianPoint | A[0:UUpper] A[0:VUpper] | Array (two-dimensional) of control points defining surface geometry. This array is constructed from the control points list. | X |

# | 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 | |||||

IfcSurface | |||||

Dim :=3 | IfcDimensionCount | The space dimensionality of IfcSurface. It is always a three-dimensional geometric representation item.
IFC4 CHANGE Derived attribute promoted from subtypes. |
X | ||

IfcBoundedSurface | |||||

IfcBSplineSurface | |||||

1 | UDegree | IfcInteger |
Algebraic degree of basis functions in u. | X | |

2 | VDegree | IfcInteger |
Algebraic degree of basis functions in v. | X | |

3 | ControlPointsList | IfcCartesianPoint | L[2:?] L[2:?] | This is a list of lists of control points. | X |

4 | SurfaceForm | IfcBSplineSurfaceForm | Indicator of special surface types. | X | |

5 | UClosed | IfcLogical |
Indication of whether the surface is closed in the u direction; this is for information only. | X | |

6 | VClosed | IfcLogical |
Indication of whether the surface is closed in the v direction; this is for information only. | X | |

7 | SelfIntersect | IfcLogical | Flag to indicate whether, or not, surface is self-intersecting; this is for information only. | X | |

UUpper :=SIZEOF(ControlPointsList) - 1 | IfcInteger | Upper index on control points in u direction. |
X | ||

VUpper :=SIZEOF(ControlPointsList[1]) - 1 | IfcInteger | Upper index on control points in v direction. |
X | ||

ControlPoints :=IfcMakeArrayOfArray(ControlPointsList, 0,UUpper,0,VUpper) | IfcCartesianPoint | A[0:UUpper] A[0:VUpper] | Array (two-dimensional) of control points defining surface geometry. This array is constructed from the control points list. | X |

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

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

<xs:complexContent>

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

<xs:sequence>

<xs:element name="ControlPointsList">

<xs:complexType>

<xs:sequence>

<xs:element ref="ifc:IfcCartesianPoint" minOccurs="4" maxOccurs="unbounded"/>

</xs:sequence>

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

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

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

</xs:complexType>

</xs:element>

</xs:sequence>

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

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

<xs:attribute name="SurfaceForm" type="ifc:IfcBSplineSurfaceForm" use="optional"/>

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

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

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

</xs:extension>

</xs:complexContent>

</xs:complexType>

```
ENTITY IfcBSplineSurface
```

ABSTRACT SUPERTYPE OF(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;