// File generated by CPPExt (Transient) // // // Copyright (C) 1991 - 2000 by // Matra Datavision SA. All rights reserved. // // Copyright (C) 2001 - 2004 by // Open CASCADE SA. All rights reserved. // // This file is part of the Open CASCADE Technology software. // // This software may be distributed and/or modified under the terms and // conditions of the Open CASCADE Public License as defined by Open CASCADE SA // and appearing in the file LICENSE included in the packaging of this file. // // This software is distributed on an "AS IS" basis, without warranty of any // kind, and Open CASCADE SA hereby disclaims all such warranties, // including without limitation, any warranties of merchantability, fitness // for a particular purpose or non-infringement. Please see the License for // the specific terms and conditions governing rights and limitations under the // License. #ifndef _Geom_BSplineCurve_HeaderFile #define _Geom_BSplineCurve_HeaderFile #ifndef _Standard_HeaderFile #include <Standard.hxx> #endif #ifndef _Handle_Geom_BSplineCurve_HeaderFile #include <Handle_Geom_BSplineCurve.hxx> #endif #ifndef _Standard_Boolean_HeaderFile #include <Standard_Boolean.hxx> #endif #ifndef _GeomAbs_BSplKnotDistribution_HeaderFile #include <GeomAbs_BSplKnotDistribution.hxx> #endif #ifndef _GeomAbs_Shape_HeaderFile #include <GeomAbs_Shape.hxx> #endif #ifndef _Standard_Integer_HeaderFile #include <Standard_Integer.hxx> #endif #ifndef _Handle_TColgp_HArray1OfPnt_HeaderFile #include <Handle_TColgp_HArray1OfPnt.hxx> #endif #ifndef _Handle_TColStd_HArray1OfReal_HeaderFile #include <Handle_TColStd_HArray1OfReal.hxx> #endif #ifndef _Handle_TColStd_HArray1OfInteger_HeaderFile #include <Handle_TColStd_HArray1OfInteger.hxx> #endif #ifndef _Standard_Real_HeaderFile #include <Standard_Real.hxx> #endif #ifndef _Geom_BoundedCurve_HeaderFile #include <Geom_BoundedCurve.hxx> #endif #ifndef _Handle_Geom_Geometry_HeaderFile #include <Handle_Geom_Geometry.hxx> #endif class TColgp_HArray1OfPnt; class TColStd_HArray1OfReal; class TColStd_HArray1OfInteger; class Standard_ConstructionError; class Standard_DimensionError; class Standard_DomainError; class Standard_OutOfRange; class Standard_RangeError; class Standard_NoSuchObject; class Geom_UndefinedDerivative; class TColgp_Array1OfPnt; class TColStd_Array1OfReal; class TColStd_Array1OfInteger; class gp_Pnt; class gp_Vec; class gp_Trsf; class Geom_Geometry; //! Definition of the B_spline curve. <br> //! A B-spline curve can be <br> //! Uniform or non-uniform <br> //! Rational or non-rational <br> //! Periodic or non-periodic <br> //! <br> //! a b-spline curve is defined by : <br> //! its degree; the degree for a <br> //! Geom_BSplineCurve is limited to a value (25) <br> //! which is defined and controlled by the system. <br> //! This value is returned by the function MaxDegree; <br> //! - its periodic or non-periodic nature; <br> //! - a table of poles (also called control points), with <br> //! their associated weights if the BSpline curve is <br> //! rational. The poles of the curve are "control <br> //! points" used to deform the curve. If the curve is <br> //! non-periodic, the first pole is the start point of <br> //! the curve, and the last pole is the end point of <br> //! the curve. The segment which joins the first pole <br> //! to the second pole is the tangent to the curve at <br> //! its start point, and the segment which joins the <br> //! last pole to the second-from-last pole is the <br> //! tangent to the curve at its end point. If the curve <br> //! is periodic, these geometric properties are not <br> //! verified. It is more difficult to give a geometric <br> //! signification to the weights but are useful for <br> //! providing exact representations of the arcs of a <br> //! circle or ellipse. Moreover, if the weights of all the <br> //! poles are equal, the curve has a polynomial <br> //! equation; it is therefore a non-rational curve. <br> //! - a table of knots with their multiplicities. For a <br> //! Geom_BSplineCurve, the table of knots is an <br> //! increasing sequence of reals without repetition; <br> //! the multiplicities define the repetition of the knots. <br> //! A BSpline curve is a piecewise polynomial or <br> //! rational curve. The knots are the parameters of <br> //! junction points between two pieces. The <br> //! multiplicity Mult(i) of the knot Knot(i) of <br> //! the BSpline curve is related to the degree of <br> //! continuity of the curve at the knot Knot(i), <br> //! which is equal to Degree - Mult(i) <br> //! where Degree is the degree of the BSpline curve. <br> //! If the knots are regularly spaced (i.e. the difference <br> //! between two consecutive knots is a constant), three <br> //! specific and