# class ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>

```
Class describing a generic position vector (point) in 3 dimensions.
This class is templated on the type of Coordinate system.
One example is the XYZPoint which is a vector based on
double precision x,y,z data members by using the
ROOT::Math::Cartesian3D<double> Coordinate system.
The class is having also an extra template parameter, the coordinate system tag,
to be able to identify (tag) vector described in different reference coordinate system,
like global or local coordinate systems.

@ingroup GenVector

```

#### This class is also known as (typedefs to this class)

ROOT::Math::Plane3D::Point, vector<ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>,allocator<ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag> > >::value_type, ROOT::Math::Transform3D::Point, ROOT::Math::PositionVector3D<Cartesian3D<double>,DefaultCoordinateSystemTag>, ROOT::Math::XYZPoint, ROOT::Math::XYZPointD, ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double> >

## Data Members

private:
 ROOT::Math::Cartesian3D fCoordinates

## Function documentation

PositionVector3D & operator=( const ForeignVector & v)
```          Assignment from a foreign 3D vector type, for example, Hep3Vector
Precondition: v must implement methods x(), y() and z()

```
const CoordSystem & Coordinates() const
```          Retrieve a copy of the coordinates object

```
PositionVector3D<CoordSystem, Tag>& SetCoordinates(const ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar* src)
```         Set internal data based on a C-style array of 3 Scalar numbers

```
`{ fCoordinates.SetCoordinates(src); return *this; }`

```         Set internal data based on 3 Scalar numbers

```
`{ fCoordinates.SetCoordinates(a, b, c); return *this; }`

```        get internal data into 3 Scalar numbers

```
`{ fCoordinates.GetCoordinates(a, b, c); }`

```         get internal data into a C-style array of 3 Scalar numbers

```
`{ fCoordinates.GetCoordinates(dest); }`

``` ------------------- Equality -----------------

Exact equality

```

Scalar X() const
``` ------ Individual element access, in various coordinate systems ------

Cartesian X, converting if necessary from internal coordinate system.

```
`{ return fCoordinates.X(); }`
Scalar Y() const
```          Cartesian Y, converting if necessary from internal coordinate system.

```
`{ return fCoordinates.Y(); }`
Scalar Z() const
```          Cartesian Z, converting if necessary from internal coordinate system.

```
`{ return fCoordinates.Z(); }`
Scalar R() const
```          Polar R, converting if necessary from internal coordinate system.

```
`{ return fCoordinates.R(); }`
Scalar Theta() const
```          Polar theta, converting if necessary from internal coordinate system.

```
`{ return fCoordinates.Theta(); }`
Scalar Phi() const
```          Polar phi, converting if necessary from internal coordinate system.

```
`{ return fCoordinates.Phi(); }`
Scalar Eta() const
```          Polar eta, converting if necessary from internal coordinate system.

```
`{ return fCoordinates.Eta(); }`
Scalar Rho() const
```          Cylindrical transverse component rho

```
`{ return fCoordinates.Rho(); }`
Scalar Mag2() const
``` ----- Other fundamental properties -----

Magnitute squared ( r^2 in spherical coordinate)

```
`{ return fCoordinates.Mag2();}`
Scalar Perp2() const
```         Transverse component squared (rho^2 in cylindrical coordinates.

```
`{ return fCoordinates.Perp2();}`
PositionVector3D<CoordSystem, Tag>& SetX(ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar xx)
``` It is physically meaningless to speak of the unit vector corresponding
to a point.
------ Setting individual elements present in coordinate system ------

Change X - Cartesian3D coordinates only

```
`{ fCoordinates.SetX(xx); return *this;}`
PositionVector3D<CoordSystem, Tag>& SetY(ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar yy)
```         Change Y - Cartesian3D coordinates only

```
`{ fCoordinates.SetY(yy); return *this;}`
PositionVector3D<CoordSystem, Tag>& SetZ(ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar zz)
```         Change Z - Cartesian3D coordinates only

```
`{ fCoordinates.SetZ(zz); return *this;}`
PositionVector3D<CoordSystem, Tag>& SetR(ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar rr)
```         Change R - Polar3D coordinates only

```
`{ fCoordinates.SetR(rr); return *this;}`
PositionVector3D<CoordSystem, Tag>& SetTheta(ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar ang)
```         Change Theta - Polar3D coordinates only

```
`{ fCoordinates.SetTheta(ang); return *this;}`
PositionVector3D<CoordSystem, Tag>& SetPhi(ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar ang)
```         Change Phi - Polar3D or CylindricalEta3D coordinates

```
`{ fCoordinates.SetPhi(ang); return *this;}`
PositionVector3D<CoordSystem, Tag>& SetRho(ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar rr)
```         Change Rho - CylindricalEta3D coordinates only

```
`{ fCoordinates.SetRho(rr); return *this;}`
PositionVector3D<CoordSystem, Tag>& SetEta(ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar etaval)
```         Change Eta - CylindricalEta3D coordinates only

```
`{ fCoordinates.SetEta(etaval); return *this;}`
Scalar Dot( const DisplacementVector3D<OtherCoords,Tag> & v)
``` ------ Operations combining two vectors ------
need to specialize to exclude those with a different tags

Return the scalar (Dot) product of this with a displacement vector in
any coordinate system, but with the same tag

```
PositionVector3D Cross( const DisplacementVector3D<OtherCoords,Tag> & v)
```         Return vector (Cross) product of this point with a displacement, as a
point vector in this coordinate system of the first.

```
PositionVector3D & operator+=(const DisplacementVector3D<OtherCoords,Tag> & v)
``` The Dot and Cross products of a pair of point vectors are physically
meaningless concepts and thus are defined as private methods
It is physically meaningless to speak of the Unit vector corresponding
to a point.

Self Addition with a displacement vector.

```
PositionVector3D & operator-=(const DisplacementVector3D<OtherCoords,Tag> & v)
```          Self Difference with a displacement vector.

```
Scalar x() const
``` Limited backward name compatibility with CLHEP
```
`{ return fCoordinates.X(); }`
Scalar y() const
`{ return fCoordinates.Y(); }`
Scalar z() const
`{ return fCoordinates.Z(); }`
Scalar theta() const
`{ return fCoordinates.Theta(); }`
Scalar phi() const
`{ return fCoordinates.Phi(); }`
Scalar eta() const
`{ return fCoordinates.Eta(); }`
Scalar rho() const
`{ return fCoordinates.Rho(); }`
Scalar mag2() const
`{ return fCoordinates.Mag2(); }`
Scalar perp2() const
`{ return fCoordinates.Perp2(); }`
PositionVector3D & operator=( const PositionVector3D<OtherCoords, OtherTag> & )
PositionVector3D & operator=( const DisplacementVector3D<OtherCoords, OtherTag> & )
PositionVector3D & operator+=(const DisplacementVector3D<OtherCoords, OtherTag> & )
PositionVector3D & operator-=(const DisplacementVector3D<OtherCoords, OtherTag> & )