Describes a sphere. <br>

A sphere is defined by its radius, and is positioned in
space by a coordinate system (a gp_Ax3 object), the
origin of which is the center of the sphere.
This coordinate system is the "local coordinate system" of the sphere. The following apply:
More...

#include <Geom_SphericalSurface.hxx>

Inheritance diagram for Geom_SphericalSurface:

[legend]

Public Member Functions
	Geom_SphericalSurface (const gp_Ax3 &A3, const Standard_Real Radius)
	A3 is the local coordinate system of the surface. At the creation the parametrization of the surface is defined such as the normal Vector (N = D1U ^ D1V) is directed away from the center of the sphere. The direction of increasing parametric value V is defined by the rotation around the "YDirection" of A2 in the trigonometric sense and the orientation of increasing parametric value U is defined by the rotation around the main direction of A2 in the trigonometric sense. Warnings : It is not forbidden to create a spherical surface with Radius = 0.0 //! Raised if Radius < 0.0. More...

	Geom_SphericalSurface (const gp_Sphere &S)
	Creates a SphericalSurface from a non persistent Sphere from package gp. More...

void	SetRadius (const Standard_Real R)
	Assigns the value R to the radius of this sphere. <br> Exceptions Standard_ConstructionError if R is less than 0.0. More...

void	SetSphere (const gp_Sphere &S)
	Converts the gp_Sphere S into this sphere. More...

gp_Sphere	Sphere () const
	Returns a non persistent sphere with the same geometric <br> properties as <me>. More...

Standard_Real	UReversedParameter (const Standard_Real U) const
	Computes the u parameter on the modified <br> surface, when reversing its u parametric direction, for any point of u parameter U on this sphere. In the case of a sphere, these functions returns 2.PI - U. More...

Standard_Real	VReversedParameter (const Standard_Real V) const
	Computes the v parameter on the modified <br> surface, when reversing its v parametric direction, for any point of v parameter V on this sphere. In the case of a sphere, these functions returns -U. More...

Standard_Real	Area () const
	Computes the aera of the spherical surface. More...

void	Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const
	Returns the parametric bounds U1, U2, V1 and V2 of this sphere. <br> For a sphere: U1 = 0, U2 = 2*PI, V1 = -PI/2, V2 = PI/2. More...

void	Coefficients (Standard_Real &A1, Standard_Real &A2, Standard_Real &A3, Standard_Real &B1, Standard_Real &B2, Standard_Real &B3, Standard_Real &C1, Standard_Real &C2, Standard_Real &C3, Standard_Real &D) const
	Returns the coefficients of the implicit equation of the <br> quadric in the absolute cartesian coordinates system : These coefficients are normalized. A1.X2 + A2.Y2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + 2.(C1.X + C2.Y + C3.Z) + D = 0.0 More...

Standard_Real	Radius () const
	Computes the coefficients of the implicit equation of <br> this quadric in the absolute Cartesian coordinate system: A1.X2 + A2.Y2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + 2.(C1.X + C2.Y + C3.Z) + D = 0.0 An implicit normalization is applied (i.e. A1 = A2 = 1. in the local coordinate system of this sphere). More...

Standard_Real	Volume () const
	Computes the volume of the spherical surface. More...

Standard_Boolean	IsUClosed () const
	Returns True. More...

Standard_Boolean	IsVClosed () const
	Returns False. More...

Standard_Boolean	IsUPeriodic () const
	Returns True. More...

Standard_Boolean	IsVPeriodic () const
	Returns False. More...

Handle_Geom_Curve	UIso (const Standard_Real U) const
	Computes the U isoparametric curve. <br> The U isoparametric curves of the surface are defined by the section of the spherical surface with plane obtained by rotation of the plane (Location, XAxis, ZAxis) around ZAxis. This plane defines the origin of parametrization u. For a SphericalSurface the UIso curve is a Circle. Warnings : The radius of this circle can be zero. More...

