Open CASCADE Technology 7.8.0
Public Member Functions | Static Public Member Functions
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. More...

#include <Geom_BSplineCurve.hxx>

Inheritance diagram for Geom_BSplineCurve:
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Public Member Functions

 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>.
 
 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.
 
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().
 
void IncreaseMultiplicity (const Standard_Integer Index, const Standard_Integer M)
 Increases the multiplicity of the knot <Index> to <M>.
 
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>.
 
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>.
 
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 is an existing knot the multiplicity is increased by <M>.
 
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.
 
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.
 
void Reverse () override
 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_Real ReversedParameter (const Standard_Real U) const override
 Returns the parameter on the reversed curve for the point of parameter U on <me>.
 
void Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real theTolerance=Precision::PConfusion())
 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.
 
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:
 
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.
 
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.
 
void PeriodicNormalization (Standard_Real &U) const
 returns the parameter normalized within the period if the curve is periodic : otherwise does not do anything
 
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.
 
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.
 
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 inserted. KnotVector and poles are modified. Raised if the curve is not periodic.
 
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.
 
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.
 
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.
 
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.
 
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:
 
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 enough degree of freedom with the constrain to deform the curve accordingly.
 
Standard_Boolean IsCN (const Standard_Integer N) const override
 Returns the continuity of the curve, the curve is at least C0. Raised if N < 0.
 
Standard_Boolean IsG1 (const Standard_Real theTf, const Standard_Real theTl, const Standard_Real theAngTol) const
 Check if curve has at least G1 continuity in interval [theTf, theTl] Returns true if IsCN(1) or angle between "left" and "right" first derivatives at knots with C0 continuity is less then theAngTol only knots in interval [theTf, theTl] is checked.
 
Standard_Boolean IsClosed () const override
 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_Boolean IsPeriodic () const override
 Returns True if the curve is periodic.
 
Standard_Boolean IsRational () const
 Returns True if the weights are not identical. The tolerance criterion is Epsilon of the class Real.
 
GeomAbs_Shape Continuity () const override
 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_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.
 
void D0 (const Standard_Real U, gp_Pnt &P) const override
 Returns in P the point of parameter U.
 
void D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const override
 Raised if the continuity of the curve is not C1.
 
void D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const override
 Raised if the continuity of the curve is not C2.
 
void D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const override
 Raised if the continuity of the curve is not C3.
 
gp_Vec DN (const Standard_Real U, const Standard_Integer N) const override
 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.
 
gp_Pnt LocalValue (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2) const
 Raised if FromK1 = ToK2.
 
void LocalD0 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P) const
 Raised if FromK1 = ToK2.
 
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.
 
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.
 
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.
 
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.
 
gp_Pnt EndPoint () const override
 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_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_Real FirstParameter () const override
 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_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.
 
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.
 
const TColStd_Array1OfReal & Knots () 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.
 
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:
 
const TColStd_Array1OfReal & KnotSequence () const
 returns the knots of the B-spline curve. Knots with multiplicit greater than 1 are repeated
 
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 :
 
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_Real LastParameter () const override
 Computes the parametric value of the end point of the curve. It is a knot value.
 
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_Integer Multiplicity (const Standard_Integer Index) const
 Returns the multiplicity of the knots of range Index. Raised if Index < 1 or Index > NbKnots.
 
void Multiplicities (TColStd_Array1OfInteger &M) const
 Returns the multiplicity of the knots of the curve.
 
const TColStd_Array1OfInteger & Multiplicities () const
 returns the multiplicity of the knots of the curve.
 
Standard_Integer NbKnots () const
 Returns the number of knots. This method returns the number of knot without repetition of multiple knots.
 