frequently used cases of knot <br> //! distribution can be identified: <br> //! - "uniform" if all multiplicities are equal to 1, <br> //! - "quasi-uniform" if all multiplicities are equal to 1, <br> //! except the first and the last knot which have a <br> //! multiplicity of Degree + 1, where Degree is <br> //! the degree of the BSpline curve, <br> //! - "Piecewise Bezier" if all multiplicities are equal to <br> //! Degree except the first and last knot which <br> //! have a multiplicity of Degree + 1, where <br> //! Degree is the degree of the BSpline curve. A <br> //! curve of this type is a concatenation of arcs of Bezier curves. <br> //! If the BSpline curve is not periodic: <br> //! - the bounds of the Poles and Weights tables are 1 <br> //! and NbPoles, where NbPoles is the number <br> //! of poles of the BSpline curve, <br> //! - the bounds of the Knots and Multiplicities tables <br> //! are 1 and NbKnots, where NbKnots is the <br> //! number of knots of the BSpline curve. <br> //! If the BSpline curve is periodic, and if there are k <br> //! periodic knots and p periodic poles, the period is: <br> //! period = Knot(k + 1) - Knot(1) <br> //! and the poles and knots tables can be considered <br> //! as infinite tables, verifying: <br> //! - Knot(i+k) = Knot(i) + period <br> //! - Pole(i+p) = Pole(i) <br> //! Note: data structures of a periodic BSpline curve <br> //! are more complex than those of a non-periodic one. <br> //! Warning <br> //! In this class, weight value is considered to be zero if <br> //! the weight is less than or equal to gp::Resolution(). <br> //! <br> //! References : <br> //! . A survey of curve and surface methods in CADG Wolfgang BOHM <br> //! CAGD 1 (1984) <br> //! . On de Boor-like algorithms and blossoming Wolfgang BOEHM <br> //! cagd 5 (1988) <br> //! . Blossoming and knot insertion algorithms for B-spline curves <br> //! Ronald N. GOLDMAN <br> //! . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA <br> //! . Curves and Surfaces for Computer Aided Geometric Design, <br> //! a practical guide Gerald Farin <br> 00168 class Geom_BSplineCurve : public Geom_BoundedCurve { public: // Methods PUBLIC // //! Creates a non-rational B_spline curve on the <br> //! basis <Knots, Multiplicities> of degree <Degree>. <br> Standard_EXPORT Geom_BSplineCurve(const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Multiplicities,const Standard_Integer Degree,const Standard_Boolean Periodic = Standard_False); //! Creates a rational B_spline curve on the basis <br> //! <Knots, Multiplicities> of degree <Degree>. <br> //! Raises ConstructionError subject to the following conditions <br> //! 0 < Degree <= MaxDegree. <br> //! <br> //! Weights.Length() == Poles.Length() <br> //! <br> //! Knots.Length() == Mults.Length() >= 2 <br> //! <br> //! Knots(i) < Knots(i+1) (Knots are increasing) <br> //! <br> //! 1 <= Mults(i) <= Degree <br> //! <br> //! On a non periodic curve the first and last multiplicities <br> //! may be Degree+1 (this is even recommanded if you want the <br> //! curve to start and finish on the first and last pole). <br> //! <br> //! On a periodic curve the first and the last multicities <br> //! must be the same. <br> //! <br> //! on non-periodic curves <br> //! <br> //! Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2 <br> //! <br> //! on periodic curves <br> //! <br> //! Poles.Length() == Sum(Mults(i)) except the first or last <br> Standard_EXPORT Geom_BSplineCurve(const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Multiplicities,const Standard_Integer Degree,const Standard_Boolean Periodic = Standard_False,const Standard_Boolean CheckRational = Standard_True); //! Increases the degree of this BSpline curve to <br> //! Degree. As a result, the poles, weights and <br> //! multiplicities tables are modified; the knots table is <br> //! not changed. Nothing is done if Degree is less than <br> //! or equal to the current degree. <br> //! Exceptions <br> //! Standard_ConstructionError if Degree is greater than <br> //! Geom_BSplineCurve::MaxDegree(). <br> Standard_EXPORT void IncreaseDegree(const Standard_Integer Degree) ; //!Increases the multiplicity of the knot <Index> to <br> //! <M>. <br> //! <br> //! If <M> is lower or equal to the current <br> //! multiplicity nothing is done. If <M> is higher than <br> //! the degree the degree is used. <br>//! If <Index> is not in [FirstUKnotIndex, LastUKnotIndex] <br> Standard_EXPORT void IncreaseMultiplicity(const Standard_Integer Index,const Standard_Integer M) ; //!Increases the multiplicities of the knots in <br> //! [I1,I2] to <M>. <br> //! <br> //! For each knot if <M> is lower or equal to the <br> //! current multiplicity nothing is done. If <M> is <br> //! higher than the degree