Handle_Geom_Curve	VIso (const Standard_Real V) const
	Computes the V isoparametric curve. <br> The V isoparametric curves of the surface are defined by the section of the spherical surface with plane parallel to the plane (Location, XAxis, YAxis). This plane defines the origin of parametrization V. Be careful if V is close to PI/2 or 3*PI/2 the radius of the circle becomes tiny. It is not forbidden in this toolkit to create circle with radius = 0.0 For a SphericalSurface the VIso curve is a Circle. Warnings : The radius of this circle can be zero. More...

void	D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const
	Computes the point P (U, V) on the surface. P (U, V) = Loc + Radius * Sin (V) * Zdir + Radius * Cos (V) * (cos (U) * XDir + sin (U) * YDir) 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 and ZDir the direction of the ZAxis. More...

void	D1 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const
	Computes the current point and the first derivatives in the directions U and V. More...

void	D2 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV) const
	Computes the current point, the first and the second derivatives in the directions U and V. More...

void	D3 (const Standard_Real U, const Standard_Real 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 current point, the first,the second and the third derivatives in the directions U and V. More...

gp_Vec	DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const
	Computes the derivative of order Nu in the direction u and Nv in the direction v. //! Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0. More...

void	Transform (const gp_Trsf &T)
	Applies the transformation T to this sphere. More...

Handle_Geom_Geometry	Copy () const
	Creates a new object which is a copy of this sphere. More...

Public Member Functions inherited from Geom_ElementarySurface
void	SetAxis (const gp_Ax1 &A1)
	Changes the main axis (ZAxis) of the elementary surface. Raised if the direction of A1 is parallel to the XAxis of the coordinate system of the surface. More...

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

void	SetPosition (const gp_Ax3 &A3)
	Changes the local coordinates system of the surface. More...

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

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

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

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

virtual void	VReverse ()
	Reverses the V parametric direction of the surface. More...

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

Standard_Boolean	IsCNu (const Standard_Integer N) const
	Returns True. More...

Standard_Boolean	IsCNv (const Standard_Integer N) const
	Returns True. More...

Public Member Functions inherited from Geom_Surface
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. More...

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. More...

virtual void	TransformParameters (Standard_Real &U, Standard_Real &V, const gp_Trsf &T) const
	Computes the parameters on the transformed surface for <br> the transform of the point of parameters U,V on <me>. <br> 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->TranformParameters(U,V,T) This methods does not change <U> and <V> It can be redefined. For example on the Plane, Cylinder, Cone, Revolved and Extruded surfaces. More...

virtual gp_GTrsf2d	ParametricTransformation (const gp_Trsf &T) const
	Returns a 2d transformation used to find the new <br> parameters of a point on the transformed surface. <br> 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 th 2d transformation returned by me->ParametricTransformation(T) This methods returns an identity transformation It can be redefined. For example on the Plane, Cylinder, Cone, Revolved and Extruded surfaces. More...

virtual Standard_Real	UPeriod () const
	Returns the period of this surface in the u <br> parametric direction. //! raises if the surface is not uperiodic. More...

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

gp_Pnt	Value (const Standard_Real U, const Standard_Real V) const
	Computes the point of parameter U on the surface. <br> It is implemented with D0 Raised only for an "OffsetSurface" if it is not possible to compute the current point. More...

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. More...

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. More...

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). More...

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

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

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

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

Handle_Geom_Geometry	Mirrored (const gp_Pnt &P) const

Handle_Geom_Geometry	Mirrored (const gp_Ax1 &A1) const

Handle_Geom_Geometry	Mirrored (const gp_Ax2 &A2) const

Handle_Geom_Geometry	Rotated (const gp_Ax1 &A1, const Standard_Real Ang) const

Handle_Geom_Geometry	Scaled (const gp_Pnt &P, const Standard_Real S) const

Handle_Geom_Geometry	Transformed (const gp_Trsf &T) const

Handle_Geom_Geometry	Translated (const gp_Vec &V) const

Handle_Geom_Geometry	Translated (const gp_Pnt &P1, const gp_Pnt &P2) const

Public Member Functions inherited from MMgt_TShared
virtual void	Delete () const
	Memory deallocator for transient classes. More...

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

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

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

virtual	~Standard_Transient ()
	Destructor must be virtual. More...

virtual void	ShallowDump (Standard_OStream &) const

virtual const Handle_Standard_Type &	DynamicType () const
	Returns a type information object about this object. More...

Standard_Boolean	IsInstance (const Handle_Standard_Type &theType) const
	Returns a true value if this is an instance of Type. More...

