mirror of
https://git.dev.opencascade.org/repos/occt.git
synced 2025-04-26 10:19:45 +03:00
438 lines
15 KiB
C++
438 lines
15 KiB
C++
// Copyright (c) 1991-1999 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 _gp_Elips_HeaderFile
|
|
#define _gp_Elips_HeaderFile
|
|
|
|
#include <gp.hxx>
|
|
#include <gp_Ax1.hxx>
|
|
#include <gp_Ax2.hxx>
|
|
#include <gp_Pnt.hxx>
|
|
#include <Standard_ConstructionError.hxx>
|
|
|
|
//! Describes an ellipse in 3D space.
|
|
//! An ellipse is defined by its major and minor radii and
|
|
//! positioned in space with a coordinate system (a gp_Ax2 object) as follows:
|
|
//! - the origin of the coordinate system is the center of the ellipse,
|
|
//! - its "X Direction" defines the major axis of the ellipse, and
|
|
//! - its "Y Direction" defines the minor axis of the ellipse.
|
|
//! Together, the origin, "X Direction" and "Y Direction" of
|
|
//! this coordinate system define the plane of the ellipse.
|
|
//! This coordinate system is the "local coordinate system"
|
|
//! of the ellipse. In this coordinate system, the equation of
|
|
//! the ellipse is:
|
|
//! @code
|
|
//! X*X / (MajorRadius**2) + Y*Y / (MinorRadius**2) = 1.0
|
|
//! @endcode
|
|
//! The "main Direction" of the local coordinate system gives
|
|
//! the normal vector to the plane of the ellipse. This vector
|
|
//! gives an implicit orientation to the ellipse (definition of the
|
|
//! trigonometric sense). We refer to the "main Axis" of the
|
|
//! local coordinate system as the "Axis" of the ellipse.
|
|
//! See Also
|
|
//! gce_MakeElips which provides functions for more
|
|
//! complex ellipse constructions
|
|
//! Geom_Ellipse which provides additional functions for
|
|
//! constructing ellipses and works, in particular, with the
|
|
//! parametric equations of ellipses
|
|
class gp_Elips
|
|
{
|
|
public:
|
|
|
|
DEFINE_STANDARD_ALLOC
|
|
|
|
//! Creates an indefinite ellipse.
|
|
gp_Elips()
|
|
: majorRadius (RealLast()),
|
|
minorRadius (RealSmall())
|
|
{}
|
|
|
|
//! The major radius of the ellipse is on the "XAxis" and the
|
|
//! minor radius is on the "YAxis" of the ellipse. The "XAxis"
|
|
//! is defined with the "XDirection" of theA2 and the "YAxis" is
|
|
//! defined with the "YDirection" of theA2.
|
|
//! Warnings :
|
|
//! It is not forbidden to create an ellipse with theMajorRadius =
|
|
//! theMinorRadius.
|
|
//! Raises ConstructionError if theMajorRadius < theMinorRadius or theMinorRadius < 0.
|
|
gp_Elips (const gp_Ax2& theA2, const Standard_Real theMajorRadius, const Standard_Real theMinorRadius)
|
|
: pos (theA2),
|
|
majorRadius (theMajorRadius),
|
|
minorRadius (theMinorRadius)
|
|
{
|
|
Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || theMajorRadius < theMinorRadius,
|
|
"gp_Elips() - invalid construction parameters");
|
|
}
|
|
|
|
//! Changes the axis normal to the plane of the ellipse.
|
|
//! It modifies the definition of this plane.
|
|
//! The "XAxis" and the "YAxis" are recomputed.
|
|
//! The local coordinate system is redefined so that:
|
|
//! - its origin and "main Direction" become those of the
|
|
//! axis theA1 (the "X Direction" and "Y Direction" are then
|
|
//! recomputed in the same way as for any gp_Ax2), or
|
|
//! Raises ConstructionError if the direction of theA1
|
|
//! is parallel to the direction of the "XAxis" of the ellipse.
|
|
void SetAxis (const gp_Ax1& theA1) { pos.SetAxis (theA1); }
|
|
|
|
//! Modifies this ellipse, by redefining its local coordinate
|
|
//! so that its origin becomes theP.
|
|
void SetLocation (const gp_Pnt& theP) { pos.SetLocation (theP); }
|
|
|
|
//! The major radius of the ellipse is on the "XAxis" (major axis)
|
|
//! of the ellipse.
|
|
//! Raises ConstructionError if theMajorRadius < MinorRadius.
|
|
void SetMajorRadius (const Standard_Real theMajorRadius)
|
|
{
|
|
Standard_ConstructionError_Raise_if (theMajorRadius < minorRadius,
|
|
"gp_Elips::SetMajorRadius() - major radius should be greater or equal to minor radius");
|
|
majorRadius = theMajorRadius;
|
|
}
|
|
|
|
//! The minor radius of the ellipse is on the "YAxis" (minor axis)
|
|
//! of the ellipse.
