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Geom


Geom_BSplineCurve Class Reference

Definition of the B_spline curve.
A B-spline curve can be
Uniform or non-uniform
Rational or non-rational
Periodic or non-periodic

a b-spline curve is defined by :
its degree; the degree for a
Geom_BSplineCurve is limited to a value (25)
which is defined and controlled by the system.
This value is returned by the function MaxDegree;
- its periodic or non-periodic nature;
- a table of poles (also called control points), with
their associated weights if the BSpline curve is
rational. The poles of the curve are "control <br> points" used to deform the curve. If the curve is
non-periodic, the first pole is the start point of
the curve, and the last pole is the end point of
the curve. The segment which joins the first pole
to the second pole is the tangent to the curve at
its start point, and the segment which joins the
last pole to the second-from-last pole is the
tangent to the curve at its end point. If the curve
is periodic, these geometric properties are not
verified. It is more difficult to give a geometric
signification to the weights but are useful for
providing exact representations of the arcs of a
circle or ellipse. Moreover, if the weights of all the
poles are equal, the curve has a polynomial
equation; it is therefore a non-rational curve.
- a table of knots with their multiplicities. For a
Geom_BSplineCurve, the table of knots is an
increasing sequence of reals without repetition;
the multiplicities define the repetition of the knots.
A BSpline curve is a piecewise polynomial or
rational curve. The knots are the parameters of
junction points between two pieces. The
multiplicity Mult(i) of the knot Knot(i) of
the BSpline curve is related to the degree of
continuity of the curve at the knot Knot(i),
which is equal to Degree - Mult(i)
where Degree is the degree of the BSpline curve.
If the knots are regularly spaced (i.e. the difference
between two consecutive knots is a constant), three
specific and frequently used cases of knot
distribution can be identified:
- "uniform" if all multiplicities are equal to 1,
- "quasi-uniform" if all multiplicities are equal to 1,
except the first and the last knot which have a
multiplicity of Degree + 1, where Degree is
the degree of the BSpline curve,
- "Piecewise Bezier" if all multiplicities are equal to
Degree except the first and last knot which
have a multiplicity of Degree + 1, where
Degree is the degree of the BSpline curve. A
curve of this type is a concatenation of arcs of Bezier curves.
If the BSpline curve is not periodic:
- the bounds of the Poles and Weights tables are 1
and NbPoles, where NbPoles is the number
of poles of the BSpline curve,
- the bounds of the Knots and Multiplicities tables
are 1 and NbKnots, where NbKnots is the
number of knots of the BSpline curve.
If the BSpline curve is periodic, and if there are k
periodic knots and p periodic poles, the period is:
period = Knot(k + 1) - Knot(1)
and the poles and knots tables can be considered
as infinite tables, verifying:
- Knot(i+k) = Knot(i) + period
- Pole(i+p) = Pole(i)
Note: data structures of a periodic BSpline curve
are more complex than those of a non-periodic one.
Warning
In this class, weight value is considered to be zero if
the weight is less than or equal to gp::Resolution().

References :
. A survey of curve and surface methods in CADG Wolfgang BOHM
CAGD 1 (1984)
. On de Boor-like algorithms and blossoming Wolfgang BOEHM
cagd 5 (1988)
. Blossoming and knot insertion algorithms for B-spline curves
Ronald N. GOLDMAN
. Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA
. Curves and Surfaces for Computer Aided Geometric Design,
a practical guide Gerald Farin
.

#include <Geom_BSplineCurve.hxx>

Inheritance diagram for Geom_BSplineCurve:

Inheritance graph
[legend]

Public Member Functions

Standard_EXPORT Geom_BSplineCurve (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, const Standard_Integer Degree, const Standard_Boolean Periodic=Standard_False)
 Creates a non-rational B_spline curve on the
basis <Knots, Multiplicities> of degree <degree>.
.
Standard_EXPORT Geom_BSplineCurve (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, const Standard_Integer Degree, const Standard_Boolean Periodic=Standard_False, const Standard_Boolean CheckRational=Standard_True)
 Creates a rational B_spline curve on the basis
<Knots, Multiplicities> of degree <degree>.
Raises ConstructionError subject to the following conditions
0 < Degree <= MaxDegree.

Weights.Length() == Poles.Length()

Knots.Length() == Mults.Length() >= 2

Knots(i) < Knots(i+1) (Knots are increasing)

1 <= Mults(i) <= Degree

On a non periodic curve the first and last multiplicities
may be Degree+1 (this is even recommanded if you want the
curve to start and finish on the first and last pole).

On a periodic curve the first and the last multicities
must be the same.

on non-periodic curves

Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2

on periodic curves

Poles.Length() == Sum(Mults(i)) except the first or last
.
Standard_EXPORT void IncreaseDegree (const Standard_Integer Degree)
 Increases the degree of this BSpline curve to
Degree. As a result, the poles, weights and
multiplicities tables are modified; the knots table is
not changed. Nothing is done if Degree is less than
or equal to the current degree.
Exceptions
Standard_ConstructionError if Degree is greater than
Geom_BSplineCurve::MaxDegree().
.
Standard_EXPORT void IncreaseMultiplicity (const Standard_Integer Index, const Standard_Integer M)
 Increases the multiplicity of the knot <index> to
<m>.