Standard_Boolean	IsInstance (const Standard_CString theTypeName) const
	Returns a true value if this is an instance of TypeName. More...

Standard_Boolean	IsKind (const 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. More...

Standard_Boolean	IsKind (const Standard_CString 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. More...

virtual Handle_Standard_Transient	This () const
	Returns a Handle which references this object. Must never be called to objects created in stack. More...

Standard_Integer	GetRefCount () const
	Get the reference counter of this object. More...

Additional Inherited Members
Protected Attributes inherited from Geom_ElementarySurface
gp_Ax3	pos

Detailed Description

Describes a sphere. <br>

A sphere is defined by its radius, and is positioned in
space by a coordinate system (a gp_Ax3 object), the
origin of which is the center of the sphere.
This coordinate system is the "local coordinate system" of the sphere. 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.
The "reference meridian" of the sphere is a
half-circle, of radius equal to the radius of the
sphere. It is located in the plane defined by the
origin, "X Direction" and "main Direction", centered
on the origin, and positioned on the positive side of the "X Axis".
Rotation around the "Y Axis" gives the v parameter
on the reference meridian.
The "X Axis" gives the origin of the v parameter on
the reference meridian.
The v parametric direction is oriented by the "main Direction", i.e. when v increases, the Z coordinate
increases. (This implies that the "Y Direction"
orients the reference meridian only when the local
coordinate system is indirect.)
The u isoparametric curve is a half-circle obtained
by rotating the reference meridian of the sphere
through an angle u around the "main Axis", in the
trigonometric sense defined by the "X Direction"
and the "Y Direction".
The parametric equation of the sphere is:
P(u,v) = O + R*cos(v)*(cos(u)*XDir + sin(u)*YDir)+R*sin(v)*ZDir
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
R is the radius of the sphere.
The parametric range of the two parameters is:
[ 0, 2.*Pi ] for u, and
[ - Pi/2., + Pi/2. ] for v.

Constructor & Destructor Documentation

Geom_SphericalSurface::Geom_SphericalSurface	(	const gp_Ax3 &	A3,
		const Standard_Real	Radius
	)

A3 is the local coordinate system of the surface.
At the creation the parametrization of the surface is defined
such as the normal Vector (N = D1U ^ D1V) is directed away from
the center of the sphere.
The direction of increasing parametric value V is defined by the
rotation around the "YDirection" of A2 in the trigonometric sense
and the orientation of increasing parametric value U is defined
by the rotation around the main direction of A2 in the
trigonometric sense.
Warnings :
It is not forbidden to create a spherical surface with
Radius = 0.0
//! Raised if Radius < 0.0.

Geom_SphericalSurface::Geom_SphericalSurface ( const gp_Sphere & S )

Creates a SphericalSurface from a non persistent Sphere from
package gp.

Member Function Documentation

Standard_Real Geom_SphericalSurface::Area ( ) const

Computes the aera of the spherical surface.

void Geom_SphericalSurface::Bounds	(	Standard_Real &	U1,
		Standard_Real &	U2,
		Standard_Real &	V1,
		Standard_Real &	V2
	)		const

virtual

 Returns the parametric bounds U1, U2, V1 and V2 of this sphere. <br>

For a sphere: U1 = 0, U2 = 2*PI, V1 = -PI/2, V2 = PI/2.

Implements Geom_Surface.

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

Returns the coefficients of the implicit equation of the <br>

quadric in the absolute cartesian coordinates 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

Handle_Geom_Geometry Geom_SphericalSurface::Copy ( ) const

virtual

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

Implements Geom_Geometry.

void Geom_SphericalSurface::D0	(	const Standard_Real	U,
		const Standard_Real	V,
		gp_Pnt &	P
	)		const

virtual

Computes the point P (U, V) on the surface.
P (U, V) = Loc + Radius * Sin (V) * Zdir +
Radius * Cos (V) * (cos (U) * XDir + sin (U) * YDir)
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 and ZDir the direction of the ZAxis.

Implements Geom_Surface.

void Geom_SphericalSurface::D1	(	const Standard_Real	U,
		const Standard_Real	V,
		gp_Pnt &	P,
		gp_Vec &	D1U,
		gp_Vec &	D1V
	)		const

virtual

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

Implements Geom_Surface.

void Geom_SphericalSurface::D2	(	const Standard_Real	U,
		const Standard_Real	V,
		gp_Pnt &	P,
		gp_Vec &	D1U,
		gp_Vec &	D1V,
		gp_Vec &	D2U,
		gp_Vec &	D2V,
		gp_Vec &	D2UV
	)		const

virtual

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

Implements Geom_Surface.

void Geom_SphericalSurface::D3	(	const Standard_Real	U,
		const Standard_Real	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

virtual

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

Implements Geom_Surface.

gp_Vec Geom_SphericalSurface::DN	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	Nu,
		const Standard_Integer	Nv
	)		const

virtual

Computes the derivative of order Nu in the direction u
and Nv in the direction v.
//! Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.

Implements Geom_Surface.

Standard_Boolean Geom_SphericalSurface::IsUClosed ( ) const

virtual

Returns True.

Implements Geom_Surface.

Standard_Boolean Geom_SphericalSurface::IsUPeriodic ( ) const

virtual

Returns True.

Implements Geom_Surface.

Standard_Boolean Geom_SphericalSurface::IsVClosed ( ) const

virtual

Returns False.

Implements Geom_Surface.

Standard_Boolean Geom_SphericalSurface::IsVPeriodic ( ) const

virtual

Returns False.

Implements Geom_Surface.

Standard_Real Geom_SphericalSurface::Radius ( ) const

 Computes the coefficients of the implicit equation of <br>

this 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 = 0.0
An implicit normalization is applied (i.e. A1 = A2 = 1.
in the local coordinate system of this sphere).

void Geom_SphericalSurface::SetRadius ( const Standard_Real R )

 Assigns the value R to the radius of this sphere. <br>

Exceptions Standard_ConstructionError if R is less than 0.0.

void Geom_SphericalSurface::SetSphere ( const gp_Sphere & S )

Converts the gp_Sphere S into this sphere.

gp_Sphere Geom_SphericalSurface::Sphere ( ) const

Returns a non persistent sphere with the same geometric <br>

properties as <me>.

void Geom_SphericalSurface::Transform ( const gp_Trsf & T )

virtual

Applies the transformation T to this sphere.

Implements Geom_Geometry.

Handle_Geom_Curve Geom_SphericalSurface::UIso ( const Standard_Real U ) const

virtual

 Computes the U isoparametric curve. <br>

The U isoparametric curves of the surface are defined by the
section of the spherical surface with plane obtained by rotation
of the plane (Location, XAxis, ZAxis) around ZAxis. This plane
defines the origin of parametrization u.
For a SphericalSurface the UIso curve is a Circle.
Warnings : The radius of this circle can be zero.

Implements Geom_Surface.

Standard_Real Geom_SphericalSurface::UReversedParameter ( const Standard_Real U ) const

virtual

 Computes the u parameter on the modified <br>

surface, when reversing its u parametric
direction, for any point of u parameter U on this sphere.
In the case of a sphere, these functions returns 2.PI - U.

Implements Geom_ElementarySurface.

Handle_Geom_Curve Geom_SphericalSurface::VIso ( const Standard_Real V ) const

virtual

Computes the V isoparametric curve. <br>

The V isoparametric curves of the surface are defined by
the section of the spherical surface with plane parallel to the
plane (Location, XAxis, YAxis). This plane defines the origin of
parametrization V.
Be careful if V is close to PI/2 or 3*PI/2 the radius of the
circle becomes tiny. It is not forbidden in this toolkit to
create circle with radius = 0.0
For a SphericalSurface the VIso curve is a Circle.
Warnings : The radius of this circle can be zero.

Implements Geom_Surface.

Standard_Real Geom_SphericalSurface::Volume ( ) const

Computes the volume of the spherical surface.

Standard_Real Geom_SphericalSurface::VReversedParameter ( const Standard_Real V ) const

virtual

 Computes the v parameter on the modified <br>

surface, when reversing its v parametric
direction, for any point of v parameter V on this sphere.
In the case of a sphere, these functions returns -U.

Implements Geom_ElementarySurface.

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

Geom_SphericalSurface.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation