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535 lines
20 KiB
C++
535 lines
20 KiB
C++
// Copyright (c) 1991-1999 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 _gp_Hypr2d_HeaderFile
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#define _gp_Hypr2d_HeaderFile
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#include <gp.hxx>
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#include <gp_Ax22d.hxx>
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#include <gp_Ax2d.hxx>
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#include <gp_Pnt2d.hxx>
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#include <Standard_DomainError.hxx>
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#include <Standard_ConstructionError.hxx>
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//! Describes a branch of a hyperbola in the plane (2D space).
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//! A hyperbola is defined by its major and minor radii, and
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//! positioned in the plane with a coordinate system (a
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//! gp_Ax22d object) of which:
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//! - the origin is the center of the hyperbola,
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//! - the "X Direction" defines the major axis of the hyperbola, and
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//! - the "Y Direction" defines the minor axis of the hyperbola.
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//! This coordinate system is the "local coordinate system"
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//! of the hyperbola. The orientation of this coordinate
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//! system (direct or indirect) gives an implicit orientation to
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//! the hyperbola. In this coordinate system, the equation of
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//! the hyperbola is:
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//! X*X/(MajorRadius**2)-Y*Y/(MinorRadius**2) = 1.0
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//! The branch of the hyperbola described is the one located
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//! on the positive side of the major axis.
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//! The following schema shows the plane of the hyperbola,
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//! and in it, the respective positions of the three branches of
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//! hyperbolas constructed with the functions OtherBranch,
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//! ConjugateBranch1, and ConjugateBranch2:
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//! @code
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//! ^YAxis
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//! |
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//! FirstConjugateBranch
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//! |
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//! Other | Main
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//! --------------------- C ------------------------------>XAxis
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//! Branch | Branch
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//! |
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//! |
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//! SecondConjugateBranch
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//! |
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//! @endcode
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//! Warning
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//! The major radius can be less than the minor radius.
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//! See Also
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//! gce_MakeHypr2d which provides functions for more
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//! complex hyperbola constructions
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//! Geom2d_Hyperbola which provides additional functions
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//! for constructing hyperbolas and works, in particular, with
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//! the parametric equations of hyperbolas
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class gp_Hypr2d
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{
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public:
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DEFINE_STANDARD_ALLOC
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//! Creates of an indefinite hyperbola.
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gp_Hypr2d()
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: majorRadius (RealLast()),
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minorRadius (RealLast())
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{}
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//! Creates a hyperbola with radii theMajorRadius and
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//! theMinorRadius, centered on the origin of theMajorAxis
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//! and where the unit vector of theMajorAxis is the "X
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//! Direction" of the local coordinate system of the
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//! hyperbola. This coordinate system is direct if theIsSense
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//! is true (the default value), and indirect if theIsSense is false.
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//! Warnings :
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//! It is yet possible to create an Hyperbola with
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//! theMajorRadius <= theMinorRadius.
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//! Raises ConstructionError if theMajorRadius < 0.0 or theMinorRadius < 0.0
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gp_Hypr2d (const gp_Ax2d& theMajorAxis, const Standard_Real theMajorRadius,
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const Standard_Real theMinorRadius, const Standard_Boolean theIsSense = Standard_True)
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: majorRadius (theMajorRadius),
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minorRadius (theMinorRadius)
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{
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pos = gp_Ax22d (theMajorAxis, theIsSense);
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Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || theMajorRadius < 0.0,
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"gp_Hypr2d() - invalid construction parameters");
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}
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//! a hyperbola with radii theMajorRadius and
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//! theMinorRadius, positioned in the plane by coordinate system theA where:
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//! - the origin of theA is the center of the hyperbola,
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//! - the "X Direction" of theA defines the major axis of
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//! the hyperbola, that is, the major radius
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//! theMajorRadius is measured along this axis, and
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//! - the "Y Direction" of theA defines the minor axis of
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//! the hyperbola, that is, the minor radius
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//! theMinorRadius is measured along this axis, and
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//! - the orientation (direct or indirect sense) of theA
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//! gives the implicit orientation of the hyperbola.
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//! Warnings :
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//! It is yet possible to create an Hyperbola with
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//! theMajorRadius <= theMinorRadius.
