Describes a triaxial ellipsoid surface. An ellipsoid is defined by three semi-axes A, B, C (all > 0) and is positioned in space by a coordinate system (a gp_Ax3 object), the origin of which is the center of the ellipsoid. More...

#include <GeomEval_EllipsoidSurface.hxx>

Inheritance diagram for GeomEval_EllipsoidSurface:

[legend]

Public Member Functions
	GeomEval_EllipsoidSurface (const gp_Ax3 &thePosition, double theA, double theB, double theC)
	Creates a triaxial ellipsoid surface with the given local coordinate system and three semi-axes.

double	SemiAxisA () const
	Returns the semi-axis A (along XDir).

double	SemiAxisB () const
	Returns the semi-axis B (along YDir).

double	SemiAxisC () const
	Returns the semi-axis C (along ZDir).

void	SetSemiAxisA (double theA)
	Assigns the value theA to the semi-axis A.

void	SetSemiAxisB (double theB)
	Assigns the value theB to the semi-axis B.

void	SetSemiAxisC (double theC)
	Assigns the value theC to the semi-axis C.

void	UReverse () final
	Reversal is not supported for this eval surface.

void	VReverse () final
	Reversal is not supported for this eval surface.

double	UReversedParameter (const double U) const final
	Reversal is not supported for this eval surface.

double	VReversedParameter (const double V) const final
	Reversal is not supported for this eval surface.

void	Bounds (double &U1, double &U2, double &V1, double &V2) const final
	Returns the parametric bounds U1, U2, V1 and V2 of this ellipsoid.

bool	IsUClosed () const final
	Returns True. The ellipsoid is closed in U (period 2*Pi).

bool	IsVClosed () const final
	Returns False.

bool	IsUPeriodic () const final
	Returns True. The ellipsoid is periodic in U (period 2*Pi).

bool	IsVPeriodic () const final
	Returns False.

occ::handle< Geom_Curve >	UIso (const double U) const final
	Computes the U isoparametric curve. For a triaxial ellipsoid, the U isoparametric curve is not a standard Geom_Curve type.

occ::handle< Geom_Curve >	VIso (const double V) const final
	Computes the V isoparametric curve. For a triaxial ellipsoid, the V isoparametric curve is not a standard Geom_Curve type (it is an ellipse only when A == B).

gp_Pnt	EvalD0 (const double U, const double V) const final
	Computes the point P(U, V) on the surface.

Geom_Surface::ResD1	EvalD1 (const double U, const double V) const final
	Computes the point and the first partial derivatives at (U, V).

Geom_Surface::ResD2	EvalD2 (const double U, const double V) const final
	Computes the point and partial derivatives up to 2nd order at (U, V).

Geom_Surface::ResD3	EvalD3 (const double U, const double V) const final
	Computes the point and partial derivatives up to 3rd order at (U, V).

gp_Vec	EvalDN (const double U, const double V, const int Nu, const int Nv) const final
	Computes the derivative of order Nu in the direction u and Nv in the direction v.

void	Transform (const gp_Trsf &T) final
	Transformation is not supported for this eval geometry.

occ::handle< Geom_Geometry >	Copy () const final
	Creates a new object which is a copy of this ellipsoid.

void	DumpJson (Standard_OStream &theOStream, int theDepth=-1) const final
	Dumps the content of me into the stream.

void	Coefficients (double &A1, double &A2, double &A3, double &B1, double &B2, double &B3, double &C1, double &C2, double &C3, double &D) const
	Returns the coefficients of the implicit equation of the quadric in the absolute Cartesian coordinate system:

Public Member Functions inherited from Geom_ElementarySurface
void	SetAxis (const gp_Ax1 &theA1)
	Changes the main axis (ZAxis) of the elementary surface.

void	SetLocation (const gp_Pnt &theLoc)
	Changes the location of the local coordinates system of the surface.

void	SetPosition (const gp_Ax3 &theAx3)
	Changes the local coordinates system of the surface.

const gp_Ax1 &	Axis () const
	Returns the main axis of the surface (ZAxis).

const gp_Pnt &	Location () const
	Returns the location point of the local coordinate system of the surface.

const gp_Ax3 &	Position () const
	Returns the local coordinates system of the surface.

