TGraphDelaunay generates a Delaunay triangulation of a TGraph2D.
This triangulation code derives from an implementation done by Luke Jones (Royal Holloway, University of London) in April 2002 in the PAW context.
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.
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.
This applet gives a nice practical view of Delaunay triangulation and Voronoi diagram.
Definition at line 30 of file TGraphDelaunay.h.
Public Member Functions | |
TGraphDelaunay () | |
TGraphDelaunay default constructor. | |
TGraphDelaunay (TGraph2D *g) | |
TGraphDelaunay normal constructor. | |
~TGraphDelaunay () override | |
TGraphDelaunay destructor. | |
Double_t | ComputeZ (Double_t x, Double_t y) |
Return the z value corresponding to the (x,y) point in fGraph2D. | |
void | FindAllTriangles () |
Attempt to find all the Delaunay triangles of the point set. | |
TGraph2D * | GetGraph2D () const |
Double_t | GetMarginBinsContent () const |
Int_t * | GetMTried () const |
Int_t | GetNdt () const |
Int_t * | GetNTried () const |
Int_t * | GetPTried () const |
Double_t * | GetXN () const |
Double_t | GetXNmax () const |
Double_t | GetXNmin () const |
Double_t * | GetYN () const |
Double_t | GetYNmax () const |
Double_t | GetYNmin () const |
Double_t | Interpolate (Double_t x, Double_t y) |
Finds the Delaunay triangle that the point (xi,yi) sits in (if any) and calculate a z-value for it by linearly interpolating the z-values that make up that triangle. | |
TClass * | IsA () const override |
void | SetMarginBinsContent (Double_t z=0.) |
Sets the histogram bin height for points lying outside the convex hull ie: the bins in the margin. | |
void | SetMaxIter (Int_t n=100000) |
Defines the number of triangles tested for a Delaunay triangle (number of iterations) before abandoning the search. | |
void | Streamer (TBuffer &) override |
Stream an object of class TObject. | |
void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
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TNamed () | |
TNamed (const char *name, const char *title) | |
TNamed (const TNamed &named) | |
TNamed copy ctor. | |
TNamed (const TString &name, const TString &title) | |
virtual | ~TNamed () |
TNamed destructor. | |
void | Clear (Option_t *option="") override |
Set name and title to empty strings (""). | |
TObject * | Clone (const char *newname="") const override |
Make a clone of an object using the Streamer facility. | |
Int_t | Compare (const TObject *obj) const override |
Compare two TNamed objects. | |
void | Copy (TObject &named) const override |
Copy this to obj. | |
virtual void | FillBuffer (char *&buffer) |
Encode TNamed into output buffer. | |
const char * | GetName () const override |
Returns name of object. | |
const char * | GetTitle () const override |
Returns title of object. | |
ULong_t | Hash () const override |
Return hash value for this object. | |
TClass * | IsA () const override |
Bool_t | IsSortable () const override |
void | ls (Option_t *option="") const override |
List TNamed name and title. | |
TNamed & | operator= (const TNamed &rhs) |
TNamed assignment operator. | |
void | Print (Option_t *option="") const override |
Print TNamed name and title. | |
virtual void | SetName (const char *name) |
Set the name of the TNamed. | |
virtual void | SetNameTitle (const char *name, const char *title) |
Set all the TNamed parameters (name and title). | |
virtual void | SetTitle (const char *title="") |
Set the title of the TNamed. | |
virtual Int_t | Sizeof () const |
Return size of the TNamed part of the TObject. | |
void | Streamer (TBuffer &) override |
Stream an object of class TObject. | |
void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
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TObject () | |
TObject constructor. | |
TObject (const TObject &object) | |
TObject copy ctor. | |
virtual | ~TObject () |
TObject destructor. | |
void | AbstractMethod (const char *method) const |
Use this method to implement an "abstract" method that you don't want to leave purely abstract. | |
virtual void | AppendPad (Option_t *option="") |
Append graphics object to current pad. | |
virtual void | Browse (TBrowser *b) |
Browse object. May be overridden for another default action. | |
ULong_t | CheckedHash () |
Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. | |
virtual const char * | ClassName () const |