If <m> is lower or equal to the current
multiplicity nothing is done. If <m> is higher than
the degree the degree is used.
//! If <index> is not in [FirstUKnotIndex, LastUKnotIndex]
.
Standard_EXPORT void IncreaseMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M)
 Increases the multiplicities of the knots in
[I1,I2] to <m>.

For each knot if <m> is lower or equal to the
current multiplicity nothing is done. If <m> is
higher than the degree the degree is used.
//! If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]
.
Standard_EXPORT void IncrementMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M)
 Increment the multiplicities of the knots in
[I1,I2] by <m>.

If <m> is not positive nithing is done.

For each knot the resulting multiplicity is
limited to the Degree.
//! If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]
.
Standard_EXPORT void InsertKnot (const Standard_Real U, const Standard_Integer M=1, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_True)
 Inserts a knot value in the sequence of knots. If
<u> is an existing knot the multiplicity is
increased by <m>.

If U is not on the parameter range nothing is
done.

If the multiplicity is negative or null nothing is
done. The new multiplicity is limited to the
degree.

The tolerance criterion for knots equality is
the max of Epsilon(U) and ParametricTolerance.
.
Standard_EXPORT void InsertKnots (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_False)
 Inserts a set of knots values in the sequence of
knots.

For each U = Knots(i), M = Mults(i)

If <u> is an existing knot the multiplicity is
increased by <m> if <add> is True, increased to
<m> if <add> is False.

If U is not on the parameter range nothing is
done.

If the multiplicity is negative or null nothing is
done. The new multiplicity is limited to the
degree.

The tolerance criterion for knots equality is
the max of Epsilon(U) and ParametricTolerance.
.
Standard_EXPORT Standard_Boolean RemoveKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance)
 Reduces the multiplicity of the knot of index Index
to M. If M is equal to 0, the knot is removed.
With a modification of this type, the array of poles is also modified.
Two different algorithms are systematically used to
compute the new poles of the curve. If, for each
pole, the distance between the pole calculated
using the first algorithm and the same pole
calculated using the second algorithm, is less than
Tolerance, this ensures that the curve is not
modified by more than Tolerance. Under these
conditions, true is returned; otherwise, false is returned.
A low tolerance is used to prevent modification of
the curve. A high tolerance is used to "smooth" the curve.
Exceptions
Standard_OutOfRange if Index is outside the
bounds of the knots table.
//! pole insertion and pole removing
this operation is limited to the Uniform or QuasiUniform
BSplineCurve. The knot values are modified . If the BSpline is
NonUniform or Piecewise Bezier an exception Construction error
is raised.
.
Standard_EXPORT void Reverse ()
 Changes the direction of parametrization of <me>. The Knot
sequence is modified, the FirstParameter and the
LastParameter are not modified. The StartPoint of the
initial curve becomes the EndPoint of the reversed curve
and the EndPoint of the initial curve becomes the StartPoint
of the reversed curve.
.
Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const
 Returns the parameter on the reversed curve for
the point of parameter U on <me>.

returns UFirst + ULast - U
.
Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2)
 Modifies this BSpline curve by segmenting it between
U1 and U2. Either of these values can be outside the
bounds of the curve, but U2 must be greater than U1.
All data structure tables of this BSpline curve are
modified, but the knots located between U1 and U2
are retained. The degree of the curve is not modified.
Warnings :
Even if <me> is not closed it can become closed after the
segmentation for example if U1 or U2 are out of the bounds
of the curve <me> or if the curve makes loop.
After the segmentation the length of a curve can be null.
//! raises if U2 < U1.
.
Standard_EXPORT void SetKnot (const Standard_Integer Index, const Standard_Real K)
 Modifies this BSpline curve by assigning the value K
to the knot of index Index in the knots table. This is a
relatively local modification because K must be such that:
Knots(Index - 1) < K < Knots(Index + 1)
The second syntax allows you also to increase the
multiplicity of the knot to M (but it is not possible to
decrease the multiplicity of the knot with this function).
Standard_ConstructionError if:
- K is not such that:
Knots(Index - 1) < K < Knots(Index + 1)
- M is greater than the degree of this BSpline curve
or lower than the previous multiplicity of knot of
index Index in the knots table.
Standard_OutOfRange if Index is outside the bounds of the knots table.
.
Standard_EXPORT void SetKnots (const TColStd_Array1OfReal &K)
 Modifies this BSpline curve by assigning the array
K to its knots table. The multiplicity of the knots is not modified.
Exceptions
Standard_ConstructionError if the values in the
array K are not in ascending order.
Standard_OutOfRange if the bounds of the array
K are not respectively 1 and the number of knots of this BSpline curve.
.
Standard_EXPORT void SetKnot (const Standard_Integer Index, const Standard_Real K, const Standard_Integer M)
 Changes the knot of range Index with its multiplicity.
You can increase the multiplicity of a knot but it is
not allowed to decrease the multiplicity of an existing knot.
Raised if K >= Knots(Index+1) or K <= Knots(Index-1).
Raised if M is greater than Degree or lower than the previous
multiplicity of knot of range Index.
//! Raised if Index < 1 || Index > NbKnots
.
Standard_EXPORT void PeriodicNormalization (Standard_Real &U) const
 returns the parameter normalized within
the period if the curve is periodic : otherwise
does not do anything

