Describes a cone. A cone is defined by the half-angle (can be negative) at its apex, and is positioned in space by a coordinate system (a gp_Ax3 object) and a reference radius as follows: More...

#include <Geom_ConicalSurface.hxx>

Inheritance diagram for Geom_ConicalSurface:

[legend]

Public Member Functions
	Geom_ConicalSurface (const gp_Ax3 &A3, const double Ang, const double Radius)
	A3 defines the local coordinate system of the conical surface. Ang is the conical surface semi-angle. Its absolute value is in range ]0, PI/2[. Radius is the radius of the circle Viso in the placement plane of the conical surface defined with "XAxis" and "YAxis". The "ZDirection" of A3 defines the direction of the surface's axis of symmetry. If the location point of A3 is the apex of the surface Radius = 0 . At the creation the parametrization of the surface is defined such that the normal Vector (N = D1U ^ D1V) is oriented towards the "outside region" of the surface.

	Geom_ConicalSurface (const gp_Cone &C)
	Creates a ConicalSurface from a non transient gp_Cone.

void	SetCone (const gp_Cone &C)
	Set <me> so that <me> has the same geometric properties as C.

void	SetRadius (const double R)
	Changes the radius of the conical surface in the placement plane (Z = 0, V = 0). The local coordinate system is not modified. Raised if R < 0.0.

void	SetSemiAngle (const double Ang)
	Changes the semi angle of the conical surface. Semi-angle can be negative. Its absolute value std::abs(Ang) is in range ]0,PI/2[. Raises ConstructionError if std::abs(Ang) < Resolution from gp or std::abs(Ang) >= PI/2 - Resolution.

gp_Cone	Cone () const
	Returns a non transient cone with the same geometric properties as <me>.

double	UReversedParameter (const double U) const final
	Eeturn 2.PI - U.

double	VReversedParameter (const double V) const final
	Computes the u (or v) parameter on the modified surface, when reversing its u (or v) parametric direction, for any point of u parameter U (or of v parameter V) on this cone. In the case of a cone, these functions return respectively:

void	VReverse () final
	Changes the orientation of this cone in the v parametric direction. The bounds of the surface are not changed but the v parametric direction is reversed. As a consequence, for a cone:

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

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

gp_Pnt	Apex () const
	Computes the apex of this cone. It is on the negative side of the axis of revolution of this cone if the half-angle at the apex is positive, and on the positive side of the "main Axis" if the half-angle is negative.

void	Bounds (double &U1, double &U2, double &V1, double &V2) const final
	The conical surface is infinite in the V direction so V1 = Realfirst from Standard and V2 = RealLast. U1 = 0 and U2 = 2*PI.

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 : These coefficients are normalized.

double	RefRadius () const
	Returns the reference radius of this cone. The reference radius is the radius of the circle formed by the intersection of this cone and its reference plane (i.e. the plane defined by the origin, "X Direction" and "Y Direction" of the local coordinate system of this cone). If the apex of this cone is on the origin of the local coordinate system of this cone, the returned value is 0.

double	SemiAngle () const
	Returns the semi-angle at the apex of this cone. Attention! Semi-angle can be negative.

bool	IsUClosed () const final
	returns True.

bool	IsVClosed () const final
	returns False.

bool	IsUPeriodic () const final
	Returns True.

bool	IsVPeriodic () const final
	Returns False.

occ::handle< Geom_Curve >	UIso (const double U) const final
	Builds the U isoparametric line of this cone. The origin of this line is on the reference plane of this cone (i.e. the plane defined by the origin, "X Direction" and "Y Direction" of the local coordinate system of this cone).

occ::handle< Geom_Curve >	VIso (const double V) const final
	Builds the V isoparametric circle of this cone. It is the circle on this cone, located in the plane of Z coordinate V*cos(Semi-Angle) in the local coordinate system of this cone. The "Axis" of this circle is the axis of revolution of this cone. Its starting point is defined by the "X Direction" of this cone. Warning If the V isoparametric circle is close to the apex of this cone, the radius of the circle becomes very small. It is possible to have a circle with radius equal to 0.0.

