| library: libPhysics #include "TRotation.h" |
| Inheritance Chart: | |||||||||
|
protected:
TRotation(Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t)
public:
TRotation()
TRotation(const TRotation&)
TRotation(const TQuaternion&)
TRotation operator*(const TRotation&) const
TRotation Inverse() const
virtual ~TRotation()
void AngleAxis(Double_t&, TVector3&) const
static TClass* Class()
Double_t GetXPhi() const
Double_t GetXPsi() const
Double_t GetXTheta() const
Double_t GetYPhi() const
Double_t GetYPsi() const
Double_t GetYTheta() const
TRotation& Invert()
virtual TClass* IsA() const
Bool_t IsIdentity() const
void MakeBasis(TVector3& xAxis, TVector3& yAxis, TVector3& zAxis) const
Bool_t operator!=(const TRotation& m) const
Double_t operator()(int, int) const
TVector3 operator*(const TVector3& p) const
TRotation& operator*=(const TRotation& m)
TRotation& operator=(const TRotation& m)
Bool_t operator==(const TRotation& m) const
TRotation::TRotationRow operator[](int i) const
Double_t PhiX() const
Double_t PhiY() const
Double_t PhiZ() const
TRotation& Rotate(Double_t, const TVector3&)
TRotation& Rotate(Double_t psi, const TVector3* p)
TRotation& RotateAxes(const TVector3& newX, const TVector3& newY, const TVector3& newZ)
TRotation& RotateX(Double_t)
TRotation& RotateXEulerAngles(Double_t phi, Double_t theta, Double_t psi)
TRotation& RotateY(Double_t)
TRotation& RotateYEulerAngles(Double_t phi, Double_t theta, Double_t psi)
TRotation& RotateZ(Double_t)
TRotation& SetToIdentity()
TRotation& SetXAxis(const TVector3& axis)
TRotation& SetXAxis(const TVector3& axis, const TVector3& xyPlane)
TRotation& SetXEulerAngles(Double_t phi, Double_t theta, Double_t psi)
void SetXPhi(Double_t)
void SetXPsi(Double_t)
void SetXTheta(Double_t)
TRotation& SetYAxis(const TVector3& axis)
TRotation& SetYAxis(const TVector3& axis, const TVector3& yzPlane)
TRotation& SetYEulerAngles(Double_t phi, Double_t theta, Double_t psi)
void SetYPhi(Double_t)
void SetYPsi(Double_t)
void SetYTheta(Double_t)
TRotation& SetZAxis(const TVector3& axis)
TRotation& SetZAxis(const TVector3& axis, const TVector3& zxPlane)
virtual void ShowMembers(TMemberInspector& insp, char* parent)
virtual void Streamer(TBuffer& b)
void StreamerNVirtual(TBuffer& b)
Double_t ThetaX() const
Double_t ThetaY() const
Double_t ThetaZ() const
TRotation& Transform(const TRotation& m)
Double_t XX() const
Double_t XY() const
Double_t XZ() const
Double_t YX() const
Double_t YY() const
Double_t YZ() const
Double_t ZX() const
Double_t ZY() const
Double_t ZZ() const
protected:
Double_t fxx
Double_t fxy
Double_t fxz
Double_t fyx
Double_t fyy
Double_t fyz
Double_t fzx
Double_t fzy
Double_t fzz
*-*-*-*-*-*-*-*-*-*-*-*The Physics Vector package *-*-*-*-*-*-*-*-*-*-*-* *-* ========================== * *-* The Physics Vector package consists of five classes: * *-* - TVector2 * *-* - TVector3 * *-* - TRotation * *-* - TLorentzVector * *-* - TLorentzRotation * *-* It is a combination of CLHEPs Vector package written by * *-* Leif Lonnblad, Andreas Nilsson and Evgueni Tcherniaev * *-* and a ROOT package written by Pasha Murat. * *-* for CLHEP see: http://wwwinfo.cern.ch/asd/lhc++/clhep/ * *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
| xx xy xz |
| yx yy yz |
| zx zy zz |
It describes a so called active rotation, i.e. rotation of objects inside a static system of coordinates. In case you want to rotate the frame and want to know the coordinates of objects in the rotated system, you should apply the inverse rotation to the objects. If you want to transform coordinates from the rotated frame to the original frame you have to apply the direct transformation.
A rotation around a specified axis means counterclockwise rotation around
the positive direction of the axis.
There is no direct way to to set the matrix elements - to ensure that a TRotation object always describes a real rotation. But you can get the values by the member functions XX()..ZZ() or the (,) operator:
Double_t xx = r.XX(); // the
same as xx=r(0,0)
xx
= r(0,0);
if (r==m) {...} // test for equality
if (r!=m) {..} // test for inequality
if (r.IsIdentity()) {...} // test for identity
| 1 0
0 |
Rx(a) = | 0 cos(a) -sin(a) |
| 0 sin(a) cos(a)
|
| cos(a) 0 sin(a)
|
Ry(a) = | 0 1
0 |
| -sin(a) 0 cos(a) |
| cos(a) -sin(a) 0 |
Rz(a) = | sin(a) cos(a) 0 |
| 0
0 1 |
and are implemented as member functions RotateX(), RotateY()
and RotateZ():
r.RotateX(TMath::Pi()); // rotation around the x-axis
r.Rotate(TMath::Pi()/3,TVector3(3,4,5));
It is possible to find a unit vector and an angle, which describe the same rotation as the current one:
Double_t angle;
TVector3 axis;
r.GetAngleAxis(angle,axis);
TVector3 newX(0,1,0);
TVector3 newY(0,0,1);
TVector3 newZ(1,0,0);
a.RotateAxes(newX,newY,newZ);
Member functions ThetaX(), ThetaY(), ThetaZ(), PhiX(), PhiY(),PhiZ() return azimuth and polar angles of the rotated axes:
Double_t tx,ty,tz,px,py,pz;
tx= a.ThetaX();
...
pz= a.PhiZ();
r = r2 * r1;
| x' | | xx xy xz | | x |
| y' | = | yx yy yz | | y |
| z' | | zx zy zz | | z |
e.g.:
TVector3 v(1,1,1);
v = r * v;
You can also use the Transform() member function or the operator
*= of the
TVector3 class:
TVector3 v;
TRotation r;
v.Transform(r);
v *= r; //Attention v = r * v
Constructor for a rotation based on a Quaternion if magnitude of quaternion is null, creates identity rotation if quaternion is non-unit, creates rotation corresponding to the normalized (unit) quaternion
Rotate using the x-convention (Landau and Lifshitz, Goldstein, &c) by doing the explicit rotations. This is slightly less efficient than directly applying the rotation, but makes the code much clearer. My presumption is that this code is not going to be a speed bottle neck.
Rotate using the y-convention.
Make the zAxis into a unit variable.
void ~TRotation()
Double_t XX() const
Double_t XY() const
Double_t XZ() const
Double_t YX() const
Double_t YY() const
Double_t YZ() const
Double_t ZX() const
Double_t ZY() const
Double_t ZZ() const
TRotation::TRotationRow operator[](int i) const
Double_t operator()(int, int) const
TRotation& operator=(const TRotation& m)
Bool_t operator==(const TRotation& m) const
Bool_t operator!=(const TRotation& m) const
Bool_t IsIdentity() const
TVector3 operator*(const TVector3& p) const
TRotation operator*(const TRotation&) const
TRotation& operator*=(const TRotation& m)
TRotation& Transform(const TRotation& m)
TRotation Inverse() const
TRotation& Invert()
TRotation& Rotate(Double_t psi, const TVector3* p)
TRotation& SetToIdentity()
TClass* Class()
TClass* IsA() const
void ShowMembers(TMemberInspector& insp, char* parent)
void Streamer(TBuffer& b)
void StreamerNVirtual(TBuffer& b)