Standard_EXPORT void SetPeriodic ()
 Changes this BSpline curve into a periodic curve.
To become periodic, the curve must first be closed.
Next, the knot sequence must be periodic. For this,
FirstUKnotIndex and LastUKnotIndex are used
to compute I1 and I2, the indexes in the knots
array of the knots corresponding to the first and
last parameters of this BSpline curve.
The period is therefore: Knots(I2) - Knots(I1).
Consequently, the knots and poles tables are modified.
Exceptions
Standard_ConstructionError if this BSpline curve is not closed.
.
Standard_EXPORT void SetOrigin (const Standard_Integer Index)
 Assigns the knot of index Index in the knots table as
the origin of this periodic BSpline curve. As a
consequence, the knots and poles tables are modified.
Exceptions
Standard_NoSuchObject if this curve is not periodic.
Standard_DomainError if Index is outside the bounds of the knots table.
.
Standard_EXPORT void SetOrigin (const Standard_Real U, const Standard_Real Tol)
 Set the origin of a periodic curve at Knot U. If U
is not a knot of the BSpline a new knot is
inseted. KnotVector and poles are modified.
//! Raised if the curve is not periodic
.
Standard_EXPORT void SetNotPeriodic ()
 Changes this BSpline curve into a non-periodic
curve. If this curve is already non-periodic, it is not modified.
Note: the poles and knots tables are modified.
Warning
If this curve is periodic, as the multiplicity of the first
and last knots is not modified, and is not equal to
Degree + 1, where Degree is the degree of
this BSpline curve, the start and end points of the
curve are not its first and last poles.
.
Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt &P)
 Modifies this BSpline curve by assigning P to the pole
of index Index in the poles table.
Exceptions
Standard_OutOfRange if Index is outside the
bounds of the poles table.
Standard_ConstructionError if Weight is negative or null.
.
Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight)
 Modifies this BSpline curve by assigning P to the pole
of index Index in the poles table.
This syntax also allows you to modify the
weight of the modified pole, which becomes Weight.
In this case, if this BSpline curve is non-rational, it
can become rational and vice versa.
Exceptions
Standard_OutOfRange if Index is outside the
bounds of the poles table.
Standard_ConstructionError if Weight is negative or null.
.
Standard_EXPORT void SetWeight (const Standard_Integer Index, const Standard_Real Weight)
 Changes the weight for the pole of range Index.
If the curve was non rational it can become rational.
If the curve was rational it can become non rational.
Raised if Index < 1 || Index > NbPoles
//! Raised if Weight <= 0.0
.
Standard_EXPORT void MovePoint (const Standard_Real U, const gp_Pnt &P, const Standard_Integer Index1, const Standard_Integer Index2, Standard_Integer &FirstModifiedPole, Standard_Integer &LastModifiedPole)
 Moves the point of parameter U of this BSpline curve
to P. Index1 and Index2 are the indexes in the table
of poles of this BSpline curve of the first and last
poles designated to be moved.
FirstModifiedPole and LastModifiedPole are the
indexes of the first and last poles which are effectively modified.
In the event of incompatibility between Index1, Index2 and the value U:
- no change is made to this BSpline curve, and
- the FirstModifiedPole and LastModifiedPole are returned null.
Exceptions
Standard_OutOfRange if:
- Index1 is greater than or equal to Index2, or
- Index1 or Index2 is less than 1 or greater than the
number of poles of this BSpline curve.
.
Standard_EXPORT void MovePointAndTangent (const Standard_Real U, const gp_Pnt &P, const gp_Vec &Tangent, const Standard_Real Tolerance, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, Standard_Integer &ErrorStatus)
 Move a point with parameter U to P.
and makes it tangent at U be Tangent.
StartingCondition = -1 means first can move
EndingCondition = -1 means last point can move
StartingCondition = 0 means the first point cannot move
EndingCondition = 0 means the last point cannot move
StartingCondition = 1 means the first point and tangent cannot move
EndingCondition = 1 means the last point and tangent cannot move
and so forth
ErrorStatus != 0 means that there are not enought degree of freedom
with the constrain to deform the curve accordingly

