// 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_BezierCurve_HeaderFile
#define _Geom2d_BezierCurve_HeaderFile
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
class Standard_ConstructionError;
class Standard_DimensionError;
class Standard_RangeError;
class Standard_OutOfRange;
class gp_Pnt2d;
class gp_Vec2d;
class gp_Trsf2d;
class Geom2d_Geometry;
class Geom2d_BezierCurve;
DEFINE_STANDARD_HANDLE(Geom2d_BezierCurve, Geom2d_BoundedCurve)
//! Describes a rational or non-rational Bezier curve
//! - a non-rational Bezier curve is defined by a table
//! of poles (also called control points),
//! - a rational Bezier curve is defined by a table of
//! poles with varying weights.
//! These data are manipulated by two parallel arrays:
//! - the poles table, which is an array of gp_Pnt2d points, and
//! - the weights table, which is an array of reals.
//! The bounds of these arrays are 1 and "the number of poles" of the curve.
//! The poles of the curve are "control points" used to deform the curve.
//! 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.
//! 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 is polynomial; it is therefore a
//! non-rational curve. The non-rational curve is a
//! special and frequently used case. The weights are
//! defined and used only in case of a rational curve.
//! The degree of a Bezier curve is equal to the
//! number of poles, minus 1. It must be greater than or
//! equal to 1. However, the degree of a
//! Geom2d_BezierCurve curve is limited to a value
//! (25) which is defined and controlled by the system.
//! This value is returned by the function MaxDegree.
//! The parameter range for a Bezier curve is [ 0, 1 ].
//! If the first and last control points of the Bezier
//! curve are the same point then the curve is closed.
//! For example, to create a closed Bezier curve with
//! four control points, you have to give a set of control
//! points P1, P2, P3 and P1.
//! The continuity of a Bezier curve is infinite.
//! It is not possible to build a Bezier curve with
//! negative weights. We consider that a weight value
//! is zero if it is less than or equal to
//! gp::Resolution(). We also consider that
//! two weight values W1 and W2 are equal if:
//! |W2 - W1| <= gp::Resolution().
//! Warning
//! - When considering the continuity of a closed
//! Bezier curve at the junction point, remember that
//! a curve of this type is never periodic. This means
//! that the derivatives for the parameter u = 0
//! have no reason to be the same as the
//! derivatives for the parameter u = 1 even if the curve is closed.
//! - The length of a Bezier curve can be null.
class Geom2d_BezierCurve : public Geom2d_BoundedCurve
{
public:
//! Creates a non rational Bezier curve with a set of poles :
//! CurvePoles. The weights are defaulted to all being 1.
//! Raises ConstructionError if the number of poles is greater than MaxDegree + 1
//! or lower than 2.
Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles);
//! Creates a rational Bezier curve with the set of poles
//! CurvePoles and the set of weights PoleWeights .
//! If all the weights are identical the curve is considered
//! as non rational. Raises ConstructionError if
//! the number of poles is greater than MaxDegree + 1 or lower
//! than 2 or CurvePoles and CurveWeights have not the same length
//! or one weight value is lower or equal to Resolution from
//! package gp.
Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles, const TColStd_Array1OfReal& PoleWeights);
//! Increases the degree of a bezier curve. Degree is the new
//! degree of .
//! raises ConstructionError if Degree is greater than MaxDegree or lower than 2
//! or lower than the initial degree of .
Standard_EXPORT void Increase (const Standard_Integer Degree);
//! Inserts a pole with its weight in the set of poles after the
//! pole of range Index. If the curve was non rational it can
//! become rational if all the weights are not identical.
//! Raised if Index is not in the range [0, NbPoles]
//!
//! Raised if the resulting number of poles is greater than
//! MaxDegree + 1.
Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0);
//! Inserts a pole with its weight in the set of poles after
//! the pole of range Index. If the curve was non rational it
//! can become rational if all the weights are not identical.
//! Raised if Index is not in the range [1, NbPoles+1]
//!
//! Raised if the resulting number of poles is greater than
//! MaxDegree + 1.
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 Index is not in the range [1, NbPoles]
Standard_EXPORT void RemovePole (const Standard_Integer Index);
//! Reverses the direction of parametrization of
//! Value (NewU) = Value (1 - OldU)
Standard_EXPORT void Reverse() Standard_OVERRIDE;
//! Returns the parameter on the reversed curve for
//! the point of parameter U on .
//!
//! returns 1-U
Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
//! Segments the curve between U1 and U2 which can be out
//! of the bounds of the curve. The curve is oriented from U1
//! to U2.
//! The control points are modified, the first and the last point
//! are not the same but the parametrization range is [0, 1]
//! else it could not be a Bezier curve.
//! 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.
Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2);
//! Substitutes the pole of range index with P.