Returns name of class to which the object belongs. | |
virtual void | Delete (Option_t *option="") |
Delete this object. | |
virtual Int_t | DistancetoPrimitive (Int_t px, Int_t py) |
Computes distance from point (px,py) to the object. | |
virtual void | Draw (Option_t *option="") |
Default Draw method for all objects. | |
virtual void | DrawClass () const |
Draw class inheritance tree of the class to which this object belongs. | |
virtual TObject * | DrawClone (Option_t *option="") const |
Draw a clone of this object in the current selected pad with: gROOT->SetSelectedPad(c1) . | |
virtual void | Dump () const |
Dump contents of object on stdout. | |
virtual void | Error (const char *method, const char *msgfmt,...) const |
Issue error message. | |
virtual void | Execute (const char *method, const char *params, Int_t *error=nullptr) |
Execute method on this object with the given parameter string, e.g. | |
virtual void | Execute (TMethod *method, TObjArray *params, Int_t *error=nullptr) |
Execute method on this object with parameters stored in the TObjArray. | |
virtual void | ExecuteEvent (Int_t event, Int_t px, Int_t py) |
Execute action corresponding to an event at (px,py). | |
virtual void | Fatal (const char *method, const char *msgfmt,...) const |
Issue fatal error message. | |
virtual TObject * | FindObject (const char *name) const |
Must be redefined in derived classes. | |
virtual TObject * | FindObject (const TObject *obj) const |
Must be redefined in derived classes. | |
virtual Option_t * | GetDrawOption () const |
Get option used by the graphics system to draw this object. | |
virtual const char * | GetIconName () const |
Returns mime type name of object. | |
virtual char * | GetObjectInfo (Int_t px, Int_t py) const |
Returns string containing info about the object at position (px,py). | |
virtual Option_t * | GetOption () const |
virtual UInt_t | GetUniqueID () const |
Return the unique object id. | |
virtual Bool_t | HandleTimer (TTimer *timer) |
Execute action in response of a timer timing out. | |
Bool_t | HasInconsistentHash () const |
Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. | |
virtual void | Info (const char *method, const char *msgfmt,...) const |
Issue info message. | |
virtual Bool_t | InheritsFrom (const char *classname) const |
Returns kTRUE if object inherits from class "classname". | |
virtual Bool_t | InheritsFrom (const TClass *cl) const |
Returns kTRUE if object inherits from TClass cl. | |
virtual void | Inspect () const |
Dump contents of this object in a graphics canvas. | |
void | InvertBit (UInt_t f) |
Bool_t | IsDestructed () const |
IsDestructed. | |
virtual Bool_t | IsEqual (const TObject *obj) const |
Default equal comparison (objects are equal if they have the same address in memory). | |
virtual Bool_t | IsFolder () const |
Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). | |
R__ALWAYS_INLINE Bool_t | IsOnHeap () const |
R__ALWAYS_INLINE Bool_t | IsZombie () const |
void | MayNotUse (const char *method) const |
Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). | |
virtual Bool_t | Notify () |
This method must be overridden to handle object notification (the base implementation is no-op). | |
void | Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const |
Use this method to declare a method obsolete. | |
void | operator delete (void *ptr) |
Operator delete. | |
void | operator delete (void *ptr, void *vp) |
Only called by placement new when throwing an exception. | |
void | operator delete[] (void *ptr) |
Operator delete []. | |
void | operator delete[] (void *ptr, void *vp) |
Only called by placement new[] when throwing an exception. | |
void * | operator new (size_t sz) |
void * | operator new (size_t sz, void *vp) |
void * | operator new[] (size_t sz) |
void * | operator new[] (size_t sz, void *vp) |
TObject & | operator= (const TObject &rhs) |
TObject assignment operator. | |
virtual void | Paint (Option_t *option="") |
This method must be overridden if a class wants to paint itself. | |
virtual void | Pop () |
Pop on object drawn in a pad to the top of the display list. | |
virtual Int_t | Read (const char *name) |
Read contents of object with specified name from the current directory. | |
virtual void | RecursiveRemove (TObject *obj) |
Recursively remove this object from a list. | |
void | ResetBit (UInt_t f) |
