s
To avoid exposing templated parameter to the users, typedefs are defined for all types of vectors based an double's and float's. To use them, one must include the header file Math/Vector3D.h. The following typedef's, defined in the header file Math/Vector3Dfwd.h, are available for the different instantiations of the template class ROOT::Math::DisplacementVector3D:
- ROOT::Math::XYZVector vector based on x,y,z coordinates (cartesian) in double precision
- ROOT::Math::XYZVectorF vector based on x,y,z coordinates (cartesian) in float precision
- ROOT::Math::Polar3DVector vector based on r,theta,phi coordinates (polar) in double precision
- ROOT::Math::Polar3DVectorF vector based on r,theta,phi coordinates (polar) in float precision
- ROOT::Math::RhoZPhiVector vector based on rho, z,phi coordinates (cylindrical) in double precision
- ROOT::Math::RhoZPhiVectorF vector based on rho, z,phi coordinates (cylindrical) in float precision
- ROOT::Math::RhoEtaPhiVector vector based on rho,eta,phi coordinates (cylindrical using eta instead of z) in double precision
- ROOT::Math::RhoEtaPhiVectorF vector based on rho,eta,phi coordinates (cylindrical using eta instead of z) in float precision
Constructors and Assignment
The following declarations are available:
XYZVector v1; // create an empty vector (x = 0, y = 0, z = 0)
XYZVector v2( 1,2,3); // create a vector with x=1, y = 2, z = 3;
Polar3DVector v3( 1, PI/2, PI); // create a vector with r = 1, theta = PI/2 and phi=PI
RhoEtaPHiVector v4( 1, 2, PI) // create a vector with rho= 1, eta = 2, phi = PI
Note that each type of vector is constructed by passing its coordinates representations, so a XYZVector(1,2,3) is different from a Polar3DVector(1,2,3).
In addition the Vector classes can be constructed by any vector, which implements the accessors x(), y() and z(). This con be another Vector3D based on a different coordinate system types or even any vector of a different package, like the CLHEP HepThreeVector that implements the required signatures.
XYZVector v1(1,2,3);
RhoEtaPhiVector r2(v1);
CLHEP::HepThreeVector q(1,2,3);
XYZVector v3(q)
Coordinate Accessors
All the same coordinate accessors are available through the interface of the class ROOT::Math::DisplacementVector3D. For example:
v1.X(); v1.X(); v1.Z() // returns cartesian components for the cartesian vector v1
v1.Rho(); v1.Eta(); v1.Phi() // returns cylindrical components for the cartesian vector v1
r2.X(); r2.Y(); r2.Z() // returns cartesian components for the cylindrical vector r2
In addition, all the 3 coordinates of the vector can be retrieved with the GetCoordinates method:
double d[3];
v1.GetCoordinates(d); // fill d array with (x,y,z) components of v1
r2.GetCoordinates(d); // fill d array with (r,eta,phi) components of r2
std::vector <double>vc(3);
v1.GetCoordinates(vc.begin(),vc.end()); // fill std::vector with (x,y,z) components of v1</double>
To get more information on all the coordinate accessors see the reference documentation of ROOT::Math::DisplacementVector3D.
Setter Methods
One can set only all the three coordinates via:
v1.SetCoordinates(c1,c2,c3); // sets the (x,y,z) for a XYZVector
r2.SetCoordinates(c1,c2,c3); // sets r,theta,phi for a Polar3DVector
r2.SetXYZ(x,y,z); // sets the three cartesian components for the Polar3DVector
Single coordinate setter methods are available for the basic vector coordinates, like SetX() for a XYZVector or SetR() for a polar vector. Attempting to do a SetX() on a polar vector will not compile.
XYZVector v1; v1.SetX(1) // OK setting x for a Cartesian vector
Polar3DVector v2; v2.SetX(1) // ERROR: cannot set X for a Polar vector. Method will not compile
v2.SetR(1) // OK setting r for a Polar vector
In addition there are setter methods from C arrays or iterators.
double d[3] = {1.,2.,3.};
XYZVector v;
v.SetCoordinates(d); // set (x,y,z) components of v using values from d
or for example from an std::vector using the iterator
std::vector <double>w(3);
v.SetCoordinates(w.begin(),w.end()); // set (x,y,z) components of v using values from w</double>
Arithmetic Operations
The following operations are possible between Vector classes, even of different coordinate system types: ( v1,v2 are any type of ROOT::Math::DisplacementVector3D classes, v3 is the same type of v1; a is a scalar value)
v1 += v2;
v1 -= v2;
v1 = - v2;
v1 *= a;
v1 /= a;
v2 = a * v1;
v2 = v1 / a;
v2 = v1 * a;
v3 = v1 + v2;
v3 = v1 - v2;
Comparison
For v1 and v2 of the same type (same coordinate system and same scalar type):
Dot and Cross Product
We support the dot and cross products, through the Dot() and Cross() method, with any Vector (q) implementing x(), y() and z()
XYZVector v1(x,y,z);
double s = v1.Dot(q);
XYZVector v2 = v1.Cross(q);
Note that the multiplication between two vectors using the operator * is not supported because is ambiguous.
Other Methods
XYZVector u = v1.Unit(); // return unit vector parallel to v1
