Describes a BSpline curve. A BSpline curve can be: More...

#include <Geom2d_BSplineCurve.hxx>

Inheritance diagram for Geom2d_BSplineCurve:

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Public Member Functions
	Geom2d_BSplineCurve (const TColgp_Array1OfPnt2d &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>. The following conditions must be verified. 0 < Degree <= MaxDegree.

	Geom2d_BSplineCurve (const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, const Standard_Integer Degree, const Standard_Boolean Periodic=Standard_False)
	Creates a rational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>. The following conditions must be verified. 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 Geom2d_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)
	Increases by M the multiplicity of the knots of indexes I1 to I2 in the knots table of this BSpline curve. For each knot, the resulting multiplicity is limited to the degree of this curve. If M is negative, nothing is done. As a result, the poles and weights tables of this BSpline curve are modified. Warning It is forbidden to modify the multiplicity of the first or last knot of a non-periodic curve. Be careful as Geom2d does not protect against this. Exceptions Standard_OutOfRange if I1 or I2 is outside the bounds of the knots table.

void	InsertKnot (const Standard_Real U, const Standard_Integer M=1, const Standard_Real ParametricTolerance=0.0)
	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 the values of the array Knots, with the respective multiplicities given by the array Mults, into the knots table of this BSpline curve. If a value of the array Knots is an existing knot, its multiplicity is:

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.

void	InsertPoleAfter (const Standard_Integer Index, const gp_Pnt2d &P, const Standard_Real Weight=1.0)
	The new pole is inserted after the pole of range Index. If the curve was non rational it can become rational.

void	InsertPoleBefore (const Standard_Integer Index, const gp_Pnt2d &P, const Standard_Real Weight=1.0)
	The new pole is inserted before the pole of range Index. If the curve was non rational it can become rational.

void	RemovePole (const Standard_Integer Index)
	Removes the pole of range Index If the curve was rational it can become non rational.

void	Reverse () override
	Reverses the orientation of this BSpline curve. As a result.

Standard_Real	ReversedParameter (const Standard_Real U) const override
	Computes the parameter on the reversed curve for the point of parameter U on this BSpline curve. The returned value is: UFirst + ULast - U, where UFirst and ULast are the values of the first and last parameters of this BSpline curve.

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) Exceptions 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)
	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). Exceptions Standard_ConstructionError if:

void	PeriodicNormalization (Standard_Real &U) const
	Computes the parameter normalized within the "first" period of this BSpline curve, if it is periodic: the returned value is in the range Param1 and Param1 + Period, where:

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 Knot(I2) - Knot(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	SetNotPeriodic ()
	Changes this BSpline curve into a non-periodic curve. If this curve is already non-periodic, it is not modified. Note that 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_Pnt2d &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_Pnt2d &P, const Standard_Real Weight)
	Modifies this BSpline curve by assigning P to the pole of index Index in the poles table. The second 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)
	Assigns the weight Weight to the pole of index Index of the poles table. If the curve was non rational it can become rational. If the curve was rational it can become non rational. Exceptions Standard_OutOfRange if Index is outside the bounds of the poles table. Standard_ConstructionError if Weight is negative or null.

void	MovePoint (const Standard_Real U, const gp_Pnt2d &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_Pnt2d &P, const gp_Vec2d &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 true if the degree of continuity of this BSpline curve is at least N. A BSpline curve is at least GeomAbs_C0. Exceptions Standard_RangeError if N is negative.

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. In this class the degree of the basis normalized B-spline functions cannot be greater than "MaxDegree" Computation of value and derivatives.

void	D0 (const Standard_Real U, gp_Pnt2d &P) const override
	Returns in P the point of parameter U. 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.

void	D1 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1) const override
	Raised if the continuity of the curve is not C1.

void	D2 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) const override
	Raised if the continuity of the curve is not C2.

void	D3 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const override
	For this BSpline curve, computes.

gp_Vec2d	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. Raises UndefinedDerivative if the continuity of the curve is not CN. RangeError if N < 1. The following functions computes 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.

gp_Pnt2d	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_Pnt2d &P) const
	Raised if FromK1 = ToK2.

void	LocalD1 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt2d &P, gp_Vec2d &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_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &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_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &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_Vec2d	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_Pnt2d	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
	For a B-spline curve the first parameter (which gives the start point of the curve) is a knot value but if the multiplicity of the first knot index is lower than Degree + 1 it is not the first knot of the curve. This method computes the index of the knot corresponding to the first parameter.

Standard_Real	FirstParameter () const override
	Computes the parametric value of the start point of the curve. It is a knot value.

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;

const TColStd_Array1OfReal &	Knots () const
	returns the knot values of the B-spline curve;

void	KnotSequence (TColStd_Array1OfReal &K) const
	Returns the knots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.

const TColStd_Array1OfReal &	KnotSequence () const
	Returns the knots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.

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_Pnt2d &	Pole (const Standard_Integer Index) const
	Returns the pole of range Index. Raised if Index < 1 or Index > NbPoles.

void	Poles (TColgp_Array1OfPnt2d &P) const
	Returns the poles of the B-spline curve;.

const TColgp_Array1OfPnt2d &	Poles () const
	Returns the poles of the B-spline curve;.

gp_Pnt2d	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_Trsf2d &T) override
	Applies the transformation T to this BSpline curve.

void	Resolution (const Standard_Real ToleranceUV, Standard_Real &UTolerance)
	Computes for this BSpline curve the parametric tolerance UTolerance for a given tolerance Tolerance3D (relative to dimensions in the plane). If f(t) is the equation of this BSpline curve, UTolerance ensures that: \| t1 - t0\| < Utolerance ===> \|f(t1) - f(t0)\| < ToleranceUV.

Handle< Geom2d_Geometry >	Copy () const override
	Creates a new object which is a copy of this BSpline curve.

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 Geom2d_BoundedCurve
Public Member Functions inherited from Geom2d_Curve
virtual Standard_Real	TransformedParameter (const Standard_Real U, const gp_Trsf2d &T) const
	Computes the parameter on the curve transformed by T for the point of parameter U on this curve. Note: this function generally returns U but it can be redefined (for example, on a line).

virtual Standard_Real	ParametricTransformation (const gp_Trsf2d &T) const
	Returns the coefficient required to compute the parametric transformation of this curve when transformation T is applied. This coefficient is the ratio between the parameter of a point on this curve and the parameter of the transformed point on the new curve transformed by T. Note: this function generally returns 1. but it can be redefined (for example, on a line).

Handle< Geom2d_Curve >	Reversed () const
	Creates a reversed duplicate Changes the orientation of this curve. The first and last parameters are not changed, but the parametric direction of the curve is reversed. If the curve is bounded:

virtual Standard_Real	Period () const
	Returns the period of this curve. raises if the curve is not periodic.

gp_Pnt2d	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.

Public Member Functions inherited from Geom2d_Geometry
void	Mirror (const gp_Pnt2d &P)
	Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry and assigns the result to this geometric object.

void	Mirror (const gp_Ax2d &A)
	Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry.

void	Rotate (const gp_Pnt2d &P, const Standard_Real Ang)
	Rotates a Geometry. P is the center of the rotation. Ang is the angular value of the rotation in radians.

void	Scale (const gp_Pnt2d &P, const Standard_Real S)
	Scales a Geometry. S is the scaling value.

void	Translate (const gp_Vec2d &V)
	Translates a Geometry. V is the vector of the translation.

void	Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2)
	Translates a Geometry from the point P1 to the point P2.

Handle< Geom2d_Geometry >	Mirrored (const gp_Pnt2d &P) const

Handle< Geom2d_Geometry >	Mirrored (const gp_Ax2d &A) const

Handle< Geom2d_Geometry >	Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const

Handle< Geom2d_Geometry >	Scaled (const gp_Pnt2d &P, const Standard_Real S) const

Handle< Geom2d_Geometry >	Transformed (const gp_Trsf2d &T) const

Handle< Geom2d_Geometry >	Translated (const gp_Vec2d &V) const

Handle< Geom2d_Geometry >	Translated (const gp_Pnt2d &P1, const gp_Pnt2d &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

Describes a BSpline curve. A BSpline curve can be:

uniform or non-uniform,
rational or non-rational,
periodic or non-periodic. A BSpline curve is defined by:
its degree; the degree for a Geom2d_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 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 they 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 Geom2d_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, such that:
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. Warnings : In this class we consider that a weight value is zero if Weight <= Resolution from package gp. For two parametric values (or two knot values) U1, U2 we consider that U1 = U2 if Abs (U2 - U1) <= Epsilon (U1). For two weights values W1, W2 we consider that W1 = W2 if Abs (W2 - W1) <= Epsilon (W1). The method Epsilon is defined in the class Real from package Standard.