the degree is used. <br>//! If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex] <br> Standard_EXPORT void IncreaseMultiplicity(const Standard_Integer I1,const Standard_Integer I2,const Standard_Integer M) ; //!Increment the multiplicities of the knots in <br> //! [I1,I2] by <M>. <br> //! <br> //! If <M> is not positive nithing is done. <br> //! <br> //! For each knot the resulting multiplicity is <br> //! limited to the Degree. <br>//! If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex] <br> Standard_EXPORT void IncrementMultiplicity(const Standard_Integer I1,const Standard_Integer I2,const Standard_Integer M) ; //! Inserts a knot value in the sequence of knots. If <br> //! <U> is an existing knot the multiplicity is <br> //! increased by <M>. <br> //! <br> //! If U is not on the parameter range nothing is <br> //! done. <br> //! <br> //! If the multiplicity is negative or null nothing is <br> //! done. The new multiplicity is limited to the <br> //! degree. <br> //! <br> //! The tolerance criterion for knots equality is <br> //! the max of Epsilon(U) and ParametricTolerance. <br> Standard_EXPORT void InsertKnot(const Standard_Real U,const Standard_Integer M = 1,const Standard_Real ParametricTolerance = 0.0,const Standard_Boolean Add = Standard_True) ; //! Inserts a set of knots values in the sequence of <br> //! knots. <br> //! <br> //! For each U = Knots(i), M = Mults(i) <br> //! <br> //! If <U> is an existing knot the multiplicity is <br> //! increased by <M> if <Add> is True, increased to <br> //! <M> if <Add> is False. <br> //! <br> //! If U is not on the parameter range nothing is <br> //! done. <br> //! <br> //! If the multiplicity is negative or null nothing is <br> //! done. The new multiplicity is limited to the <br> //! degree. <br> //! <br> //! The tolerance criterion for knots equality is <br> //! the max of Epsilon(U) and ParametricTolerance. <br> Standard_EXPORT void InsertKnots(const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const Standard_Real ParametricTolerance = 0.0,const Standard_Boolean Add = Standard_False) ; //! Reduces the multiplicity of the knot of index Index <br> //! to M. If M is equal to 0, the knot is removed. <br> //! With a modification of this type, the array of poles is also modified. <br> //! Two different algorithms are systematically used to <br> //! compute the new poles of the curve. If, for each <br> //! pole, the distance between the pole calculated <br> //! using the first algorithm and the same pole <br> //! calculated using the second algorithm, is less than <br> //! Tolerance, this ensures that the curve is not <br> //! modified by more than Tolerance. Under these <br> //! conditions, true is returned; otherwise, false is returned. <br> //! A low tolerance is used to prevent modification of <br> //! the curve. A high tolerance is used to "smooth" the curve. <br> //! Exceptions <br> //! Standard_OutOfRange if Index is outside the <br> //! bounds of the knots table. <br>//! pole insertion and pole removing <br> //! this operation is limited to the Uniform or QuasiUniform <br> //! BSplineCurve. The knot values are modified . If the BSpline is <br> //! NonUniform or Piecewise Bezier an exception Construction error <br> //! is raised. <br> Standard_EXPORT Standard_Boolean RemoveKnot(const Standard_Integer Index,const Standard_Integer M,const Standard_Real Tolerance) ; //! Changes the direction of parametrization of <me>. The Knot <br> //! sequence is modified, the FirstParameter and the <br> //! LastParameter are not modified. The StartPoint of the <br> //! initial curve becomes the EndPoint of the reversed curve <br> //! and the EndPoint of the initial curve becomes the StartPoint <br> //! of the reversed curve. <br> Standard_EXPORT void Reverse() ; //! Returns the parameter on the reversed curve for <br> //! the point of parameter U on <me>. <br> //! <br> //! returns UFirst + ULast - U <br> Standard_EXPORT Standard_Real ReversedParameter(const Standard_Real U) const; //! Modifies this BSpline curve by segmenting it between <br> //! U1 and U2. Either of these values can be outside the <br> //! bounds of the curve, but U2 must be greater than U1. <br> //! All data structure tables of this BSpline curve are <br> //! modified, but the knots located between U1 and U2 <br> //! are retained. The degree of the curve is not modified. <br> //! Warnings : <br> //! Even if <me> is not closed it can become closed after the <br> //! segmentation for example if U1 or U2 are out of the bounds <br> //! of the curve <me> or if the curve makes loop. <br> //! After the segmentation the length of a curve can be null. <br>//! raises if U2 < U1. <br> Standard_EXPORT void Segment(const Standard_Real U1,const Standard_Real