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 current point and the first derivatives in the directions U and V.

Geom_Surface::ResD2	EvalD2 (const double U, const double V) const final
	Computes the current point, the first and the second derivatives in the directions U and V.

Geom_Surface::ResD3	EvalD3 (const double U, const double V) const final
	Computes the current point, the first,the second and the third derivatives in the directions U and 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 u parametric direction, and Nv in the v parametric direction at the point of parameters (U, V) of this cone. Exceptions Standard_RangeError if:

void	Transform (const gp_Trsf &T) final
	Applies the transformation T to this cone.

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

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

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.

void	UReverse () override
	Reverses the U parametric direction of the surface.

void	VReverse () override
	Reverses the V parametric direction 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.

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

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 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.

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

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 cone. A cone is defined by the half-angle (can be negative) at its apex, and is positioned in space by a coordinate system (a gp_Ax3 object) and a reference radius as follows:

The "main Axis" of the coordinate system is the axis of revolution of the cone.
The plane defined by the origin, the "X Direction" and the "Y Direction" of the coordinate system is the reference plane of the cone. The intersection of the cone with this reference plane is a circle of radius equal to the reference radius.
The apex of the cone is on the negative side of the "main Axis" of the coordinate system if the half-angle is positive, and on the positive side if the half-angle is negative. This coordinate system is the "local coordinate system" of the cone. The following apply:
Rotation around its "main Axis", in the trigonometric sense given by the "X Direction" and the "Y Direction", defines the u parametric direction.
Its "X Axis" gives the origin for the u parameter.
Its "main Direction" is the v parametric direction of the cone.
Its origin is the origin of the v parameter. The parametric range of the two parameters is:
- [ 0, 2.*Pi ] for u, and

- ] -infinity, +infinity [ for v

NCollection_ForwardRangeIterator
STL input iterator that wraps an OCCT More()/Next() iterator.
Definition NCollection_ForwardRange.hxx:142

The parametric equation of the cone is:
P(u, v) = O + (R + v*sin(Ang)) * (cos(u)*XDir + sin(u)*YDir) + v*cos(Ang)*ZDir

where:
O, XDir, YDir and ZDir are respectively the origin, the "X Direction", the "Y Direction" and the "Z Direction" of the cone's local coordinate system,
Ang is the half-angle at the apex of the cone, and
R is the reference radius.

Constructor & Destructor Documentation

◆ Geom_ConicalSurface() [1/2]

Geom_ConicalSurface::Geom_ConicalSurface	(	const gp_Ax3 &	A3,
		const double	Ang,
		const double	Radius )

A3 defines the local coordinate system of the conical surface. Ang is the conical surface semi-angle. Its absolute value is in range ]0, PI/2[. Radius is the radius of the circle Viso in the placement plane of the conical surface defined with "XAxis" and "YAxis". The "ZDirection" of A3 defines the direction of the surface's axis of symmetry. If the location point of A3 is the apex of the surface Radius = 0 . At the creation the parametrization of the surface is defined such that the normal Vector (N = D1U ^ D1V) is oriented towards the "outside region" of the surface.

Raised if Radius < 0.0 or std::abs(Ang) < Resolution from gp or std::abs(Ang) >= PI/2 - Resolution

◆ Geom_ConicalSurface() [2/2]

Geom_ConicalSurface::Geom_ConicalSurface ( const gp_Cone & C )

Creates a ConicalSurface from a non transient gp_Cone.

Member Function Documentation

◆ Apex()

gp_Pnt Geom_ConicalSurface::Apex ( ) const

Computes the apex of this cone. It is on the negative side of the axis of revolution of this cone if the half-angle at the apex is positive, and on the positive side of the "main Axis" if the half-angle is negative.

◆ Bounds()

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

finalvirtual

The conical surface is infinite in the V direction so V1 = Realfirst from Standard and V2 = RealLast. U1 = 0 and U2 = 2*PI.

Implements Geom_Surface.

◆ Coefficients()

void Geom_ConicalSurface::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 : These coefficients are normalized.

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 =

0.0

◆ Cone()

gp_Cone Geom_ConicalSurface::Cone ( ) const

Returns a non transient cone with the same geometric properties as <me>.

◆ Copy()

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

finalvirtual

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

Implements Geom_Geometry.

◆ DumpJson()

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

finalvirtual

Dumps the content of me into the stream.

Reimplemented from Geom_Geometry.

◆ EvalD0()

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

finalvirtual

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

P (U, V) = Loc +
           (RefRadius + V * sin (Semi-Angle)) * (cos (U) * XDir + sin (U) * YDir) +
           V * cos (Semi-Angle) * ZDir

where Loc is the origin of the placement plane (XAxis, YAxis) XDir is the direction of the XAxis and YDir the direction of the YAxis.

Implements Geom_Surface.

◆ EvalD1()

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

finalvirtual

Computes the current point and the first derivatives in the directions U and V.

Implements Geom_Surface.

◆ EvalD2()

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

finalvirtual

Computes the current point, the first and the second derivatives in the directions U and V.

Implements Geom_Surface.

◆ EvalD3()

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

finalvirtual

Computes the current point, the first,the second and the third derivatives in the directions U and V.

Implements Geom_Surface.

◆ EvalDN()

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

finalvirtual

Computes the derivative of order Nu in the u parametric direction, and Nv in the v parametric direction at the point of parameters (U, V) of this cone. Exceptions Standard_RangeError if:

Nu + Nv is less than 1,
Nu or Nv is negative.

Implements Geom_Surface.

◆ IsUClosed()

bool Geom_ConicalSurface::IsUClosed ( ) const

finalvirtual

returns True.

Implements Geom_Surface.

◆ IsUPeriodic()

bool Geom_ConicalSurface::IsUPeriodic ( ) const

finalvirtual

Returns True.

Implements Geom_Surface.

◆ IsVClosed()

bool Geom_ConicalSurface::IsVClosed ( ) const

finalvirtual

returns False.

Implements Geom_Surface.

◆ IsVPeriodic()

bool Geom_ConicalSurface::IsVPeriodic ( ) const

finalvirtual

Returns False.

Implements Geom_Surface.

◆ ParametricTransformation()

gp_GTrsf2d Geom_ConicalSurface::ParametricTransformation ( const gp_Trsf & T ) const

finalvirtual

Returns a 2d transformation used to find the new parameters of a point on the transformed surface.

me->Transformed(T)->Value(U',V')

is the same point as

me->Value(U,V).Transformed(T)

Where U',V' are obtained by transforming U,V with the 2d transformation returned by

me->ParametricTransformation(T)

This method returns a scale centered on the U axis with T.ScaleFactor

Reimplemented from Geom_Surface.

◆ RefRadius()

double Geom_ConicalSurface::RefRadius ( ) const

Returns the reference radius of this cone. The reference radius is the radius of the circle formed by the intersection of this cone and its reference plane (i.e. the plane defined by the origin, "X Direction" and "Y Direction" of the local coordinate system of this cone). If the apex of this cone is on the origin of the local coordinate system of this cone, the returned value is 0.

◆ SemiAngle()

double Geom_ConicalSurface::SemiAngle ( ) const

Returns the semi-angle at the apex of this cone. Attention! Semi-angle can be negative.

◆ SetCone()

void Geom_ConicalSurface::SetCone ( const gp_Cone & C )

Set <me> so that <me> has the same geometric properties as C.

◆ SetRadius()

void Geom_ConicalSurface::SetRadius ( const double R )

Changes the radius of the conical surface in the placement plane (Z = 0, V = 0). The local coordinate system is not modified. Raised if R < 0.0.

◆ SetSemiAngle()

void Geom_ConicalSurface::SetSemiAngle ( const double Ang )

Changes the semi angle of the conical surface. Semi-angle can be negative. Its absolute value std::abs(Ang) is in range ]0,PI/2[. Raises ConstructionError if std::abs(Ang) < Resolution from gp or std::abs(Ang) >= PI/2 - Resolution.

◆ Transform()

void Geom_ConicalSurface::Transform ( const gp_Trsf & T )

finalvirtual

Applies the transformation T to this cone.

Implements Geom_Geometry.

◆ TransformParameters()

void Geom_ConicalSurface::TransformParameters	(	double &	U,
		double &	V,
		const gp_Trsf &	T ) const

finalvirtual

Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.

me->Transformed(T)->Value(U',V')

is the same point as

me->Value(U,V).Transformed(T)

Where U',V' are the new values of U,V after calling

me->TransformParameters(U,V,T)

This method multiplies V by T.ScaleFactor()

Reimplemented from Geom_Surface.

◆ UIso()

occ::handle< Geom_Curve > Geom_ConicalSurface::UIso ( const double U ) const

finalvirtual

Builds the U isoparametric line of this cone. The origin of this line is on the reference plane of this cone (i.e. the plane defined by the origin, "X Direction" and "Y Direction" of the local coordinate system of this cone).

Implements Geom_Surface.

◆ UReversedParameter()

double Geom_ConicalSurface::UReversedParameter ( const double U ) const

finalvirtual

Eeturn 2.PI - U.

Implements Geom_ElementarySurface.

◆ VIso()

occ::handle< Geom_Curve > Geom_ConicalSurface::VIso ( const double V ) const

finalvirtual

Builds the V isoparametric circle of this cone. It is the circle on this cone, located in the plane of Z coordinate V*cos(Semi-Angle) in the local coordinate system of this cone. The "Axis" of this circle is the axis of revolution of this cone. Its starting point is defined by the "X Direction" of this cone. Warning If the V isoparametric circle is close to the apex of this cone, the radius of the circle becomes very small. It is possible to have a circle with radius equal to 0.0.

Implements Geom_Surface.

◆ VReverse()

void Geom_ConicalSurface::VReverse ( )

finalvirtual

Changes the orientation of this cone in the v parametric direction. The bounds of the surface are not changed but the v parametric direction is reversed. As a consequence, for a cone:

the "main Direction" of the local coordinate system is reversed, and
the half-angle at the apex is inverted.

Implements Geom_Surface.

◆ VReversedParameter()

double Geom_ConicalSurface::VReversedParameter ( const double V ) const

finalvirtual

Computes the u (or v) parameter on the modified surface, when reversing its u (or v) parametric direction, for any point of u parameter U (or of v parameter V) on this cone. In the case of a cone, these functions return respectively:

2.*Pi - U, -V.

Implements Geom_ElementarySurface.

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

Geom_ConicalSurface.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Geom_ConicalSurface() [1/2]

◆ Geom_ConicalSurface() [2/2]

Member Function Documentation

◆ Apex()

◆ Bounds()

◆ Coefficients()

◆ Cone()

◆ Copy()

◆ DumpJson()

◆ EvalD0()

◆ EvalD1()

◆ EvalD2()

◆ EvalD3()

◆ EvalDN()

◆ IsUClosed()

◆ IsUPeriodic()

◆ IsVClosed()

◆ IsVPeriodic()

◆ ParametricTransformation()

◆ RefRadius()

◆ SemiAngle()

◆ SetCone()

◆ SetRadius()

◆ SetSemiAngle()

◆ Transform()

◆ TransformParameters()

◆ UIso()

◆ UReversedParameter()

◆ VIso()

◆ VReverse()

◆ VReversedParameter()