TGraph2D

class TGraph2D : public TNamed, public TAttLine, public TAttFill, public TAttMarker

    protected:

      void Build(Int_t n)

    public:

                       TGraph2D()
                       TGraph2D(Int_t n)
                       TGraph2D(Int_t n, Int_t* x, Int_t* y, Int_t* z)
                       TGraph2D(Int_t n, Float_t* x, Float_t* y, Float_t* z)
                       TGraph2D(Int_t n, Double_t* x, Double_t* y, Double_t* z)
                       TGraph2D(TH2* h2)
                       TGraph2D(const char* name, const char* title, Int_t n, Double_t* x, Double_t* y, Double_t* z)
                       TGraph2D(const char* filename, const char* format = "%lg %lg %lg", Option_t* option = "")
                       TGraph2D(const TGraph2D&)
              TGraph2D operator=(const TGraph2D&)
               virtual ~TGraph2D()
        static TClass* Class()
         virtual Int_t DistancetoPrimitive(Int_t px, Int_t py)
          virtual void Draw(Option_t* option = "")
          virtual void ExecuteEvent(Int_t event, Int_t px, Int_t py)
      virtual TObject* FindObject(const char* name) const
      virtual TObject* FindObject(const TObject* obj) const
         virtual Int_t Fit(const char* formula, Option_t* option = "", Option_t* goption = "")
         virtual Int_t Fit(TF2* f2, Option_t* option = "", Option_t* goption = "")
                TList* GetContourList(Double_t contour)
           TDirectory* GetDirectory() const
      virtual Double_t GetErrorX(Int_t bin) const
      virtual Double_t GetErrorY(Int_t bin) const
      virtual Double_t GetErrorZ(Int_t bin) const
                 TH2D* GetHistogram(Option_t* option = "")
                TList* GetListOfFunctions() const
              Double_t GetMargin() const
                 Int_t GetN() const
                 Int_t GetNpx() const
                 Int_t GetNpy() const
             Double_t* GetX() const
                TAxis* GetXaxis() const
              Double_t GetXmax() const
              Double_t GetXmin() const
             Double_t* GetY() const
                TAxis* GetYaxis() const
              Double_t GetYmax() const
              Double_t GetYmin() const
             Double_t* GetZ() const
                TAxis* GetZaxis() const
              Double_t GetZmax() const
              Double_t GetZmin() const
              Double_t Interpolate(Double_t x, Double_t y)
       virtual TClass* IsA() const
          virtual void Paint(Option_t* option = "")
                  TH1* Project(Option_t* option = "x") const
                 Int_t RemovePoint(Int_t ipoint)
          virtual void SavePrimitive(ofstream& out, Option_t* option)
          virtual void SetDirectory(TDirectory* dir)
          virtual void SetHistogram(TH2* h)
                  void SetMargin(Double_t m = 0.1)
                  void SetMarginBinsContent(Double_t z = 0.)
                  void SetMaximum(Double_t maximum = -1111)
                  void SetMaxIter(Int_t n = 100000)
                  void SetMinimum(Double_t minimum = -1111)
          virtual void SetName(const char* name)
                  void SetNpx(Int_t npx = 40)
                  void SetNpy(Int_t npx = 40)
                  void SetPoint(Int_t point, Double_t x, Double_t y, Double_t z)
          virtual void SetTitle(const char* title = "")
          virtual void ShowMembers(TMemberInspector& insp, char* parent)
          virtual void Streamer(TBuffer& b)
                  void StreamerNVirtual(TBuffer& b)

Data Members

    private:

      Bool_t fUserHisto  True when SetHistogram has been called

    protected:

                     Int_t fNpoints    Number of points in the data set
                     Int_t fNpx        Number of bins along X in fHistogram
                     Int_t fNpy        Number of bins along Y in fHistogram
                     Int_t fMaxIter    Maximum number of iterations to find Delaunay t>
                     Int_t fSize       !Real size of fX, fY and fZ
                 Double_t* fX          [fNpoints]
                 Double_t* fY          [fNpoints] Data set to be plotted
                 Double_t* fZ          [fNpoints]
                  Double_t fMinimum    Minimum value for plotting along z
                  Double_t fMaximum    Maximum value for plotting along z
                  Double_t fMargin     Extra space (in %) around interpolated area for fHistogram
                  Double_t fZout       fHistogram bin height for points lying outside the interpolated area
                    TList* fFunctions  Pointer to list of functions (fits and user)
                     TH2D* fHistogram  !2D histogram of z values linearly interpolated
               TDirectory* fDirectory  !Pointer to directory holding this 2D graph
      TVirtualHistPainter* fPainter    !pointer to histogram painter

Class Description

 A Graph2D is a graphics object made of three arrays X, Y and Z with the same
 number of points each.