U2) ; //! Modifies this BSpline curve by assigning the value K <br> //! to the knot of index Index in the knots table. This is a <br> //! relatively local modification because K must be such that: <br> //! Knots(Index - 1) < K < Knots(Index + 1) <br> //! The second syntax allows you also to increase the <br> //! multiplicity of the knot to M (but it is not possible to <br> //! decrease the multiplicity of the knot with this function). <br> //! Standard_ConstructionError if: <br> //! - K is not such that: <br> //! Knots(Index - 1) < K < Knots(Index + 1) <br> //! - M is greater than the degree of this BSpline curve <br> //! or lower than the previous multiplicity of knot of <br> //! index Index in the knots table. <br> //! Standard_OutOfRange if Index is outside the bounds of the knots table. <br> Standard_EXPORT void SetKnot(const Standard_Integer Index,const Standard_Real K) ; //! Modifies this BSpline curve by assigning the array <br> //! K to its knots table. The multiplicity of the knots is not modified. <br> //! Exceptions <br> //! Standard_ConstructionError if the values in the <br> //! array K are not in ascending order. <br> //! Standard_OutOfRange if the bounds of the array <br> //! K are not respectively 1 and the number of knots of this BSpline curve. <br> Standard_EXPORT void SetKnots(const TColStd_Array1OfReal& K) ; //! Changes the knot of range Index with its multiplicity. <br> //! You can increase the multiplicity of a knot but it is <br> //! not allowed to decrease the multiplicity of an existing knot. <br> //! Raised if K >= Knots(Index+1) or K <= Knots(Index-1). <br> //! Raised if M is greater than Degree or lower than the previous <br> //! multiplicity of knot of range Index. <br>//! Raised if Index < 1 || Index > NbKnots <br> Standard_EXPORT void SetKnot(const Standard_Integer Index,const Standard_Real K,const Standard_Integer M) ; //! returns the parameter normalized within <br> //! the period if the curve is periodic : otherwise <br> //! does not do anything <br> Standard_EXPORT void PeriodicNormalization(Standard_Real& U) const; //! Changes this BSpline curve into a periodic curve. <br> //! To become periodic, the curve must first be closed. <br> //! Next, the knot sequence must be periodic. For this, <br> //! FirstUKnotIndex and LastUKnotIndex are used <br> //! to compute I1 and I2, the indexes in the knots <br> //! array of the knots corresponding to the first and <br> //! last parameters of this BSpline curve. <br> //! The period is therefore: Knots(I2) - Knots(I1). <br> //! Consequently, the knots and poles tables are modified. <br> //! Exceptions <br> //! Standard_ConstructionError if this BSpline curve is not closed. <br> Standard_EXPORT void SetPeriodic() ; //! Assigns the knot of index Index in the knots table as <br> //! the origin of this periodic BSpline curve. As a <br> //! consequence, the knots and poles tables are modified. <br> //! Exceptions <br> //! Standard_NoSuchObject if this curve is not periodic. <br> //! Standard_DomainError if Index is outside the bounds of the knots table. <br> Standard_EXPORT void SetOrigin(const Standard_Integer Index) ; //! Set the origin of a periodic curve at Knot U. If U <br> //! is not a knot of the BSpline a new knot is <br> //! inseted. KnotVector and poles are modified. <br>//! Raised if the curve is not periodic <br> Standard_EXPORT void SetOrigin(const Standard_Real U,const Standard_Real Tol) ; //! Changes this BSpline curve into a non-periodic <br> //! curve. If this curve is already non-periodic, it is not modified. <br> //! Note: the poles and knots tables are modified. <br> //! Warning <br> //! If this curve is periodic, as the multiplicity of the first <br> //! and last knots is not modified, and is not equal to <br> //! Degree + 1, where Degree is the degree of <br> //! this BSpline curve, the start and end points of the <br> //! curve are not its first and last poles. <br> Standard_EXPORT void SetNotPeriodic() ; //! Modifies this BSpline curve by assigning P to the pole <br> //! of index Index in the poles table. <br> //! Exceptions <br> //! Standard_OutOfRange if Index is outside the <br> //! bounds of the poles table. <br> //! Standard_ConstructionError if Weight is negative or null. <br> Standard_EXPORT void SetPole(const Standard_Integer Index,const gp_Pnt& P) ; //! Modifies this BSpline curve by assigning P to the pole <br> //! of index Index in the poles table. <br> //! This syntax also allows you to modify the <br> //! weight of the modified pole, which becomes Weight. <br> //! In this case, if this BSpline curve is non-rational, it <br> //! can become rational and vice versa. <br> //! Exceptions <br> //! Standard_OutOfRange if Index is outside the <br> //! bounds of the poles