.
Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const
 Returns the continuity of the curve, the curve is at least C0.
//! Raised if N < 0.
.
Standard_EXPORT Standard_Boolean IsClosed () const
 Returns true if the distance between the first point and the
last point of the curve is lower or equal to Resolution
from package gp.
Warnings :
The first and the last point can be different from the first
pole and the last pole of the curve.
.
Standard_EXPORT Standard_Boolean IsPeriodic () const
 Returns True if the curve is periodic.
.
Standard_EXPORT Standard_Boolean IsRational () const
 Returns True if the weights are not identical.
The tolerance criterion is Epsilon of the class Real.
.
Standard_EXPORT GeomAbs_Shape Continuity () const
 Returns the global continuity of the curve :
C0 : only geometric continuity,
C1 : continuity of the first derivative all along the Curve,
C2 : continuity of the second derivative all along the Curve,
C3 : continuity of the third derivative all along the Curve,
CN : the order of continuity is infinite.
For a B-spline curve of degree d if a knot Ui has a
multiplicity p the B-spline curve is only Cd-p continuous
at Ui. So the global continuity of the curve can't be greater
than Cd-p where p is the maximum multiplicity of the interior
Knots. In the interior of a knot span the curve is infinitely
continuously differentiable.
.
Standard_EXPORT Standard_Integer Degree () const
 Returns the degree of this BSpline curve.
The degree of a Geom_BSplineCurve curve cannot
be greater than Geom_BSplineCurve::MaxDegree().
//! Computation of value and derivatives
.
Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt &P) const
 Returns in P the point of parameter U.
.
Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const
 Raised if the continuity of the curve is not C1.
.
Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const
 Raised if the continuity of the curve is not C2.
.
Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const
 Raised if the continuity of the curve is not C3.
.
Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Integer N) const
 For the point of parameter U of this BSpline curve,
computes the vector corresponding to the Nth derivative.
Warning
On a point where the continuity of the curve is not the
one requested, this function impacts the part defined
by the parameter with a value greater than U, i.e. the
part of the curve to the "right" of the singularity.
Exceptions
Standard_RangeError if N is less than 1.
The following functions compute the point of parameter U
and the derivatives at this point on the B-spline curve
arc defined between the knot FromK1 and the knot ToK2.
U can be out of bounds [Knot (FromK1), Knot (ToK2)] but
for the computation we only use the definition of the curve
between these two knots. This method is useful to compute
local derivative, if the order of continuity of the whole
curve is not greater enough. Inside the parametric
domain Knot (FromK1), Knot (ToK2) the evaluations are
the same as if we consider the whole definition of the
curve. Of course the evaluations are different outside
this parametric domain.
.
Standard_EXPORT gp_Pnt LocalValue (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2) const
 Raised if FromK1 = ToK2.
Raised if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].
.
Standard_EXPORT void LocalD0 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P) const
 Raised if FromK1 = ToK2.
Raised if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].
.
Standard_EXPORT void LocalD1 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P, gp_Vec &V1) const
 Raised if the local continuity of the curve is not C1
between the knot K1 and the knot K2.
//! Raised if FromK1 = ToK2.
Raised if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].
.
Standard_EXPORT void LocalD2 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const
 Raised if the local continuity of the curve is not C2
between the knot K1 and the knot K2.
//! Raised if FromK1 = ToK2.
Raised if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].
.
Standard_EXPORT void LocalD3 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const
 Raised if the local continuity of the curve is not C3
between the knot K1 and the knot K2.
//! Raised if FromK1 = ToK2.
Raised if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].
.
Standard_EXPORT gp_Vec LocalDN (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, const Standard_Integer N) const
 Raised if the local continuity of the curve is not CN
between the knot K1 and the knot K2.
//! Raised if FromK1 = ToK2.
//! Raised if N < 1.
Raises if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].
.
Standard_EXPORT gp_Pnt EndPoint () const
 Returns the last point of the curve.
Warnings :
The last point of the curve is different from the last
pole of the curve if the multiplicity of the last knot
is lower than Degree.
.
Standard_EXPORT Standard_Integer FirstUKnotIndex () const
 Returns the index in the knot array of the knot
corresponding to the first or last parameter of this BSpline curve.
For a BSpline curve, the first (or last) parameter
(which gives the start (or end) point of the curve) is a
knot value. However, if the multiplicity of the first (or
last) knot is less than Degree + 1, where
Degree is the degree of the curve, it is not the first
(or last) knot of the curve.
.
Standard_EXPORT Standard_Real FirstParameter () const
 Returns the value of the first parameter of this
BSpline curve. This is a knot value.
The first parameter is the one of the start point of the BSpline curve.
.
Standard_EXPORT Standard_Real Knot (const Standard_Integer Index) const
 Returns the knot of range Index. When there is a knot
with a multiplicity greater than 1 the knot is not repeated.
The method Multiplicity can be used to get the multiplicity
of the Knot.
//! Raised if Index < 1 or Index > NbKnots
.
Standard_EXPORT void Knots (TColStd_Array1OfReal &K) const
 returns the knot values of the B-spline curve;
Warning
A knot with a multiplicity greater than 1 is not
repeated in the knot table. The Multiplicity function
can be used to obtain the multiplicity of each knot.
Raised if the length of K is not equal to the number of knots.