 This class has different constructors:

 1) With an array's dimension and three arrays x, y, and z:

    TGraph2D *g = new TGraph2D(n, x, y, z);

    x, y, z arrays can be doubles, floats, or ints.

 2) With an array's dimension only:

    TGraph2D *g = new TGraph2D(n);

    The internal arrays are then filled with SetPoint. The following line
    fills the the internal arrays at the position "i" with the values x,y,z.

    g->SetPoint(i, x, y, z);

 3) Without parameters:

    TGraph2D *g = new TGraph2D();

    again SetPoint must be used to fill the internal arrays.

 4) From a file:

    TGraph2D *g = new TGraph2D("graph.dat");

    Arrays are read from the ASCII file "graph.dat" according to a specifies
    format. The format's default value is "%lg %lg %lg"

 Note that in any of these three cases, SetPoint can be used to change a data
 point or add a new one. If the data point index (i) is greater than the
 current size of the internal arrays, they are automatically extended.

 Specific drawing options can be used to paint a TGraph2D:
   "TRI"  : The Delaunay triangles are drawn using filled area.
            An hidden surface drawing technique is used. The surface is
            painted with the current fill area color. The edges of each
            triangles are painted with the current line color.
   "TRIW" : The Delaunay triangles are drawn as wire frame
   "TRI1" : The Delaunay triangles are painted with color levels. The edges
            of each triangles are painted with the current line color.
   "TRI2" : the Delaunay triangles are painted with color levels.
   "P"    : Draw a marker at each vertex
   "P0"   : Draw a circle at each vertex. Each circle background is white.

 A TGraph2D can be also drawn with ANY options valid to draw a 2D histogram.

 When a TGraph2D is drawn with one of the 2D histogram drawing option,
 a intermediate 2D histogram is filled using the Delaunay triangles
 technique to interpolate the data set.

 TGraph2D linearly interpolate a Z value for any (X,Y) point given some
 existing (X,Y,Z) points. The existing (X,Y,Z) points can be randomly
 scattered. The algorithm works by joining the existing points to make
 Delaunay triangles in (X,Y). These are then used to define flat planes
 in (X,Y,Z) over which to interpolate. The interpolated surface thus takes
 the form of tessellating triangles at various angles. Output can take the
 form of a 2D histogram or a vector. The triangles found can be drawn in 3D.

 This software cannot be guaranteed to work under all circumstances. They
 were originally written to work with a few hundred points in an XY space
 with similar X and Y ranges.

  The picture below has been generated by the following macro:

{
   TCanvas *c = new TCanvas("c","Graph2D example",0,0,700,600);
   Double_t x, y, z, P = 6.;
   Int_t np = 200;
   TGraph2D *dt = new TGraph2D();
   TRandom *r = new TRandom();
   for (Int_t N=0; N<np; N++) {
      x = 2*P*(r->Rndm(N))-P;
      y = 2*P*(r->Rndm(N))-P;
      z = (sin(x)/x)*(sin(y)/y)+0.2;
      dt->SetPoint(N,x,y,z);
   }
   gStyle->SetPalette(1);
   dt->Draw("surf1");
}

 A more complete example can be find in $ROOTSYS/tutorial/graph2dfit.C. It
 produces the following output:

 Definition of Delaunay triangulation (After B. Delaunay):
 For a set S of points in the Euclidean plane, the unique triangulation DT(S)
 of S such that no point in S is inside the circumcircle of any triangle in
 DT(S). DT(S) is the dual of the Voronoi diagram of S.
 If n is the number of points in S, the Voronoi diagram of S is the partitioning
 of the plane containing S points into n convex polygons such that each polygon
 contains exactly one point and every point in a given polygon is closer to its
 central point than to any other. A Voronoi diagram is sometimes also known as
 a Dirichlet tessellation.

 Graph2D default constructor

 Graph2D constructor with three vectors of ints as input.

 Graph2D constructor with three vectors of floats as input.

 Graph2D constructor with three vectors of doubles as input.

 Graph2D constructor with a TH2 (h2) as input.
 Only the h2's bins within the X and Y axis ranges are used.

