Class to generate a Delaunay triangulation of a 2D set of points.

Algorithm based on Triangle, a two-dimensional quality mesh generator and Delaunay triangulator from Jonathan Richard Shewchuk.

See [http://www.cs.cmu.edu/~quake/triangle.html]

Definition at line 71 of file Delaunay2D.h.

Classes
struct	Triangle

Public Types
typedef std::vector< Triangle >	Triangles

Public Member Functions
	Delaunay2D (int n, const double x, const double y, const double *z, double xmin=0, double xmax=0, double ymin=0, double ymax=0)
	class constructor from array of data points More...

Triangles::const_iterator	begin () const

Triangles::const_iterator	end () const

void	FindAllTriangles ()
	Find all triangles. More...

double	Interpolate (double x, double y)
	Return the Interpolated z value corresponding to the (x,y) point. More...

Int_t	NumberOfTriangles () const
	return the number of triangles More...

void	SetInputPoints (int n, const double x, const double y, const double *z, double xmin=0, double xmax=0, double ymin=0, double ymax=0)
	set the input points for building the graph More...

void	SetZOuterValue (double z=0.)
	set z value to be returned for points outside the region More...

double	XMax () const

double	XMin () const

double	YMax () const

double	YMin () const

double	ZOuterValue () const
	return the user defined Z-outer value More...

Protected Member Functions
unsigned int	Cell (UInt_t x, UInt_t y) const
	grid cells with containing triangles More...

int	CellX (double x) const

int	CellY (double y) const

Protected Attributes
std::set< UInt_t >	fCells [(fNCells+1) *(fNCells+1)]
	inverse denominator to calculate X cell = fNCells / (fYNmax - fYNmin) More...

Bool_t	fInit
	Height for points lying outside the convex hull. More...

Int_t	fNdt

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

double	fOffsetX
	Maximum value of fYN. More...

double	fOffsetY
	Normalization offset X. More...

double	fScaleFactorX
	Normalization offset Y. More...

double	fScaleFactorY
	Normalization factor X. More...

Triangles	fTriangles
	True if FindAllTriangels() has been performed. More...

const double *	fX
	Number of data points. More...

double	fXCellStep
	number of cells to divide the normalized space More...

std::vector< double >	fXN
	Triangles of Triangulation. More...

double	fXNmax
	Minimum value of fXN. More...

double	fXNmin
	Pointer to Z array. More...

const double *	fY
	Pointer to X array (managed externally) More...

double	fYCellStep
	inverse denominator to calculate X cell = fNCells / (fXNmax - fXNmin) More...

std::vector< double >	fYN
	normalized X More...

double	fYNmax
	Minimum value of fYN. More...

double	fYNmin
	Maximum value of fXN. More...

const double *	fZ
	Pointer to Y array. More...

double	fZout
	Normalization factor Y. More...

Static Protected Attributes
static const int	fNCells = 25
	normalized Y More...

Private Member Functions
	Delaunay2D (const Delaunay2D &)

void	DoFindTriangles ()
	internal function to find the triangle use Triangle or CGAL if flag is set More...

double	DoInterpolateNormalized (double x, double y)
	internal method to compute the interpolation More...

void	DoNormalizePoints ()
	internal function to normalize the points More...

double	Linear_transform (double x, double offset, double factor)

Delaunay2D &	operator= (const Delaunay2D &)

#include <Math/Delaunay2D.h>

Member Typedef Documentation

◆ Triangles

typedef std::vector<Triangle> ROOT::Math::Delaunay2D::Triangles

Definition at line 85 of file Delaunay2D.h.

Constructor & Destructor Documentation

◆ Delaunay2D() [1/2]

ROOT::Math::Delaunay2D::Delaunay2D	(	int	n,
		const double *	x,
		const double *	y,
		const double *	z,
		double	xmin = `0`,
		double	xmax = `0`,
		double	ymin = `0`,
		double	ymax = `0`
	)

class constructor from array of data points

Definition at line 34 of file Delaunay2D.cxx.

◆ Delaunay2D() [2/2]

ROOT::Math::Delaunay2D::Delaunay2D ( const Delaunay2D & )

private

Member Function Documentation

◆ begin()

Triangles::const_iterator ROOT::Math::Delaunay2D::begin ( ) const

inline

Definition at line 116 of file Delaunay2D.h.

◆ Cell()

unsigned int ROOT::Math::Delaunay2D::Cell	(	UInt_t	x,
		UInt_t	y
	)		const

inlineprotected

grid cells with containing triangles

Definition at line 274 of file Delaunay2D.h.

◆ CellX()

int ROOT::Math::Delaunay2D::CellX ( double x ) const

inlineprotected

Definition at line 278 of file Delaunay2D.h.

◆ CellY()

int ROOT::Math::Delaunay2D::CellY ( double y ) const

inlineprotected

Definition at line 282 of file Delaunay2D.h.

◆ DoFindTriangles()

void ROOT::Math::Delaunay2D::DoFindTriangles ( )

private

internal function to find the triangle use Triangle or CGAL if flag is set

Triangle implementation for finding all the triangles.

Definition at line 256 of file Delaunay2D.cxx.

◆ DoInterpolateNormalized()

double ROOT::Math::Delaunay2D::DoInterpolateNormalized	(	double	x,
		double	y
	)

private

internal method to compute the interpolation

Triangle implementation for interpolation 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 379 of file Delaunay2D.cxx.

◆ DoNormalizePoints()

void ROOT::Math::Delaunay2D::DoNormalizePoints ( )

private

internal function to normalize the points

Triangle implementation for normalizing the points.

Definition at line 244 of file Delaunay2D.cxx.

◆ end()

Triangles::const_iterator ROOT::Math::Delaunay2D::end ( ) const

inline

Definition at line 117 of file Delaunay2D.h.

