// Created on: 1993-03-09 // Created by: JCV // Copyright (c) 1993-1999 Matra Datavision // Copyright (c) 1999-2014 OPEN CASCADE SAS // // This file is part of Open CASCADE Technology software library. // // This library is free software; you can redistribute it and/or modify it under // the terms of the GNU Lesser General Public License version 2.1 as published // by the Free Software Foundation, with special exception defined in the file // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT // distribution for complete text of the license and disclaimer of any warranty. // // Alternatively, this file may be used under the terms of Open CASCADE // commercial license or contractual agreement. #ifndef _Geom_BSplineCurve_HeaderFile #define _Geom_BSplineCurve_HeaderFile #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include class Standard_ConstructionError; class Standard_DimensionError; class Standard_DomainError; class Standard_OutOfRange; class Standard_RangeError; class Standard_NoSuchObject; class Geom_UndefinedDerivative; class gp_Pnt; class gp_Vec; class gp_Trsf; class Geom_Geometry; class Geom_BSplineCurve; DEFINE_STANDARD_HANDLE(Geom_BSplineCurve, Geom_BoundedCurve) //! Definition of the B_spline curve. //! A B-spline curve can be //! Uniform or non-uniform //! Rational or non-rational //! Periodic or non-periodic //! //! a b-spline curve is defined by : //! its degree; the degree for a //! Geom_BSplineCurve is limited to a value (25) //! which is defined and controlled by the system. //! This value is returned by the function MaxDegree; //! - its periodic or non-periodic nature; //! - a table of poles (also called control points), with //! their associated weights if the BSpline curve is //! rational. The poles of the curve are "control //! points" used to deform the curve. If the curve is //! non-periodic, the first pole is the start point of //! the curve, and the last pole is the end point of //! the curve. The segment which joins the first pole //! to the second pole is the tangent to the curve at //! its start point, and the segment which joins the //! last pole to the second-from-last pole is the //! tangent to the curve at its end point. If the curve //! is periodic, these geometric properties are not //! verified. It is more difficult to give a geometric //! signification to the weights but are useful for //! providing exact representations of the arcs of a //! circle or ellipse. Moreover, if the weights of all the //! poles are equal, the curve has a polynomial //! equation; it is therefore a non-rational curve. //! - a table of knots with their multiplicities. For a //! Geom_BSplineCurve, the table of knots is an //! increasing sequence of reals without repetition; //! the multiplicities define the repetition of the knots. //! A BSpline curve is a piecewise polynomial or //! rational curve. The knots are the parameters of //! junction points between two pieces. The //! multiplicity Mult(i) of the knot Knot(i) of //! the BSpline curve is related to the degree of //! continuity of the curve at the knot Knot(i), //! which is equal to Degree - Mult(i) //! where Degree is the degree of the BSpline curve. //! If the knots are regularly spaced (i.e. the difference //! between two consecutive knots is a constant), three //! specific and frequently used cases of knot //! distribution can be identified: //! - "uniform" if all multiplicities are equal to 1, //! - "quasi-uniform" if all multiplicities are equal to 1, //! except the first and the last knot which have a //! multiplicity of Degree + 1, where Degree is //! the degree of the BSpline curve, //! - "Piecewise Bezier" if all multiplicities are equal to //! Degree except the first and last knot which //! have a multiplicity of Degree + 1, where //! Degree is the degree of the BSpline curve. A //! curve of this type is a concatenation of arcs of Bezier curves. //! If the BSpline curve is not periodic: //! - the bounds of the Poles and Weights tables are 1 //! and NbPoles, where NbPoles is the number //! of poles of the BSpline curve, //! - the bounds of the Knots and Multiplicities tables //! are 1 and NbKnots, where NbKnots is the //! number of knots of the BSpline curve. //! If the BSpline curve is periodic, and if there are k //! periodic knots and p periodic poles, the period is: //! period = Knot(k + 1) - Knot(1) //! and the poles and knots tables can be considered //! as infinite tables, verifying: //! - Knot(i+k) = Knot(i) + period //! - Pole(i+p) = Pole(i) //! Note: data structures of a periodic BSpline curve //! are more complex than those of a non-periodic one. //! Warning //! In this class, weight value is considered to be zero if //! the weight is less than or equal to gp::Resolution(). //! //! References : //! . A survey of curve and surface methods in CADG Wolfgang BOHM //! CAGD 1 (1984) //! . On de Boor-like algorithms and blossoming Wolfgang BOEHM //! cagd 5 (1988) //! . Blossoming and knot insertion algorithms for B-spline curves //! Ronald N. GOLDMAN //! . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA //! . Curves and Surfaces for Computer Aided Geometric Design, //! a practical guide Gerald Farin class Geom_BSplineCurve : public Geom_BoundedCurve { public: //! Creates a non-rational B_spline curve on the //! basis of degree . 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 //! of degree . //! Raises ConstructionError subject to the following conditions //! 0 < Degree <= MaxDegree. //! //! Weights.Length() == Poles.Length() //! //! Knots.Length() == Mults.Length() >= 2 //! //! Knots(i) < Knots(i+1) (Knots are increasing) //! //! 1 <= Mults(i) <= Degree //! //! On a non periodic curve the first and last multiplicities //! may be Degree+1 (this is even recommanded if you want the //! curve to start and finish on the first and last pole). //! //! On a periodic curve the first and the last multicities //! must be the same. //! //! on non-periodic curves //! //! Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2 //! //! on periodic curves //! //! Poles.Length() == Sum(Mults(i)) except the first or last Standard_EXPORT 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 //! Degree. As a result, the poles, weights and //! multiplicities tables are modified; the knots table is //! not changed. Nothing is done if Degree is less than //! or equal to the current degree. //! Exceptions //! Standard_ConstructionError if Degree is greater than //! Geom_BSplineCurve::MaxDegree(). Standard_EXPORT void IncreaseDegree (const Standard_Integer Degree); //! Increases the multiplicity of the knot to //! . //! //! If is lower or equal to the current //! multiplicity nothing is done. If is higher than //! the degree the degree is used. //! If is not in [FirstUKnotIndex, LastUKnotIndex] Standard_EXPORT void IncreaseMultiplicity (const Standard_Integer Index, const Standard_Integer M); //! Increases the multiplicities of the knots in //! [I1,I2] to . //! //! For each knot if is lower or equal to the //! current multiplicity nothing is done. If is //! higher than the degree the degree is used. //! If are not in [FirstUKnotIndex, LastUKnotIndex] Standard_EXPORT void IncreaseMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M); //! Increment the multiplicities of the knots in //! [I1,I2] by . //! //! If is not positive nithing is done. //! //! For each knot the resulting multiplicity is //! limited to the Degree. //! If are not in [FirstUKnotIndex, LastUKnotIndex] 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 //! is an existing knot the multiplicity is //! increased by . //! //! If U is not on the parameter range nothing is //! done. //! //! If the multiplicity is negative or null nothing is //! done. The new multiplicity is limited to the //! degree. //! //! The tolerance criterion for knots equality is //! the max of Epsilon(U) and ParametricTolerance. Standard_EXPORT void 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 //! knots. //! //! For each U = Knots(i), M = Mults(i) //! //! If is an existing knot the multiplicity is //! increased by if is True, increased to //! if is False. //! //! If U is not on the parameter range nothing is //! done. //! //! If the multiplicity is negative or null nothing is //! done. The new multiplicity is limited to the //! degree. //! //! The tolerance criterion for knots equality is //! the max of Epsilon(U) and ParametricTolerance. Standard_EXPORT 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 //! to M. If M is equal to 0, the knot is removed. //! With a modification of this type, the array of poles is also modified. //! Two different algorithms are systematically used to //! compute the new poles of the curve. If, for each //! pole, the distance between the pole calculated //! using the first algorithm and the same pole //! calculated using the second algorithm, is less than //! Tolerance, this ensures