virtual void | SaveAs (const char *filename="", Option_t *option="") const |
Save this object in the file specified by filename. | |
virtual void | SavePrimitive (std::ostream &out, Option_t *option="") |
Save a primitive as a C++ statement(s) on output stream "out". | |
void | SetBit (UInt_t f) |
void | SetBit (UInt_t f, Bool_t set) |
Set or unset the user status bits as specified in f. | |
virtual void | SetDrawOption (Option_t *option="") |
Set drawing option for object. | |
virtual void | SetUniqueID (UInt_t uid) |
Set the unique object id. | |
void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
virtual void | SysError (const char *method, const char *msgfmt,...) const |
Issue system error message. | |
R__ALWAYS_INLINE Bool_t | TestBit (UInt_t f) const |
Int_t | TestBits (UInt_t f) const |
virtual void | UseCurrentStyle () |
Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. | |
virtual void | Warning (const char *method, const char *msgfmt,...) const |
Issue warning message. | |
virtual Int_t | Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) |
Write this object to the current directory. | |
virtual Int_t | Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const |
Write this object to the current directory. | |
Static Public Member Functions | |
static TClass * | Class () |
static const char * | Class_Name () |
static constexpr Version_t | Class_Version () |
static const char * | DeclFileName () |
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static TClass * | Class () |
static const char * | Class_Name () |
static constexpr Version_t | Class_Version () |
static const char * | DeclFileName () |
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static TClass * | Class () |
static const char * | Class_Name () |
static constexpr Version_t | Class_Version () |
static const char * | DeclFileName () |
static Longptr_t | GetDtorOnly () |
Return destructor only flag. | |
static Bool_t | GetObjectStat () |
Get status of object stat flag. | |
static void | SetDtorOnly (void *obj) |
Set destructor only flag. | |
static void | SetObjectStat (Bool_t stat) |
Turn on/off tracking of objects in the TObjectTable. | |
Protected Member Functions | |
void | CreateTrianglesDataStructure () |
Function used internally only. | |
Bool_t | Enclose (Int_t T1, Int_t T2, Int_t T3, Int_t Ex) const |
Is point e inside the triangle t1-t2-t3 ? | |
void | FileIt (Int_t P, Int_t N, Int_t M) |
Files the triangle defined by the 3 vertices p, n and m into the fxTried arrays. | |
void | FindHull () |
Finds those points which make up the convex hull of the set. | |
Bool_t | InHull (Int_t E, Int_t X) const |
Is point e inside the hull defined by all points apart from x ? | |
Double_t | InterpolateOnPlane (Int_t TI1, Int_t TI2, Int_t TI3, Int_t E) const |
Finds the z-value at point e given that it lies on the plane defined by t1,t2,t3. | |
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virtual void | DoError (int level, const char *location, const char *fmt, va_list va) const |
Interface to ErrorHandler (protected). | |
void | MakeZombie () |
Protected Attributes | |
Bool_t | fAllTri |
! True if FindAllTriangles() has been performed on fGraph2D | |
Double_t * | fDist |
! Array used to order mass points by distance | |
TGraph2D * | fGraph2D |
! 2D graph containing the user data | |
Int_t * | fHullPoints |
! Hull points of size fNhull | |
Bool_t | fInit |
! True if CreateTrianglesDataStructure() and FindHull() have been performed | |
Int_t | fMaxIter |
! Maximum number of iterations to find Delaunay triangles | |
Int_t * | fMTried |
! | |
Int_t | fNdt |
! Number of Delaunay triangles found | |
Int_t | fNhull |
! Number of points in the hull | |
Int_t | fNpoints |
! Number of data points in fGraph2D | |
Int_t * | fNTried |
! Delaunay triangles storage of size fNdt | |
Int_t * | fOrder |
! Array used to order mass points by distance | |
Int_t * | fPTried |
! | |
Int_t | fTriedSize |
! Real size of the fxTried arrays | |
Double_t * | fX |
! Pointer to fGraph2D->fX | |
Double_t * | fXN |
! fGraph2D vectors normalized of size fNpoints | |
Double_t | fXNmax |
! Maximum value of fXN | |
Double_t | fXNmin |
! Minimum value of fXN | |
Double_t | fXoffset |
! | |
Double_t | fXScaleFactor |
! | |
Double_t * | fY |
! Pointer to fGraph2D->fY | |
Double_t * | fYN |
! fGraph2D vectors normalized of size fNpoints | |