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//! Raises ConstructionError if theMajorRadius < 0.0 or theMinorRadius < 0.0
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gp_Hypr2d (const gp_Ax22d& theA, const Standard_Real theMajorRadius, const Standard_Real theMinorRadius)
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: pos (theA),
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majorRadius (theMajorRadius),
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minorRadius (theMinorRadius)
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{
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Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || theMajorRadius < 0.0,
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"gp_Hypr2d() - invalid construction parameters");
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}
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//! Modifies this hyperbola, by redefining its local
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//! coordinate system so that its origin becomes theP.
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void SetLocation (const gp_Pnt2d& theP) { pos.SetLocation (theP); }
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//! Modifies the major or minor radius of this hyperbola.
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//! Exceptions
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//! Standard_ConstructionError if theMajorRadius or
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//! MinorRadius is negative.
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void SetMajorRadius (const Standard_Real theMajorRadius)
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{
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Standard_ConstructionError_Raise_if (theMajorRadius < 0.0,
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"gp_Hypr2d::SetMajorRadius() - major radius should be greater or equal zero");
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majorRadius = theMajorRadius;
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}
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//! Modifies the major or minor radius of this hyperbola.
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//! Exceptions
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//! Standard_ConstructionError if MajorRadius or
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//! theMinorRadius is negative.
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void SetMinorRadius (const Standard_Real theMinorRadius)
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{
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Standard_ConstructionError_Raise_if (theMinorRadius < 0.0,
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"gp_Hypr2d::SetMinorRadius() - minor radius should be greater or equal zero");
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minorRadius = theMinorRadius;
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}
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//! Modifies this hyperbola, by redefining its local
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//! coordinate system so that it becomes theA.
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void SetAxis (const gp_Ax22d& theA) { pos.SetAxis (theA); }
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//! Changes the major axis of the hyperbola. The minor axis is
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//! recomputed and the location of the hyperbola too.
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void SetXAxis (const gp_Ax2d& theA) { pos.SetXAxis (theA); }
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//! Changes the minor axis of the hyperbola.The minor axis is
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//! recomputed and the location of the hyperbola too.
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void SetYAxis (const gp_Ax2d& theA) { pos.SetYAxis (theA); }
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//! In the local coordinate system of the hyperbola the equation of
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//! the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 and the
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//! equation of the first asymptote is Y = (B/A)*X
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//! where A is the major radius of the hyperbola and B the minor
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//! radius of the hyperbola.
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//! Raises ConstructionError if MajorRadius = 0.0
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gp_Ax2d Asymptote1() const;
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//! In the local coordinate system of the hyperbola the equation of
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//! the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 and the
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//! equation of the first asymptote is Y = -(B/A)*X
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//! where A is the major radius of the hyperbola and B the minor
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//! radius of the hyperbola.
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//! Raises ConstructionError if MajorRadius = 0.0
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gp_Ax2d Asymptote2() const;
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//! Computes the coefficients of the implicit equation of
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//! the hyperbola :
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//! theA * (X**2) + theB * (Y**2) + 2*theC*(X*Y) + 2*theD*X + 2*theE*Y + theF = 0.
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Standard_EXPORT void Coefficients (Standard_Real& theA, Standard_Real& theB, Standard_Real& theC,
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Standard_Real& theD, Standard_Real& theE, Standard_Real& theF) const;
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//! Computes the branch of hyperbola which is on the positive side of the
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//! "YAxis" of <me>.
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gp_Hypr2d ConjugateBranch1() const
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{
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gp_Dir2d aV (pos.YDirection());
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Standard_Boolean isSign = (pos.XDirection().Crossed (pos.YDirection())) >= 0.0;
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return gp_Hypr2d (gp_Ax2d (pos.Location(), aV), minorRadius, majorRadius, isSign);
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}
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//! Computes the branch of hyperbola which is on the negative side of the
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//! "YAxis" of <me>.
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gp_Hypr2d ConjugateBranch2() const
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{
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gp_Dir2d aV (pos.YDirection().Reversed());
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Standard_Boolean isSign = (pos.XDirection().Crossed (pos.YDirection())) >= 0.0;
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return gp_Hypr2d (gp_Ax2d (pos.Location(), aV), minorRadius, majorRadius, isSign);
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}
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//! Computes the directrix which is the line normal to the XAxis of the hyperbola
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//! in the local plane (Z = 0) at a distance d = MajorRadius / e
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//! from the center of the hyperbola, where e is the eccentricity of
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//! the hyperbola.
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//! This line is parallel to the "YAxis". The intersection point
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//! between the "Directrix1" and the "XAxis" is the "Location" point
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//! of the "Directrix1".
