Defined in File Ifc4x3_rc1.h
IfcBSplineSurface: public Ifc4x3_rc1::IfcBoundedSurface¶
Definition from 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
Pij = control_points
wij = weights
d1 = u_degree
d2 = v_degree
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]; sj ≤ sj+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:
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:
In the rational case the surface equation is:
NOTE Corresponding ISO 10303 entity: b_spline_surface. Please refer to ISO/IS 10303-42:1994, p. 78 for the final definition of the formal standard.
HISTORY New entity in IFC2x4.
Subclassed by Ifc4x3_rc1::IfcBSplineSurfaceWithKnots
Algebraic degree of basis functions in u.
Algebraic degree of basis functions in v.
This is a list of lists of control points.
Indication of whether the surface is closed in the u direction; this is for information only.
Indication of whether the surface is closed in the v direction; this is for information only.
Flag to indicate whether, or not, surface is self-intersecting; this is for information only.