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365 lines
14 KiB
C++
365 lines
14 KiB
C++
// Created on: 1993-03-24
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// Created by: JCV
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// Copyright (c) 1993-1999 Matra Datavision
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// Copyright (c) 1999-2014 OPEN CASCADE SAS
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//
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// This file is part of Open CASCADE Technology software library.
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//
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// This library is free software; you can redistribute it and/or modify it under
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// the terms of the GNU Lesser General Public License version 2.1 as published
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// by the Free Software Foundation, with special exception defined in the file
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// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
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// distribution for complete text of the license and disclaimer of any warranty.
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//
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// Alternatively, this file may be used under the terms of Open CASCADE
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// commercial license or contractual agreement.
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#ifndef _Geom2d_BezierCurve_HeaderFile
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#define _Geom2d_BezierCurve_HeaderFile
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#include <Standard.hxx>
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#include <Standard_Type.hxx>
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#include <Standard_Boolean.hxx>
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#include <TColgp_HArray1OfPnt2d.hxx>
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#include <TColStd_HArray1OfReal.hxx>
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#include <Standard_Integer.hxx>
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#include <Standard_Real.hxx>
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#include <Geom2d_BoundedCurve.hxx>
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#include <TColgp_Array1OfPnt2d.hxx>
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#include <TColStd_Array1OfReal.hxx>
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#include <GeomAbs_Shape.hxx>
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#include <BSplCLib.hxx>
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class Standard_ConstructionError;
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class Standard_DimensionError;
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class Standard_RangeError;
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class Standard_OutOfRange;
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class gp_Pnt2d;
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class gp_Vec2d;
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class gp_Trsf2d;
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class Geom2d_Geometry;
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class Geom2d_BezierCurve;
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DEFINE_STANDARD_HANDLE(Geom2d_BezierCurve, Geom2d_BoundedCurve)
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//! Describes a rational or non-rational Bezier curve
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//! - a non-rational Bezier curve is defined by a table
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//! of poles (also called control points),
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//! - a rational Bezier curve is defined by a table of
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//! poles with varying weights.
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//! These data are manipulated by two parallel arrays:
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//! - the poles table, which is an array of gp_Pnt2d points, and
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//! - the weights table, which is an array of reals.
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//! The bounds of these arrays are 1 and "the number of poles" of the curve.
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//! The poles of the curve are "control points" used to deform the curve.
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//! The first pole is the start point of the curve, and the
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//! last pole is the end point of the curve. The segment
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//! which joins the first pole to the second pole is the
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//! tangent to the curve at its start point, and the
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//! segment which joins the last pole to the
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//! second-from-last pole is the tangent to the curve
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//! at its end point.
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//! It is more difficult to give a geometric signification
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//! to the weights but they are useful for providing
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//! exact representations of the arcs of a circle or
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//! ellipse. Moreover, if the weights of all the poles are
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//! equal, the curve is polynomial; it is therefore a
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//! non-rational curve. The non-rational curve is a
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//! special and frequently used case. The weights are
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//! defined and used only in case of a rational curve.
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//! The degree of a Bezier curve is equal to the
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//! number of poles, minus 1. It must be greater than or
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//! equal to 1. However, the degree of a
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//! Geom2d_BezierCurve curve is limited to a value
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//! (25) which is defined and controlled by the system.
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//! This value is returned by the function MaxDegree.
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//! The parameter range for a Bezier curve is [ 0, 1 ].
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//! If the first and last control points of the Bezier
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//! curve are the same point then the curve is closed.
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//! For example, to create a closed Bezier curve with
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//! four control points, you have to give a set of control
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//! points P1, P2, P3 and P1.
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//! The continuity of a Bezier curve is infinite.
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//! It is not possible to build a Bezier curve with
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//! negative weights. We consider that a weight value
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//! is zero if it is less than or equal to
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//! gp::Resolution(). We also consider that
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//! two weight values W1 and W2 are equal if:
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//! |W2 - W1| <= gp::Resolution().
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//! Warning
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//! - When considering the continuity of a closed
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//! Bezier curve at the junction point, remember that
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//! a curve of this type is never periodic. This means
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//! that the derivatives for the parameter u = 0
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//! have no reason to be the same as the
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//! derivatives for the parameter u = 1 even if the curve is closed.
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//! - The length of a Bezier curve can be null.
