IFC 4.3.0.1 (IFC4X3) development

8.9.3.7 IfcBSplineSurface

ABSTRACT This definition may not be instantiated

8.9.3.7.1 Semantic definition

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

The symbology used here is:

Variable Definition
K1 upper_index_on_u_control_points
K2 upper_index_on_v_control_points
Pij control_points
wij weights
d1 u_degree
d2 v_degree
Table 8.9.3.7.D

The control points are ordered as: P00, P01, P02, ..., PK1(K2-1), PK1K2

The weights, in the case of the rational subtype, are ordered similarly.

For each parameter, s = u or v, if k is the upper index on the control points and d is the degree for s, the knot array is an array of (k + d + 2) real numbers [s-d, ...., sk+1], such that for all indices j in [-d, k]; sjsj+1. This array is obtained from the appropriate u_knots or v_knots list by repeating each multiple knot according to the multiplicity.

Nid, the ith normalised B-spline basis function of degree d, is defined on the subset [si-d, ...., si+1] of this array.

Let L denote the number of distinct values amongst the knots in the knot list; L will be referred to as the ‘upper index on knots’. Let mj denote the multiplicity (i.e., number of repetitions) of the jth distinct knot value. Then:

formula
Figure 8.9.3.7.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.

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:

formula
Figure 8.9.3.7.B

In the rational case the surface equation is:

formula
Figure 8.9.3.7.C

8.9.3.7.2 Entity inheritance

8.9.3.7.3 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.

IfcSurface (1)
* Dim IfcDimensionCount

This attribute is formally derived.

3

The space dimensionality of IfcSurface. It is always a three-dimensional geometric representation item.

Click to show 3 hidden inherited attributes Click to hide 3 inherited attributes
IfcBSplineSurface (10)
1 UDegree IfcInteger

Algebraic degree of basis functions in u.

2 VDegree IfcInteger

Algebraic degree of basis functions in v.

3 ControlPointsList LIST [2:?] OF LIST [2:?] OF IfcCartesianPoint

This is a list of lists of control points.

4 SurfaceForm IfcBSplineSurfaceForm

Indicator of special surface types.

5 UClosed IfcLogical

Indication of whether the surface is closed in the u direction; this is for information only.

6 VClosed IfcLogical

Indication of whether the surface is closed in the v direction; this is for information only.

7 SelfIntersect IfcLogical

Flag to indicate whether, or not, surface is self-intersecting; this is for information only.

* UUpper IfcInteger

This attribute is formally derived.

SIZEOF(ControlPointsList) - 1

Upper index on control points in u direction.

* VUpper IfcInteger

This attribute is formally derived.

SIZEOF(ControlPointsList[1]) - 1

Upper index on control points in v direction.

* ControlPoints ARRAY [0:UUpper] OF ARRAY [0:VUpper] OF IfcCartesianPoint

This attribute is formally derived.

IfcMakeArrayOfArray(ControlPointsList,
0,UUpper,0,VUpper)

Array (two-dimensional) of control points defining surface geometry. This array is constructed from the control points list.

Table 8.9.3.7.E

8.9.3.7.4 Formal representation

ENTITY IfcBSplineSurface
 ABSTRACT SUPERTYPE OF (ONEOF
	(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;

8.9.3.7.5 References

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8.9.3.7.6 Changelog

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