Standard_Integer NbPoles () const
 Returns the number of poles.
 
const gp_Pnt & Pole (const Standard_Integer Index) const
 Returns the pole of range Index. Raised if Index < 1 or Index > NbPoles.
 
void Poles (TColgp_Array1OfPnt &P) const
 Returns the poles of the B-spline curve;.
 
const TColgp_Array1OfPnt & Poles () const
 Returns the poles of the B-spline curve;.
 
gp_Pnt StartPoint () const override
 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_Real Weight (const Standard_Integer Index) const
 Returns the weight of the pole of range Index . Raised if Index < 1 or Index > NbPoles.
 
void Weights (TColStd_Array1OfReal &W) const
 Returns the weights of the B-spline curve;.
 
const TColStd_Array1OfReal * Weights () const
 Returns the weights of the B-spline curve;.
 
void Transform (const gp_Trsf &T) override
 Applies the transformation T to this BSpline curve.
 
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.
 
Handle< Geom_Geometry > Copy () const override
 Creates a new object which is a copy of this BSpline curve.
 
Standard_Boolean IsEqual (const Handle< Geom_BSplineCurve > &theOther, const Standard_Real thePreci) const
 Comapare two Bspline curve on identity;.
 
virtual void DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const override
 Dumps the content of me into the stream.
 
- Public Member Functions inherited from Geom_Curve
virtual Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf &T) const
 Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.
 
virtual Standard_Real ParametricTransformation (const gp_Trsf &T) const
 Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.
 
Handle< Geom_Curve > Reversed () const
 Returns a copy of <me> reversed.
 
virtual Standard_Real Period () const
 Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic.
 
gp_Pnt Value (const Standard_Real U) const
 Computes the point of parameter U on <me>. If the curve is periodic then the returned point is P(U) with U = Ustart + (U - Uend) where Ustart and Uend are the parametric bounds of the curve. it is implemented with D0.
 
- Public Member Functions inherited from Geom_Geometry
void Mirror (const gp_Pnt &P)
 Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry.
 
void Mirror (const gp_Ax1 &A1)
 Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry.
 
void Mirror (const gp_Ax2 &A2)
 Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection).
 
void Rotate (const gp_Ax1 &A1, const Standard_Real Ang)
 Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians.
 
void Scale (const gp_Pnt &P, const Standard_Real S)
 Scales a Geometry. S is the scaling value.
 
void Translate (const gp_Vec &V)
 Translates a Geometry. V is the vector of the translation.
 
void Translate (const gp_Pnt &P1, const gp_Pnt &P2)
 Translates a Geometry from the point P1 to the point P2.
 
Handle< Geom_Geometry > Mirrored (const gp_Pnt &P) const
 
Handle< Geom_Geometry > Mirrored (const gp_Ax1 &A1) const
 
Handle< Geom_Geometry > Mirrored (const gp_Ax2 &A2) const
 
Handle< Geom_Geometry > Rotated (const gp_Ax1 &A1, const Standard_Real Ang) const
 
Handle< Geom_Geometry > Scaled (const gp_Pnt &P, const Standard_Real S) const
 
Handle< Geom_Geometry > Transformed (const gp_Trsf &T) const
 
Handle< Geom_Geometry > Translated (const gp_Vec &V) const
 
Handle< Geom_Geometry > Translated (const gp_Pnt &P1, const gp_Pnt &P2) const
 
- Public Member Functions inherited from Standard_Transient
 Standard_Transient ()
 Empty constructor.
 
 Standard_Transient (const Standard_Transient &)
 Copy constructor – does nothing.
 
Standard_Transient & operator= (const Standard_Transient &)
 Assignment operator, needed to avoid copying reference counter.
 
virtual ~Standard_Transient ()
 Destructor must be virtual.
 
virtual const opencascade::handle< Standard_Type > & DynamicType () const
 Returns a type descriptor about this object.
 
Standard_Boolean IsInstance (const opencascade::handle< Standard_Type > &theType) const
 Returns a true value if this is an instance of Type.
 
Standard_Boolean IsInstance (const Standard_CString theTypeName) const
 Returns a true value if this is an instance of TypeName.
 
Standard_Boolean IsKind (const opencascade::handle< Standard_Type > &theType) const
 Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism.
 