Standard_EXPORT void KnotSequence (TColStd_Array1OfReal &K) const
 Returns K, the knots sequence of this BSpline curve.
In this sequence, knots with a multiplicity greater than 1 are repeated.
In the case of a non-periodic curve the length of the
sequence must be equal to the sum of the NbKnots
multiplicities of the knots of the curve (where
NbKnots is the number of knots of this BSpline
curve). This sum is also equal to : NbPoles + Degree + 1
where NbPoles is the number of poles and
Degree the degree of this BSpline curve.
In the case of a periodic curve, if there are k periodic
knots, the period is Knot(k+1) - Knot(1).
The initial sequence is built by writing knots 1 to k+1,
which are repeated according to their corresponding multiplicities.
If Degree is the degree of the curve, the degree of
continuity of the curve at the knot of index 1 (or k+1)
is equal to c = Degree + 1 - Mult(1). c
knots are then inserted at the beginning and end of
the initial sequence:
- the c values of knots preceding the first item
Knot(k+1) in the initial sequence are inserted
at the beginning; the period is subtracted from these c values;
- the c values of knots following the last item
Knot(1) in the initial sequence are inserted at
the end; the period is added to these c values.
The length of the sequence must therefore be equal to:
NbPoles + 2*Degree - Mult(1) + 2.
Example
For a non-periodic BSpline curve of degree 2 where:
- the array of knots is: { k1 k2 k3 k4 },
- with associated multiplicities: { 3 1 2 3 },
the knot sequence is:
K = { k1 k1 k1 k2 k3 k3 k4 k4 k4 }
For a periodic BSpline curve of degree 4 , which is
"C1" continuous at the first knot, and where :
- the periodic knots are: { k1 k2 k3 (k4) }
(3 periodic knots: the points of parameter k1 and k4
are identical, the period is p = k4 - k1),
- with associated multiplicities: { 3 1 2 (3) },
the degree of continuity at knots k1 and k4 is:
Degree + 1 - Mult(i) = 2.
2 supplementary knots are added at the beginning
and end of the sequence:
- at the beginning: the 2 knots preceding k4 minus
the period; in this example, this is k3 - p both times;
- at the end: the 2 knots following k1 plus the period;
in this example, this is k2 + p and k3 + p.
The knot sequence is therefore:
K = { k3-p k3-p k1 k1 k1 k2 k3 k3
k4 k4 k4 k2+p k3+p }
Exceptions
Standard_DimensionError if the array K is not of
the appropriate length.Returns the knots sequence.
.
Standard_EXPORT GeomAbs_BSplKnotDistribution KnotDistribution () const
 Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier.
If all the knots differ by a positive constant from the
preceding knot the BSpline Curve can be :
- Uniform if all the knots are of multiplicity 1,
- QuasiUniform if all the knots are of multiplicity 1 except for
the first and last knot which are of multiplicity Degree + 1,
- PiecewiseBezier if the first and last knots have multiplicity
Degree + 1 and if interior knots have multiplicity Degree
A piecewise Bezier with only two knots is a BezierCurve.
else the curve is non uniform.
The tolerance criterion is Epsilon from class Real.
.
Standard_EXPORT Standard_Integer LastUKnotIndex () const
 For a BSpline curve the last parameter (which gives the
end point of the curve) is a knot value but if the
multiplicity of the last knot index is lower than
Degree + 1 it is not the last knot of the curve. This
method computes the index of the knot corresponding to
the last parameter.
.
Standard_EXPORT Standard_Real LastParameter () const
 Computes the parametric value of the end point of the curve.
It is a knot value.
.
Standard_EXPORT void LocateU (const Standard_Real U, const Standard_Real ParametricTolerance, Standard_Integer &I1, Standard_Integer &I2, const Standard_Boolean WithKnotRepetition=Standard_False) const
 Locates the parametric value U in the sequence of knots.
If "WithKnotRepetition" is True we consider the knot's
representation with repetition of multiple knot value,
otherwise we consider the knot's representation with
no repetition of multiple knot values.
Knots (I1) <= U <= Knots (I2)
. if I1 = I2 U is a knot value (the tolerance criterion
ParametricTolerance is used).
. if I1 < 1 => U < Knots (1) - Abs(ParametricTolerance)
. if I2 > NbKnots => U > Knots (NbKnots) + Abs(ParametricTolerance)
.
Standard_EXPORT Standard_Integer Multiplicity (const Standard_Integer Index) const
 Returns the multiplicity of the knots of range Index.
//! Raised if Index < 1 or Index > NbKnots
.
Standard_EXPORT void Multiplicities (TColStd_Array1OfInteger &M) const
 Returns the multiplicity of the knots of the curve.
Raised if the length of M is not equal to NbKnots.
.
Standard_EXPORT Standard_Integer NbKnots () const
 Returns the number of knots. This method returns the number of
knot without repetition of multiple knots.
.
Standard_EXPORT Standard_Integer NbPoles () const
 Returns the number of poles
.
Standard_EXPORT gp_Pnt Pole (const Standard_Integer Index) const
 Returns the pole of range Index.
//! Raised if Index < 1 or Index > NbPoles.
.
Standard_EXPORT void Poles (TColgp_Array1OfPnt &P) const
 Returns the poles of the B-spline curve;
Raised if the length of P is not equal to the number of poles.
.
Standard_EXPORT gp_Pnt StartPoint () const
 Returns the start point of the curve.
Warnings :
This point is different from the first pole of the curve if the
multiplicity of the first knot is lower than Degree.
.
Standard_EXPORT Standard_Real Weight (const Standard_Integer Index) const
 Returns the weight of the pole of range Index .
//! Raised if Index < 1 or Index > NbPoles.
.
Standard_EXPORT void Weights (TColStd_Array1OfReal &W) const
 Returns the weights of the B-spline curve;
Raised if the length of W is not equal to NbPoles.
.
Standard_EXPORT void Transform (const gp_Trsf &T)
 Applies the transformation T to this BSpline curve.
.
Standard_EXPORT void Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance)
 Computes for this BSpline curve the parametric
tolerance UTolerance for a given 3D tolerance Tolerance3D.
If f(t) is the equation of this BSpline curve,
UTolerance ensures that:
| t1 - t0| < Utolerance ===>
|f(t1) - f(t0)| < Tolerance3D
.
Standard_EXPORT Handle_Geom_Geometry Copy () const
 Creates a new object which is a copy of this BSpline curve.
.
Standard_EXPORT const Handle (Standard_Type)&DynamicType() const