 Graph2D constructor with name, title and three vectors of doubles as input.
 name   : name of 2D graph (avoid blanks)
 title  : 2D graph title
          if title is of the form "stringt;stringx;stringy;stringz"
          the 2D graph title is set to stringt, the x axis title to stringy,
          the y axis title to stringy,etc

 Graph2D constructor. The arrays fX, fY and fZ should be filled via
 calls to SetPoint

 Graph2D constructor reading input from filename
 filename is assumed to contain at least three columns of numbers

 Graph2D copy constructor.

 TGraph2D destructor.

 Creates the 2D graph basic data structure

 Computes distance from point px,py to a graph

 Specific drawing options can be used to paint a TGraph2D:
   "TRI"  : The Delaunay triangles are drawn using filled area.
            An hidden surface drawing technique is used. The surface is
            painted with the current fill area color. The edges of each
            triangles are painted with the current line color.
   "TRIW" : The Delaunay triangles are drawn as wire frame
   "TRI1" : The Delaunay triangles are painted with color levels. The edges
            of each triangles are painted with the current line color.
   "TRI2" : the Delaunay triangles are painted with color levels.
   "P"    : Draw a marker at each vertex
   "P0"   : Draw a circle at each vertex. Each circle background is white.

 A TGraph2D can be also drawn with ANY options valid to draw a 2D histogram.

 When a TGraph2D is drawn with one of the 2D histogram drawing option,
 a intermediate 2D histogram is filled using the Delaunay triangles
 technique to interpolate the data set.

 Executes action corresponding to one event

 search object named name in the list of functions

 search object obj in the list of functions

 Fits this graph with function with name fname
 Predefined functions such as gaus, expo and poln are automatically
 created by ROOT.
 fname can also be a formula, accepted by the linear fitter (linear parts divided
 by "++" sign), for example "x++sin(x)" for fitting "[0]*x+[1]*sin(x)"

 Fits this 2D graph with function f2

  f2 is an already predefined function created by TF2.
  Predefined functions such as gaus, expo and poln are automatically
  created by ROOT.

  The list of fit options is given in parameter option.
     option = "W"  Set all errors to 1
            = "U" Use a User specified fitting algorithm (via SetFCN)
            = "Q" Quiet mode (minimum printing)
            = "V" Verbose mode (default is between Q and V)
            = "R" Use the Range specified in the function range
            = "N" Do not store the graphics function, do not draw
            = "0" Do not plot the result of the fit. By default the fitted function
                  is drawn unless the option"N" above is specified.
            = "+" Add this new fitted function to the list of fitted functions
                  (by default, any previous function is deleted)
            = "C" In case of linear fitting, not calculate the chisquare
                  (saves time)
            = "ROB" In case of linear fitting, compute the LTS regression
                     coefficients (robust(resistant) regression), using
                     the default fraction of good points
              "ROB=0.x" - compute the LTS regression coefficients, using
                           0.x as a fraction of good points

  In order to use the Range option, one must first create a function
  with the expression to be fitted. For example, if your graph2d
  has a defined range between -4 and 4 and you want to fit a gaussian
  only in the interval 1 to 3, you can do:
       TF2 *f2 = new TF2("f2","gaus",1,3);
       graph2d->Fit("f2","R");


  Setting initial conditions
  ==========================
  Parameters must be initialized before invoking the Fit function.
  The setting of the parameter initial values is automatic for the
  predefined functions : poln, expo, gaus. One can however disable
  this automatic computation by specifying the option "B".
  You can specify boundary limits for some or all parameters via
       f2->SetParLimits(p_number, parmin, parmax);
  if parmin>=parmax, the parameter is fixed
  Note that you are not forced to fix the limits for all parameters.
  For example, if you fit a function with 6 parameters, you can do:
    func->SetParameters(0,3.1,1.e-6,0.1,-8,100);
    func->SetParLimits(4,-10,-4);
    func->SetParLimits(5, 1,1);
  With this setup, parameters 0->3 can vary freely
  Parameter 4 has boundaries [-10,-4] with initial value -8
  Parameter 5 is fixed to 100.

  Fit range
  =========
  The fit range can be specified in two ways:
    - specify rxmax > rxmin (default is rxmin=rxmax=0)
    - specify the option "R". In this case, the function will be taken
      instead of the full graph range.