Standard_Boolean IsKind (const Standard_CString theTypeName) const
 Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism.
 
Standard_Transient * This () const
 Returns non-const pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero.
 
Standard_Integer GetRefCount () const noexcept
 Get the reference counter of this object.
 
void IncrementRefCounter () noexcept
 Increments the reference counter of this object.
 
Standard_Integer DecrementRefCounter () noexcept
 Decrements the reference counter of this object; returns the decremented value.
 
virtual void Delete () const
 Memory deallocator for transient classes.
 

Static Public Member Functions

static Standard_Integer MaxDegree ()
 Returns the value of the maximum degree of the normalized B-spline basis functions in this package.
 
- Static Public Member Functions inherited from Standard_Transient
static constexpr const char * get_type_name ()
 Returns a type descriptor about this object.
 
static const opencascade::handle< Standard_Type > & get_type_descriptor ()
 Returns type descriptor of Standard_Transient class.
 

Additional Inherited Members

- Public Types inherited from Standard_Transient
typedef void base_type
 Returns a type descriptor about this object.
 

Detailed Description

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;

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

Constructor & Destructor Documentation

◆ Geom_BSplineCurve() [1/2]

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 
)

Creates a non-rational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>.

◆ Geom_BSplineCurve() [2/2]

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 
)

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 recommended 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

Member Function Documentation

◆ Continuity()

GeomAbs_Shape Geom_BSplineCurve::Continuity ( ) const
overridevirtual

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.

Implements Geom_Curve.

◆ Copy()

Handle< Geom_Geometry > Geom_BSplineCurve::Copy ( ) const
overridevirtual

Creates a new object which is a copy of this BSpline curve.

Implements Geom_Geometry.

◆ D0()

void Geom_BSplineCurve::D0 ( const Standard_Real  U,
gp_Pnt &  P 
) const
overridevirtual

Returns in P the point of parameter U.

Implements Geom_Curve.

◆ D1()

void Geom_BSplineCurve::D1 ( const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1 
) const
overridevirtual

Raised if the continuity of the curve is not C1.

Implements Geom_Curve.

◆ D2()

void Geom_BSplineCurve::D2 ( const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1,
gp_Vec &  V2 
) const
overridevirtual

Raised if the continuity of the curve is not C2.

Implements Geom_Curve.

◆ D3()

void Geom_BSplineCurve::D3 ( const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1,
gp_Vec &  V2,
gp_Vec &  V3 
) const
overridevirtual

Raised if the continuity of the curve is not C3.

Implements Geom_Curve.

◆ Degree()

Standard_Integer Geom_BSplineCurve::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.

◆ DN()

gp_Vec Geom_BSplineCurve::DN ( const Standard_Real  U,
const Standard_Integer  N 
) const
overridevirtual

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.

Implements Geom_Curve.

◆ DumpJson()

virtual void Geom_BSplineCurve::DumpJson ( Standard_OStream &  theOStream,
Standard_Integer  theDepth = -1 
) const
overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom_BoundedCurve.

◆ EndPoint()

gp_Pnt Geom_BSplineCurve::EndPoint ( ) const
overridevirtual

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.

Implements Geom_BoundedCurve.

◆ FirstParameter()

Standard_Real Geom_BSplineCurve::FirstParameter ( ) const
overridevirtual

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.

Implements Geom_Curve.

◆ FirstUKnotIndex()

Standard_Integer Geom_BSplineCurve::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.

◆ IncreaseDegree()

void Geom_BSplineCurve::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().

◆ IncreaseMultiplicity() [1/2]

void Geom_BSplineCurve::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]

◆ IncreaseMultiplicity() [2/2]

void Geom_BSplineCurve::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]

◆ IncrementMultiplicity()

void Geom_BSplineCurve::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]

◆ InsertKnot()

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 
)

Inserts a knot value in the sequence of knots. If 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.

◆ InsertKnots()

void Geom_BSplineCurve::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 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.

