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IfcBSplineCurve

Definition from ISO/CD 10303-42:1992: A B-spline curve is a piecewise parametric polynominal 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 polynominal 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:

  1. All weights shall be positive and the curve is given by

    k+1 = number of control points
    Pi = control points
    wi = weights
    d = degree

    The knot array is an array of (k+d+2) real numbers [u-d ... uk+1], such that for all indices j in [-d,k], uj <= uj+1. This array is obtained from the knot data list by repeating each multiple knot according to the multiplicity. N di, the ith normalised B-spline basis function of degree d, is defined on the subset [ui-d, ... , ui+1] of this array.

  2. Let L denote the number of distinct values amongst the d+k+2 knots in the knot array; 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. Then

    All 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 u of e.g. multiplicity 3 is interpreted as a string u, u, u, in the knot array. The B-spline curve has 3 special subtypes (IAI note: only 1, Bezier curve, included in this IFC release) where the knots and knot multiplicities are derived to provide simple default capabilities.

  3. Logical flag is provided to indicate whether the curve self intersects or not.

Illustration from ISO 10303-42:

control points

NOTE: Corresponding STEP entity: b_spline_curve. Please refer to ISO/IS 10303-42:1994, p. 45 for the final definition of the formal standard.

HISTORY: New entity in Release IFC2x Edition 2.

EXPRESS specification:

ENTITY IfcBSplineCurve
ABSTRACT SUPERTYPE OF (IfcBezierCurve)
SUBTYPE OF ( IfcBoundedCurve);
Degree  :  INTEGER;
ControlPointsList  :  LIST [2:?] OF IfcCartesianPoint;
CurveForm  :  IfcBSplineCurveForm;
ClosedCurve  :  LOGICAL;
SelfIntersect  :  LOGICAL;
DERIVE
ControlPoints  :  ARRAY [0:255] OF IfcCartesianPoint :=  IfcListToArray(ControlPointsList,0,UpperIndexOnControlPoints);
UpperIndexOnControlPoints  :  INTEGER :=  (SIZEOF(ControlPointsList) - 1);
WHERE
WR41  :  SIZEOF(QUERY(Temp <* ControlPointsList | Temp.Dim <> ControlPointsList[1].Dim)) = 0;
END_ENTITY;

Attribute definitions:

Degree  :  The algebraic degree of the basis functions.
ControlPointsList  :  The list of control points for the curve.
CurveForm  :  Used to identify particular types of curve; it is for information only.
ClosedCurve  :  Indication of whether the curve is closed; it is for information only.
SelfIntersect  :  Indication whether the curve self-intersects or not; it is for information only.
ControlPoints  :  The array of control points used to define the geometry of the curve. This is derived from the list of control points.
UpperIndexOnControlPoints  :  The upper index on the array of control points; the lower index is 0.
This value is derived from the control points list.

Formal Propositions:

WR41  :  All control points shall have the same dimensionality.

Inheritance graph

ENTITY IfcBSplineCurve;
ENTITY IfcRepresentationItem;
ENTITY IfcGeometricRepresentationItem;
ENTITY IfcCurve;
DERIVE
Dim  :  IfcDimensionCount :=  IfcCurveDim(SELF);
ENTITY IfcBoundedCurve;
ENTITY IfcBSplineCurve;
Degree  :  INTEGER;
ControlPointsList  :  LIST [2:?] OF IfcCartesianPoint;
CurveForm  :  IfcBSplineCurveForm;
ClosedCurve  :  LOGICAL;
SelfIntersect  :  LOGICAL;
DERIVE
ControlPoints  :  ARRAY [0:255] OF IfcCartesianPoint :=  IfcListToArray(ControlPointsList,0,UpperIndexOnControlPoints);
UpperIndexOnControlPoints  :  INTEGER :=  (SIZEOF(ControlPointsList) - 1);
END_ENTITY;