// Created on: 1993-03-24
// 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 _Geom2d_BSplineCurve_HeaderFile
#define _Geom2d_BSplineCurve_HeaderFile
#include
#include
#include
#include
#include
#include
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#include
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class Standard_ConstructionError;
class Standard_DimensionError;
class Standard_DomainError;
class Standard_OutOfRange;
class Standard_RangeError;
class Standard_NoSuchObject;
class Geom2d_UndefinedDerivative;
class gp_Pnt2d;
class gp_Vec2d;
class gp_Trsf2d;
class Geom2d_Geometry;
class Geom2d_BSplineCurve;
DEFINE_STANDARD_HANDLE(Geom2d_BSplineCurve, Geom2d_BoundedCurve)
//! 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
class Geom2d_BSplineCurve : public Geom2d_BoundedCurve
{
public:
//! Creates a non-rational B_spline curve on the
//! basis of 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
Standard_EXPORT 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 rational B_spline curve on the basis
//! of 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
Standard_EXPORT 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);
//! 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().
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.
//! 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.
Standard_EXPORT void IncreaseMultiplicity (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.
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.
//! 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.
Standard_EXPORT void InsertKnot (const Standard_Real U, const Standard_Integer M = 1, const Standard_Real ParametricTolerance = 0.0);
//! 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.
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.
Standard_EXPORT Standard_Boolean RemoveKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance);
//! 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]
Standard_EXPORT void InsertPoleAfter (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]
Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0);
//! 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]
Standard_EXPORT void RemovePole (const Standard_Integer Index);
//! 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.
Standard_EXPORT void Reverse() Standard_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.
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.
//! - 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().
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)
//! 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.
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);
//! 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.
Standard_EXPORT void SetKnot (const Standard_Integer Index, const Standard_Real K, const Standard_Integer M);
//! 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.
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 Knot(I2) - Knot(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);
//! 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.
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_Pnt2d& P);
//! 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.
Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P, 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.
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_Pnt2d& 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_Pnt2d& P, const gp_Vec2d& Tangent, const Standard_Real Tolerance, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, Standard_Integer& ErrorStatus);
//! 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_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.
//! In this class the degree of the basis normalized B-spline
//! functions cannot be greater than "MaxDegree"
//! Computation of value and derivatives
Standard_EXPORT Standard_Integer Degree() const;
Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE;
//! Raised if the continuity of the curve is not C1.
Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE;
//! Raised if the continuity of the curve is not C2.
Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE;
//! 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.
Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& 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.
//! 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.
Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE;
//! Raised if FromK1 = ToK2.
Standard_EXPORT gp_Pnt2d 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_Pnt2d& 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_Pnt2d& P, gp_Vec2d& 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_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& 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_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& 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_Vec2d 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_Pnt2d EndPoint() const Standard_OVERRIDE;
//! 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_EXPORT Standard_Integer FirstUKnotIndex() const;
//! Computes the parametric value of the start point of the curve.
//! It is a knot value.
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;
//!
//! 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;
Standard_EXPORT const TColStd_Array1OfReal& Knots() 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.
Standard_EXPORT 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}
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_Pnt2d& 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_Array1OfPnt2d& P) const;
//! Returns the poles of the B-spline curve;
Standard_EXPORT const TColgp_Array1OfPnt2d& 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_Pnt2d 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_Trsf2d& 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 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
Standard_EXPORT void Resolution (const Standard_Real ToleranceUV, Standard_Real& UTolerance);
//! Creates a new object which is a copy of this BSpline curve.
Standard_EXPORT Handle(Geom2d_Geometry) Copy() const Standard_OVERRIDE;
//! 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(Geom2d_BSplineCurve,Geom2d_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_HArray1OfPnt2d) poles;
Handle(TColStd_HArray1OfReal) weights;
Handle(TColStd_HArray1OfReal) flatknots;
Handle(TColStd_HArray1OfReal) knots;
Handle(TColStd_HArray1OfInteger) mults;
Standard_Real maxderivinv;
Standard_Boolean maxderivinvok;
};
#endif // _Geom2d_BSplineCurve_HeaderFile
__