◆ IsClosed()

Standard_Boolean Geom_BSplineCurve::IsClosed ( ) const
overridevirtual

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.

Implements Geom_Curve.

◆ IsCN()

Standard_Boolean Geom_BSplineCurve::IsCN ( const Standard_Integer  N) const
overridevirtual

Returns the continuity of the curve, the curve is at least C0. Raised if N < 0.

Implements Geom_Curve.

◆ IsEqual()

Standard_Boolean Geom_BSplineCurve::IsEqual ( const Handle< Geom_BSplineCurve > &  theOther,
const Standard_Real  thePreci 
) const

Comapare two Bspline curve on identity;.

◆ IsG1()

Standard_Boolean Geom_BSplineCurve::IsG1 ( const Standard_Real  theTf,
const Standard_Real  theTl,
const Standard_Real  theAngTol 
) const

Check if curve has at least G1 continuity in interval [theTf, theTl] Returns true if IsCN(1) or angle between "left" and "right" first derivatives at knots with C0 continuity is less then theAngTol only knots in interval [theTf, theTl] is checked.

◆ IsPeriodic()

Standard_Boolean Geom_BSplineCurve::IsPeriodic ( ) const
overridevirtual

Returns True if the curve is periodic.

Implements Geom_Curve.

◆ IsRational()

Standard_Boolean Geom_BSplineCurve::IsRational ( ) const

Returns True if the weights are not identical. The tolerance criterion is Epsilon of the class Real.

◆ Knot()

Standard_Real Geom_BSplineCurve::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.

◆ KnotDistribution()

GeomAbs_BSplKnotDistribution Geom_BSplineCurve::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.

◆ Knots() [1/2]

const TColStd_Array1OfReal & Geom_BSplineCurve::Knots ( ) 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.

◆ Knots() [2/2]

void Geom_BSplineCurve::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 K.Lower() is less than number of first knot or K.Upper() is more than number of last knot.

◆ KnotSequence() [1/2]

const TColStd_Array1OfReal & Geom_BSplineCurve::KnotSequence ( ) const

returns the knots of the B-spline curve. Knots with multiplicit greater than 1 are repeated

◆ KnotSequence() [2/2]

void Geom_BSplineCurve::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 Raised if K.Lower() is less than number of first knot in knot sequence with repetitions or K.Upper() is more than number of last knot in knot sequence with repetitions.

◆ LastParameter()

Standard_Real Geom_BSplineCurve::LastParameter ( ) const
overridevirtual

Computes the parametric value of the end point of the curve. It is a knot value.

Implements Geom_Curve.

◆ LastUKnotIndex()

Standard_Integer Geom_BSplineCurve::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.

◆ LocalD0()

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

Raised if FromK1 = ToK2.

◆ LocalD1()

void Geom_BSplineCurve::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.

◆ LocalD2()

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

Raised if the local continuity of the curve is not C2 between the knot K1 and the knot K2. Raised if FromK1 = ToK2.

◆ LocalD3()

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

Raised if the local continuity of the curve is not C3 between the knot K1 and the knot K2. Raised if FromK1 = ToK2.

◆ LocalDN()

gp_Vec Geom_BSplineCurve::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.

◆ LocalValue()

gp_Pnt Geom_BSplineCurve::LocalValue ( const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2 
) const

Raised if FromK1 = ToK2.

◆ LocateU()

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

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)

◆ MaxDegree()

static Standard_Integer Geom_BSplineCurve::MaxDegree ( )
static

Returns the value of the maximum degree of the normalized B-spline basis functions in this package.

◆ MovePoint()

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 
)

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.

◆ MovePointAndTangent()

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 
)

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 enough degree of freedom with the constrain to deform the curve accordingly.

◆ Multiplicities() [1/2]

const TColStd_Array1OfInteger & Geom_BSplineCurve::Multiplicities ( ) const

returns the multiplicity of the knots of the curve.

◆ Multiplicities() [2/2]

void Geom_BSplineCurve::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.