table. <br> //! Standard_ConstructionError if Weight is negative or null. <br> Standard_EXPORT void SetPole(const Standard_Integer Index,const gp_Pnt& P,const Standard_Real Weight) ; //! Changes the weight for the pole of range Index. <br> //! If the curve was non rational it can become rational. <br> //! If the curve was rational it can become non rational. <br> //! Raised if Index < 1 || Index > NbPoles <br>//! Raised if Weight <= 0.0 <br> Standard_EXPORT void SetWeight(const Standard_Integer Index,const Standard_Real Weight) ; //! Moves the point of parameter U of this BSpline curve <br> //! to P. Index1 and Index2 are the indexes in the table <br> //! of poles of this BSpline curve of the first and last <br> //! poles designated to be moved. <br> //! FirstModifiedPole and LastModifiedPole are the <br> //! indexes of the first and last poles which are effectively modified. <br> //! In the event of incompatibility between Index1, Index2 and the value U: <br> //! - no change is made to this BSpline curve, and <br> //! - the FirstModifiedPole and LastModifiedPole are returned null. <br> //! Exceptions <br> //! Standard_OutOfRange if: <br> //! - Index1 is greater than or equal to Index2, or <br> //! - Index1 or Index2 is less than 1 or greater than the <br> //! number of poles of this BSpline curve. <br> Standard_EXPORT void MovePoint(const Standard_Real U,const gp_Pnt& P,const Standard_Integer Index1,const Standard_Integer Index2,Standard_Integer& FirstModifiedPole,Standard_Integer& LastModifiedPole) ; //! Move a point with parameter U to P. <br> //! and makes it tangent at U be Tangent. <br> //! StartingCondition = -1 means first can move <br> //! EndingCondition = -1 means last point can move <br> //! StartingCondition = 0 means the first point cannot move <br> //! EndingCondition = 0 means the last point cannot move <br> //! StartingCondition = 1 means the first point and tangent cannot move <br> //! EndingCondition = 1 means the last point and tangent cannot move <br> //! and so forth <br> //! ErrorStatus != 0 means that there are not enought degree of freedom <br> //! with the constrain to deform the curve accordingly <br> //! <br> Standard_EXPORT void MovePointAndTangent(const Standard_Real U,const gp_Pnt& P,const gp_Vec& Tangent,const Standard_Real Tolerance,const Standard_Integer StartingCondition,const Standard_Integer EndingCondition,Standard_Integer& ErrorStatus) ; //! Returns the continuity of the curve, the curve is at least C0. <br>//! Raised if N < 0. <br> Standard_EXPORT Standard_Boolean IsCN(const Standard_Integer N) const; //! Returns true if the distance between the first point and the <br> //! last point of the curve is lower or equal to Resolution <br> //! from package gp. <br> //! Warnings : <br> //! The first and the last point can be different from the first <br> //! pole and the last pole of the curve. <br> Standard_EXPORT Standard_Boolean IsClosed() const; //! Returns True if the curve is periodic. <br> Standard_EXPORT Standard_Boolean IsPeriodic() const; //! Returns True if the weights are not identical. <br> //! The tolerance criterion is Epsilon of the class Real. <br> Standard_EXPORT Standard_Boolean IsRational() const; //! Returns the global continuity of the curve : <br> //! C0 : only geometric continuity, <br> //! C1 : continuity of the first derivative all along the Curve, <br> //! C2 : continuity of the second derivative all along the Curve, <br> //! C3 : continuity of the third derivative all along the Curve, <br> //! CN : the order of continuity is infinite. <br> //! For a B-spline curve of degree d if a knot Ui has a <br> //! multiplicity p the B-spline curve is only Cd-p continuous <br> //! at Ui. So the global continuity of the curve can't be greater <br> //! than Cd-p where p is the maximum multiplicity of the interior <br> //! Knots. In the interior of a knot span the curve is infinitely <br> //! continuously differentiable. <br> Standard_EXPORT GeomAbs_Shape Continuity() const; //! Returns the degree of this BSpline curve. <br> //! The degree of a Geom_BSplineCurve curve cannot <br> //! be greater than Geom_BSplineCurve::MaxDegree(). <br>//! Computation of value and derivatives <br> Standard_EXPORT Standard_Integer Degree() const; //! Returns in P the point of parameter U. <br> Standard_EXPORT void D0(const Standard_Real U,gp_Pnt& P) const; //! Raised if the continuity of the curve is not C1. <br> Standard_EXPORT void D1(const Standard_Real U,gp_Pnt& P,gp_Vec& V1) const; //! Raised if the continuity of the curve is not C2. <br> Standard_EXPORT void D2(const Standard_Real U,gp_Pnt& P,gp_Vec& V1,gp_Vec& V2) const; //! Raised if the continuity of the curve is not C3. <br> Standard_EXPORT void D3(const Standard_Real