|
|
//! Raises ConstructionError if theMinorRadius > MajorRadius or MinorRadius < 0.
|
|
void SetMinorRadius (const Standard_Real theMinorRadius)
|
|
{
|
|
Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || majorRadius < theMinorRadius,
|
|
"gp_Elips::SetMinorRadius() - minor radius should be a positive number lesser or equal to major radius");
|
|
minorRadius = theMinorRadius;
|
|
}
|
|
|
|
//! Modifies this ellipse, by redefining its local coordinate
|
|
//! so that it becomes theA2.
|
|
void SetPosition (const gp_Ax2& theA2) { pos = theA2; }
|
|
|
|
//! Computes the area of the Ellipse.
|
|
Standard_Real Area() const { return M_PI * majorRadius * minorRadius; }
|
|
|
|
//! Computes the axis normal to the plane of the ellipse.
|
|
const gp_Ax1& Axis() const { return pos.Axis(); }
|
|
|
|
//! Computes the first or second directrix of this ellipse.
|
|
//! These are the lines, in the plane of the ellipse, normal to
|
|
//! the major axis, at a distance equal to
|
|
//! MajorRadius/e from the center of the ellipse, where
|
|
//! e is the eccentricity of the ellipse.
|
|
//! The first directrix (Directrix1) is on the positive side of
|
|
//! the major axis. The second directrix (Directrix2) is on
|
|
//! the negative side.
|
|
//! The directrix is returned as an axis (gp_Ax1 object), the
|
|
//! origin of which is situated on the "X Axis" of the local
|
|
//! coordinate system of this ellipse.
|
|
//! Exceptions
|
|
//! Standard_ConstructionError if the eccentricity is null
|
|
//! (the ellipse has degenerated into a circle).
|
|
gp_Ax1 Directrix1() const;
|
|
|
|
//! This line is obtained by the symmetrical transformation
|
|
//! of "Directrix1" with respect to the "YAxis" of the ellipse.
|
|
//! Exceptions
|
|
//! Standard_ConstructionError if the eccentricity is null
|
|
//! (the ellipse has degenerated into a circle).
|
|
gp_Ax1 Directrix2() const;
|
|
|
|
//! Returns the eccentricity of the ellipse between 0.0 and 1.0
|
|
//! If f is the distance between the center of the ellipse and
|
|
//! the Focus1 then the eccentricity e = f / MajorRadius.
|
|
//! Raises ConstructionError if MajorRadius = 0.0
|
|
Standard_Real Eccentricity() const;
|
|
|
|
//! Computes the focal distance. It is the distance between the
|
|
//! two focus focus1 and focus2 of the ellipse.
|
|
Standard_Real Focal() const
|
|
{
|
|
return 2.0 * sqrt (majorRadius * majorRadius - minorRadius * minorRadius);
|
|
}
|
|
|
|
//! Returns the first focus of the ellipse. This focus is on the
|
|
//! positive side of the "XAxis" of the ellipse.
|
|
gp_Pnt Focus1() const;
|
|
|
|
//! Returns the second focus of the ellipse. This focus is on the
|
|
//! negative side of the "XAxis" of the ellipse.
|
|
gp_Pnt Focus2() const;
|
|
|
|
//! Returns the center of the ellipse. It is the "Location"
|
|
//! point of the coordinate system of the ellipse.
|
|
const gp_Pnt& Location() const { return pos.Location(); }
|
|
|
|
//! Returns the major radius of the ellipse.
|
|
Standard_Real MajorRadius() const { return majorRadius; }
|
|
|
|
//! Returns the minor radius of the ellipse.
|
|
Standard_Real MinorRadius() const { return minorRadius; }
|
|
|
|
//! Returns p = (1 - e * e) * MajorRadius where e is the eccentricity
|
|
//! of the ellipse.
|
|
//! Returns 0 if MajorRadius = 0
|
|
Standard_Real Parameter() const;
|
|
|
|
//! Returns the coordinate system of the ellipse.
|
|
const gp_Ax2& Position() const { return pos; }
|
|
|
|
//! Returns the "XAxis" of the ellipse whose origin
|
|
//! is the center of this ellipse. It is the major axis of the
|
|
//! ellipse.
|
|
gp_Ax1 XAxis() const { return gp_Ax1 (pos.Location(), pos.XDirection()); }
|
|
|
|
//! Returns the "YAxis" of the ellipse whose unit vector is the "X Direction" or the "Y Direction"
|
|
//! of the local coordinate system of this ellipse.
|
|
//! This is the minor axis of the ellipse.
|
|
gp_Ax1 YAxis() const { return gp_Ax1 (pos.Location(), pos.YDirection()); }
|
|
|
|
Standard_EXPORT void Mirror (const gp_Pnt& theP);
|
|
|
|
//! Performs the symmetrical transformation of an ellipse with
|
|
//! respect to the point theP which is the center of the symmetry.
|
|
Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Pnt& theP) const;
|
|
|
|
Standard_EXPORT void Mirror (const gp_Ax1& theA1);
|
|
|
|
//! Performs the symmetrical transformation of an ellipse with
|
|
//! respect to an axis placement which is the axis of the symmetry.
|
|
Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Ax1& theA1) const;
|
|
|
|
Standard_EXPORT void Mirror (const gp_Ax2& theA2);
|
|
|
|
//! Performs the symmetrical transformation of an ellipse with
|
|
//! respect to a plane. The axis placement theA2 locates the plane
|
|
//! of the symmetry (Location, XDirection, YDirection).
|
|
Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Ax2& theA2) const;
|
|
|
|
void Rotate (const gp_Ax1& theA1, const Standard_Real theAng) { pos.Rotate (theA1, theAng); }
|
|
|
|
//! Rotates an ellipse. theA1 is the axis of the rotation.
|
|
//! theAng is the angular value of the rotation in radians.
|
|
Standard_NODISCARD gp_Elips Rotated (const gp_Ax1& theA1, const Standard_Real theAng) const
|
|
{
|
|
gp_Elips anE = *this;
|
|
anE.pos.Rotate (theA1, theAng);
|
|
return anE;
|
|
}
|
|
|
|
void Scale (const gp_Pnt& theP, const Standard_Real theS);
|
|
|
|
//! Scales an ellipse. theS is the scaling value.
|
|
Standard_NODISCARD gp_Elips Scaled (const gp_Pnt& theP, const Standard_Real theS) const;
|
|
|
|
void Transform (const gp_Trsf& theT);
|
|
|
|
//! Transforms an ellipse with the transformation theT from class Trsf.
|
|
Standard_NODISCARD gp_Elips Transformed (const gp_Trsf& theT) const;
|
|
|
|
void Translate (const gp_Vec& theV) { pos.Translate (theV); }
|
|
|
|
//! Translates an ellipse in the direction of the vector theV.
|
|
//! The magnitude of the translation is the vector's magnitude.
|
|
Standard_NODISCARD gp_Elips Translated (const gp_Vec& theV) const
|
|
{
|
|
gp_Elips anE = *this;
|
|
anE.pos.Translate (theV);
|
|
return anE;
|
|
}
|
|
|
|
void Translate (const gp_Pnt& theP1, const gp_Pnt& theP2) { pos.Translate (theP1, theP2); }
|
|
|
|
//! Translates an ellipse from the point theP1 to the point theP2.
|
|
Standard_NODISCARD gp_Elips Translated (const gp_Pnt& theP1, const gp_Pnt& theP2) const
|
|
{
|
|
gp_Elips anE = *this;
|
|
anE.pos.Translate (theP1, theP2);
|
|
return anE;
|
|
}
|
|
|
|
private:
|
|
|
|
gp_Ax2 pos;
|
|
Standard_Real majorRadius;
|
|
Standard_Real minorRadius;
|
|
|
|
};
|
|
|
|
// =======================================================================
|
|
// function : Directrix1
|
|
// purpose :
|
|
// =======================================================================
|
|
inline gp_Ax1 gp_Elips::Directrix1() const
|
|
{
|
|
Standard_Real anE = Eccentricity();
|
|
Standard_ConstructionError_Raise_if (anE <= gp::Resolution(), "gp_Elips::Directrix1() - zero eccentricity");
|
|
gp_XYZ anOrig = pos.XDirection().XYZ();
|
|
anOrig.Multiply (majorRadius / anE);
|
|
anOrig.Add (pos.Location().XYZ());
|
|
return gp_Ax1 (gp_Pnt (anOrig), pos.YDirection());
|
|
}
|
|
|
|
// =======================================================================
|
|
// function : Directrix2
|
|
// purpose :
|
|
// =======================================================================
|
|
inline gp_Ax1 gp_Elips::Directrix2() const
|
|
{
|
|
Standard_Real anE = Eccentricity();
|
|
Standard_ConstructionError_Raise_if (anE <= gp::Resolution(), "gp_Elips::Directrix2() - zero eccentricity");
|
|
gp_XYZ anOrig = pos.XDirection().XYZ();
|
|
anOrig.Multiply (-majorRadius / anE);
|
|
anOrig.Add (pos.Location().XYZ());
|
|
return gp_Ax1 (gp_Pnt (anOrig), pos.YDirection());
|
|
}
|
|
|
|
// =======================================================================
|
|
// function : Eccentricity
|
|
// purpose :
|
|
// =======================================================================
|
|
inline Standard_Real gp_Elips::Eccentricity() const
|
|
{
|
|
if (majorRadius == 0.0)
|
|
{
|
|
return 0.0;
|
|
}
|
|
else
|
|
{
|
|
return sqrt (majorRadius * majorRadius - minorRadius * minorRadius) / majorRadius;
|
|
}
|
|
}
|
|
|
|
// =======================================================================
|
|
// function : Focus1
|
|
// purpose :
|
|
// =======================================================================
|
|
inline gp_Pnt gp_Elips::Focus1() const
|
|
{
|
|
Standard_Real aC = sqrt (majorRadius * majorRadius - minorRadius * minorRadius);
|
|
const gp_Pnt& aPP = pos.Location();
|
|
const gp_Dir& aDD = pos.XDirection();
|
|
return gp_Pnt (aPP.X() + aC * aDD.X(),
|
|
aPP.Y() + aC * aDD.Y(),
|
|
aPP.Z() + aC * aDD.Z());
|
|
}
|
|
|
|
// =======================================================================
|
|
// function : Focus2
|
|
// purpose :
|
|
// =======================================================================
|
|
inline gp_Pnt gp_Elips::Focus2() const
|
|
{
|
|
Standard_Real aC = sqrt (majorRadius * majorRadius - minorRadius * minorRadius);
|
|
const gp_Pnt& aPP = pos.Location();
|
|
const gp_Dir& aDD = pos.XDirection();
|
|
return gp_Pnt (aPP.X() - aC * aDD.X(),
|
|
aPP.Y() - aC * aDD.Y(),
|
|
aPP.Z() - aC * aDD.Z());
|
|
}
|
|
|
|
// =======================================================================
|
|
// function : Parameter
|
|
// purpose :
|
|
// =======================================================================
|
|
inline Standard_Real gp_Elips::Parameter() const
|
|
{
|
|
if (majorRadius == 0.0)
|
|
{
|
|
return 0.0;
|
|
}
|
|
else
|
|
{
|
|
return (minorRadius * minorRadius) / majorRadius;
|
|
}
|
|
}
|
|
|
|
// =======================================================================
|
|
// function : Scale
|
|
// purpose :
|
|
// =======================================================================
|
|
inline void gp_Elips::Scale (const gp_Pnt& theP,
|
|
const Standard_Real theS)
|
|
// Modified by skv - Fri Apr 8 10:28:10 2005 OCC8559 Begin
|
|
// { pos.Scale(P, S); }
|
|
{
|
|
majorRadius *= theS;
|
|
if (majorRadius < 0)
|
|
{
|
|
majorRadius = -majorRadius;
|
|
}
|
|
minorRadius *= theS;
|
|
if (minorRadius < 0)
|
|
{
|
|
minorRadius = -minorRadius;
|
|
}
|
|
pos.Scale (theP, theS);
|
|
}
|
|
// Modified by skv - Fri Apr 8 10:28:10 2005 OCC8559 End
|
|
|
|
// =======================================================================
|
|
// function : Scaled
|
|
// purpose :
|
|
// =======================================================================
|
|
inline gp_Elips gp_Elips::Scaled (const gp_Pnt& theP,
|
|
const Standard_Real theS) const
|
|
{
|
|
gp_Elips anE = *this;
|
|
anE.majorRadius *= theS;
|
|
if (anE.majorRadius < 0)
|
|
{
|
|
anE.majorRadius = -anE.majorRadius;
|
|
}
|
|
anE.minorRadius *= theS;
|
|
if (anE.minorRadius < 0)
|
|
{
|
|
anE.minorRadius = -anE.minorRadius;
|
|
}
|
|
anE.pos.Scale (theP, theS);
|
|
return anE;
|
|
}
|
|
|
|
// =======================================================================
|
|
// function : Transform
|
|
// purpose :
|
|
// =======================================================================
|
|
inline void gp_Elips::Transform (const gp_Trsf& 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_Elips gp_Elips::Transformed (const gp_Trsf& theT) const
|
|
{
|
|
gp_Elips anE = *this;
|
|
anE.majorRadius *= theT.ScaleFactor();
|
|
if (anE.majorRadius < 0)
|
|
{
|
|
anE.majorRadius = -anE.majorRadius;
|
|
}
|
|
anE.minorRadius *= theT.ScaleFactor();
|
|
if (anE.minorRadius < 0)
|
|
{
|
|
anE.minorRadius = -anE.minorRadius;
|
|
}
|
|
anE.pos.Transform (theT);
|
|
return anE;
|
|
}
|
|
|
|
#endif // _gp_Elips_HeaderFile
|