THelix

    protected:

      Double_t FindClosestPhase(Double_t phi0, Double_t cosine)
       THelix& operator=(const THelix&)
          void SetRotMatrix()

    public:

                        THelix()
                        THelix(Double_t x, Double_t y, Double_t z, Double_t vx, Double_t vy, Double_t vz, Double_t w)
                        THelix(Double_t* xyz, Double_t* v, Double_t w, Double_t* range = 0, EHelixRangeType rtype = kHelixZ, Double_t* axis = 0)
                        THelix(const THelix& helix)
                virtual ~THelix()
         static TClass* Class()
           virtual void Copy(TObject& helix) const
           virtual void Draw(Option_t* option = "")
      virtual Option_t* GetOption() const
        virtual TClass* IsA() const
           virtual void Print(Option_t* option = "") const
           virtual void SavePrimitive(ostream& out, Option_t* option = "")
           virtual void SetAxis(Double_t* axis)
           virtual void SetAxis(Double_t x, Double_t y, Double_t z)
                   void SetHelix(Double_t* xyz, Double_t* v, Double_t w, Double_t* range = 0, EHelixRangeType type = kUnchanged, Double_t* axis = 0)
           virtual void SetOption(Option_t* option = "")
           virtual void SetRange(Double_t* range, EHelixRangeType rtype = kHelixZ)
           virtual void SetRange(Double_t r1, Double_t r2, EHelixRangeType rtype = kHelixZ)
           virtual void ShowMembers(TMemberInspector& insp, char* parent)
           virtual void Streamer(TBuffer& b)
                   void StreamerNVirtual(TBuffer& b)

    protected:

          Double_t fX0        Initial X position
          Double_t fY0        Initial Y position
          Double_t fZ0        Initial Z position
          Double_t fVt        Transverse velocity (constant of motion)
          Double_t fPhi0      Initial phase, so vx0 = fVt*cos(fPhi0)
          Double_t fVz        Z velocity (constant of motion)
          Double_t fW         Angular frequency
          Double_t fAxis[3]   Direction unit vector of the helix axis
       TRotMatrix* fRotMat    Rotation matrix: axis // z  -->  axis // fAxis
          Double_t fRange[2]  Range of helix parameter t
      static Int_t fgMinNSeg  minimal number of segments in polyline

Class Description

______________________________________________________________________________
 Helix is, hmmm, well, a helix.  It has 3 different constructors.

 Comments/suggestions/etc on this class should be sent to the author:
             pyeh@cdfsga.fnal.gov (Ping Yeh)

   If a particle with charge q passes through a point (x,y,z)
   with momentum (px,py,pz) with magnetic field B along an axis (nx,ny,nz),
   this helix can be constrcuted like

      THelix p(x0,y0,z0, px,py,pz, q*B, nx,ny,nz);

     (nx,ny,nz) defaults to (0,0,1).

   A helix in its own frame can be defined with initial position
   (x0,y0,z0) and "velocity" (vx0,vy0,vz0), both 3-vectors, and
   an angular frequency w.  The parametric equation of the helix is

    x = x0 - vt / w * sin(-w * t + phi0)
    y = y0 + vt / w * cos(-w * t + phi0)
    z = z0 + vz * t


   The 'normal constructor' has 6 parameters,

       Example:
                 THelix pl1(xyz0, v0, w, range, rtype, axis);

         where:
             xyz0  : array of initial position
             v0    : array of initial velocity
             w     : angular frequency
             range : helix range
             rtype : kHelixZ specifies allowed drawing range in helix Z direction, i.e., along B field.
                     kLabZ specifies drawing range in lab frame.
                     kHelixX, kHelixY, kLabX, kLabY, kUnchanged ... etc can also be specified
             axis  : helix axis



 A Third constructor uses several default values:

       Example:
   c1 = new TCanvas("c1");
   TView *view = new TView(1);
   view->SetRange(-1,-1,-1,1,1,1);
   THelix *helix = new THelix(0.0, 0.0, 0.0, 1.0, 0.0, 0.3, 10.0);
   helix->Draw();

 will initializes a helix with its axis in Z direction (rtype=kHelixZ).
 range[0] = 0 and range[1] = 1

 Set all helix parameters.

 Helix default constructor.

 Helix normal constructor.

 Helix normal constructor.

 Helix copy constructor.

assignement operator

 Helix destructor.

 Copy this helix to obj.

 Draw this helix with its current attributes.

 Dump this helix with its attributes.

 Save primitive as a C++ statement(s) on output stream out.

 Set a new axis for the helix.  This will make a new rotation matrix.

 Set axis.

 Set a new range for the helix.  This will remake the polyline.

 Set range.

 Set the rotational matrix according to the helix axis.

 Finds the closest phase to phi0 that gives cos(phase) = cosine

 Stream an object of class THelix.