Static Public Member Functions

static Standard_EXPORT Standard_Integer MaxDegree ()
 Returns the value of the maximum degree of the normalized
B-spline basis functions in this package.
.

Private Member Functions

Standard_EXPORT Standard_Boolean IsCacheValid (const Standard_Real Parameter) const
 Tells whether the Cache is valid for the
given parameter
Warnings : the parameter must be normalized within
the period if the curve is periodic. Otherwise
the answer will be false

.
Standard_EXPORT void InvalidateCache ()
 Invalidates the cache. This has to be private
this has to be private
.
Standard_EXPORT void UpdateKnots ()
 Recompute the flatknots, the knotsdistribution, the continuity.
.
Standard_EXPORT void ValidateCache (const Standard_Real Parameter)
 updates the cache and validates it


Private Attributes

Standard_Boolean rational
Standard_Boolean periodic
GeomAbs_BSplKnotDistribution knotSet
GeomAbs_Shape smooth
Standard_Integer deg
Handle_TColgp_HArray1OfPnt poles
Handle_TColStd_HArray1OfReal weights
Handle_TColStd_HArray1OfReal flatknots
Handle_TColStd_HArray1OfReal knots
Handle_TColStd_HArray1OfInteger mults
Handle_TColgp_HArray1OfPnt cachepoles
Handle_TColStd_HArray1OfReal cacheweights
Standard_Integer validcache
Standard_Real parametercache
Standard_Real spanlenghtcache
Standard_Integer spanindexcache
Standard_Real maxderivinv
Standard_Boolean maxderivinvok

Constructor & Destructor Documentation

Standard_EXPORT Geom_BSplineCurve::Geom_BSplineCurve const TColgp_Array1OfPnt &  Poles,
const TColStd_Array1OfReal &  Knots,
const TColStd_Array1OfInteger &  Multiplicities,
const Standard_Integer  Degree,
const Standard_Boolean  Periodic = Standard_False
 

Standard_EXPORT Geom_BSplineCurve::Geom_BSplineCurve const TColgp_Array1OfPnt &  Poles,
const TColStd_Array1OfReal &  Weights,
const TColStd_Array1OfReal &  Knots,
const TColStd_Array1OfInteger &  Multiplicities,
const Standard_Integer  Degree,
const Standard_Boolean  Periodic = Standard_False,
const Standard_Boolean  CheckRational = Standard_True
 


Member Function Documentation

Standard_EXPORT GeomAbs_Shape Geom_BSplineCurve::Continuity  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Handle_Geom_Geometry Geom_BSplineCurve::Copy  )  const [virtual]
 

Implements Geom_Geometry.

Standard_EXPORT void Geom_BSplineCurve::D0 const Standard_Real  U,
gp_Pnt &  P
const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT void Geom_BSplineCurve::D1 const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1
const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT void Geom_BSplineCurve::D2 const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1,
gp_Vec &  V2
const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT void Geom_BSplineCurve::D3 const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1,
gp_Vec &  V2,
gp_Vec &  V3
const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Integer Geom_BSplineCurve::Degree  )  const
 

Standard_EXPORT gp_Vec Geom_BSplineCurve::DN const Standard_Real  U,
const Standard_Integer  N
const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT gp_Pnt Geom_BSplineCurve::EndPoint  )  const [virtual]
 

Implements Geom_BoundedCurve.