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class Geom2d_BezierCurve : public Geom2d_BoundedCurve
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{
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public:
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//! Creates a non rational Bezier curve with a set of poles :
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//! CurvePoles. The weights are defaulted to all being 1.
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//! Raises ConstructionError if the number of poles is greater than MaxDegree + 1
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//! or lower than 2.
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Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles);
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//! Creates a rational Bezier curve with the set of poles
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//! CurvePoles and the set of weights PoleWeights .
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//! If all the weights are identical the curve is considered
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//! as non rational. Raises ConstructionError if
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//! the number of poles is greater than MaxDegree + 1 or lower
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//! than 2 or CurvePoles and CurveWeights have not the same length
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//! or one weight value is lower or equal to Resolution from
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//! package gp.
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Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles, const TColStd_Array1OfReal& PoleWeights);
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//! Increases the degree of a bezier curve. Degree is the new
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//! degree of <me>.
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//! raises ConstructionError if Degree is greater than MaxDegree or lower than 2
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//! or lower than the initial degree of <me>.
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Standard_EXPORT void Increase (const Standard_Integer Degree);
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//! Inserts a pole with its weight in the set of poles after the
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//! pole of range Index. If the curve was non rational it can
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//! become rational if all the weights are not identical.
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//! Raised if Index is not in the range [0, NbPoles]
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//!
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//! Raised if the resulting number of poles is greater than
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//! MaxDegree + 1.
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Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0);
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//! Inserts a pole with its weight in the set of poles after
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//! the pole of range Index. If the curve was non rational it
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//! can become rational if all the weights are not identical.
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//! Raised if Index is not in the range [1, NbPoles+1]
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//!
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//! Raised if the resulting number of poles is greater than
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//! MaxDegree + 1.
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Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0);
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//! Removes the pole of range Index.
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//! If the curve was rational it can become non rational.
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//! Raised if Index is not in the range [1, NbPoles]
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Standard_EXPORT void RemovePole (const Standard_Integer Index);
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//! Reverses the direction of parametrization of <me>
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//! Value (NewU) = Value (1 - OldU)
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Standard_EXPORT void Reverse() Standard_OVERRIDE;
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//! Returns the parameter on the reversed curve for
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//! the point of parameter U on <me>.
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//!
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//! returns 1-U
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Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
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//! Segments the curve between U1 and U2 which can be out
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//! of the bounds of the curve. The curve is oriented from U1
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//! to U2.
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//! The control points are modified, the first and the last point
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//! are not the same but the parametrization range is [0, 1]
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//! else it could not be a Bezier curve.
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//! Warnings :
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//! Even if <me> is not closed it can become closed after the
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//! segmentation for example if U1 or U2 are out of the bounds
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//! of the curve <me> or if the curve makes loop.
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//! After the segmentation the length of a curve can be null.
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Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2);
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//! Substitutes the pole of range index with P.
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//! If the curve <me> is rational the weight of range Index
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//! is not modified.
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//! raiseD if Index is not in the range [1, NbPoles]
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Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P);
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//! Substitutes the pole and the weights of range Index.
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//! If the curve <me> is not rational it can become rational
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//! if all the weights are not identical.
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//! If the curve was rational it can become non rational if
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//! all the weights are identical.
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//! Raised if Index is not in the range [1, NbPoles]
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//! Raised if Weight <= Resolution from package gp
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Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight);
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//! Changes the weight of the pole of range Index.
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//! If the curve <me> is not rational it can become rational
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//! if all the weights are not identical.
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//! If the curve was rational it can become non rational if
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//! all the weights are identical.
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//! Raised if Index is not in the range [1, NbPoles]
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//! Raised if Weight <= Resolution from package gp
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Standard_EXPORT void SetWeight (const Standard_Integer Index, const Standard_Real Weight);
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//! Returns True if the distance between the first point
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//! and the last point of the curve is lower or equal to
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//! the Resolution from package gp.
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Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE;
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//! Continuity of the curve, returns True.
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Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE;
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//! Returns False. A BezierCurve cannot be periodic in this
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//! package
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Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE;
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//! Returns false if all the weights are identical. The tolerance
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//! criterion is Resolution from package gp.
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Standard_EXPORT Standard_Boolean IsRational() const;
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//! Returns GeomAbs_CN, which is the continuity of any Bezier curve.