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//! This point is on the positive side of the "XAxis".
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gp_Ax2d Directrix1() const;
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//! This line is obtained by the symmetrical transformation
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//! of "Directrix1" with respect to the "YAxis" of the hyperbola.
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gp_Ax2d Directrix2() const;
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//! Returns the eccentricity of the hyperbola (e > 1).
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//! If f is the distance between the location of the hyperbola
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//! and the Focus1 then the eccentricity e = f / MajorRadius. Raises DomainError if MajorRadius = 0.0.
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Standard_Real Eccentricity() const
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{
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Standard_DomainError_Raise_if (majorRadius <= gp::Resolution(),
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"gp_Hypr2d::Eccentricity() - major radius is zero");
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return sqrt (majorRadius * majorRadius + minorRadius * minorRadius) / majorRadius;
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}
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//! Computes the focal distance. It is the distance between the
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//! "Location" of the hyperbola and "Focus1" or "Focus2".
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Standard_Real Focal() const
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{
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return 2.0 * sqrt (majorRadius * majorRadius + minorRadius * minorRadius);
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}
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//! Returns the first focus of the hyperbola. This focus is on the
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//! positive side of the "XAxis" of the hyperbola.
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gp_Pnt2d Focus1() const
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{
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Standard_Real aC = sqrt (majorRadius * majorRadius + minorRadius * minorRadius);
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return gp_Pnt2d (pos.Location().X() + aC * pos.XDirection().X(), pos.Location().Y() + aC * pos.XDirection().Y());
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}
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//! Returns the second focus of the hyperbola. This focus is on the
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//! negative side of the "XAxis" of the hyperbola.
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gp_Pnt2d Focus2() const
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{
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Standard_Real aC = sqrt(majorRadius * majorRadius + minorRadius * minorRadius);
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return gp_Pnt2d(pos.Location().X() - aC * pos.XDirection().X(), pos.Location().Y() - aC * pos.XDirection().Y());
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}
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//! Returns the location point of the hyperbola.
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//! It is the intersection point between the "XAxis" and
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//! the "YAxis".
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const gp_Pnt2d& Location() const { return pos.Location(); }
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//! Returns the major radius of the hyperbola (it is the radius
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//! corresponding to the "XAxis" of the hyperbola).
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Standard_Real MajorRadius() const { return majorRadius; }
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//! Returns the minor radius of the hyperbola (it is the radius
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//! corresponding to the "YAxis" of the hyperbola).
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Standard_Real MinorRadius() const { return minorRadius; }
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//! Returns the branch of hyperbola obtained by doing the
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//! symmetrical transformation of <me> with respect to the
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//! "YAxis" of <me>.
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gp_Hypr2d OtherBranch() const
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{
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Standard_Boolean isSign = (pos.XDirection().Crossed (pos.YDirection())) >= 0.0;
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return gp_Hypr2d (gp_Ax2d (pos.Location(), pos.XDirection().Reversed()), majorRadius, minorRadius, isSign);
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}
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//! Returns p = (e * e - 1) * MajorRadius where e is the
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//! eccentricity of the hyperbola.
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//! Raises DomainError if MajorRadius = 0.0
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Standard_Real Parameter() const
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{
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Standard_DomainError_Raise_if (majorRadius <= gp::Resolution(),
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"gp_Hypr2d::Parameter() - major radius is zero");
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return (minorRadius * minorRadius) / majorRadius;
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}
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//! Returns the axisplacement of the hyperbola.
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const gp_Ax22d& Axis() const { return pos; }
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//! Computes an axis whose
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//! - the origin is the center of this hyperbola, and
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//! - the unit vector is the "X Direction" or "Y Direction"
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//! respectively of the local coordinate system of this hyperbola
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//! Returns the major axis of the hyperbola.
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gp_Ax2d XAxis() const { return pos.XAxis(); }
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//! Computes an axis whose
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//! - the origin is the center of this hyperbola, and
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//! - the unit vector is the "X Direction" or "Y Direction"
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//! respectively of the local coordinate system of this hyperbola
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//! Returns the minor axis of the hyperbola.
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gp_Ax2d YAxis() const { return pos.YAxis(); }
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void Reverse()
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{
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gp_Dir2d aTemp = pos.YDirection();
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aTemp.Reverse();
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pos.SetAxis (gp_Ax22d(pos.Location(), pos.XDirection(), aTemp));
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}
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//! Reverses the orientation of the local coordinate system
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//! of this hyperbola (the "Y Axis" is reversed). Therefore,
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//! the implicit orientation of this hyperbola is reversed.