Double_t | fYNmax |
! Maximum value of fYN | |
Double_t | fYNmin |
! Minimum value of fYN | |
Double_t | fYoffset |
! Parameters used to normalize user data | |
Double_t | fYScaleFactor |
! | |
Double_t * | fZ |
! Pointer to fGraph2D->fZ | |
Double_t | fZout |
! Histogram bin height for points lying outside the convex hull | |
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TString | fName |
TString | fTitle |
Private Member Functions | |
TGraphDelaunay (const TGraphDelaunay &)=delete | |
TGraphDelaunay & | operator= (const TGraphDelaunay &)=delete |
Additional Inherited Members | |
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enum | { kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff } |
enum | { kSingleKey = (1ULL << ( 0 )) , kOverwrite = (1ULL << ( 1 )) , kWriteDelete = (1ULL << ( 2 )) } |
enum | EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) } |
enum | EStatusBits { kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) , kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 13 )) } |
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enum | { kOnlyPrepStep = (1ULL << ( 3 )) } |
#include <TGraphDelaunay.h>
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TGraphDelaunay::TGraphDelaunay | ( | ) |
TGraphDelaunay default constructor.
Definition at line 49 of file TGraphDelaunay.cxx.
TGraphDelaunay::TGraphDelaunay | ( | TGraph2D * | g | ) |
TGraphDelaunay normal constructor.
Definition at line 86 of file TGraphDelaunay.cxx.
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TGraphDelaunay destructor.
Definition at line 123 of file TGraphDelaunay.cxx.
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Definition at line 100 of file TGraphDelaunay.h.
Return the z value corresponding to the (x,y) point in fGraph2D.
Definition at line 148 of file TGraphDelaunay.cxx.
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Function used internally only.
It creates the data structures needed to compute the Delaunay triangles.
Definition at line 178 of file TGraphDelaunay.cxx.
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Definition at line 100 of file TGraphDelaunay.h.
Is point e inside the triangle t1-t2-t3 ?
Definition at line 215 of file TGraphDelaunay.cxx.
Files the triangle defined by the 3 vertices p, n and m into the fxTried arrays.
If these arrays are to small they are automatically expanded.
Definition at line 237 of file TGraphDelaunay.cxx.
void TGraphDelaunay::FindAllTriangles | ( | ) |
Attempt to find all the Delaunay triangles of the point set.
It is not guaranteed that it will fully succeed, and no check is made that it has fully succeeded (such a check would be possible by referencing the points that make up the convex hull). The method is to check if each triangle shares all three of its sides with other triangles. If not, a point is generated just outside the triangle on the side(s) not shared, and a new triangle is found for that point. If this method is not working properly (many triangles are not being found) it's probably because the new points are too far beyond or too close to the non-shared sides. Fiddling with the size of the ‘alittlebit’ parameter may help.
Definition at line 290 of file TGraphDelaunay.cxx.
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Finds those points which make up the convex hull of the set.
If the xy plane were a sheet of wood, and the points were nails hammered into it at the respective coordinates, then if an elastic band were stretched over all the nails it would form the shape of the convex hull. Those nails in contact with it are the points that make up the hull.
Definition at line 421 of file TGraphDelaunay.cxx.
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Definition at line 84 of file TGraphDelaunay.h.
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Definition at line 85 of file TGraphDelaunay.h.
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Definition at line 89 of file TGraphDelaunay.h.
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Definition at line 86 of file TGraphDelaunay.h.
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Definition at line 88 of file TGraphDelaunay.h.
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Definition at line 87 of file TGraphDelaunay.h.
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Definition at line 90 of file TGraphDelaunay.h.
