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 (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...

TGraph2D *	GetGraph2D () const

Double_t	GetMarginBinsContent () const

Int_t	GetNdt () const

Int_t *	GetPTried () const

Int_t *	GetNTried () const

Int_t *	GetMTried () const

Double_t *	GetXN () const

Double_t *	GetYN () const

Double_t	GetXNmin () const

Double_t	GetXNmax () const

Double_t	GetYNmin () const

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

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

virtual	~TNamed ()

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

virtual TObject *	Clone (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	SetName (const char *name)
	Change (i.e. More...

virtual void	SetNameTitle (const char name, const char title)
	Change (i.e. set) all the TNamed parameters (name and title). More...

virtual void	SetTitle (const char *title="")
	Change (i.e. set) the title of the TNamed. More...

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

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

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

Public Member Functions inherited from TObject
	TObject ()

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

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

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

virtual void	AppendPad (Option_t *option="")
	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 TObject *	DrawClone (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	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 TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

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

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

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

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

virtual Option_t *	GetOption () const

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

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

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

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

Bool_t	IsOnHeap () const

Bool_t	IsZombie () const

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

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...

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	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. 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...

void *	operator new (size_t sz)

void *	operator new[] (size_t sz)

void *	operator new (size_t sz, void *vp)

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

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

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

void	ResetBit (UInt_t f)

Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

void	InvertBit (UInt_t f)

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

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

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

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

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

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...

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

virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

Protected Attributes
Int_t	fNdt

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

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

Double_t *	fX
	Number of points in the hull. More...

Double_t *	fY
	Pointer to fGraph2D->fX. More...

Double_t *	fZ
	Pointer to fGraph2D->fY. More...

Double_t *	fXN
	Pointer to fGraph2D->fZ. More...

Double_t *	fYN
	fGraph2D vectors normalized of size fNpoints More...

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

Double_t	fXNmax
	Minimum value of fXN. More...

Double_t	fYNmin
	Maximum value of fXN. More...

Double_t	fYNmax
	Minimum value of fYN. More...

Double_t	fXoffset
	Maximum value of fYN. More...

Double_t	fYoffset

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

Double_t	fYScaleFactor

Double_t	fZout

Double_t *	fDist
	Histogram bin height for points lying outside the convex hull. More...

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

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

Int_t *	fPTried
	Real size of the fxTried arrays. More...

Int_t *	fNTried

Int_t *	fMTried
	Delaunay triangles storage of size fNdt. More...

Int_t *	fHullPoints

Int_t *	fOrder
	Hull points of size fNhull. More...

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

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

TGraph2D *	fGraph2D
	True if CreateTrianglesDataStructure() and FindHull() have been performed. More...

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

Private Member Functions
	TGraphDelaunay (const TGraphDelaunay &)

TGraphDelaunay &	operator= (const TGraphDelaunay &)

Additional Inherited Members
Public Types inherited from TObject
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) }

enum	{ kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff }

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

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

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

static Bool_t	GetObjectStat ()
	Get status of object stat 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]

Constructor & Destructor Documentation

TGraphDelaunay::TGraphDelaunay ( const TGraphDelaunay & )

private

TGraphDelaunay::TGraphDelaunay ( )

TGraphDelaunay::TGraphDelaunay ( TGraph2D * g )

TGraphDelaunay normal constructor.

Definition at line 86 of file TGraphDelaunay.cxx.

TGraphDelaunay::~TGraphDelaunay ( )

virtual

TGraphDelaunay destructor.

Definition at line 123 of file TGraphDelaunay.cxx.

Member Function Documentation

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.

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.

Referenced by ComputeZ(), and Interpolate().

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.

Referenced by Interpolate().

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.

Referenced by Interpolate().

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.

Referenced by TGraph2DPainter::FindTriangles().

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.

Referenced by ComputeZ(), and Interpolate().

TGraph2D* TGraphDelaunay::GetGraph2D ( ) const

inline

Definition at line 86 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::TGraph2DPainter().

Double_t TGraphDelaunay::GetMarginBinsContent ( ) const

inline

Definition at line 87 of file TGraphDelaunay.h.

Int_t* TGraphDelaunay::GetMTried ( ) const

inline

Definition at line 91 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::FindTriangles().

Int_t TGraphDelaunay::GetNdt ( ) const

inline

Definition at line 88 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::FindTriangles().

Int_t* TGraphDelaunay::GetNTried ( ) const

inline

Definition at line 90 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::FindTriangles().

Int_t* TGraphDelaunay::GetPTried ( ) const

inline

Definition at line 89 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::FindTriangles().

Double_t* TGraphDelaunay::GetXN ( ) const

inline

Definition at line 92 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::FindTriangles().

Double_t TGraphDelaunay::GetXNmax ( ) const

inline

Definition at line 95 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::FindTriangles().

Double_t TGraphDelaunay::GetXNmin ( ) const

inline

Definition at line 94 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::FindTriangles().

Double_t* TGraphDelaunay::GetYN ( ) const

inline

Definition at line 93 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::FindTriangles().

Double_t TGraphDelaunay::GetYNmax ( ) const

inline

Definition at line 97 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::FindTriangles().

Double_t TGraphDelaunay::GetYNmin ( ) const

inline

Definition at line 96 of file TGraphDelaunay.h.

Referenced by TGraph2DPainter::FindTriangles().

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.

Referenced by FindHull(), and 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.

Referenced by ComputeZ(), and FindAllTriangles().