GeomAbs_Shape	Continuity () const override
	Returns GeomAbs_CN, the global continuity of any elementary surface.

bool	IsCNu (const int N) const override
	Returns True.

bool	IsCNv (const int N) const override
	Returns True.

Public Member Functions inherited from Geom_Surface
occ::handle< Geom_Surface >	UReversed () const
	Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned.

occ::handle< Geom_Surface >	VReversed () const
	Reverses the V direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned.

virtual void	TransformParameters (double &U, double &V, const gp_Trsf &T) const
	Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.

virtual gp_GTrsf2d	ParametricTransformation (const gp_Trsf &T) const
	Returns a 2d transformation used to find the new parameters of a point on the transformed surface.

virtual double	UPeriod () const
	Returns the period of this surface in the u parametric direction. Raises if the surface is not uperiodic.

virtual double	VPeriod () const
	Returns the period of this surface in the v parametric direction. raises if the surface is not vperiodic.

void	D0 (const double U, const double V, gp_Pnt &P) const
	Computes the point of parameter (U, V).

void	D1 (const double U, const double V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const
	Computes the point and first partial derivatives.

void	D2 (const double U, const double V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV) const
	Computes the point and partial derivatives up to 2nd order.

void	D3 (const double U, const double V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV, gp_Vec &D3U, gp_Vec &D3V, gp_Vec &D3UUV, gp_Vec &D3UVV) const
	Computes the point and partial derivatives up to 3rd order.

gp_Vec	DN (const double U, const double V, const int Nu, const int Nv) const
	Computes the derivative of order Nu in U and Nv in V.

gp_Pnt	Value (const double U, const double V) const
	Computes the point of parameter (U, V) on the surface.

Public Member Functions inherited from Geom_Geometry
void	Mirror (const gp_Pnt &P)
	Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry.

void	Mirror (const gp_Ax1 &A1)
	Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry.

void	Mirror (const gp_Ax2 &A2)
	Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection).

void	Rotate (const gp_Ax1 &A1, const double Ang)
	Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians.

void	Scale (const gp_Pnt &P, const double S)
	Scales a Geometry. S is the scaling value.

void	Translate (const gp_Vec &V)
	Translates a Geometry. V is the vector of the translation.

void	Translate (const gp_Pnt &P1, const gp_Pnt &P2)
	Translates a Geometry from the point P1 to the point P2.

occ::handle< Geom_Geometry >	Mirrored (const gp_Pnt &P) const

occ::handle< Geom_Geometry >	Mirrored (const gp_Ax1 &A1) const

occ::handle< Geom_Geometry >	Mirrored (const gp_Ax2 &A2) const

occ::handle< Geom_Geometry >	Rotated (const gp_Ax1 &A1, const double Ang) const

occ::handle< Geom_Geometry >	Scaled (const gp_Pnt &P, const double S) const

occ::handle< Geom_Geometry >	Transformed (const gp_Trsf &T) const

occ::handle< Geom_Geometry >	Translated (const gp_Vec &V) const

occ::handle< Geom_Geometry >	Translated (const gp_Pnt &P1, const gp_Pnt &P2) const

Public Member Functions inherited from Standard_Transient
	Standard_Transient ()
	Empty constructor.

	Standard_Transient (const Standard_Transient &)
	Copy constructor – does nothing.

Standard_Transient &	operator= (const Standard_Transient &)
	Assignment operator, needed to avoid copying reference counter.

virtual	~Standard_Transient ()=default
	Destructor must be virtual.

virtual const opencascade::handle< Standard_Type > &	DynamicType () const
	Returns a type descriptor about this object.

bool	IsInstance (const opencascade::handle< Standard_Type > &theType) const
	Returns a true value if this is an instance of Type.

bool	IsInstance (const char *const theTypeName) const
	Returns a true value if this is an instance of TypeName.

bool	IsKind (const opencascade::handle< Standard_Type > &theType) const
	Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism.

bool	IsKind (const char *const theTypeName) const
	Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism.