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Definition at line 93 of file TGraphDelaunay.h.
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Definition at line 92 of file TGraphDelaunay.h.
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Definition at line 91 of file TGraphDelaunay.h.
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Definition at line 95 of file TGraphDelaunay.h.
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Definition at line 94 of file TGraphDelaunay.h.
Is point e inside the hull defined by all points apart from x ?
Definition at line 448 of file TGraphDelaunay.cxx.
Finds the Delaunay triangle that the point (xi,yi) sits in (if any) and calculate a z-value for it by linearly interpolating the z-values that make up that triangle.
Definition at line 595 of file TGraphDelaunay.cxx.
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Finds the z-value at point e given that it lies on the plane defined by t1,t2,t3.
Definition at line 556 of file TGraphDelaunay.cxx.
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Reimplemented from TObject.
Definition at line 100 of file TGraphDelaunay.h.
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void TGraphDelaunay::SetMarginBinsContent | ( | Double_t | z = 0. | ) |
Sets the histogram bin height for points lying outside the convex hull ie: the bins in the margin.
Definition at line 943 of file TGraphDelaunay.cxx.
void TGraphDelaunay::SetMaxIter | ( | Int_t | n = 100000 | ) |
Defines the number of triangles tested for a Delaunay triangle (number of iterations) before abandoning the search.
Definition at line 932 of file TGraphDelaunay.cxx.
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Definition at line 100 of file TGraphDelaunay.h.
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! True if FindAllTriangles() has been performed on fGraph2D
Definition at line 64 of file TGraphDelaunay.h.
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! Array used to order mass points by distance
Definition at line 56 of file TGraphDelaunay.h.
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! 2D graph containing the user data
Definition at line 66 of file TGraphDelaunay.h.
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! Hull points of size fNhull
Definition at line 62 of file TGraphDelaunay.h.
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! True if CreateTrianglesDataStructure() and FindHull() have been performed
Definition at line 65 of file TGraphDelaunay.h.
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! Maximum number of iterations to find Delaunay triangles
Definition at line 57 of file TGraphDelaunay.h.
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!
Definition at line 61 of file TGraphDelaunay.h.
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! Number of Delaunay triangles found
Definition at line 39 of file TGraphDelaunay.h.
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! Number of points in the hull
Definition at line 41 of file TGraphDelaunay.h.
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! Number of data points in fGraph2D
Definition at line 40 of file TGraphDelaunay.h.
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! Delaunay triangles storage of size fNdt
Definition at line 60 of file TGraphDelaunay.h.
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! Array used to order mass points by distance
Definition at line 63 of file TGraphDelaunay.h.
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!
Definition at line 59 of file TGraphDelaunay.h.
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! Real size of the fxTried arrays
Definition at line 58 of file TGraphDelaunay.h.
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! Pointer to fGraph2D->fX
Definition at line 42 of file TGraphDelaunay.h.
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! fGraph2D vectors normalized of size fNpoints
Definition at line 45 of file TGraphDelaunay.h.
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! Maximum value of fXN
Definition at line 48 of file TGraphDelaunay.h.
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! Minimum value of fXN
Definition at line 47 of file TGraphDelaunay.h.
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!
Definition at line 51 of file TGraphDelaunay.h.
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!
Definition at line 53 of file TGraphDelaunay.h.
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! Pointer to fGraph2D->fY
Definition at line 43 of file TGraphDelaunay.h.
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! fGraph2D vectors normalized of size fNpoints
Definition at line 46 of file TGraphDelaunay.h.
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! Maximum value of fYN
Definition at line 50 of file TGraphDelaunay.h.
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! Minimum value of fYN
Definition at line 49 of file TGraphDelaunay.h.
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! Parameters used to normalize user data
Definition at line 52 of file TGraphDelaunay.h.
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!
Definition at line 54 of file TGraphDelaunay.h.
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! Pointer to fGraph2D->fZ
Definition at line 44 of file TGraphDelaunay.h.
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! Histogram bin height for points lying outside the convex hull
Definition at line 55 of file TGraphDelaunay.h.