U,gp_Pnt& P,gp_Vec& V1,gp_Vec& V2,gp_Vec& V3) const; //! For the point of parameter U of this BSpline curve, <br> //! computes the vector corresponding to the Nth derivative. <br> //! Warning <br> //! On a point where the continuity of the curve is not the <br> //! one requested, this function impacts the part defined <br> //! by the parameter with a value greater than U, i.e. the <br> //! part of the curve to the "right" of the singularity. <br> //! Exceptions <br> //! Standard_RangeError if N is less than 1. <br> //! The following functions compute the point of parameter U <br> //! and the derivatives at this point on the B-spline curve <br> //! arc defined between the knot FromK1 and the knot ToK2. <br> //! U can be out of bounds [Knot (FromK1), Knot (ToK2)] but <br> //! for the computation we only use the definition of the curve <br> //! between these two knots. This method is useful to compute <br> //! local derivative, if the order of continuity of the whole <br> //! curve is not greater enough. Inside the parametric <br> //! domain Knot (FromK1), Knot (ToK2) the evaluations are <br> //! the same as if we consider the whole definition of the <br> //! curve. Of course the evaluations are different outside <br> //! this parametric domain. <br> Standard_EXPORT gp_Vec DN(const Standard_Real U,const Standard_Integer N) const; //! Raised if FromK1 = ToK2. <br> //! Raised if FromK1 and ToK2 are not in the range <br> //! [FirstUKnotIndex, LastUKnotIndex]. <br> Standard_EXPORT gp_Pnt LocalValue(const Standard_Real U,const Standard_Integer FromK1,const Standard_Integer ToK2) const; //! Raised if FromK1 = ToK2. <br> //! Raised if FromK1 and ToK2 are not in the range <br> //! [FirstUKnotIndex, LastUKnotIndex]. <br> Standard_EXPORT void LocalD0(const Standard_Real U,const Standard_Integer FromK1,const Standard_Integer ToK2,gp_Pnt& P) const; //! Raised if the local continuity of the curve is not C1 <br> //! between the knot K1 and the knot K2. <br>//! Raised if FromK1 = ToK2. <br> //! Raised if FromK1 and ToK2 are not in the range <br> //! [FirstUKnotIndex, LastUKnotIndex]. <br> Standard_EXPORT void LocalD1(const Standard_Real U,const Standard_Integer FromK1,const Standard_Integer ToK2,gp_Pnt& P,gp_Vec& V1) const; //! Raised if the local continuity of the curve is not C2 <br> //! between the knot K1 and the knot K2. <br>//! Raised if FromK1 = ToK2. <br> //! Raised if FromK1 and ToK2 are not in the range <br> //! [FirstUKnotIndex, LastUKnotIndex]. <br> Standard_EXPORT void LocalD2(const Standard_Real U,const Standard_Integer FromK1,const Standard_Integer ToK2,gp_Pnt& P,gp_Vec& V1,gp_Vec& V2) const; //! Raised if the local continuity of the curve is not C3 <br> //! between the knot K1 and the knot K2. <br>//! Raised if FromK1 = ToK2. <br> //! Raised if FromK1 and ToK2 are not in the range <br> //! [FirstUKnotIndex, LastUKnotIndex]. <br> Standard_EXPORT void LocalD3(const Standard_Real U,const Standard_Integer FromK1,const Standard_Integer ToK2,gp_Pnt& P,gp_Vec& V1,gp_Vec& V2,gp_Vec& V3) const; //! Raised if the local continuity of the curve is not CN <br> //! between the knot K1 and the knot K2. <br>//! Raised if FromK1 = ToK2. <br>//! Raised if N < 1. <br> //! Raises if FromK1 and ToK2 are not in the range <br> //! [FirstUKnotIndex, LastUKnotIndex]. <br> Standard_EXPORT gp_Vec LocalDN(const Standard_Real U,const Standard_Integer FromK1,const Standard_Integer ToK2,const Standard_Integer N) const; //! Returns the last point of the curve. <br> //! Warnings : <br> //! The last point of the curve is different from the last <br> //! pole of the curve if the multiplicity of the last knot <br> //! is lower than Degree. <br> Standard_EXPORT gp_Pnt EndPoint() const; //! Returns the index in the knot array of the knot <br> //! corresponding to the first or last parameter of this BSpline curve. <br> //! For a BSpline curve, the first (or last) parameter <br> //! (which gives the start (or end) point of the curve) is a <br> //! knot value. However, if the multiplicity of the first (or <br> //! last) knot is less than Degree + 1, where <br> //! Degree is the degree of the curve, it is not the first <br> //! (or last) knot of the curve. <br> Standard_EXPORT Standard_Integer FirstUKnotIndex() const; //! Returns the value of the first parameter of this <br> //! BSpline curve. This is a knot value. <br> //! The first parameter is the one of the start point of the BSpline curve. <br> Standard_EXPORT Standard_Real FirstParameter() const; //! Returns the knot of range Index. When there is a knot <br> //! with a multiplicity greater than 1 the knot is not repeated. <br> //! The method Multiplicity can be used to get the multiplicity <br> //! of the Knot. <br>//! Raised if Index < 1 or Index > NbKnots <br> Standard_EXPORT