Describes a torus. A torus is defined by its major and minor radii and positioned in space with a coordinate system (a gp_Ax3 object) as follows: More...

#include <gp_Torus.hxx>

Public Member Functions
constexpr	gp_Torus () noexcept
	creates an indefinite Torus.
constexpr	gp_Torus (const gp_Ax3 &theA3, const double theMajorRadius, const double theMinorRadius)
	a torus centered on the origin of coordinate system theA3, with major radius theMajorRadius and minor radius theMinorRadius, and with the reference plane defined by the origin, the "X Direction" and the "Y Direction" of theA3. Warnings : It is not forbidden to create a torus with theMajorRadius = theMinorRadius = 0.0 Raises ConstructionError if theMinorRadius < 0.0 or if theMajorRadius < 0.0
void	SetAxis (const gp_Ax1 &theA1)
	Modifies this torus, by redefining its local coordinate system so that:
constexpr void	SetLocation (const gp_Pnt &theLoc) noexcept
	Changes the location of the torus.
void	SetMajorRadius (const double theMajorRadius)
	Assigns value to the major radius of this torus. Raises ConstructionError if theMajorRadius - MinorRadius <= Resolution().
void	SetMinorRadius (const double theMinorRadius)
	Assigns value to the minor radius of this torus. Raises ConstructionError if theMinorRadius < 0.0 or if MajorRadius - theMinorRadius <= Resolution from gp.
constexpr void	SetPosition (const gp_Ax3 &theA3) noexcept
	Changes the local coordinate system of the surface.
constexpr double	Area () const noexcept
	Computes the area of the torus.
constexpr void	UReverse () noexcept
	Reverses the U parametrization of the torus reversing the YAxis.
constexpr void	VReverse () noexcept
	Reverses the V parametrization of the torus reversing the ZAxis.
bool	Direct () const
	returns true if the Ax3, the local coordinate system of this torus, is right handed.
constexpr const gp_Ax1 &	Axis () const noexcept
	returns the symmetry axis of the torus.
void	Coefficients (NCollection_Array1< double > &theCoef) const
	Computes the coefficients of the implicit equation of the surface in the absolute Cartesian coordinate system:
constexpr const gp_Pnt &	Location () const noexcept
	Returns the Torus's location.
constexpr const gp_Ax3 &	Position () const noexcept
	Returns the local coordinates system of the torus.
constexpr double	MajorRadius () const noexcept
	returns the major radius of the torus.
constexpr double	MinorRadius () const noexcept
	returns the minor radius of the torus.
constexpr double	Volume () const noexcept
	Computes the volume of the torus.
constexpr gp_Ax1	XAxis () const noexcept
	returns the axis X of the torus.
constexpr gp_Ax1	YAxis () const noexcept
	returns the axis Y of the torus.
void	Mirror (const gp_Pnt &theP) noexcept
gp_Torus	Mirrored (const gp_Pnt &theP) const noexcept
	Performs the symmetrical transformation of a torus with respect to the point theP which is the center of the symmetry.
void	Mirror (const gp_Ax1 &theA1) noexcept
gp_Torus	Mirrored (const gp_Ax1 &theA1) const noexcept
	Performs the symmetrical transformation of a torus with respect to an axis placement which is the axis of the symmetry.
void	Mirror (const gp_Ax2 &theA2) noexcept
gp_Torus	Mirrored (const gp_Ax2 &theA2) const noexcept
	Performs the symmetrical transformation of a torus with respect to a plane. The axis placement theA2 locates the plane of the of the symmetry : (Location, XDirection, YDirection).
void	Rotate (const gp_Ax1 &theA1, const double theAng)
gp_Torus	Rotated (const gp_Ax1 &theA1, const double theAng) const
	Rotates a torus. theA1 is the axis of the rotation. theAng is the angular value of the rotation in radians.
void	Scale (const gp_Pnt &theP, const double theS)
gp_Torus	Scaled (const gp_Pnt &theP, const double theS) const
	Scales a torus. S is the scaling value. The absolute value of S is used to scale the torus.
void	Transform (const gp_Trsf &theT)
gp_Torus	Transformed (const gp_Trsf &theT) const
	Transforms a torus with the transformation theT from class Trsf.
constexpr void	Translate (const gp_Vec &theV) noexcept
constexpr gp_Torus	Translated (const gp_Vec &theV) const noexcept
	Translates a torus in the direction of the vector theV. The magnitude of the translation is the vector's magnitude.
constexpr void	Translate (const gp_Pnt &theP1, const gp_Pnt &theP2) noexcept
constexpr gp_Torus	Translated (const gp_Pnt &theP1, const gp_Pnt &theP2) const noexcept
	Translates a torus from the point theP1 to the point theP2.

Detailed Description

Describes a torus. A torus is defined by its major and minor radii and positioned in space with a coordinate system (a gp_Ax3 object) as follows:

The origin of the coordinate system is the center of the torus;
The surface is obtained by rotating a circle of radius equal to the minor radius of the torus about the "main Direction" of the coordinate system. This circle is located in the plane defined by the origin, the "X Direction" and the "main Direction" of the coordinate system. It is centered on the "X Axis" of this coordinate system, and located at a distance, from the origin of this coordinate system, equal to the major radius of the torus;
The "X Direction" and "Y Direction" define the reference plane of the torus. The coordinate system described above is the "local coordinate system" of the torus. Note: when a gp_Torus torus is converted into a Geom_ToroidalSurface torus, some implicit properties of its local coordinate system are used explicitly:
its origin, "X Direction", "Y Direction" and "main Direction" are used directly to define the parametric directions on the torus and the origin of the parameters,
its implicit orientation (right-handed or left-handed) gives the orientation (direct, indirect) to the Geom_ToroidalSurface torus. See Also gce_MakeTorus which provides functions for more complex torus constructions Geom_ToroidalSurface which provides additional functions for constructing tori and works, in particular, with the parametric equations of tori.

Constructor & Destructor Documentation

◆ gp_Torus() [1/2]

gp_Torus::gp_Torus ( )

inlineconstexprnoexcept

creates an indefinite Torus.

◆ gp_Torus() [2/2]

gp_Torus::gp_Torus	(	const gp_Ax3 &	theA3,
		const double	theMajorRadius,
		const double	theMinorRadius )

inlineconstexpr

a torus centered on the origin of coordinate system theA3, with major radius theMajorRadius and minor radius theMinorRadius, and with the reference plane defined by the origin, the "X Direction" and the "Y Direction" of theA3. Warnings : It is not forbidden to create a torus with theMajorRadius = theMinorRadius = 0.0 Raises ConstructionError if theMinorRadius < 0.0 or if theMajorRadius < 0.0

Member Function Documentation

◆ Area()

double gp_Torus::Area ( ) const

inlineconstexprnoexcept

Computes the area of the torus.

◆ Axis()

const gp_Ax1 & gp_Torus::Axis ( ) const

inlineconstexprnoexcept

returns the symmetry axis of the torus.

◆ Coefficients()

void gp_Torus::Coefficients ( NCollection_Array1< double > & theCoef ) const

Computes the coefficients of the implicit equation of the surface in the absolute Cartesian coordinate system:

Coef(1) * X^4 + Coef(2) * Y^4 + Coef(3) * Z^4 +
Coef(4) * X^3 * Y + Coef(5) * X^3 * Z + Coef(6) * Y^3 * X +
Coef(7) * Y^3 * Z + Coef(8) * Z^3 * X + Coef(9) * Z^3 * Y +
Coef(10) * X^2 * Y^2 + Coef(11) * X^2 * Z^2 +
Coef(12) * Y^2 * Z^2 + Coef(13) * X^2 * Y * Z +
Coef(14) * X * Y^2 * Z + Coef(15) * X * Y * Z^2 +
Coef(16) * X^3 + Coef(17) * Y^3 + Coef(18) * Z^3 +
Coef(19) * X^2 * Y + Coef(20) * X^2 * Z + Coef(21) * Y^2 * X +
Coef(22) * Y^2 * Z + Coef(23) * Z^2 * X + Coef(24) * Z^2 * Y +
Coef(25) * X * Y * Z +
Coef(26) * X^2 + Coef(27) * Y^2 + Coef(28) * Z^2 +
Coef(29) * X * Y + Coef(30) * X * Z + Coef(31) * Y * Z +
Coef(32) * X + Coef(33) * Y + Coef(34) * Z +
Coef(35) = 0.0

Raises DimensionError if the length of theCoef is lower than 35.

◆ Direct()

bool gp_Torus::Direct ( ) const

inline

returns true if the Ax3, the local coordinate system of this torus, is right handed.

◆ Location()

const gp_Pnt & gp_Torus::Location ( ) const

inlineconstexprnoexcept

Returns the Torus's location.

◆ MajorRadius()

double gp_Torus::MajorRadius ( ) const

inlineconstexprnoexcept

returns the major radius of the torus.

◆ MinorRadius()

double gp_Torus::MinorRadius ( ) const

inlineconstexprnoexcept

returns the minor radius of the torus.

◆ Mirror() [1/3]

void gp_Torus::Mirror ( const gp_Ax1 & theA1 )

noexcept

◆ Mirror() [2/3]

void gp_Torus::Mirror ( const gp_Ax2 & theA2 )

noexcept

◆ Mirror() [3/3]

void gp_Torus::Mirror ( const gp_Pnt & theP )

noexcept

◆ Mirrored() [1/3]

gp_Torus gp_Torus::Mirrored ( const gp_Ax1 & theA1 ) const

nodiscardnoexcept

Performs the symmetrical transformation of a torus with respect to an axis placement which is the axis of the symmetry.

◆ Mirrored() [2/3]

gp_Torus gp_Torus::Mirrored ( const gp_Ax2 & theA2 ) const

nodiscardnoexcept

Performs the symmetrical transformation of a torus with respect to a plane. The axis placement theA2 locates the plane of the of the symmetry : (Location, XDirection, YDirection).

◆ Mirrored() [3/3]

gp_Torus gp_Torus::Mirrored ( const gp_Pnt & theP ) const

nodiscardnoexcept

Performs the symmetrical transformation of a torus with respect to the point theP which is the center of the symmetry.

◆ Position()

const gp_Ax3 & gp_Torus::Position ( ) const

inlineconstexprnoexcept

Returns the local coordinates system of the torus.

◆ Rotate()

void gp_Torus::Rotate	(	const gp_Ax1 &	theA1,
		const double	theAng )

inline

◆ Rotated()

gp_Torus gp_Torus::Rotated	(	const gp_Ax1 &	theA1,
		const double	theAng ) const

inlinenodiscard

Rotates a torus. theA1 is the axis of the rotation. theAng is the angular value of the rotation in radians.

◆ Scale()

void gp_Torus::Scale	(	const gp_Pnt &	theP,
		const double	theS )

inline

◆ Scaled()

gp_Torus gp_Torus::Scaled	(	const gp_Pnt &	theP,
		const double	theS ) const

inlinenodiscard

Scales a torus. S is the scaling value. The absolute value of S is used to scale the torus.

◆ SetAxis()

void gp_Torus::SetAxis ( const gp_Ax1 & theA1 )

inline

Modifies this torus, by redefining its local coordinate system so that:

its origin and "main Direction" become those of the axis theA1 (the "X Direction" and "Y Direction" are then recomputed). Raises ConstructionError if the direction of theA1 is parallel to the "XDirection" of the coordinate system of the toroidal surface.

◆ SetLocation()

void gp_Torus::SetLocation ( const gp_Pnt & theLoc )

inlineconstexprnoexcept

Changes the location of the torus.

◆ SetMajorRadius()

void gp_Torus::SetMajorRadius ( const double theMajorRadius )

inline

Assigns value to the major radius of this torus. Raises ConstructionError if theMajorRadius - MinorRadius <= Resolution().

◆ SetMinorRadius()

void gp_Torus::SetMinorRadius ( const double theMinorRadius )

inline

Assigns value to the minor radius of this torus. Raises ConstructionError if theMinorRadius < 0.0 or if MajorRadius - theMinorRadius <= Resolution from gp.

◆ SetPosition()

void gp_Torus::SetPosition ( const gp_Ax3 & theA3 )

inlineconstexprnoexcept

Changes the local coordinate system of the surface.

◆ Transform()

void gp_Torus::Transform ( const gp_Trsf & theT )

inline

◆ Transformed()

gp_Torus gp_Torus::Transformed ( const gp_Trsf & theT ) const

inlinenodiscard

Transforms a torus with the transformation theT from class Trsf.

◆ Translate() [1/2]

void gp_Torus::Translate	(	const gp_Pnt &	theP1,
		const gp_Pnt &	theP2 )

inlineconstexprnoexcept

◆ Translate() [2/2]

void gp_Torus::Translate ( const gp_Vec & theV )

inlineconstexprnoexcept

◆ Translated() [1/2]

gp_Torus gp_Torus::Translated	(	const gp_Pnt &	theP1,
		const gp_Pnt &	theP2 ) const

inlinenodiscardconstexprnoexcept

Translates a torus from the point theP1 to the point theP2.

◆ Translated() [2/2]

gp_Torus gp_Torus::Translated ( const gp_Vec & theV ) const

inlinenodiscardconstexprnoexcept

Translates a torus in the direction of the vector theV. The magnitude of the translation is the vector's magnitude.

◆ UReverse()

void gp_Torus::UReverse ( )

inlineconstexprnoexcept

Reverses the U parametrization of the torus reversing the YAxis.

◆ Volume()

double gp_Torus::Volume ( ) const

inlineconstexprnoexcept

Computes the volume of the torus.

◆ VReverse()

void gp_Torus::VReverse ( )

inlineconstexprnoexcept

Reverses the V parametrization of the torus reversing the ZAxis.

◆ XAxis()

gp_Ax1 gp_Torus::XAxis ( ) const

inlineconstexprnoexcept

returns the axis X of the torus.

◆ YAxis()

gp_Ax1 gp_Torus::YAxis ( ) const

inlineconstexprnoexcept

returns the axis Y of the torus.

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

gp_Torus.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ gp_Torus() [1/2]

◆ gp_Torus() [2/2]

Member Function Documentation

◆ Area()

◆ Axis()

◆ Coefficients()

◆ Direct()

◆ Location()

◆ MajorRadius()

◆ MinorRadius()

◆ Mirror() [1/3]

◆ Mirror() [2/3]

◆ Mirror() [3/3]

◆ Mirrored() [1/3]

◆ Mirrored() [2/3]

◆ Mirrored() [3/3]

◆ Position()

◆ Rotate()

◆ Rotated()

◆ Scale()

◆ Scaled()

◆ SetAxis()

◆ SetLocation()

◆ SetMajorRadius()

◆ SetMinorRadius()

◆ SetPosition()

◆ Transform()

◆ Transformed()

◆ Translate() [1/2]

◆ Translate() [2/2]

◆ Translated() [1/2]

◆ Translated() [2/2]

◆ UReverse()

◆ Volume()

◆ VReverse()

◆ XAxis()

◆ YAxis()