that the curve is not //! modified by more than Tolerance. Under these //! conditions, true is returned; otherwise, false is returned. //! A low tolerance is used to prevent modification of //! the curve. A high tolerance is used to "smooth" the curve. //! Exceptions //! Standard_OutOfRange if Index is outside the //! bounds of the knots table. //! pole insertion and pole removing //! this operation is limited to the Uniform or QuasiUniform //! BSplineCurve. The knot values are modified . If the BSpline is //! NonUniform or Piecewise Bezier an exception Construction error //! is raised. Standard_EXPORT Standard_Boolean RemoveKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance); //! Changes the direction of parametrization of . The Knot //! sequence is modified, the FirstParameter and the //! LastParameter are not modified. The StartPoint of the //! initial curve becomes the EndPoint of the reversed curve //! and the EndPoint of the initial curve becomes the StartPoint //! of the reversed curve. Standard_EXPORT void Reverse() Standard_OVERRIDE; //! Returns the parameter on the reversed curve for //! the point of parameter U on . //! //! returns UFirst + ULast - U Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE; //! 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 is not closed it can become closed after the //! segmentation for example if U1 or U2 are out of the bounds //! of the curve or if the curve makes loop. //! After the segmentation the length of a curve can be null. //! raises if U2 < U1. //! Standard_DomainError if U2 - U1 exceeds the period for periodic curves. //! i.e. ((U2 - U1) - Period) > Precision::PConfusion(). Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real theTolerance = Precision::PConfusion()); //! Modifies this BSpline curve by assigning the value K //! to the knot of index Index in the knots table. This is a //! relatively local modification because K must be such that: //! Knots(Index - 1) < K < Knots(Index + 1) //! The second syntax allows you also to increase the //! multiplicity of the knot to M (but it is not possible to //! decrease the multiplicity of the knot with this function). //! Standard_ConstructionError if: //! - K is not such that: //! Knots(Index - 1) < K < Knots(Index + 1) //! - M is greater than the degree of this BSpline curve //! or lower than the previous multiplicity of knot of //! index Index in the knots table. //! Standard_OutOfRange if Index is outside the bounds of the knots table. Standard_EXPORT void SetKnot (const Standard_Integer Index, const Standard_Real K); //! Modifies this BSpline curve by assigning the array //! K to its knots table. The multiplicity of the knots is not modified. //! Exceptions //! Standard_ConstructionError if the values in the //! array K are not in ascending order. //! Standard_OutOfRange if the bounds of the array //! K are not respectively 1 and the number of knots of this BSpline curve. Standard_EXPORT void SetKnots (const TColStd_Array1OfReal& K); //! Changes the knot of range Index with its multiplicity. //! You can increase the multiplicity of a knot but it is //! not allowed to decrease the multiplicity of an existing knot. //! //! Raised if K >= Knots(Index+1) or K <= Knots(Index-1). //! Raised if M is greater than Degree or lower than the previous //! multiplicity of knot of range Index. //! Raised if Index < 1 || Index > NbKnots Standard_EXPORT void SetKnot (const Standard_Integer Index, const Standard_Real K, const Standard_Integer M); //! returns the parameter normalized within //! the period if the curve is periodic : otherwise //! does not do anything Standard_EXPORT void PeriodicNormalization (Standard_Real& U) const; //! Changes this BSpline curve into a periodic curve. //! To become periodic, the curve must first be closed. //! Next, the knot sequence must be periodic. For this, //! FirstUKnotIndex and LastUKnotIndex are used //! to compute I1 and I2, the indexes in the knots //! array of the knots corresponding to the first and //! last parameters of this BSpline curve. //! The period is therefore: Knots(I2) - Knots(I1). //! Consequently, the knots and poles tables are modified. //! Exceptions //! Standard_ConstructionError if this BSpline curve is not closed. Standard_EXPORT void SetPeriodic(); //! Assigns the knot of index Index in the knots table as //! the origin of this periodic BSpline curve. As a //! consequence, the knots and poles tables are modified. //! Exceptions //! Standard_NoSuchObject if this curve is not periodic. //! Standard_DomainError if Index is outside the bounds of the knots table. Standard_EXPORT void SetOrigin (const Standard_Integer Index); //! Set the origin of a periodic curve at Knot U. If U //! is not a knot of the BSpline a new knot is //! inseted. KnotVector and poles are modified. //! Raised if the curve is not periodic Standard_EXPORT void SetOrigin (const Standard_Real U, const Standard_Real Tol); //! Changes this BSpline curve into a non-periodic //! curve. If this curve is already non-periodic, it is not modified. //! Note: the poles and knots tables are modified. //! Warning //! If this curve is periodic, as the multiplicity of the first //! and last knots is not modified, and is not equal to //! Degree + 1, where Degree is the degree of //! this BSpline curve, the start and end points of the //! curve are not its first and last poles. Standard_EXPORT void SetNotPeriodic(); //! Modifies this BSpline curve by assigning P to the pole //! of index Index in the poles table. //! Exceptions //! Standard_OutOfRange if Index is outside the //! bounds of the poles table. //! Standard_ConstructionError if Weight is negative or null. Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt& P); //! Modifies this BSpline curve by assigning P to the pole //! of index Index in the poles table. //! This syntax also allows you to modify the //! weight of the modified pole, which becomes Weight. //! In this case, if this BSpline curve is non-rational, it //! can become rational and vice versa. //! Exceptions //! Standard_OutOfRange if Index is outside the //! bounds of the poles table. //! Standard_ConstructionError if Weight is negative or null. Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt& P, const Standard_Real Weight); //! Changes the weight for the pole of range Index. //! If the curve was non rational it can become rational. //! If the curve was rational it can become non rational. //! //! Raised if Index < 1 || Index > NbPoles //! Raised if Weight <= 0.0 Standard_EXPORT void SetWeight (const Standard_Integer Index, const Standard_Real Weight); //! Moves the point of parameter U of this BSpline curve //! to P. Index1 and Index2 are the indexes in the table //! of poles of this BSpline curve of the first and last //! poles designated to be moved. //! FirstModifiedPole and LastModifiedPole are the //! indexes of the first and last poles which are effectively modified. //! In the event of incompatibility between Index1, Index2 and the value U: //! - no change is made to this BSpline curve, and //! - the FirstModifiedPole and LastModifiedPole are returned null. //! Exceptions //! Standard_OutOfRange if: //! - Index1 is greater than or equal to Index2, or //! - Index1 or Index2 is less than 1 or greater than the //! number of poles of this BSpline curve. Standard_EXPORT void 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. //! and makes it tangent at U be Tangent. //! StartingCondition = -1 means first can move //! EndingCondition = -1 means last point can move //! StartingCondition = 0 means the first point cannot move //! EndingCondition = 0 means the last point cannot move //! StartingCondition = 1 means the first point and tangent cannot move //! EndingCondition = 1 means the last point and tangent cannot move //! and so forth //! ErrorStatus != 0 means that there are not enought degree of freedom //! with the constrain to deform the curve accordingly Standard_EXPORT 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. //! Raised if N < 0. Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE; //! Check if curve has at least G1 continuity in interval [theTf, theTl] //! Returns true if IsCN(1) //! or //! angle betweem "left" and "right" first derivatives at //! knots with C0 continuity is less then theAngTol //! only knots in interval [theTf, theTl] is checked Standard_EXPORT Standard_Boolean IsG1 (const Standard_Real theTf, const Standard_Real theTl, const Standard_Real theAngTol) const; //! Returns true if the distance between the first point and the //! last point of the curve is lower or equal to Resolution //! from package gp. //! Warnings : //! The first and the last point can be different from the first //! pole and the last pole of the curve. Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; //! Returns True if the curve is periodic. Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; //! Returns True if the weights are not identical. //! The tolerance criterion is Epsilon of the class Real. Standard_EXPORT Standard_Boolean IsRational() const; //! Returns the global continuity of the curve : //! C0 : only geometric continuity, //! C1 : continuity of the first derivative all along the Curve, //! C2 : continuity of the second derivative all along the Curve, //! C3 : continuity of the third derivative all along the Curve, //! CN : the order of continuity is infinite. //! For a B-spline curve of degree d if a knot Ui has a //! multiplicity p the B-spline curve is only Cd-p continuous //! at Ui. So the global continuity of the curve can't be greater //! than Cd-p where p is the maximum multiplicity of the interior //! Knots. In the interior of a knot span the curve is infinitely //! continuously differentiable. Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE; //! Returns the degree of this BSpline curve. //! The degree of a Geom_BSplineCurve curve cannot //! be greater than Geom_BSplineCurve::MaxDegree(). //! Computation of value and derivatives Standard_EXPORT Standard_Integer Degree() const; //! Returns in P the point of parameter U. Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt& P) const Standard_OVERRIDE; //! Raised if the continuity of the curve is not C1. Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1) const Standard_OVERRIDE; //! Raised if the continuity of the curve is not C2. Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2) const Standard_OVERRIDE; //! Raised if the continuity of the curve is not C3. Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const Standard_OVERRIDE; //! For the point of parameter U of this BSpline curve, //! computes the vector corresponding to the Nth derivative. //! Warning //! On a point where the continuity of the curve is not the //! one requested, this function impacts the part defined //! by the parameter with a value greater than U, i.e. the //! part of the curve to the "right" of the singularity. //! Exceptions //! Standard_RangeError if N is less than 1. //! //! The following functions compute the point of parameter U //! and the derivatives at this point on the B-spline curve //! arc defined between the knot FromK1 and the knot ToK2. //! U can be out of bounds [Knot (FromK1), Knot (ToK2)] but //! for the computation we only use the definition of the curve //! between these two knots. This method is useful to compute //! local derivative, if the order of continuity of the whole //! curve is not greater enough. Inside the parametric //! domain Knot (FromK1), Knot (ToK2) the evaluations are //! the same as if we consider the whole definition of the //! curve. Of course the evaluations are different outside //! this parametric domain. Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE; //! Raised if FromK1 = ToK2. Standard_EXPORT gp_Pnt LocalValue (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2) const; //! Raised if FromK1 = ToK2. 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 //! between the knot K1 and the knot K2. //! Raised if FromK1 = ToK2. 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 //! between the knot K1 and the knot K2. //! Raised if FromK1 = ToK2. 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 //! between the knot K1 and the knot K2. //! Raised if FromK1 = ToK2. 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 //! between the knot K1 and the knot K2. //! Raised if FromK1 = ToK2. //! Raised if N < 1. 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. //! Warnings : //! The last point of the curve is different from the last //! pole of the curve if the multiplicity of the last knot //! is lower than Degree. Standard_EXPORT gp_Pnt EndPoint() const Standard_OVERRIDE; //! Returns the index in the knot array of the knot //! corresponding to the first or last parameter of this BSpline curve. //! For a BSpline curve, the first (or last) parameter //! (which gives the start (or end) point of the curve) is a //! knot value. However, if the multiplicity of the first (or //! last) knot is less than Degree + 1, where //! Degree is the degree of the curve, it is not the first //! (or last) knot of the curve. Standard_EXPORT Standard_Integer FirstUKnotIndex() const; //! Returns the value of the first parameter of this //! BSpline curve. This is a knot value. //! The first parameter is the one of the start point of the BSpline curve. Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; //! Returns the knot of range Index. When there is a knot //! with a multiplicity greater than 1 the knot is not repeated. //! The method Multiplicity can be used to get the multiplicity //! of the Knot. //! Raised if Index < 1 or Index > NbKnots Standard_EXPORT Standard_Real Knot (const Standard_Integer Index) const; //! returns the knot values of the B-spline curve; //! Warning //! A knot with a multiplicity greater than 1 is not //! repeated in the knot table. The Multiplicity function //! can be used to obtain the multiplicity of each knot. //! //! Raised K.Lower() is less than number of first knot or //! K.Upper() is more than number of last knot. Standard_EXPORT void Knots (TColStd_Array1OfReal& K) const; //! returns the knot values of the B-spline curve; //! Warning //! A knot with a multiplicity greater than 1 is not //! repeated in the knot table. The Multiplicity function //! can be used to obtain the multiplicity of each knot. Standard_EXPORT const TColStd_Array1OfReal& Knots() const; //! Returns K, the knots sequence of this BSpline curve. //! In this sequence, knots with a multiplicity greater than 1 are repeated. //! In the case of a non-periodic curve the length of the //! sequence must be equal to the sum of the NbKnots //! multiplicities of the knots of the curve (where //! NbKnots is the number of knots of this BSpline //! curve). This sum is also equal to : NbPoles + Degree + 1 //! where NbPoles is the number of poles and //! Degree the degree of this BSpline curve. //! In the case of a periodic curve, if there are k periodic //! knots, the period is Knot(k+1) - Knot(1). //! The initial sequence is built by writing knots 1 to k+1, //! which are repeated according to their corresponding multiplicities. //! If Degree is the degree of the curve, the degree of //! continuity of the curve at the knot of index 1 (or k+1) //! is equal to c = Degree + 1 - Mult(1). c //! knots are then inserted at the beginning and end of //! the initial sequence: //! - the c values of knots preceding the first item //! Knot(k+1) in the initial sequence are inserted //! at the beginning; the period is subtracted from these c values; //! - the c values of knots following the last item //! Knot(1) in the initial sequence are inserted at //! the end; the period is added to these c values. //! The length of the sequence must therefore be equal to: //! NbPoles + 2*Degree - Mult(1) + 2. //! Example //! For a non-periodic BSpline curve of degree 2 where: //! - the array of knots is: { k1 k2 k3 k4 }, //! - with associated multiplicities: { 3 1 2 3 }, //! the knot sequence is: //! K = { k1 k1 k1 k2 k3 k3 k4 k4 k4 } //! For a periodic BSpline curve of degree 4 , which is //! "C1" continuous at the first knot, and where : //! - the periodic knots are: { k1 k2 k3 (k4) } //! (3 periodic knots: the points of parameter k1 and k4 //! are identical, the period is p = k4 - k1), //! - with associated multiplicities: { 3 1 2 (3) }, //! the degree of continuity at knots k1 and k4 is: //! Degree + 1 - Mult(i) = 2. //! 2 supplementary knots are added at the beginning //! and end of the sequence: //! - at the beginning: the 2 knots preceding k4 minus //! the period; in this example, this is k3 - p both times; //! - at the end: the 2 knots following k1 plus the period; //! in this example, this is k2 + p and k3 + p. //! The knot sequence is therefore: //! K = { k3-p k3-p k1 k1 k1 k2 k3 k3 //! k4 k4 k4 k2+p k3+p } //! Exceptions //! Raised if K.Lower() is less than number of first knot //! in knot sequence with repetitions or K.Upper() is more //! than number of last knot in knot sequence with repetitions. Standard_EXPORT void KnotSequence (TColStd_Array1OfReal& K) const; //! returns the knots of the B-spline curve. //! Knots with multiplicit greater than 1 are repeated Standard_EXPORT const TColStd_Array1OfReal& KnotSequence() const; //! Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. //! If all the knots differ by a positive constant from the //! preceding knot the BSpline Curve can be : //! - Uniform if all the knots are of multiplicity 1, //! - QuasiUniform if all the knots are of multiplicity 1 except for //! the first and last knot which are of multiplicity Degree + 1, //! - PiecewiseBezier if the first and last knots have multiplicity //! Degree + 1 and if interior knots have multiplicity Degree //! A piecewise Bezier with only two knots is a BezierCurve. //! else the curve is non uniform. //! The tolerance criterion is Epsilon from class Real. Standard_EXPORT GeomAbs_BSplKnotDistribution KnotDistribution() const; //! For a BSpline curve the last parameter (which gives the //! end point of the curve) is a knot value but if the //! multiplicity of the last knot index is lower than //! Degree + 1 it is not the last knot of the curve. This //! method computes the index of the knot corresponding to //! the last parameter. Standard_EXPORT Standard_Integer LastUKnotIndex() const; //! Computes the parametric value of the end point of the curve. //! It is a knot value. Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; //! Locates the parametric value U in the sequence of knots. //! If "WithKnotRepetition" is True we consider the knot's //! representation with repetition of multiple knot value, //! otherwise we consider the knot's representation with //! no repetition of multiple knot values. //! Knots (I1) <= U <= Knots (I2) //! . if I1 = I2 U is a knot value (the tolerance criterion //! ParametricTolerance is used). //! . if I1 < 1 => U < Knots (1) - Abs(ParametricTolerance) //! . if I2 > NbKnots => U > Knots (NbKnots) + Abs(ParametricTolerance) Standard_EXPORT 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. //! Raised if Index < 1 or Index > NbKnots Standard_EXPORT Standard_Integer Multiplicity (const Standard_Integer Index) const; //! Returns the multiplicity of the knots of the curve. //! //! Raised if the length of M is not equal to NbKnots. Standard_EXPORT void Multiplicities (TColStd_Array1OfInteger& M) const; //! returns the multiplicity of the knots of the curve. Standard_EXPORT const TColStd_Array1OfInteger& Multiplicities() const; //! Returns the number of knots. This method returns the number of //! knot without repetition of multiple knots. Standard_EXPORT Standard_Integer NbKnots() const; //! Returns the number of poles Standard_EXPORT Standard_Integer NbPoles() const; //! Returns the pole of range Index. //! Raised if Index < 1 or Index > NbPoles. Standard_EXPORT const gp_Pnt& Pole(const Standard_Integer Index) const; //! Returns the poles of the B-spline curve; //! //! Raised if the length of P is not equal to the number of poles. Standard_EXPORT void Poles (TColgp_Array1OfPnt& P) const; //! Returns the poles of the B-spline curve; Standard_EXPORT const TColgp_Array1OfPnt& Poles() const; //! Returns the start point of the curve. //! Warnings : //! This point is different from the first pole of the curve if the //! multiplicity of the first knot is lower than Degree. Standard_EXPORT gp_Pnt StartPoint() const Standard_OVERRIDE; //! Returns the weight of the pole of range Index . //! Raised if Index < 1 or Index > NbPoles. Standard_EXPORT Standard_Real Weight (const Standard_Integer Index) const; //! Returns the weights of the B-spline curve; //! //! Raised if the length of W is not equal to NbPoles. Standard_EXPORT void Weights (TColStd_Array1OfReal& W) const; //! Returns the weights of the B-spline curve; Standard_EXPORT const TColStd_Array1OfReal* Weights() const; //! Applies the transformation T to this BSpline curve. Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE; //! Returns the value of the maximum degree of the normalized //! B-spline basis functions in this package. Standard_EXPORT static Standard_Integer MaxDegree(); //! Computes for this BSpline curve the parametric //! tolerance UTolerance for a given 3D tolerance Tolerance3D. //! If f(t) is the equation of this BSpline curve, //! UTolerance ensures that: //! | t1 - t0| < Utolerance ===> //! |f(t1) - f(t0)| < Tolerance3D Standard_EXPORT void Resolution (const Standard_Real Tolerance3D, Standard_Real& UTolerance); //! Creates a new object which is a copy of this BSpline curve. Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE; //! Comapare two Bspline curve on identity; Standard_EXPORT Standard_Boolean IsEqual (const Handle(Geom_BSplineCurve)& theOther, const Standard_Real thePreci) const; //! Dumps the content of me into the stream Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE; DEFINE_STANDARD_RTTIEXT(Geom_BSplineCurve,Geom_BoundedCurve) protected: private: //! Recompute the flatknots, the knotsdistribution, the continuity. Standard_EXPORT void UpdateKnots(); 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; Standard_Real maxderivinv; Standard_Boolean maxderivinvok; }; #endif // _Geom_BSplineCurve_HeaderFile