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//! Note:
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//! - Reverse assigns the result to this hyperbola, while
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//! - Reversed creates a new one.
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Standard_NODISCARD gp_Hypr2d Reversed() const;
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//! Returns true if the local coordinate system is direct
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//! and false in the other case.
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Standard_Boolean IsDirect() const
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{
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return (pos.XDirection().Crossed (pos.YDirection())) >= 0.0;
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}
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Standard_EXPORT void Mirror (const gp_Pnt2d& theP);
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//! Performs the symmetrical transformation of an hyperbola with
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//! respect to the point theP which is the center of the symmetry.
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Standard_NODISCARD Standard_EXPORT gp_Hypr2d Mirrored (const gp_Pnt2d& theP) const;
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Standard_EXPORT void Mirror (const gp_Ax2d& theA);
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//! Performs the symmetrical transformation of an hyperbola with
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//! respect to an axis placement which is the axis of the symmetry.
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Standard_NODISCARD Standard_EXPORT gp_Hypr2d Mirrored (const gp_Ax2d& theA) const;
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void Rotate (const gp_Pnt2d& theP, const Standard_Real theAng) { pos.Rotate (theP, theAng); }
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//! Rotates an hyperbola. theP is the center of the rotation.
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//! theAng is the angular value of the rotation in radians.
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Standard_NODISCARD gp_Hypr2d Rotated (const gp_Pnt2d& theP, const Standard_Real theAng) const
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{
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gp_Hypr2d aH = *this;
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aH.pos.Rotate (theP, theAng);
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return aH;
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}
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void Scale (const gp_Pnt2d& theP, const Standard_Real theS);
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//! Scales an hyperbola. <theS> is the scaling value.
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//! If <theS> is positive only the location point is
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//! modified. But if <theS> is negative the "XAxis" is
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//! reversed and the "YAxis" too.
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Standard_NODISCARD gp_Hypr2d Scaled (const gp_Pnt2d& theP, const Standard_Real theS) const;
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void Transform (const gp_Trsf2d& theT);
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//! Transforms an hyperbola with the transformation theT from
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//! class Trsf2d.
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Standard_NODISCARD gp_Hypr2d Transformed (const gp_Trsf2d& theT) const;
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void Translate (const gp_Vec2d& theV) { pos.Translate (theV); }
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//! Translates an hyperbola in the direction of the vector theV.
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//! The magnitude of the translation is the vector's magnitude.
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Standard_NODISCARD gp_Hypr2d Translated (const gp_Vec2d& theV) const
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{
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gp_Hypr2d aH = *this;
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aH.pos.Translate (theV);
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return aH;
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}
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void Translate(const gp_Pnt2d& theP1, const gp_Pnt2d& theP2) { pos.Translate (theP1, theP2); }
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//! Translates an hyperbola from the point theP1 to the point theP2.
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Standard_NODISCARD gp_Hypr2d Translated (const gp_Pnt2d& theP1, const gp_Pnt2d& theP2) const
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{
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gp_Hypr2d aH = *this;
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aH.pos.Translate (theP1, theP2);
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return aH;
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}
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private:
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gp_Ax22d pos;
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Standard_Real majorRadius;
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Standard_Real minorRadius;
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};
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//=======================================================================
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//function : Asymptote1
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// purpose :
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//=======================================================================
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inline gp_Ax2d gp_Hypr2d::Asymptote1() const
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{
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Standard_ConstructionError_Raise_if (majorRadius <= gp::Resolution(),
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"gp_Hypr2d::Asymptote1() - major radius is zero");
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gp_Dir2d aVdir = pos.XDirection();
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gp_XY aCoord1 (pos.YDirection().XY());
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gp_XY aCoord2 = aCoord1.Multiplied (minorRadius / majorRadius);
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aCoord1.Add (aCoord2);
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aVdir.SetXY (aCoord1);
