THelix

class THelix : public TPolyLine3D

    protected:

      Double_t FindClosestPhase(Double_t phi0, Double_t cosine)
          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 THelix(Double_t* xyz, Double_t* v, Double_t w, Double_t* range = 0, EHelixRangeType rtype = kHelixZ, Double_t* axis = 0)
                 THelix THelix()
                 THelix THelix(const THelix& helix)
           virtual void ~THelix()
                TClass* Class()
           virtual void Copy(TObject& helix)
           virtual void Draw(Option_t* option)
      virtual Option_t* GetOption() const
        virtual TClass* IsA() const
           virtual void Paint(Option_t* option)
           virtual void Print(Option_t* option)
           virtual void SavePrimitive(ofstream& out, Option_t* option)
           virtual void SetAxis(Double_t x, Double_t y, Double_t z)
           virtual void SetAxis(Double_t* axis)
                   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 r1, Double_t r2, EHelixRangeType rtype = kHelixZ)
           virtual void SetRange(Double_t* range, EHelixRangeType rtype = kHelixZ)
           virtual void ShowMembers(TMemberInspector& insp, char* parent)
           virtual void Sizeof3D() const
           virtual void Streamer(TBuffer& b)

  Data Members

    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.

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

 Return total X3D size of this shape with its attributes.

 set the rotational matrix according to the helix axis

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

Inline Functions

          Option_t* GetOption() const
               void Paint(Option_t* option)
               void SetOption(Option_t* option)
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void Streamer(TBuffer& b)