  Changing the fitting function
  =============================
  By default the fitting function Graph2DFitChisquare is used.
  To specify a User defined fitting function, specify option "U" and
  call the following functions:
    TVirtualFitter::Fitter(mygraph)->SetFCN(MyFittingFunction)
  where MyFittingFunction is of type:
  extern void MyFittingFunction(Int_t &npar, Double_t *gin, Double_t &f, Double_t *u, Int_t flag);

  Associated functions
  ====================
  One or more object (typically a TF2*) can be added to the list
  of functions (fFunctions) associated to each graph.
  When TGraph::Fit is invoked, the fitted function is added to this list.
  Given a graph gr, one can retrieve an associated function
  with:  TF2 *myfunc = gr->GetFunction("myfunc");

  Access to the fit results
  =========================
  If the graph is made persistent, the list of
  associated functions is also persistent. Given a pointer (see above)
  to an associated function myfunc, one can retrieve the function/fit
  parameters with calls such as:
    Double_t chi2 = myfunc->GetChisquare();
    Double_t par0 = myfunc->GetParameter(0); //value of 1st parameter
    Double_t err0 = myfunc->GetParError(0);  //error on first parameter

  Fit Statistics
  ==============
  You can change the statistics box to display the fit parameters with
  the TStyle::SetOptFit(mode) method. This mode has four digits.
  mode = pcev  (default = 0111)
    v = 1;  print name/values of parameters
    e = 1;  print errors (if e=1, v must be 1)
    c = 1;  print Chisquare/Number of degress of freedom
    p = 1;  print Probability

  For example: gStyle->SetOptFit(1011);
  prints the fit probability, parameter names/values, and errors.
  You can change the position of the statistics box with these lines
  (where g is a pointer to the TGraph):

  Root > TPaveStats *st = (TPaveStats*)g->GetListOfFunctions()->FindObject("stats")
  Root > st->SetX1NDC(newx1); //new x start position
  Root > st->SetX2NDC(newx2); //new x end position

 Get x axis of the graph.

 Get y axis of the graph.

 Get z axis of the graph.

 Returns the X and Y graphs building a contour. A contour level may
 consist in several parts not connected to each other. This function
 returns them in a graphs' list.

 This function is called by Graph2DFitChisquare.
 It always returns a negative value. Real implementation in TGraph2DErrors

 This function is called by Graph2DFitChisquare.
 It always returns a negative value. Real implementation in TGraph2DErrors

 This function is called by Graph2DFitChisquare.
 It always returns a negative value. Real implementation in TGraph2DErrors

 By default returns a pointer to the Delaunay histogram. If fHistogram
 doesn't exist, books the 2D histogram fHistogram with a margin around
 the hull. Calls TGraphDelaunay::Interpolate at each bin centre to build up
 an interpolated 2D histogram.
 If the "empty" option is selected, returns an empty histogram booked with
 the limits of fX, fY and fZ. This option is used when the data set is
 drawn with markers only. In that particular case there is no need to
 find the Delaunay triangles.

 Returns the X maximum

 Returns the X minimum

 Returns the Y maximum

 Returns the Y minimum

 Returns the Z maximum

 Returns the Z minimum

 Finds the z value at the position (x,y) thanks to
 the Delaunay interpolation.

 Paints this 2D graph with its current attributes

 Projects a 2-d graph into 1 or 2-d histograms depending on the
 option parameter
 option may contain a combination of the characters x,y,z
 option = "x" return the x projection into a TH1D histogram
 option = "y" return the y projection into a TH1D histogram
 option = "xy" return the x versus y projection into a TH2D histogram
 option = "yx" return the y versus x projection into a TH2D histogram

 Deletes point number ipoint

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

 By default when an 2D graph is created, it is added to the list
 of 2D graph objects in the current directory in memory.
 Remove reference to this 2D graph from current directory and add
 reference to new directory dir. dir can be 0 in which case the
 2D graph does not belong to any directory.

 Sets the histogram to be filled

 Sets the extra space (in %) around interpolated area for the 2D histogram

 Sets the histogram bin height for points lying outside the TGraphDelaunay
 convex hull ie: the bins in the margin.

 Changes the name of this 2D graph

 Sets the number of bins along X used to draw the function

 Sets the number of bins along Y used to draw the function

 Sets point number n.
 If n is greater than the current size, the arrays are automatically
 extended.

 Sets graph title

 Stream a class object

Inline Functions

           TGraph2D operator=(const TGraph2D&)
        TDirectory* GetDirectory() const
              Int_t GetNpx() const
              Int_t GetNpy() const
             TList* GetListOfFunctions() const
           Double_t GetMargin() const
              Int_t GetN() const
          Double_t* GetX() const
          Double_t* GetY() const
          Double_t* GetZ() const
               void SetMaxIter(Int_t n = 100000)
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void StreamerNVirtual(TBuffer& b)