# class ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>

```
Class describing a generic displacement vector in 3 dimensions.
This class is templated on the type of Coordinate system.
One example is the XYZVector 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::RhoZPhiVectorD, ROOT::Math::RhoZPhiVector, ROOT::Math::DisplacementVector3D<Cylindrical3D<double>,DefaultCoordinateSystemTag>, ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double> >

## Data Members

private:
 ROOT::Math::Cylindrical3D fCoordinates internal coordinate system

## Function documentation

DisplacementVector3D & operator=( const ForeignVector & v)
```          Assignment from a foreign 3D vector type, for example, Hep3Vector
Precondition: v must implement methods x(), y() and z()

```
CoordSystem Coordinates() const
``` ------ Set, Get, and access coordinate data ------

Retrieve a copy of the coordinates object

```
DisplacementVector3D<CoordSystem, Tag>& SetCoordinates(const ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<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();}`
DisplacementVector3D Unit() const
```         return unit vector parallel to this

```
DisplacementVector3D<CoordSystem, Tag>& SetX(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar xx)
``` ------ Setting of individual elements present in coordinate system ------

Change X - Cartesian3D coordinates only

```
`{ fCoordinates.SetX(xx); return *this;}`
DisplacementVector3D<CoordSystem, Tag>& SetY(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar yy)
```         Change Y - Cartesian3D coordinates only

```
`{ fCoordinates.SetY(yy); return *this;}`
DisplacementVector3D<CoordSystem, Tag>& SetZ(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar zz)
```         Change Z - Cartesian3D coordinates only

```
`{ fCoordinates.SetZ(zz); return *this;}`
DisplacementVector3D<CoordSystem, Tag>& SetR(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar rr)
```         Change R - Polar3D coordinates only

```
`{ fCoordinates.SetR(rr); return *this;}`
DisplacementVector3D<CoordSystem, Tag>& SetTheta(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar ang)
```         Change Theta - Polar3D coordinates only

```
`{ fCoordinates.SetTheta(ang); return *this;}`
DisplacementVector3D<CoordSystem, Tag>& SetPhi(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar ang)
```         Change Phi - Polar3D or CylindricalEta3D coordinates

```
`{ fCoordinates.SetPhi(ang); return *this;}`
DisplacementVector3D<CoordSystem, Tag>& SetRho(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar rr)
```         Change Rho - CylindricalEta3D coordinates only

```
`{ fCoordinates.SetRho(rr); return *this;}`
DisplacementVector3D<CoordSystem, Tag>& SetEta(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar etaval)
```         Change Eta - CylindricalEta3D coordinates only

```
`{ fCoordinates.SetEta(etaval); return *this;}`

``` ------ Operations combining two vectors ------
-- need to have the specialized version in order to avoid

Return the scalar (dot) product of two displacement vectors.
It is possible to perform the product for any type of vector coordinates,
but they must have the same coordinate system tag

```
DisplacementVector3D Cross( const DisplacementVector3D<OtherCoords,Tag> & v)
```         Return vector (cross) product of two displacement vectors,
as a vector in the coordinate system of this class.
It is possible to perform the product for any type of vector coordinates,
but they must have the same coordinate system tag

```
DisplacementVector3D Cross( const OtherVector & v)
```         Return vector (cross) product of two  vectors,
as a vector in the coordinate system of this class.
It is possible to perform the product for any classes
implementing X(), Y() and Z() member functions

```
DisplacementVector3D & operator*=(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar a)
```         multiply this vector by a scalar quantity

```
DisplacementVector3D & operator/=(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar a)
```         divide this vector by a scalar quantity

```
return operator*( Scalar(-1) )
DisplacementVector3D operator/(ROOT::Math::DisplacementVector3D<ROOT::Math::Cylindrical3D<double>,ROOT::Math::DefaultCoordinateSystemTag>::Scalar a) const
```         Division of a vector with a real number

```
Scalar x() const
``` Methods providing 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(); }`
DisplacementVector3D unit() const
`{return Unit();}`
DisplacementVector3D Cross( const PositionVector3D<T2> & )
```         Cross product involving a position vector is inappropriate

```
DisplacementVector3D & operator=( const DisplacementVector3D<OtherCoords, OtherTag> & )
DisplacementVector3D & operator=( const PositionVector3D<OtherCoords, OtherTag> & )
DisplacementVector3D & operator+=(const DisplacementVector3D<OtherCoords, OtherTag> & )
DisplacementVector3D & operator-=(const DisplacementVector3D<OtherCoords, OtherTag> & )
operator+( DisplacementVector3D<CoordSystem1,U> v1, const DisplacementVector3D<CoordSystem2,U> & v2)
``` ---------- DisplacementVector3D class template ends here ------------

Addition of DisplacementVector3D vectors.
The (coordinate system) type of the returned vector is defined to
be identical to that of the first vector, which is passed by value

```
operator-( DisplacementVector3D<CoordSystem1,U> v1, DisplacementVector3D<CoordSystem2,U> const & v2)
```        Difference between two DisplacementVector3D vectors.
The (coordinate system) type of the returned vector is defined to
be identical to that of the first vector.

```