Standard_EXPORT Standard_Real Geom_BSplineCurve::FirstParameter  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Integer Geom_BSplineCurve::FirstUKnotIndex  )  const
 

Standard_EXPORT const Geom_BSplineCurve::Handle Standard_Type   )  const
 

Reimplemented from Geom_BoundedCurve.

Standard_EXPORT void Geom_BSplineCurve::IncreaseDegree const Standard_Integer  Degree  ) 
 

Standard_EXPORT void Geom_BSplineCurve::IncreaseMultiplicity const Standard_Integer  I1,
const Standard_Integer  I2,
const Standard_Integer  M
 

Standard_EXPORT void Geom_BSplineCurve::IncreaseMultiplicity const Standard_Integer  Index,
const Standard_Integer  M
 

Standard_EXPORT void Geom_BSplineCurve::IncrementMultiplicity const Standard_Integer  I1,
const Standard_Integer  I2,
const Standard_Integer  M
 

Standard_EXPORT void Geom_BSplineCurve::InsertKnot const Standard_Real  U,
const Standard_Integer  M = 1,
const Standard_Real  ParametricTolerance = 0.0,
const Standard_Boolean  Add = Standard_True
 

Standard_EXPORT void Geom_BSplineCurve::InsertKnots const TColStd_Array1OfReal &  Knots,
const TColStd_Array1OfInteger &  Mults,
const Standard_Real  ParametricTolerance = 0.0,
const Standard_Boolean  Add = Standard_False
 

Standard_EXPORT void Geom_BSplineCurve::InvalidateCache  )  [private]
 

Standard_EXPORT Standard_Boolean Geom_BSplineCurve::IsCacheValid const Standard_Real  Parameter  )  const [private]
 

Standard_EXPORT Standard_Boolean Geom_BSplineCurve::IsClosed  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Boolean Geom_BSplineCurve::IsCN const Standard_Integer  N  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Boolean Geom_BSplineCurve::IsPeriodic  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Boolean Geom_BSplineCurve::IsRational  )  const
 

Standard_EXPORT Standard_Real Geom_BSplineCurve::Knot const Standard_Integer  Index  )  const
 

Standard_EXPORT GeomAbs_BSplKnotDistribution Geom_BSplineCurve::KnotDistribution  )  const
 

Standard_EXPORT void Geom_BSplineCurve::Knots TColStd_Array1OfReal &  K  )  const
 

Standard_EXPORT void Geom_BSplineCurve::KnotSequence TColStd_Array1OfReal &  K  )  const
 

Standard_EXPORT Standard_Real Geom_BSplineCurve::LastParameter  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Integer Geom_BSplineCurve::LastUKnotIndex  )  const
 

Standard_EXPORT void Geom_BSplineCurve::LocalD0 const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
gp_Pnt &  P
const
 

Standard_EXPORT void Geom_BSplineCurve::LocalD1 const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
gp_Pnt &  P,
gp_Vec &  V1
const
 

Standard_EXPORT void Geom_BSplineCurve::LocalD2 const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
gp_Pnt &  P,
gp_Vec &  V1,
gp_Vec &  V2
const
 

Standard_EXPORT void Geom_BSplineCurve::LocalD3 const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
gp_Pnt &  P,
gp_Vec &  V1,
gp_Vec &  V2,
gp_Vec &  V3
const
 

Standard_EXPORT gp_Vec Geom_BSplineCurve::LocalDN const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
const Standard_Integer  N
const
 

Standard_EXPORT gp_Pnt Geom_BSplineCurve::LocalValue const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2
const
 

Standard_EXPORT void Geom_BSplineCurve::LocateU const Standard_Real  U,
const Standard_Real  ParametricTolerance,
Standard_Integer &  I1,
Standard_Integer &  I2,
const Standard_Boolean  WithKnotRepetition = Standard_False
const
 

static Standard_EXPORT Standard_Integer Geom_BSplineCurve::MaxDegree  )  [static]
 

Standard_EXPORT void Geom_BSplineCurve::MovePoint const Standard_Real  U,
const gp_Pnt &  P,
const Standard_Integer  Index1,
const Standard_Integer  Index2,
Standard_Integer &  FirstModifiedPole,
Standard_Integer &  LastModifiedPole
 

Standard_EXPORT void Geom_BSplineCurve::MovePointAndTangent const Standard_Real  U,
const gp_Pnt &  P,
const gp_Vec &  Tangent,
const Standard_Real  Tolerance,
const Standard_Integer  StartingCondition,
const Standard_Integer  EndingCondition,
Standard_Integer &  ErrorStatus
 

Standard_EXPORT void Geom_BSplineCurve::Multiplicities TColStd_Array1OfInteger &  M  )  const
 