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

◆ Geom2d_BSplineCurve() [1/2]

Geom2d_BSplineCurve::Geom2d_BSplineCurve	(	const TColgp_Array1OfPnt2d &	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>. The following conditions must be verified. 0 < Degree <= MaxDegree.

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

◆ Geom2d_BSplineCurve() [2/2]

Geom2d_BSplineCurve::Geom2d_BSplineCurve	(	const TColgp_Array1OfPnt2d &	Poles,
		const TColStd_Array1OfReal &	Weights,
		const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Multiplicities,
		const Standard_Integer	Degree,
		const Standard_Boolean	Periodic = Standard_False )

Creates a rational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>. The following conditions must be verified. 0 < Degree <= MaxDegree.

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 Geom2d_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 Geom2d_Curve.

◆ Copy()

Handle< Geom2d_Geometry > Geom2d_BSplineCurve::Copy ( ) const

overridevirtual

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

Implements Geom2d_Geometry.

◆ D0()

void Geom2d_BSplineCurve::D0	(	const Standard_Real	U,
		gp_Pnt2d &	P ) const

overridevirtual

Returns in P the point of parameter U. 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.

Raised only for the "OffsetCurve" if it is not possible to compute the current point. For example when the first derivative on the basis curve and the offset direction are parallel.

Implements Geom2d_Curve.

◆ D1()

void Geom2d_BSplineCurve::D1	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1 ) const

overridevirtual

Raised if the continuity of the curve is not C1.

Implements Geom2d_Curve.

◆ D2()

void Geom2d_BSplineCurve::D2	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1,
		gp_Vec2d &	V2 ) const

overridevirtual

Raised if the continuity of the curve is not C2.

Implements Geom2d_Curve.

◆ D3()

void Geom2d_BSplineCurve::D3	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1,
		gp_Vec2d &	V2,
		gp_Vec2d &	V3 ) const

overridevirtual

For this BSpline curve, computes.

the point P of parameter U, or
the point P and one or more of the following values:
V1, the first derivative vector,
V2, the second derivative vector,
V3, the third derivative vector. Warning On a point where the continuity of the curve is not the one requested, these functions impact 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. Raises UndefinedDerivative if the continuity of the curve is not C3.

Implements Geom2d_Curve.

◆ Degree()

Standard_Integer Geom2d_BSplineCurve::Degree ( ) const

Returns the degree of this BSpline curve. In this class the degree of the basis normalized B-spline functions cannot be greater than "MaxDegree" Computation of value and derivatives.

◆ DN()

gp_Vec2d Geom2d_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. Raises UndefinedDerivative if the continuity of the curve is not CN. RangeError if N < 1. The following functions computes 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 Geom2d_Curve.

◆ DumpJson()

virtual void Geom2d_BSplineCurve::DumpJson	(	Standard_OStream &	theOStream,
		Standard_Integer	theDepth = -1 ) const

overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom2d_BoundedCurve.

◆ EndPoint()

gp_Pnt2d Geom2d_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 Geom2d_BoundedCurve.

◆ FirstParameter()

Standard_Real Geom2d_BSplineCurve::FirstParameter ( ) const

overridevirtual

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

Implements Geom2d_Curve.

◆ FirstUKnotIndex()

Standard_Integer Geom2d_BSplineCurve::FirstUKnotIndex ( ) const

For a B-spline curve the first parameter (which gives the start point of the curve) is a knot value but if the multiplicity of the first knot index is lower than Degree + 1 it is not the first knot of the curve. This method computes the index of the knot corresponding to the first parameter.

◆ IncreaseDegree()

void Geom2d_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 Geom2d_BSplineCurve::MaxDegree().

◆ IncreaseMultiplicity() [1/2]

void Geom2d_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. As a result, the poles and weights tables of this curve are modified. Warning It is forbidden to modify the multiplicity of the first or last knot of a non-periodic curve. Be careful as Geom2d does not protect against this. Exceptions Standard_OutOfRange if either Index, I1 or I2 is outside the bounds of the knots table.