◆ Multiplicity()

Standard_Integer Geom_BSplineCurve::Multiplicity ( const Standard_Integer  Index) const

Returns the multiplicity of the knots of range Index. Raised if Index < 1 or Index > NbKnots.

◆ NbKnots()

Standard_Integer Geom_BSplineCurve::NbKnots ( ) const

Returns the number of knots. This method returns the number of knot without repetition of multiple knots.

◆ NbPoles()

Standard_Integer Geom_BSplineCurve::NbPoles ( ) const

Returns the number of poles.

◆ PeriodicNormalization()

void Geom_BSplineCurve::PeriodicNormalization ( Standard_Real &  U) const

returns the parameter normalized within the period if the curve is periodic : otherwise does not do anything

◆ Pole()

const gp_Pnt & Geom_BSplineCurve::Pole ( const Standard_Integer  Index) const

Returns the pole of range Index. Raised if Index < 1 or Index > NbPoles.

◆ Poles() [1/2]

const TColgp_Array1OfPnt & Geom_BSplineCurve::Poles ( ) const

Returns the poles of the B-spline curve;.

◆ Poles() [2/2]

void Geom_BSplineCurve::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.

◆ RemoveKnot()

Standard_Boolean Geom_BSplineCurve::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.

◆ Resolution()

void Geom_BSplineCurve::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.

◆ Reverse()

void Geom_BSplineCurve::Reverse ( )
overridevirtual

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.

Implements Geom_Curve.

◆ ReversedParameter()

Standard_Real Geom_BSplineCurve::ReversedParameter ( const Standard_Real  U) const
overridevirtual

Returns the parameter on the reversed curve for the point of parameter U on <me>.

returns UFirst + ULast - U

Implements Geom_Curve.

◆ Segment()

void Geom_BSplineCurve::Segment ( const Standard_Real  U1,
const Standard_Real  U2,
const Standard_Real  theTolerance = Precision::PConfusion() 
)

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.

Parameter theTolerance defines the possible proximity of the segment boundaries and B-spline knots to treat them as equal.

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_DomainError if U2 - U1 exceeds the period for periodic curves. i.e. ((U2 - U1) - Period) > Precision::PConfusion().

◆ SetKnot() [1/2]

void Geom_BSplineCurve::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.

◆ SetKnot() [2/2]

void Geom_BSplineCurve::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

◆ SetKnots()

void Geom_BSplineCurve::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.

◆ SetNotPeriodic()

void Geom_BSplineCurve::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.

◆ SetOrigin() [1/2]

void Geom_BSplineCurve::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.

◆ SetOrigin() [2/2]

void Geom_BSplineCurve::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 inserted. KnotVector and poles are modified. Raised if the curve is not periodic.

◆ SetPeriodic()

void Geom_BSplineCurve::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.

◆ SetPole() [1/2]

void Geom_BSplineCurve::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.

◆ SetPole() [2/2]

void Geom_BSplineCurve::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.

◆ SetWeight()

void Geom_BSplineCurve::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

◆ StartPoint()

gp_Pnt Geom_BSplineCurve::StartPoint ( ) const
overridevirtual

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.

Implements Geom_BoundedCurve.

◆ Transform()

void Geom_BSplineCurve::Transform ( const gp_Trsf &  T)
overridevirtual

Applies the transformation T to this BSpline curve.

Implements Geom_Geometry.

◆ Weight()

Standard_Real Geom_BSplineCurve::Weight ( const Standard_Integer  Index) const

Returns the weight of the pole of range Index . Raised if Index < 1 or Index > NbPoles.

◆ Weights() [1/2]

const TColStd_Array1OfReal * Geom_BSplineCurve::Weights ( ) const

Returns the weights of the B-spline curve;.

◆ Weights() [2/2]

void Geom_BSplineCurve::Weights ( TColStd_Array1OfReal &  W) const

Returns the weights of the B-spline curve;.

Raised if the length of W is not equal to NbPoles.

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