Standard_Real Knot(const Standard_Integer Index) const; //! returns the knot values of the B-spline curve; <br> //! Warning <br> //! A knot with a multiplicity greater than 1 is not <br> //! repeated in the knot table. The Multiplicity function <br> //! can be used to obtain the multiplicity of each knot. <br> //! Raised if the length of K is not equal to the number of knots. <br> Standard_EXPORT void Knots(TColStd_Array1OfReal& K) const; //! Returns K, the knots sequence of this BSpline curve. <br> //! In this sequence, knots with a multiplicity greater than 1 are repeated. <br> //! In the case of a non-periodic curve the length of the <br> //! sequence must be equal to the sum of the NbKnots <br> //! multiplicities of the knots of the curve (where <br> //! NbKnots is the number of knots of this BSpline <br> //! curve). This sum is also equal to : NbPoles + Degree + 1 <br> //! where NbPoles is the number of poles and <br> //! Degree the degree of this BSpline curve. <br> //! In the case of a periodic curve, if there are k periodic <br> //! knots, the period is Knot(k+1) - Knot(1). <br> //! The initial sequence is built by writing knots 1 to k+1, <br> //! which are repeated according to their corresponding multiplicities. <br> //! If Degree is the degree of the curve, the degree of <br> //! continuity of the curve at the knot of index 1 (or k+1) <br> //! is equal to c = Degree + 1 - Mult(1). c <br> //! knots are then inserted at the beginning and end of <br> //! the initial sequence: <br> //! - the c values of knots preceding the first item <br> //! Knot(k+1) in the initial sequence are inserted <br> //! at the beginning; the period is subtracted from these c values; <br> //! - the c values of knots following the last item <br> //! Knot(1) in the initial sequence are inserted at <br> //! the end; the period is added to these c values. <br> //! The length of the sequence must therefore be equal to: <br> //! NbPoles + 2*Degree - Mult(1) + 2. <br> //! Example <br> //! For a non-periodic BSpline curve of degree 2 where: <br> //! - the array of knots is: { k1 k2 k3 k4 }, <br> //! - with associated multiplicities: { 3 1 2 3 }, <br> //! the knot sequence is: <br> //! K = { k1 k1 k1 k2 k3 k3 k4 k4 k4 } <br> //! For a periodic BSpline curve of degree 4 , which is <br> //! "C1" continuous at the first knot, and where : <br> //! - the periodic knots are: { k1 k2 k3 (k4) } <br> //! (3 periodic knots: the points of parameter k1 and k4 <br> //! are identical, the period is p = k4 - k1), <br> //! - with associated multiplicities: { 3 1 2 (3) }, <br> //! the degree of continuity at knots k1 and k4 is: <br> //! Degree + 1 - Mult(i) = 2. <br> //! 2 supplementary knots are added at the beginning <br> //! and end of the sequence: <br> //! - at the beginning: the 2 knots preceding k4 minus <br> //! the period; in this example, this is k3 - p both times; <br> //! - at the end: the 2 knots following k1 plus the period; <br> //! in this example, this is k2 + p and k3 + p. <br> //! The knot sequence is therefore: <br> //! K = { k3-p k3-p k1 k1 k1 k2 k3 k3 <br> //! k4 k4 k4 k2+p k3+p } <br> //! Exceptions <br> //! Standard_DimensionError if the array K is not of <br> //! the appropriate length.Returns the knots sequence. <br> Standard_EXPORT void KnotSequence(TColStd_Array1OfReal& K) const; //! Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. <br> //! If all the knots differ by a positive constant from the <br> //! preceding knot the BSpline Curve can be : <br> //! - Uniform if all the knots are of multiplicity 1, <br> //! - QuasiUniform if all the knots are of multiplicity 1 except for <br> //! the first and last knot which are of multiplicity Degree + 1, <br> //! - PiecewiseBezier if the first and last knots have multiplicity <br> //! Degree + 1 and if interior knots have multiplicity Degree <br> //! A piecewise Bezier with only two knots is a BezierCurve. <br> //! else the curve is non uniform. <br> //! The tolerance criterion is Epsilon from class Real. <br> Standard_EXPORT GeomAbs_BSplKnotDistribution KnotDistribution() const; //! For a BSpline curve the last parameter (which gives the <br> //! end point of the curve) is a knot value but if the <br> //! multiplicity of the last knot index is lower than <br> //! Degree + 1 it is not the last knot of the curve. This <br> //! method computes the index of the knot corresponding to <br> //! the last parameter. <br> Standard_EXPORT Standard_Integer LastUKnotIndex() const; //! Computes the parametric value of the end point of the curve. <br> //! It is a knot value. <br> Standard_EXPORT Standard_Real LastParameter() const; //! Locates the parametric value U in the sequence of knots. <br> //! If "WithKnotRepetition" is True we consider