ROOT   6.08/07 Reference Guide
TGraphDelaunay Class Reference

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 32 of file TGraphDelaunay.h.

## Public Member Functions

TGraphDelaunay ()
TGraphDelaunay default constructor. More...

TGraphDelaunay (TGraph2D *g)
TGraphDelaunay normal constructor. More...

virtual ~TGraphDelaunay ()
TGraphDelaunay destructor. More...

Double_t ComputeZ (Double_t x, Double_t y)
Return the z value corresponding to the (x,y) point in fGraph2D. More...

void FindAllTriangles ()
Attempt to find all the Delaunay triangles of the point set. More...

TGraph2DGetGraph2D () const

Double_t GetMarginBinsContent () const

Int_tGetMTried () const

Int_t GetNdt () const

Int_tGetNTried () const

Int_tGetPTried () const

Double_tGetXN () const

Double_t GetXNmax () const

Double_t GetXNmin () const

Double_tGetYN () 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. More...

void SetMarginBinsContent (Double_t z=0.)
Sets the histogram bin height for points lying outside the convex hull ie: the bins in the margin. More...

void SetMaxIter (Int_t n=100000)
Defines the number of triangles tested for a Delaunay triangle (number of iterations) before abandoning the search. More...

Public Member Functions inherited from TNamed
TNamed ()

TNamed (const char *name, const char *title)

TNamed (const TString &name, const TString &title)

TNamed (const TNamed &named)
TNamed copy ctor. More...

virtual ~TNamed ()

virtual void Clear (Option_t *option="")
Set name and title to empty strings (""). More...

virtual TObjectClone (const char *newname="") const
Make a clone of an object using the Streamer facility. More...

virtual Int_t Compare (const TObject *obj) const
Compare two TNamed objects. More...

virtual void Copy (TObject &named) const
Copy this to obj. More...

virtual void FillBuffer (char *&buffer)
Encode TNamed into output buffer. More...

virtual const char * GetName () const
Returns name of object. More...

virtual const char * GetTitle () const
Returns title of object. More...

virtual ULong_t Hash () const
Return hash value for this object. More...

virtual Bool_t IsSortable () const

virtual void ls (Option_t *option="") const
List TNamed name and title. More...

TNamedoperator= (const TNamed &rhs)
TNamed assignment operator. More...

virtual void Print (Option_t *option="") const
Print TNamed name and title. More...

virtual void SetName (const char *name)
Set the name of the TNamed. More...

virtual void SetNameTitle (const char *name, const char *title)
Set all the TNamed parameters (name and title). More...

virtual void SetTitle (const char *title="")
Set the title of the TNamed. More...

virtual Int_t Sizeof () const
Return size of the TNamed part of the TObject. More...

Public Member Functions inherited from TObject
TObject ()
TObject constructor. More...

TObject (const TObject &object)
TObject copy ctor. More...

virtual ~TObject ()
TObject destructor. More...

void AbstractMethod (const char *method) const
Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

Append graphics object to current pad. More...

virtual void Browse (TBrowser *b)
Browse object. May be overridden for another default action. More...

virtual const char * ClassName () const
Returns name of class to which the object belongs. More...

virtual void Delete (Option_t *option="")
Delete this object. More...

virtual Int_t DistancetoPrimitive (Int_t px, Int_t py)
Computes distance from point (px,py) to the object. More...

virtual void Draw (Option_t *option="")
Default Draw method for all objects. More...

virtual void DrawClass () const
Draw class inheritance tree of the class to which this object belongs. More...

virtual TObjectDrawClone (Option_t *option="") const
Draw a clone of this object in the current pad. More...

virtual void Dump () const
Dump contents of object on stdout. More...

virtual void Error (const char *method, const char *msgfmt,...) const
Issue error message. More...

virtual void Execute (const char *method, const char *params, Int_t *error=0)
Execute method on this object with the given parameter string, e.g. More...

virtual void Execute (TMethod *method, TObjArray *params, Int_t *error=0)
Execute method on this object with parameters stored in the TObjArray. More...

virtual void ExecuteEvent (Int_t event, Int_t px, Int_t py)
Execute action corresponding to an event at (px,py). More...

virtual void Fatal (const char *method, const char *msgfmt,...) const
Issue fatal error message. More...

virtual TObjectFindObject (const char *name) const
Must be redefined in derived classes. More...

virtual TObjectFindObject (const TObject *obj) const
Must be redefined in derived classes. More...

virtual Option_tGetDrawOption () const
Get option used by the graphics system to draw this object. More...

virtual const char * GetIconName () const
Returns mime type name of object. More...

virtual char * GetObjectInfo (Int_t px, Int_t py) const
Returns string containing info about the object at position (px,py). More...

virtual Option_tGetOption () const

virtual UInt_t GetUniqueID () const
Return the unique object id. More...

virtual Bool_t HandleTimer (TTimer *timer)
Execute action in response of a timer timing out. More...

virtual void Info (const char *method, const char *msgfmt,...) const
Issue info message. More...

virtual Bool_t InheritsFrom (const char *classname) const
Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t InheritsFrom (const TClass *cl) const
Returns kTRUE if object inherits from TClass cl. More...

virtual void Inspect () const
Dump contents of this object in a graphics canvas. More...

void InvertBit (UInt_t f)

virtual Bool_t IsEqual (const TObject *obj) const
Default equal comparison (objects are equal if they have the same address in memory). More...

virtual Bool_t IsFolder () const
Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

Bool_t IsOnHeap () const

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). More...

virtual Bool_t Notify ()
This method must be overridden to handle object notification. More...

void Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const
Use this method to declare a method obsolete. More...

void operator delete (void *ptr)
Operator delete. More...

void operator delete[] (void *ptr)
Operator delete []. More...

voidoperator new (size_t sz)

voidoperator new (size_t sz, void *vp)

voidoperator new[] (size_t sz)

voidoperator new[] (size_t sz, void *vp)

TObjectoperator= (const TObject &rhs)
TObject assignment operator. More...

virtual void Paint (Option_t *option="")
This method must be overridden if a class wants to paint itself. More...

virtual void Pop ()
Pop on object drawn in a pad to the top of the display list. More...

virtual Int_t Read (const char *name)
Read contents of object with specified name from the current directory. More...

virtual void RecursiveRemove (TObject *obj)
Recursively remove this object from a list. More...

void ResetBit (UInt_t f)

virtual void SaveAs (const char *filename="", Option_t *option="") const
Save this object in the file specified by filename. More...

virtual void SavePrimitive (std::ostream &out, Option_t *option="")
Save a primitive as a C++ statement(s) on output stream "out". More...

void SetBit (UInt_t f, Bool_t set)
Set or unset the user status bits as specified in f. More...

void SetBit (UInt_t f)

virtual void SetDrawOption (Option_t *option="")
Set drawing option for object. More...

virtual void SetUniqueID (UInt_t uid)
Set the unique object id. More...

virtual void SysError (const char *method, const char *msgfmt,...) const
Issue system error message. More...

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. More...

virtual void Warning (const char *method, const char *msgfmt,...) const
Issue warning message. More...

virtual Int_t Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
Write this object to the current directory. More...

virtual Int_t Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
Write this object to the current directory. More...

## Protected Member Functions

void CreateTrianglesDataStructure ()
2D graph containing the user data More...

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 ? More...

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. More...

void FindHull ()
Finds those points which make up the convex hull of the set. More...

Bool_t InHull (Int_t E, Int_t X) const
Is point e inside the hull defined by all points apart from x ? More...

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. More...

Protected Member Functions inherited from TObject
virtual void DoError (int level, const char *location, const char *fmt, va_list va) const
Interface to ErrorHandler (protected). More...

void MakeZombie ()

## Protected Attributes

Bool_t fAllTri
Array used to order mass points by distance. More...

Double_tfDist
Histogram bin height for points lying outside the convex hull. More...

TGraph2DfGraph2D
True if CreateTrianglesDataStructure() and FindHull() have been performed. More...

Int_tfHullPoints

Bool_t fInit
True if FindAllTriangles() has been performed on fGraph2D. More...

Int_t fMaxIter
Array used to order mass points by distance. More...

Int_tfMTried
Delaunay triangles storage of size fNdt. More...

Int_t fNdt

Int_t fNhull
Number of data points in fGraph2D. More...

Int_t fNpoints
Number of Delaunay triangles found. More...

Int_tfNTried

Int_tfOrder
Hull points of size fNhull. More...

Int_tfPTried
Real size of the fxTried arrays. More...

Int_t fTriedSize
Maximum number of iterations to find Delaunay triangles. More...

Double_tfX
Number of points in the hull. More...

Double_tfXN
Pointer to fGraph2D->fZ. More...

Double_t fXNmax
Minimum value of fXN. More...

Double_t fXNmin
fGraph2D vectors normalized of size fNpoints More...

Double_t fXoffset
Maximum value of fYN. More...

Double_t fXScaleFactor
Parameters used to normalize user data. More...

Double_tfY
Pointer to fGraph2D->fX. More...

Double_tfYN
fGraph2D vectors normalized of size fNpoints More...

Double_t fYNmax
Minimum value of fYN. More...

Double_t fYNmin
Maximum value of fXN. More...

Double_t fYoffset

Double_t fYScaleFactor

Double_tfZ
Pointer to fGraph2D->fY. More...

Double_t fZout

Protected Attributes inherited from TNamed
TString fName

TString fTitle

## Private Member Functions

TGraphDelaunay (const TGraphDelaunay &)

TGraphDelaunayoperator= (const TGraphDelaunay &)

Public Types inherited from TObject
enum  { kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff }

enum  { kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) }

enum  EStatusBits {
kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4),
kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13)
}

Static Public Member Functions inherited from TObject
static Long_t GetDtorOnly ()
Return destructor only flag. More...

static Bool_t GetObjectStat ()
Get status of object stat flag. More...

static void SetDtorOnly (void *obj)
Set destructor only flag. More...

static void SetObjectStat (Bool_t stat)
Turn on/off tracking of objects in the TObjectTable. More...

#include <TGraphDelaunay.h>

Inheritance diagram for TGraphDelaunay:
[legend]

## ◆ TGraphDelaunay() [1/3]

 TGraphDelaunay::TGraphDelaunay ( const TGraphDelaunay & )
private

## ◆ TGraphDelaunay() [2/3]

 TGraphDelaunay::TGraphDelaunay ( )

TGraphDelaunay default constructor.

Definition at line 49 of file TGraphDelaunay.cxx.

## ◆ TGraphDelaunay() [3/3]

 TGraphDelaunay::TGraphDelaunay ( TGraph2D * g )

TGraphDelaunay normal constructor.

Definition at line 86 of file TGraphDelaunay.cxx.

## ◆ ~TGraphDelaunay()

 TGraphDelaunay::~TGraphDelaunay ( )
virtual

TGraphDelaunay destructor.

Definition at line 123 of file TGraphDelaunay.cxx.

## ◆ ComputeZ()

 Double_t TGraphDelaunay::ComputeZ ( Double_t x, Double_t y )

Return the z value corresponding to the (x,y) point in fGraph2D.

Definition at line 148 of file TGraphDelaunay.cxx.

## ◆ CreateTrianglesDataStructure()

 void TGraphDelaunay::CreateTrianglesDataStructure ( )
protected

2D graph containing the user data

Function used internally only.

It creates the data structures needed to compute the Delaunay triangles.

Definition at line 178 of file TGraphDelaunay.cxx.

## ◆ Enclose()

 Bool_t TGraphDelaunay::Enclose ( Int_t T1, Int_t T2, Int_t T3, Int_t Ex ) const
protected

Is point e inside the triangle t1-t2-t3 ?

Definition at line 215 of file TGraphDelaunay.cxx.

## ◆ FileIt()

 void TGraphDelaunay::FileIt ( Int_t p, Int_t n, Int_t m )
protected

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.

## ◆ FindAllTriangles()

 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.

## ◆ FindHull()

 void TGraphDelaunay::FindHull ( )
protected

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.

## ◆ GetGraph2D()

 TGraph2D* TGraphDelaunay::GetGraph2D ( ) const
inline

Definition at line 86 of file TGraphDelaunay.h.

## ◆ GetMarginBinsContent()

 Double_t TGraphDelaunay::GetMarginBinsContent ( ) const
inline

Definition at line 87 of file TGraphDelaunay.h.

## ◆ GetMTried()

 Int_t* TGraphDelaunay::GetMTried ( ) const
inline

Definition at line 91 of file TGraphDelaunay.h.

## ◆ GetNdt()

 Int_t TGraphDelaunay::GetNdt ( ) const
inline

Definition at line 88 of file TGraphDelaunay.h.

## ◆ GetNTried()

 Int_t* TGraphDelaunay::GetNTried ( ) const
inline

Definition at line 90 of file TGraphDelaunay.h.

## ◆ GetPTried()

 Int_t* TGraphDelaunay::GetPTried ( ) const
inline

Definition at line 89 of file TGraphDelaunay.h.

## ◆ GetXN()

 Double_t* TGraphDelaunay::GetXN ( ) const
inline

Definition at line 92 of file TGraphDelaunay.h.

## ◆ GetXNmax()

 Double_t TGraphDelaunay::GetXNmax ( ) const
inline

Definition at line 95 of file TGraphDelaunay.h.

## ◆ GetXNmin()

 Double_t TGraphDelaunay::GetXNmin ( ) const
inline

Definition at line 94 of file TGraphDelaunay.h.

## ◆ GetYN()

 Double_t* TGraphDelaunay::GetYN ( ) const
inline

Definition at line 93 of file TGraphDelaunay.h.

## ◆ GetYNmax()

 Double_t TGraphDelaunay::GetYNmax ( ) const
inline

Definition at line 97 of file TGraphDelaunay.h.

## ◆ GetYNmin()

 Double_t TGraphDelaunay::GetYNmin ( ) const
inline

Definition at line 96 of file TGraphDelaunay.h.

## ◆ InHull()

 Bool_t TGraphDelaunay::InHull ( Int_t E, Int_t X ) const
protected

Is point e inside the hull defined by all points apart from x ?

Definition at line 448 of file TGraphDelaunay.cxx.

## ◆ Interpolate()

 Double_t TGraphDelaunay::Interpolate ( Double_t xx, Double_t yy )

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.

## ◆ InterpolateOnPlane()

 Double_t TGraphDelaunay::InterpolateOnPlane ( Int_t TI1, Int_t TI2, Int_t TI3, Int_t E ) const
protected

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.

## ◆ operator=()

 TGraphDelaunay& TGraphDelaunay::operator= ( const TGraphDelaunay & )
private

## ◆ SetMarginBinsContent()

 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.

## ◆ SetMaxIter()

 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.

## ◆ fAllTri

 Bool_t TGraphDelaunay::fAllTri
protected

Array used to order mass points by distance.

Definition at line 66 of file TGraphDelaunay.h.

## ◆ fDist

 Double_t* TGraphDelaunay::fDist
protected

Histogram bin height for points lying outside the convex hull.

Definition at line 58 of file TGraphDelaunay.h.

## ◆ fGraph2D

 TGraph2D* TGraphDelaunay::fGraph2D
protected

True if CreateTrianglesDataStructure() and FindHull() have been performed.

Definition at line 68 of file TGraphDelaunay.h.

## ◆ fHullPoints

 Int_t* TGraphDelaunay::fHullPoints
protected

Definition at line 64 of file TGraphDelaunay.h.

## ◆ fInit

 Bool_t TGraphDelaunay::fInit
protected

True if FindAllTriangles() has been performed on fGraph2D.

Definition at line 67 of file TGraphDelaunay.h.