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Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE;
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//! Returns the polynomial degree of the curve. It is the number
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//! of poles less one. In this package the Degree of a Bezier
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//! curve cannot be greater than "MaxDegree".
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Standard_EXPORT Standard_Integer Degree() const;
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Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE;
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Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE;
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Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE;
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Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const Standard_OVERRIDE;
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//! For this Bezier curve, computes
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//! - the point P of parameter U, or
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//! - the point P and one or more of the following values:
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//! - V1, the first derivative vector,
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//! - V2, the second derivative vector,
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//! - V3, the third derivative vector.
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//! Note: the parameter U can be outside the bounds of the curve.
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//! Raises RangeError if N < 1.
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Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE;
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//! Returns the end point or start point of this Bezier curve.
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Standard_EXPORT gp_Pnt2d EndPoint() const Standard_OVERRIDE;
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//! Returns the value of the first parameter of this
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//! Bezier curve. This is 0.0, which gives the start point of this Bezier curve.
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Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE;
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//! Returns the value of the last parameter of this
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//! Bezier curve. This is 1.0, which gives the end point of this Bezier curve.
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Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE;
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//! Returns the number of poles for this Bezier curve.
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Standard_EXPORT Standard_Integer NbPoles() const;
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//! Returns the pole of range Index.
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//! Raised if Index is not in the range [1, NbPoles]
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Standard_EXPORT gp_Pnt2d Pole (const Standard_Integer Index) const;
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//! Returns all the poles of the curve.
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//!
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//! Raised if the length of P is not equal to the number of poles.
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Standard_EXPORT void Poles (TColgp_Array1OfPnt2d& P) const;
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//! Returns all the poles of the curve.
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const TColgp_Array1OfPnt2d& Poles() const
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{
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return poles->Array1();
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}
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//! Returns Value (U=1), it is the first control point
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//! of the curve.
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Standard_EXPORT gp_Pnt2d StartPoint() const Standard_OVERRIDE;
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//! Returns the weight of range Index.
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//! Raised if Index is not in the range [1, NbPoles]
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Standard_EXPORT Standard_Real Weight (const Standard_Integer Index) const;
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//! Returns all the weights of the curve.
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//!
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//! Raised if the length of W is not equal to the number of poles.
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Standard_EXPORT void Weights (TColStd_Array1OfReal& W) const;
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//! Returns all the weights of the curve.
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const TColStd_Array1OfReal* Weights() const
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{
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if (!weights.IsNull())
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return &weights->Array1();
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return BSplCLib::NoWeights();
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}
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//! Applies the transformation T to this Bezier curve.
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Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE;
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//! Returns the value of the maximum polynomial degree of a
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//! BezierCurve. This value is 25.
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Standard_EXPORT static Standard_Integer MaxDegree();
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//! Computes for this Bezier curve the parametric
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//! tolerance UTolerance for a given tolerance
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//! Tolerance3D (relative to dimensions in the plane).
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//! If f(t) is the equation of this Bezier curve,
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//! UTolerance ensures that
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//! | t1 - t0| < Utolerance ===>
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//! |f(t1) - f(t0)| < ToleranceUV
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Standard_EXPORT void Resolution (const Standard_Real ToleranceUV, Standard_Real& UTolerance);
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//! Creates a new object which is a copy of this Bezier curve.
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Standard_EXPORT Handle(Geom2d_Geometry) Copy() const Standard_OVERRIDE;
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DEFINE_STANDARD_RTTIEXT(Geom2d_BezierCurve,Geom2d_BoundedCurve)
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protected:
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private:
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//! Set poles to Poles, weights to Weights (not
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//! copied). If Weights is null the curve is non
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//! rational. Create the arrays of coefficients. Poles
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//! and Weights are assumed to have the first
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//! coefficient 1.
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//!
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//! Update rational and closed.
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//!
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//! if nbpoles < 2 or nbboles > MaDegree + 1
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void Init (const Handle(TColgp_HArray1OfPnt2d)& Poles, const Handle(TColStd_HArray1OfReal)& Weights);
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Standard_Boolean rational;
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Standard_Boolean closed;
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Handle(TColgp_HArray1OfPnt2d) poles;
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Handle(TColStd_HArray1OfReal) weights;
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Standard_Real maxderivinv;
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Standard_Boolean maxderivinvok;
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};
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#endif // _Geom2d_BezierCurve_HeaderFile
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