the knot's <br> //! representation with repetition of multiple knot value, <br> //! otherwise we consider the knot's representation with <br> //! no repetition of multiple knot values. <br> //! Knots (I1) <= U <= Knots (I2) <br> //! . if I1 = I2 U is a knot value (the tolerance criterion <br> //! ParametricTolerance is used). <br> //! . if I1 < 1 => U < Knots (1) - Abs(ParametricTolerance) <br> //! . if I2 > NbKnots => U > Knots (NbKnots) + Abs(ParametricTolerance) <br> Standard_EXPORT void LocateU(const Standard_Real U,const Standard_Real ParametricTolerance,Standard_Integer& I1,Standard_Integer& I2,const Standard_Boolean WithKnotRepetition = Standard_False) const; //! Returns the multiplicity of the knots of range Index. <br>//! Raised if Index < 1 or Index > NbKnots <br> Standard_EXPORT Standard_Integer Multiplicity(const Standard_Integer Index) const; //! Returns the multiplicity of the knots of the curve. <br> //! Raised if the length of M is not equal to NbKnots. <br> Standard_EXPORT void Multiplicities(TColStd_Array1OfInteger& M) const; //! Returns the number of knots. This method returns the number of <br> //! knot without repetition of multiple knots. <br> Standard_EXPORT Standard_Integer NbKnots() const; //! Returns the number of poles <br> Standard_EXPORT Standard_Integer NbPoles() const; //! Returns the pole of range Index. <br>//! Raised if Index < 1 or Index > NbPoles. <br> Standard_EXPORT gp_Pnt Pole(const Standard_Integer Index) const; //! Returns the poles of the B-spline curve; <br> //! Raised if the length of P is not equal to the number of poles. <br> Standard_EXPORT void Poles(TColgp_Array1OfPnt& P) const; //! Returns the start point of the curve. <br> //! Warnings : <br> //! This point is different from the first pole of the curve if the <br> //! multiplicity of the first knot is lower than Degree. <br> Standard_EXPORT gp_Pnt StartPoint() const; //! Returns the weight of the pole of range Index . <br>//! Raised if Index < 1 or Index > NbPoles. <br> Standard_EXPORT Standard_Real Weight(const Standard_Integer Index) const; //! Returns the weights of the B-spline curve; <br> //! Raised if the length of W is not equal to NbPoles. <br> Standard_EXPORT void Weights(TColStd_Array1OfReal& W) const; //! Applies the transformation T to this BSpline curve. <br> Standard_EXPORT void Transform(const gp_Trsf& T) ; //! Returns the value of the maximum degree of the normalized <br> //! B-spline basis functions in this package. <br> Standard_EXPORT static Standard_Integer MaxDegree() ; //! Computes for this BSpline curve the parametric <br> //! tolerance UTolerance for a given 3D tolerance Tolerance3D. <br> //! If f(t) is the equation of this BSpline curve, <br> //! UTolerance ensures that: <br> //! | t1 - t0| < Utolerance ===> <br> //! |f(t1) - f(t0)| < Tolerance3D <br> Standard_EXPORT void Resolution(const Standard_Real Tolerance3D,Standard_Real& UTolerance) ; //! Creates a new object which is a copy of this BSpline curve. <br> Standard_EXPORT Handle_Geom_Geometry Copy() const; //Standard_EXPORT ~Geom_BSplineCurve(); // Type management // Standard_EXPORT const Handle(Standard_Type)& DynamicType() const; //Standard_EXPORT Standard_Boolean IsKind(const Handle(Standard_Type)&) const; protected: // Methods PROTECTED // // Fields PROTECTED // private: // Methods PRIVATE // //! Tells whether the Cache is valid for the <br> //! given parameter <br> //! Warnings : the parameter must be normalized within <br> //! the period if the curve is periodic. Otherwise <br> //! the answer will be false <br> //! <br> Standard_EXPORT Standard_Boolean IsCacheValid(const Standard_Real Parameter) const; //! Invalidates the cache. This has to be private <br> //! this has to be private <br> Standard_EXPORT void InvalidateCache() ; //! Recompute the flatknots, the knotsdistribution, the continuity. <br> Standard_EXPORT void UpdateKnots() ; //! updates the cache and validates it <br> Standard_EXPORT void ValidateCache(const Standard_Real Parameter) ; // Fields PRIVATE // Standard_Boolean rational; Standard_Boolean periodic; GeomAbs_BSplKnotDistribution knotSet; GeomAbs_Shape smooth; Standard_Integer deg; Handle_TColgp_HArray1OfPnt poles; Handle_TColStd_HArray1OfReal weights; Handle_TColStd_HArray1OfReal flatknots; Handle_TColStd_HArray1OfReal knots; Handle_TColStd_HArray1OfInteger mults; Handle_TColgp_HArray1OfPnt cachepoles; Handle_TColStd_HArray1OfReal cacheweights; Standard_Integer validcache; Standard_Real parametercache; Standard_Real spanlenghtcache; Standard_Integer spanindexcache; Standard_Real maxderivinv; Standard_Boolean maxderivinvok; }; // other Inline functions and methods (like "C++: function call" methods) // #endif

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