Standard_EXPORT Standard_Integer Geom_BSplineCurve::Multiplicity const Standard_Integer  Index  )  const
 

Standard_EXPORT Standard_Integer Geom_BSplineCurve::NbKnots  )  const
 

Standard_EXPORT Standard_Integer Geom_BSplineCurve::NbPoles  )  const
 

Standard_EXPORT void Geom_BSplineCurve::PeriodicNormalization Standard_Real &  U  )  const
 

Standard_EXPORT gp_Pnt Geom_BSplineCurve::Pole const Standard_Integer  Index  )  const
 

Standard_EXPORT void Geom_BSplineCurve::Poles TColgp_Array1OfPnt &  P  )  const
 

Standard_EXPORT Standard_Boolean Geom_BSplineCurve::RemoveKnot const Standard_Integer  Index,
const Standard_Integer  M,
const Standard_Real  Tolerance
 

Standard_EXPORT void Geom_BSplineCurve::Resolution const Standard_Real  Tolerance3D,
Standard_Real &  UTolerance
 

Standard_EXPORT void Geom_BSplineCurve::Reverse  )  [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Real Geom_BSplineCurve::ReversedParameter const Standard_Real  U  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT void Geom_BSplineCurve::Segment const Standard_Real  U1,
const Standard_Real  U2
 

Standard_EXPORT void Geom_BSplineCurve::SetKnot const Standard_Integer  Index,
const Standard_Real  K,
const Standard_Integer  M
 

Standard_EXPORT void Geom_BSplineCurve::SetKnot const Standard_Integer  Index,
const Standard_Real  K
 

Standard_EXPORT void Geom_BSplineCurve::SetKnots const TColStd_Array1OfReal &  K  ) 
 

Standard_EXPORT void Geom_BSplineCurve::SetNotPeriodic  ) 
 

Standard_EXPORT void Geom_BSplineCurve::SetOrigin const Standard_Real  U,
const Standard_Real  Tol
 

Standard_EXPORT void Geom_BSplineCurve::SetOrigin const Standard_Integer  Index  ) 
 

Standard_EXPORT void Geom_BSplineCurve::SetPeriodic  ) 
 

Standard_EXPORT void Geom_BSplineCurve::SetPole const Standard_Integer  Index,
const gp_Pnt &  P,
const Standard_Real  Weight
 

Standard_EXPORT void Geom_BSplineCurve::SetPole const Standard_Integer  Index,
const gp_Pnt &  P
 

Standard_EXPORT void Geom_BSplineCurve::SetWeight const Standard_Integer  Index,
const Standard_Real  Weight
 

Standard_EXPORT gp_Pnt Geom_BSplineCurve::StartPoint  )  const [virtual]
 

Implements Geom_BoundedCurve.

Standard_EXPORT void Geom_BSplineCurve::Transform const gp_Trsf &  T  )  [virtual]
 

Implements Geom_Geometry.

Standard_EXPORT void Geom_BSplineCurve::UpdateKnots  )  [private]
 

Standard_EXPORT void Geom_BSplineCurve::ValidateCache const Standard_Real  Parameter  )  [private]
 

Standard_EXPORT Standard_Real Geom_BSplineCurve::Weight const Standard_Integer  Index  )  const
 

Standard_EXPORT void Geom_BSplineCurve::Weights TColStd_Array1OfReal &  W  )  const
 


Field Documentation

Handle_TColgp_HArray1OfPnt Geom_BSplineCurve::cachepoles [private]
 

Handle_TColStd_HArray1OfReal Geom_BSplineCurve::cacheweights [private]
 

Standard_Integer Geom_BSplineCurve::deg [private]
 

Handle_TColStd_HArray1OfReal Geom_BSplineCurve::flatknots [private]
 

Handle_TColStd_HArray1OfReal Geom_BSplineCurve::knots [private]
 

GeomAbs_BSplKnotDistribution Geom_BSplineCurve::knotSet [private]
 

Standard_Real Geom_BSplineCurve::maxderivinv [private]
 

Standard_Boolean Geom_BSplineCurve::maxderivinvok [private]
 

Handle_TColStd_HArray1OfInteger Geom_BSplineCurve::mults [private]
 

Standard_Real Geom_BSplineCurve::parametercache [private]
 

Standard_Boolean Geom_BSplineCurve::periodic [private]
 

Handle_TColgp_HArray1OfPnt Geom_BSplineCurve::poles [private]
 

Standard_Boolean Geom_BSplineCurve::rational [private]
 

GeomAbs_Shape Geom_BSplineCurve::smooth [private]
 

Standard_Integer Geom_BSplineCurve::spanindexcache [private]
 

Standard_Real Geom_BSplineCurve::spanlenghtcache [private]
 

Standard_Integer Geom_BSplineCurve::validcache [private]
 

Handle_TColStd_HArray1OfReal Geom_BSplineCurve::weights [private]
 


The documentation for this class was generated from the following file:
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