//! If the curve is rational the weight of range Index
//! is not modified.
//! raiseD if Index is not in the range [1, NbPoles]
Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P);
//! Substitutes the pole and the weights of range Index.
//! If the curve is not rational it can become rational
//! if all the weights are not identical.
//! If the curve was rational it can become non rational if
//! all the weights are identical.
//! Raised if Index is not in the range [1, NbPoles]
//! Raised if Weight <= Resolution from package gp
Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight);
//! Changes the weight of the pole of range Index.
//! If the curve is not rational it can become rational
//! if all the weights are not identical.
//! If the curve was rational it can become non rational if
//! all the weights are identical.
//! Raised if Index is not in the range [1, NbPoles]
//! Raised if Weight <= Resolution from package gp
Standard_EXPORT void SetWeight (const Standard_Integer Index, const Standard_Real Weight);
//! Returns True if the distance between the first point
//! and the last point of the curve is lower or equal to
//! the Resolution from package gp.
Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE;
//! Continuity of the curve, returns True.
Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE;
//! Returns False. A BezierCurve cannot be periodic in this
//! package
Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE;
//! Returns false if all the weights are identical. The tolerance
//! criterion is Resolution from package gp.
Standard_EXPORT Standard_Boolean IsRational() const;
//! Returns GeomAbs_CN, which is the continuity of any Bezier curve.
Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE;
//! Returns the polynomial degree of the curve. It is the number
//! of poles less one. In this package the Degree of a Bezier
//! curve cannot be greater than "MaxDegree".
Standard_EXPORT Standard_Integer Degree() const;
Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE;
Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE;
Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE;
Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const Standard_OVERRIDE;
//! For this Bezier 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.
//! Note: the parameter U can be outside the bounds of the curve.
//! Raises RangeError if N < 1.
Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE;
//! Returns the end point or start point of this Bezier curve.
Standard_EXPORT gp_Pnt2d EndPoint() const Standard_OVERRIDE;
//! Returns the value of the first parameter of this
//! Bezier curve. This is 0.0, which gives the start point of this Bezier curve.
Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE;
//! Returns the value of the last parameter of this
//! Bezier curve. This is 1.0, which gives the end point of this Bezier curve.
Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE;
//! Returns the number of poles for this Bezier curve.
Standard_EXPORT Standard_Integer NbPoles() const;
//! Returns the pole of range Index.
//! Raised if Index is not in the range [1, NbPoles]
Standard_EXPORT const gp_Pnt2d& Pole (const Standard_Integer Index) const;
//! Returns all the poles of the curve.
//!
//! Raised if the length of P is not equal to the number of poles.
Standard_EXPORT void Poles (TColgp_Array1OfPnt2d& P) const;
//! Returns all the poles of the curve.
const TColgp_Array1OfPnt2d& Poles() const
{
return poles->Array1();
}
//! Returns Value (U=1), it is the first control point
//! of the curve.
Standard_EXPORT gp_Pnt2d StartPoint() const Standard_OVERRIDE;
//! Returns the weight of range Index.
//! Raised if Index is not in the range [1, NbPoles]
Standard_EXPORT Standard_Real Weight (const Standard_Integer Index) const;
//! Returns all the weights of the curve.
//!
//! Raised if the length of W is not equal to the number of poles.
Standard_EXPORT void Weights (TColStd_Array1OfReal& W) const;
//! Returns all the weights of the curve.
const TColStd_Array1OfReal* Weights() const
{
if (!weights.IsNull())
return &weights->Array1();
return BSplCLib::NoWeights();
}
//! Applies the transformation T to this Bezier curve.
Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE;
//! Returns the value of the maximum polynomial degree of a
//! BezierCurve. This value is 25.
Standard_EXPORT static Standard_Integer MaxDegree();
//! Computes for this Bezier curve the parametric
//! tolerance UTolerance for a given tolerance
//! Tolerance3D (relative to dimensions in the plane).
//! If f(t) is the equation of this Bezier 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 Bezier 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_BezierCurve,Geom2d_BoundedCurve)
protected:
private:
//! Set poles to Poles, weights to Weights (not
//! copied). If Weights is null the curve is non
//! rational. Create the arrays of coefficients. Poles
//! and Weights are assumed to have the first
//! coefficient 1.
//!
//! Update rational and closed.
//!
//! if nbpoles < 2 or nbboles > MaDegree + 1
void Init (const Handle(TColgp_HArray1OfPnt2d)& Poles, const Handle(TColStd_HArray1OfReal)& Weights);
Standard_Boolean rational;
Standard_Boolean closed;
Handle(TColgp_HArray1OfPnt2d) poles;
Handle(TColStd_HArray1OfReal) weights;
Standard_Real maxderivinv;
Standard_Boolean maxderivinvok;
};
#endif // _Geom2d_BezierCurve_HeaderFile