## ◆ fMaxIter

 Int_t TGraphDelaunay::fMaxIter
protected

Array used to order mass points by distance.

Definition at line 59 of file TGraphDelaunay.h.

## ◆ fMTried

 Int_t* TGraphDelaunay::fMTried
protected

Delaunay triangles storage of size fNdt.

Definition at line 63 of file TGraphDelaunay.h.

## ◆ fNdt

 Int_t TGraphDelaunay::fNdt
protected

Definition at line 41 of file TGraphDelaunay.h.

## ◆ fNhull

 Int_t TGraphDelaunay::fNhull
protected

Number of data points in fGraph2D.

Definition at line 43 of file TGraphDelaunay.h.

## ◆ fNpoints

 Int_t TGraphDelaunay::fNpoints
protected

Number of Delaunay triangles found.

Definition at line 42 of file TGraphDelaunay.h.

## ◆ fNTried

 Int_t* TGraphDelaunay::fNTried
protected

Definition at line 62 of file TGraphDelaunay.h.

## ◆ fOrder

 Int_t* TGraphDelaunay::fOrder
protected

Hull points of size fNhull.

Definition at line 65 of file TGraphDelaunay.h.

## ◆ fPTried

 Int_t* TGraphDelaunay::fPTried
protected

Real size of the fxTried arrays.

Definition at line 61 of file TGraphDelaunay.h.

## ◆ fTriedSize

 Int_t TGraphDelaunay::fTriedSize
protected

Maximum number of iterations to find Delaunay triangles.

Definition at line 60 of file TGraphDelaunay.h.

## ◆ fX

 Double_t* TGraphDelaunay::fX
protected

Number of points in the hull.

Definition at line 44 of file TGraphDelaunay.h.

## ◆ fXN

 Double_t* TGraphDelaunay::fXN
protected

Pointer to fGraph2D->fZ.

Definition at line 47 of file TGraphDelaunay.h.

## ◆ fXNmax

 Double_t TGraphDelaunay::fXNmax
protected

Minimum value of fXN.

Definition at line 50 of file TGraphDelaunay.h.

## ◆ fXNmin

 Double_t TGraphDelaunay::fXNmin
protected

fGraph2D vectors normalized of size fNpoints

Definition at line 49 of file TGraphDelaunay.h.

## ◆ fXoffset

 Double_t TGraphDelaunay::fXoffset
protected

Maximum value of fYN.

Definition at line 53 of file TGraphDelaunay.h.

## ◆ fXScaleFactor

 Double_t TGraphDelaunay::fXScaleFactor
protected

Parameters used to normalize user data.

Definition at line 55 of file TGraphDelaunay.h.

## ◆ fY

 Double_t* TGraphDelaunay::fY
protected

Pointer to fGraph2D->fX.

Definition at line 45 of file TGraphDelaunay.h.

## ◆ fYN

 Double_t* TGraphDelaunay::fYN
protected

fGraph2D vectors normalized of size fNpoints

Definition at line 48 of file TGraphDelaunay.h.

## ◆ fYNmax

 Double_t TGraphDelaunay::fYNmax
protected

Minimum value of fYN.

Definition at line 52 of file TGraphDelaunay.h.

## ◆ fYNmin

 Double_t TGraphDelaunay::fYNmin
protected

Maximum value of fXN.

Definition at line 51 of file TGraphDelaunay.h.

## ◆ fYoffset

 Double_t TGraphDelaunay::fYoffset
protected

Definition at line 54 of file TGraphDelaunay.h.

## ◆ fYScaleFactor

 Double_t TGraphDelaunay::fYScaleFactor
protected

Definition at line 56 of file TGraphDelaunay.h.

## ◆ fZ

 Double_t* TGraphDelaunay::fZ
protected

Pointer to fGraph2D->fY.

Definition at line 46 of file TGraphDelaunay.h.

## ◆ fZout

 Double_t TGraphDelaunay::fZout
protected

Definition at line 57 of file TGraphDelaunay.h.

The documentation for this class was generated from the following files: