gp_Torus Class Reference

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
	gp_Torus ()
	creates an indefinite Torus. More...
	gp_Torus (const gp_Ax3 &A3, const Standard_Real MajorRadius, const Standard_Real MinorRadius)
	a torus centered on the origin of coordinate system A3, with major radius MajorRadius and minor radius MinorRadius, and with the reference plane defined by the origin, the "X Direction" and the "Y Direction" of A3. Warnings : It is not forbidden to create a torus with MajorRadius = MinorRadius = 0.0 Raises ConstructionError if MinorRadius < 0.0 or if MajorRadius < 0.0 More...
void	SetAxis (const gp_Ax1 &A1)
	Modifies this torus, by redefining its local coordinate system so that: More...
void	SetLocation (const gp_Pnt &Loc)
	Changes the location of the torus. More...
void	SetMajorRadius (const Standard_Real MajorRadius)
	Assigns value to the major radius of this torus. Raises ConstructionError if MajorRadius - MinorRadius <= Resolution() More...
void	SetMinorRadius (const Standard_Real MinorRadius)
	Assigns value to the minor radius of this torus. Raises ConstructionError if MinorRadius < 0.0 or if MajorRadius - MinorRadius <= Resolution from gp. More...
void	SetPosition (const gp_Ax3 &A3)
	Changes the local coordinate system of the surface. More...
Standard_Real	Area () const
	Computes the area of the torus. More...
void	UReverse ()
	Reverses the U parametrization of the torus reversing the YAxis. More...
void	VReverse ()
	Reverses the V parametrization of the torus reversing the ZAxis. More...
Standard_Boolean	Direct () const
	returns true if the Ax3, the local coordinate system of this torus, is right handed. More...
const gp_Ax1 &	Axis () const
	returns the symmetry axis of the torus. More...
void	Coefficients (TColStd_Array1OfReal &Coef) 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 Coef is lower than 35. More...
const gp_Pnt &	Location () const
	Returns the Torus's location. More...
const gp_Ax3 &	Position () const
	Returns the local coordinates system of the torus. More...
Standard_Real	MajorRadius () const
	returns the major radius of the torus. More...
Standard_Real	MinorRadius () const
	returns the minor radius of the torus. More...
Standard_Real	Volume () const
	Computes the volume of the torus. More...
gp_Ax1	XAxis () const
	returns the axis X of the torus. More...
gp_Ax1	YAxis () const
	returns the axis Y of the torus. More...
void	Mirror (const gp_Pnt &P)
gp_Torus	Mirrored (const gp_Pnt &P) const
	Performs the symmetrical transformation of a torus with respect to the point P which is the center of the symmetry. More...
void	Mirror (const gp_Ax1 &A1)
gp_Torus	Mirrored (const gp_Ax1 &A1) const
	Performs the symmetrical transformation of a torus with respect to an axis placement which is the axis of the symmetry. More...
void	Mirror (const gp_Ax2 &A2)
gp_Torus	Mirrored (const gp_Ax2 &A2) const
	Performs the symmetrical transformation of a torus with respect to a plane. The axis placement A2 locates the plane of the of the symmetry : (Location, XDirection, YDirection). More...
void	Rotate (const gp_Ax1 &A1, const Standard_Real Ang)
gp_Torus	Rotated (const gp_Ax1 &A1, const Standard_Real Ang) const
	Rotates a torus. 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)
gp_Torus	Scaled (const gp_Pnt &P, const Standard_Real S) const
	Scales a torus. S is the scaling value. The absolute value of S is used to scale the torus. More...
void	Transform (const gp_Trsf &T)
gp_Torus	Transformed (const gp_Trsf &T) const
	Transforms a torus with the transformation T from class Trsf. More...
void	Translate (const gp_Vec &V)
gp_Torus	Translated (const gp_Vec &V) const
	Translates a torus in the direction of the vector V. The magnitude of the translation is the vector's magnitude. More...
void	Translate (const gp_Pnt &P1, const gp_Pnt &P2)
gp_Torus	Translated (const gp_Pnt &P1, const gp_Pnt &P2) const
	Translates a torus from the point P1 to the point P2. More...

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

(

)

creates an indefinite Torus.

gp_Torus() [2/2]

gp_Torus::gp_Torus	(	const gp_Ax3 &	A3,
		const Standard_Real	MajorRadius,
		const Standard_Real	MinorRadius
	)

a torus centered on the origin of coordinate system A3, with major radius MajorRadius and minor radius MinorRadius, and with the reference plane defined by the origin, the "X Direction" and the "Y Direction" of A3. Warnings : It is not forbidden to create a torus with MajorRadius = MinorRadius = 0.0 Raises ConstructionError if MinorRadius < 0.0 or if MajorRadius < 0.0

Member Function Documentation

Area()

Standard_Real gp_Torus::Area

(

)

const

Computes the area of the torus.

Axis()

const gp_Ax1& gp_Torus::Axis

(

)

const

returns the symmetry axis of the torus.

Coefficients()

void gp_Torus::Coefficients

(

TColStd_Array1OfReal &

Coef

)

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 Coef is lower than 35.

Direct()

Standard_Boolean gp_Torus::Direct

(

)

const

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

Location()

const gp_Pnt& gp_Torus::Location

(

)

const

Returns the Torus's location.

MajorRadius()

Standard_Real gp_Torus::MajorRadius

(

)

const

returns the major radius of the torus.

MinorRadius()

Standard_Real gp_Torus::MinorRadius

(

)

const

returns the minor radius of the torus.

Mirror() [1/3]

void gp_Torus::Mirror

(

const gp_Pnt &

P

)

Mirror() [2/3]

void gp_Torus::Mirror

(

const gp_Ax1 &

A1

)

Mirror() [3/3]

void gp_Torus::Mirror

(

const gp_Ax2 &

A2

)

Mirrored() [1/3]

gp_Torus gp_Torus::Mirrored

(

const gp_Pnt &

P

)

const

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

Mirrored() [2/3]

gp_Torus gp_Torus::Mirrored

(

const gp_Ax1 &

A1

)

const

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

Mirrored() [3/3]

gp_Torus gp_Torus::Mirrored

(

const gp_Ax2 &

A2

)

const

Performs the symmetrical transformation of a torus with respect to a plane. The axis placement A2 locates the plane of the of the symmetry : (Location, XDirection, YDirection).

Position()

const gp_Ax3& gp_Torus::Position

(

)

const

Returns the local coordinates system of the torus.

Rotate()

void gp_Torus::Rotate	(	const gp_Ax1 &	A1,
		const Standard_Real	Ang
	)

Rotated()

gp_Torus gp_Torus::Rotated	(	const gp_Ax1 &	A1,
		const Standard_Real	Ang
	)		const

Rotates a torus. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians.

Scale()

void gp_Torus::Scale	(	const gp_Pnt &	P,
		const Standard_Real	S
	)

Scaled()

gp_Torus gp_Torus::Scaled	(	const gp_Pnt &	P,
		const Standard_Real	S
	)		const

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 &

A1

)

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

• its origin and "main Direction" become those of the axis A1 (the "X Direction" and "Y Direction" are then recomputed). Raises ConstructionError if the direction of A1 is parallel to the "XDirection" of the coordinate system of the toroidal surface.

SetLocation()

void gp_Torus::SetLocation

(

const gp_Pnt &

Loc

)

Changes the location of the torus.

SetMajorRadius()

void gp_Torus::SetMajorRadius

(

const Standard_Real

MajorRadius

)

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

SetMinorRadius()

void gp_Torus::SetMinorRadius

(

const Standard_Real

MinorRadius

)

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

SetPosition()

void gp_Torus::SetPosition

(

const gp_Ax3 &

A3

)

Changes the local coordinate system of the surface.

Transform()

void gp_Torus::Transform

(

const gp_Trsf &

T

)

Transformed()

gp_Torus gp_Torus::Transformed

(

const gp_Trsf &

T

)

const

Transforms a torus with the transformation T from class Trsf.

Translate() [1/2]

void gp_Torus::Translate

(

const gp_Vec &

V

)

Translate() [2/2]

void gp_Torus::Translate	(	const gp_Pnt &	P1,
		const gp_Pnt &	P2
	)

Translated() [1/2]

gp_Torus gp_Torus::Translated

(

const gp_Vec &

V

)

const

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

Translated() [2/2]

gp_Torus gp_Torus::Translated	(	const gp_Pnt &	P1,
		const gp_Pnt &	P2
	)		const

Translates a torus from the point P1 to the point P2.

UReverse()

void gp_Torus::UReverse

(

)

Reverses the U parametrization of the torus reversing the YAxis.

Volume()

Standard_Real gp_Torus::Volume

(

)

const

Computes the volume of the torus.

VReverse()

void gp_Torus::VReverse

(

)

Reverses the V parametrization of the torus reversing the ZAxis.

XAxis()

gp_Ax1 gp_Torus::XAxis

(

)

const

returns the axis X of the torus.

YAxis()

gp_Ax1 gp_Torus::YAxis

(

)

const

returns the axis Y of the torus.

---

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

• gp_Torus.hxx