◆ IncreaseMultiplicity() [2/2]

void Geom2d_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 Geom2d_BSplineCurve::IncrementMultiplicity	(	const Standard_Integer	I1,
		const Standard_Integer	I2,
		const Standard_Integer	M )

Increases by M the multiplicity of the knots of indexes I1 to I2 in the knots table of this BSpline curve. For each knot, the resulting multiplicity is limited to the degree of this curve. If M is negative, nothing is done. As a result, the poles and weights tables of this BSpline curve are modified. Warning It is forbidden to modify the multiplicity of the first or last knot of a non-periodic curve. Be careful as Geom2d does not protect against this. Exceptions Standard_OutOfRange if I1 or I2 is outside the bounds of the knots table.

◆ InsertKnot()

void Geom2d_BSplineCurve::InsertKnot	(	const Standard_Real	U,
		const Standard_Integer	M = 1,
		const Standard_Real	ParametricTolerance = 0.0 )

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. Warning

If U is less than the first parameter or greater than the last parameter of this BSpline curve, nothing is done.
If M is negative or null, nothing is done.
The multiplicity of a knot is limited to the degree of this BSpline curve.

◆ InsertKnots()

void Geom2d_BSplineCurve::InsertKnots	(	const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Mults,
		const Standard_Real	ParametricTolerance = 0.0,
		const Standard_Boolean	Add = Standard_False )

Inserts the values of the array Knots, with the respective multiplicities given by the array Mults, into the knots table of this BSpline curve. If a value of the array Knots is an existing knot, its multiplicity is:

increased by M, if Add is true, or
increased to M, if Add is false (default value). The tolerance criterion used for knot equality is the larger of the values ParametricTolerance (defaulted to 0.) and Standard_Real::Epsilon(U), where U is the current knot value. Warning
For a value of the array Knots which is less than the first parameter or greater than the last parameter of this BSpline curve, nothing is done.
For a value of the array Mults which is negative or null, nothing is done.
The multiplicity of a knot is limited to the degree of this BSpline curve.

◆ InsertPoleAfter()

void Geom2d_BSplineCurve::InsertPoleAfter	(	const Standard_Integer	Index,
		const gp_Pnt2d &	P,
		const Standard_Real	Weight = 1.0 )

The new pole is inserted after the pole of range Index. If the curve was non rational it can become rational.

Raised if the B-spline is NonUniform or PiecewiseBezier or if Weight <= 0.0 Raised if Index is not in the range [1, Number of Poles]

◆ InsertPoleBefore()

void Geom2d_BSplineCurve::InsertPoleBefore	(	const Standard_Integer	Index,
		const gp_Pnt2d &	P,
		const Standard_Real	Weight = 1.0 )

The new pole is inserted before the pole of range Index. If the curve was non rational it can become rational.

Raised if the B-spline is NonUniform or PiecewiseBezier or if Weight <= 0.0 Raised if Index is not in the range [1, Number of Poles]

◆ IsClosed()

Standard_Boolean Geom2d_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 Geom2d_Curve.

◆ IsCN()

Standard_Boolean Geom2d_BSplineCurve::IsCN ( const Standard_Integer N ) const

overridevirtual

Returns true if the degree of continuity of this BSpline curve is at least N. A BSpline curve is at least GeomAbs_C0. Exceptions Standard_RangeError if N is negative.

Implements Geom2d_Curve.

◆ IsG1()

Standard_Boolean Geom2d_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 Geom2d_BSplineCurve::IsPeriodic ( ) const

overridevirtual

Returns True if the curve is periodic.

Implements Geom2d_Curve.

◆ IsRational()

Standard_Boolean Geom2d_BSplineCurve::IsRational ( ) const

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

◆ Knot()

Standard_Real Geom2d_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 Geom2d_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 & Geom2d_BSplineCurve::Knots ( ) const

returns the knot values of the B-spline curve;

◆ Knots() [2/2]

void Geom2d_BSplineCurve::Knots ( TColStd_Array1OfReal & K ) const

returns the knot values of the B-spline curve;

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 & Geom2d_BSplineCurve::KnotSequence ( ) const

Returns the knots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.

◆ KnotSequence() [2/2]

void Geom2d_BSplineCurve::KnotSequence ( TColStd_Array1OfReal & K ) const

Returns the knots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.

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 Geom2d_BSplineCurve::LastParameter ( ) const

overridevirtual

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

Implements Geom2d_Curve.

◆ LastUKnotIndex()

Standard_Integer Geom2d_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 Geom2d_BSplineCurve::LocalD0	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2,
		gp_Pnt2d &	P ) const

Raised if FromK1 = ToK2.

◆ LocalD1()

void Geom2d_BSplineCurve::LocalD1	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2,
		gp_Pnt2d &	P,
		gp_Vec2d &	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 Geom2d_BSplineCurve::LocalD2	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1,
		gp_Vec2d &	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 Geom2d_BSplineCurve::LocalD3	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1,
		gp_Vec2d &	V2,
		gp_Vec2d &	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_Vec2d Geom2d_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_Pnt2d Geom2d_BSplineCurve::LocalValue	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2 ) const

Raised if FromK1 = ToK2.

◆ LocateU()

void Geom2d_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 Geom2d_BSplineCurve::MaxDegree ( )

static

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

◆ MovePoint()

void Geom2d_BSplineCurve::MovePoint	(	const Standard_Real	U,
		const gp_Pnt2d &	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 Geom2d_BSplineCurve::MovePointAndTangent	(	const Standard_Real	U,
		const gp_Pnt2d &	P,
		const gp_Vec2d &	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 & Geom2d_BSplineCurve::Multiplicities ( ) const

returns the multiplicity of the knots of the curve.

◆ Multiplicities() [2/2]

void Geom2d_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 Geom2d_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 Geom2d_BSplineCurve::NbKnots ( ) const

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

◆ NbPoles()

Standard_Integer Geom2d_BSplineCurve::NbPoles ( ) const

Returns the number of poles.

◆ PeriodicNormalization()

void Geom2d_BSplineCurve::PeriodicNormalization ( Standard_Real & U ) const

Computes the parameter normalized within the "first" period of this BSpline curve, if it is periodic: the returned value is in the range Param1 and Param1 + Period, where:

Param1 is the "first parameter", and
Period the period of this BSpline curve. Note: If this curve is not periodic, U is not modified.

◆ Pole()

const gp_Pnt2d & Geom2d_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_Array1OfPnt2d & Geom2d_BSplineCurve::Poles ( ) const

Returns the poles of the B-spline curve;.

◆ Poles() [2/2]

void Geom2d_BSplineCurve::Poles ( TColgp_Array1OfPnt2d & 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 Geom2d_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.

◆ RemovePole()

void Geom2d_BSplineCurve::RemovePole ( const Standard_Integer Index )

Removes the pole of range Index If the curve was rational it can become non rational.

Raised if the B-spline is NonUniform or PiecewiseBezier. Raised if the number of poles of the B-spline curve is lower or equal to 2 before removing. Raised if Index is not in the range [1, Number of Poles]

◆ Resolution()

void Geom2d_BSplineCurve::Resolution	(	const Standard_Real	ToleranceUV,
		Standard_Real &	UTolerance )

Computes for this BSpline curve the parametric tolerance UTolerance for a given tolerance Tolerance3D (relative to dimensions in the plane). If f(t) is the equation of this BSpline curve, UTolerance ensures that: | t1 - t0| < Utolerance ===> |f(t1) - f(t0)| < ToleranceUV.

◆ Reverse()

void Geom2d_BSplineCurve::Reverse ( )

overridevirtual

Reverses the orientation of this BSpline curve. As a result.

the knots and poles tables are modified;
the start point of the initial curve becomes the end point of the reversed curve;
the end point of the initial curve becomes the start point of the reversed curve.

Implements Geom2d_Curve.

◆ ReversedParameter()

Standard_Real Geom2d_BSplineCurve::ReversedParameter ( const Standard_Real U ) const

overridevirtual

Computes the parameter on the reversed curve for the point of parameter U on this BSpline curve. The returned value is: UFirst + ULast - U, where UFirst and ULast are the values of the first and last parameters of this BSpline curve.

Implements Geom2d_Curve.

◆ Segment()

void Geom2d_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.

The segmentation of a periodic curve over an interval corresponding to its period generates a non-periodic curve with equivalent geometry. Exceptions Standard_DomainError if U2 is less than U1. 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 Geom2d_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) Exceptions 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 Geom2d_BSplineCurve::SetKnot	(	const Standard_Integer	Index,
		const Standard_Real	K,
		const Standard_Integer	M )

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). Exceptions 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.

◆ SetKnots()

void Geom2d_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 Geom2d_BSplineCurve::SetNotPeriodic ( )

Changes this BSpline curve into a non-periodic curve. If this curve is already non-periodic, it is not modified. Note that 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()

void Geom2d_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.

◆ SetPeriodic()

void Geom2d_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 Knot(I2) - Knot(I1). Consequently, the knots and poles tables are modified. Exceptions Standard_ConstructionError if this BSpline curve is not closed.

◆ SetPole() [1/2]

void Geom2d_BSplineCurve::SetPole	(	const Standard_Integer	Index,
		const gp_Pnt2d &	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 Geom2d_BSplineCurve::SetPole	(	const Standard_Integer	Index,
		const gp_Pnt2d &	P,
		const Standard_Real	Weight )

Modifies this BSpline curve by assigning P to the pole of index Index in the poles table. The second 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 Geom2d_BSplineCurve::SetWeight	(	const Standard_Integer	Index,
		const Standard_Real	Weight )

Assigns the weight Weight to the pole of index Index of the poles table. If the curve was non rational it can become rational. If the curve was rational it can become non rational. Exceptions Standard_OutOfRange if Index is outside the bounds of the poles table. Standard_ConstructionError if Weight is negative or null.

◆ StartPoint()

gp_Pnt2d Geom2d_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 Geom2d_BoundedCurve.

◆ Transform()

void Geom2d_BSplineCurve::Transform ( const gp_Trsf2d & T )

overridevirtual

Applies the transformation T to this BSpline curve.

Implements Geom2d_Geometry.

◆ Weight()

Standard_Real Geom2d_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 * Geom2d_BSplineCurve::Weights ( ) const

Returns the weights of the B-spline curve;.

◆ Weights() [2/2]

void Geom2d_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.

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

Geom2d_BSplineCurve.hxx

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Geom2d_BSplineCurve() [1/2]

◆ Geom2d_BSplineCurve() [2/2]

Member Function Documentation

◆ Continuity()

◆ Copy()

◆ D0()

◆ D1()

◆ D2()

◆ D3()

◆ Degree()

◆ DN()

◆ DumpJson()

◆ EndPoint()

◆ FirstParameter()

◆ FirstUKnotIndex()

◆ IncreaseDegree()

◆ IncreaseMultiplicity() [1/2]

◆ IncreaseMultiplicity() [2/2]

◆ IncrementMultiplicity()

◆ InsertKnot()

◆ InsertKnots()

◆ InsertPoleAfter()

◆ InsertPoleBefore()

◆ IsClosed()

◆ IsCN()

◆ IsG1()

◆ IsPeriodic()

◆ IsRational()

◆ Knot()

◆ KnotDistribution()

◆ Knots() [1/2]

◆ Knots() [2/2]

◆ KnotSequence() [1/2]

◆ KnotSequence() [2/2]

◆ LastParameter()

◆ LastUKnotIndex()

◆ LocalD0()

◆ LocalD1()

◆ LocalD2()

◆ LocalD3()

◆ LocalDN()

◆ LocalValue()

◆ LocateU()

◆ MaxDegree()

◆ MovePoint()

◆ MovePointAndTangent()

◆ Multiplicities() [1/2]

◆ Multiplicities() [2/2]

◆ Multiplicity()

◆ NbKnots()

◆ NbPoles()

◆ PeriodicNormalization()

◆ Pole()

◆ Poles() [1/2]

◆ Poles() [2/2]

◆ RemoveKnot()

◆ RemovePole()

◆ Resolution()

◆ Reverse()

◆ ReversedParameter()

◆ Segment()

◆ SetKnot() [1/2]

◆ SetKnot() [2/2]

◆ SetKnots()

◆ SetNotPeriodic()

◆ SetOrigin()

◆ SetPeriodic()

◆ SetPole() [1/2]

◆ SetPole() [2/2]

◆ SetWeight()

◆ StartPoint()

◆ Transform()

◆ Weight()

◆ Weights() [1/2]

◆ Weights() [2/2]