Standard_Transient *	This () const
	Returns non-const pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero.

int	GetRefCount () const noexcept
	Get the reference counter of this object.

void	IncrementRefCounter () noexcept
	Increments the reference counter of this object. Uses relaxed memory ordering since incrementing only requires atomicity, not synchronization with other memory operations.

int	DecrementRefCounter () noexcept
	Decrements the reference counter of this object; returns the decremented value. Uses release ordering for the decrement to ensure all writes to the object are visible before the count reaches zero. An acquire fence is added only when the count reaches zero, ensuring proper synchronization before deletion. This is more efficient than using acq_rel for every decrement.

virtual void	Delete () const
	Memory deallocator for transient classes.

Additional Inherited Members
Public Types inherited from Standard_Transient
typedef void	base_type
	Returns a type descriptor about this object.

Static Public Member Functions inherited from Standard_Transient
static constexpr const char *	get_type_name ()
	Returns a type descriptor about this object.

static const opencascade::handle< Standard_Type > &	get_type_descriptor ()
	Returns type descriptor of Standard_Transient class.

Protected Attributes inherited from Geom_ElementarySurface
gp_Ax3	pos

Detailed Description

Describes a triaxial ellipsoid surface. An ellipsoid is defined by three semi-axes A, B, C (all > 0) and is positioned in space by a coordinate system (a gp_Ax3 object), the origin of which is the center of the ellipsoid.

The parametric equation of the ellipsoid is:

P(u,v) = O + A*cos(v)*cos(u)*XDir + B*cos(v)*sin(u)*YDir + C*sin(v)*ZDir

NCollection_ForwardRangeIterator

STL input iterator that wraps an OCCT More()/Next() iterator.

Definition NCollection_ForwardRange.hxx:142

where:

O, XDir, YDir and ZDir are respectively the origin, the "X Direction", the "Y Direction" and the "Z Direction" of its local coordinate system, and
A, B, C are the three semi-axes.

The parametric range is:

[0, 2*Pi] for u, and
[-Pi/2, Pi/2] for v.

When A == B the surface degenerates to a spheroid (ellipsoid of revolution).

The implicit equation in local coordinates is:

X^2/A^2 + Y^2/B^2 + Z^2/C^2 - 1 = 0

Constructor & Destructor Documentation

◆ GeomEval_EllipsoidSurface()

GeomEval_EllipsoidSurface::GeomEval_EllipsoidSurface	(	const gp_Ax3 &	thePosition,
		double	theA,
		double	theB,
		double	theC )

Creates a triaxial ellipsoid surface with the given local coordinate system and three semi-axes.

Parameters

[in]	thePosition	the local coordinate system
[in]	theA	the semi-axis along XDir (must be > 0)
[in]	theB	the semi-axis along YDir (must be > 0)
[in]	theC	the semi-axis along ZDir (must be > 0)

Exceptions

Standard_ConstructionError if any semi-axis <= 0

Member Function Documentation

◆ Bounds()

void GeomEval_EllipsoidSurface::Bounds	(	double &	U1,
		double &	U2,
		double &	V1,
		double &	V2 ) const

finalvirtual

Returns the parametric bounds U1, U2, V1 and V2 of this ellipsoid.

Parameters

[out]	U1	lower U bound (0)
[out]	U2	upper U bound (2*Pi)
[out]	V1	lower V bound (-Pi/2)
[out]	V2	upper V bound (Pi/2)

Implements Geom_Surface.

◆ Coefficients()

void GeomEval_EllipsoidSurface::Coefficients	(	double &	A1,
		double &	A2,
		double &	A3,
		double &	B1,
		double &	B2,
		double &	B3,
		double &	C1,
		double &	C2,
		double &	C3,
		double &	D ) const

Returns the coefficients of the implicit equation of the quadric in the absolute Cartesian coordinate system:

A1*X^2 + A2*Y^2 + A3*Z^2 + 2*(B1*X*Y + B2*X*Z + B3*Y*Z) +

2*(C1*X + C2*Y + C3*Z) + D = 0

In local coordinates the equation is: X^2/A^2 + Y^2/B^2 + Z^2/C^2 - 1 = 0.

◆ Copy()

occ::handle< Geom_Geometry > GeomEval_EllipsoidSurface::Copy ( ) const

finalvirtual

Creates a new object which is a copy of this ellipsoid.

Implements Geom_Geometry.

◆ DumpJson()

void GeomEval_EllipsoidSurface::DumpJson	(	Standard_OStream &	theOStream,
		int	theDepth = -1 ) const

finalvirtual

Dumps the content of me into the stream.

Reimplemented from Geom_ElementarySurface.

◆ EvalD0()

gp_Pnt GeomEval_EllipsoidSurface::EvalD0	(	const double	U,
		const double	V ) const

finalvirtual

Computes the point P(U, V) on the surface.

P(U, V) = O + A*cos(V)*cos(U)*XDir + B*cos(V)*sin(U)*YDir + C*sin(V)*ZDir

Implements Geom_Surface.

◆ EvalD1()

Geom_Surface::ResD1 GeomEval_EllipsoidSurface::EvalD1	(	const double	U,
		const double	V ) const

finalvirtual

Computes the point and the first partial derivatives at (U, V).

Implements Geom_Surface.

◆ EvalD2()

Geom_Surface::ResD2 GeomEval_EllipsoidSurface::EvalD2	(	const double	U,
		const double	V ) const

finalvirtual

Computes the point and partial derivatives up to 2nd order at (U, V).

Implements Geom_Surface.

◆ EvalD3()

Geom_Surface::ResD3 GeomEval_EllipsoidSurface::EvalD3	(	const double	U,
		const double	V ) const

finalvirtual

Computes the point and partial derivatives up to 3rd order at (U, V).

Implements Geom_Surface.

◆ EvalDN()

gp_Vec GeomEval_EllipsoidSurface::EvalDN	(	const double	U,
		const double	V,
		const int	Nu,
		const int	Nv ) const

finalvirtual

Computes the derivative of order Nu in the direction u and Nv in the direction v.

Parameters

[in]	U	the u parameter
[in]	V	the v parameter
[in]	Nu	derivative order in u (must be >= 0)
[in]	Nv	derivative order in v (must be >= 0)

Returns: the derivative vector

Exceptions

Geom_UndefinedDerivative if Nu + Nv < 1 or Nu < 0 or Nv < 0

Implements Geom_Surface.

◆ IsUClosed()

bool GeomEval_EllipsoidSurface::IsUClosed ( ) const

finalvirtual

Returns True. The ellipsoid is closed in U (period 2*Pi).

Implements Geom_Surface.

◆ IsUPeriodic()

bool GeomEval_EllipsoidSurface::IsUPeriodic ( ) const

finalvirtual

Returns True. The ellipsoid is periodic in U (period 2*Pi).

Implements Geom_Surface.

◆ IsVClosed()

bool GeomEval_EllipsoidSurface::IsVClosed ( ) const

finalvirtual

Returns False.

Implements Geom_Surface.

◆ IsVPeriodic()

bool GeomEval_EllipsoidSurface::IsVPeriodic ( ) const

finalvirtual

Returns False.

Implements Geom_Surface.

◆ SemiAxisA()

double GeomEval_EllipsoidSurface::SemiAxisA ( ) const

Returns the semi-axis A (along XDir).

◆ SemiAxisB()

finalvirtual

Reversal is not supported for this eval surface.

Exceptions

Standard_NotImplemented

Implements Geom_ElementarySurface.

The documentation for this class was generated from the following file:

GeomEval_EllipsoidSurface.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ GeomEval_EllipsoidSurface()

Member Function Documentation

◆ Bounds()

◆ Coefficients()

◆ Copy()

◆ DumpJson()

◆ EvalD0()

◆ EvalD1()

◆ EvalD2()

◆ EvalD3()

◆ EvalDN()

◆ IsUClosed()

◆ IsUPeriodic()

◆ IsVClosed()

◆ IsVPeriodic()

◆ SemiAxisA()

◆ SemiAxisB()

◆ SemiAxisC()

◆ SetSemiAxisA()

◆ SetSemiAxisB()

◆ SetSemiAxisC()

◆ Transform()

◆ UIso()

◆ UReverse()

◆ UReversedParameter()

◆ VIso()

◆ VReverse()

◆ VReversedParameter()