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return gp_Ax2d (pos.Location(), aVdir);
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}
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//=======================================================================
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//function : Asymptote2
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// purpose :
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//=======================================================================
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inline gp_Ax2d gp_Hypr2d::Asymptote2() const
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{
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Standard_ConstructionError_Raise_if (majorRadius <= gp::Resolution(),
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"gp_Hypr2d::Asymptote2() - major radius is zero");
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gp_Vec2d aVdir = pos.XDirection();
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gp_XY aCoord1 (pos.YDirection().XY());
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gp_XY aCoord2 = aCoord1.Multiplied (-minorRadius / majorRadius);
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aCoord1.Add (aCoord2);
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aVdir.SetXY (aCoord1);
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return gp_Ax2d (pos.Location(), aVdir);
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}
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//=======================================================================
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//function : Directrix1
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// purpose :
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//=======================================================================
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inline gp_Ax2d gp_Hypr2d::Directrix1() const
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{
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Standard_Real anE = Eccentricity();
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gp_XY anOrig = pos.XDirection().XY();
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anOrig.Multiply (majorRadius / anE);
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anOrig.Add (pos.Location().XY());
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return gp_Ax2d (gp_Pnt2d (anOrig), gp_Dir2d (pos.YDirection()));
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}
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//=======================================================================
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//function : Directrix2
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// purpose :
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//=======================================================================
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inline gp_Ax2d gp_Hypr2d::Directrix2() const
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{
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Standard_Real anE = Eccentricity();
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gp_XY anOrig = pos.XDirection().XY();
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anOrig.Multiply (Parameter() / anE);
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anOrig.Add (Focus1().XY());
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return gp_Ax2d (gp_Pnt2d (anOrig), gp_Dir2d (pos.YDirection()));
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}
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//=======================================================================
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//function : Reversed
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// purpose :
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//=======================================================================
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inline gp_Hypr2d gp_Hypr2d::Reversed() const
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{
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gp_Hypr2d aH = *this;
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|
gp_Dir2d aTemp = pos.YDirection();
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aTemp.Reverse ();
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aH.pos.SetAxis (gp_Ax22d (pos.Location(),pos.XDirection(), aTemp));
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|
return aH;
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|
}
|
|
|
|
//=======================================================================
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|
//function : Scale
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|
// purpose :
|
|
//=======================================================================
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|
inline void gp_Hypr2d::Scale (const gp_Pnt2d& theP, const Standard_Real theS)
|
|
{
|
|
majorRadius *= theS;
|
|
if (majorRadius < 0)
|
|
{
|
|
majorRadius = -majorRadius;
|
|
}
|
|
minorRadius *= theS;
|
|
if (minorRadius < 0)
|
|
{
|
|
minorRadius = -minorRadius;
|
|
}
|
|
pos.Scale (theP, theS);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : Scaled
|
|
// purpose :
|
|
//=======================================================================
|
|
inline gp_Hypr2d gp_Hypr2d::Scaled (const gp_Pnt2d& theP, const Standard_Real theS) const
|
|
{
|
|
gp_Hypr2d aH = *this;
|
|
aH.majorRadius *= theS;
|
|
if (aH.majorRadius < 0)
|
|
{
|
|
aH.majorRadius = -aH.majorRadius;
|
|
}
|
|
aH.minorRadius *= theS;
|
|
if (aH.minorRadius < 0)
|
|
{
|
|
aH.minorRadius = -aH.minorRadius;
|
|
}
|
|
aH.pos.Scale (theP, theS);
|
|
return aH;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : Transform
|
|
// purpose :
|
|
//=======================================================================
|
|
inline void gp_Hypr2d::Transform (const gp_Trsf2d& theT)
|
|
{
|
|
majorRadius *= theT.ScaleFactor();
|
|
if (majorRadius < 0)
|
|
{
|
|
majorRadius = -majorRadius;
|
|
}
|
|
minorRadius *= theT.ScaleFactor();
|
|
if (minorRadius < 0)
|
|
{
|
|
minorRadius = -minorRadius;
|
|
}
|
|
pos.Transform (theT);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : Transformed
|
|
// purpose :
|
|
//=======================================================================
|
|
inline gp_Hypr2d gp_Hypr2d::Transformed (const gp_Trsf2d& theT) const
|
|
{
|
|
gp_Hypr2d aH = *this;
|
|
aH.majorRadius *= theT.ScaleFactor();
|
|
if (aH.majorRadius < 0)
|
|
{
|
|
aH.majorRadius = -aH.majorRadius;
|
|
}
|
|
aH.minorRadius *= theT.ScaleFactor();
|
|
if (aH.minorRadius < 0)
|
|
{
|
|
aH.minorRadius = -aH.minorRadius;
|
|
}
|
|
aH.pos.Transform (theT);
|
|
return aH;
|
|
}
|
|
|
|
#endif // _gp_Hypr2d_HeaderFile
|