◆ FindAllTriangles()

void ROOT::Math::Delaunay2D::FindAllTriangles ( )

Find all triangles.

Definition at line 128 of file Delaunay2D.cxx.

◆ Interpolate()

double ROOT::Math::Delaunay2D::Interpolate	(	double	x,
		double	y
	)

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

Definition at line 104 of file Delaunay2D.cxx.

◆ Linear_transform()

double ROOT::Math::Delaunay2D::Linear_transform	(	double	x,
		double	offset,
		double	factor
	)

inlineprivate

Definition at line 125 of file Delaunay2D.h.

◆ NumberOfTriangles()

Int_t ROOT::Math::Delaunay2D::NumberOfTriangles ( ) const

inline

return the number of triangles

Definition at line 102 of file Delaunay2D.h.

◆ operator=()

Delaunay2D & ROOT::Math::Delaunay2D::operator= ( const Delaunay2D & )

private

◆ SetInputPoints()

void ROOT::Math::Delaunay2D::SetInputPoints	(	int	n,
		const double *	x,
		const double *	y,
		const double *	z,
		double	xmin = `0`,
		double	xmax = `0`,
		double	ymin = `0`,
		double	ymax = `0`
	)

set the input points for building the graph

set the input points

Definition at line 59 of file Delaunay2D.cxx.

◆ SetZOuterValue()

void ROOT::Math::Delaunay2D::SetZOuterValue ( double z = 0. )

inline

set z value to be returned for points outside the region

Definition at line 110 of file Delaunay2D.h.

◆ XMax()

double ROOT::Math::Delaunay2D::XMax ( ) const

inline

Definition at line 105 of file Delaunay2D.h.

◆ XMin()

double ROOT::Math::Delaunay2D::XMin ( ) const

inline

Definition at line 104 of file Delaunay2D.h.

◆ YMax()

double ROOT::Math::Delaunay2D::YMax ( ) const

inline

Definition at line 107 of file Delaunay2D.h.

◆ YMin()

double ROOT::Math::Delaunay2D::YMin ( ) const

inline

Definition at line 106 of file Delaunay2D.h.

◆ ZOuterValue()

double ROOT::Math::Delaunay2D::ZOuterValue ( ) const

inline

return the user defined Z-outer value

Definition at line 113 of file Delaunay2D.h.

Member Data Documentation

◆ fCells

std::set<UInt_t> ROOT::Math::Delaunay2D::fCells[(fNCells+1) *(fNCells+1)]

protected

inverse denominator to calculate X cell = fNCells / (fYNmax - fYNmin)

Definition at line 272 of file Delaunay2D.h.

◆ fInit

Bool_t ROOT::Math::Delaunay2D::fInit

protected

Height for points lying outside the convex hull.

Definition at line 179 of file Delaunay2D.h.

◆ fNCells

const int ROOT::Math::Delaunay2D::fNCells = 25

staticprotected

normalized Y

Definition at line 269 of file Delaunay2D.h.

◆ fNdt

Int_t ROOT::Math::Delaunay2D::fNdt

protected

Definition at line 150 of file Delaunay2D.h.

◆ fNpoints

Int_t ROOT::Math::Delaunay2D::fNpoints

protected

Number of Delaunay triangles found.

Definition at line 151 of file Delaunay2D.h.

◆ fOffsetX

double ROOT::Math::Delaunay2D::fOffsetX

protected

Maximum value of fYN.

Definition at line 165 of file Delaunay2D.h.

◆ fOffsetY

double ROOT::Math::Delaunay2D::fOffsetY

protected

Normalization offset X.

Definition at line 166 of file Delaunay2D.h.

◆ fScaleFactorX

double ROOT::Math::Delaunay2D::fScaleFactorX

protected

Normalization offset Y.

Definition at line 168 of file Delaunay2D.h.

◆ fScaleFactorY

double ROOT::Math::Delaunay2D::fScaleFactorY

protected

Normalization factor X.

Definition at line 169 of file Delaunay2D.h.

◆ fTriangles

Triangles ROOT::Math::Delaunay2D::fTriangles

protected

True if FindAllTriangels() has been performed.

Definition at line 183 of file Delaunay2D.h.

◆ fX

const double* ROOT::Math::Delaunay2D::fX

protected

Number of data points.

Definition at line 153 of file Delaunay2D.h.

◆ fXCellStep

double ROOT::Math::Delaunay2D::fXCellStep

protected

number of cells to divide the normalized space

Definition at line 270 of file Delaunay2D.h.

◆ fXN

std::vector<double> ROOT::Math::Delaunay2D::fXN

protected

Triangles of Triangulation.

Definition at line 261 of file Delaunay2D.h.

◆ fXNmax

double ROOT::Math::Delaunay2D::fXNmax

protected

Minimum value of fXN.

Definition at line 158 of file Delaunay2D.h.

◆ fXNmin

double ROOT::Math::Delaunay2D::fXNmin

protected

Pointer to Z array.

Definition at line 157 of file Delaunay2D.h.

◆ fY

const double* ROOT::Math::Delaunay2D::fY

protected

Pointer to X array (managed externally)

Definition at line 154 of file Delaunay2D.h.

◆ fYCellStep

double ROOT::Math::Delaunay2D::fYCellStep

protected

inverse denominator to calculate X cell = fNCells / (fXNmax - fXNmin)

Definition at line 271 of file Delaunay2D.h.

◆ fYN

std::vector<double> ROOT::Math::Delaunay2D::fYN

protected

normalized X

Definition at line 262 of file Delaunay2D.h.

◆ fYNmax

double ROOT::Math::Delaunay2D::fYNmax

protected

Minimum value of fYN.

Definition at line 160 of file Delaunay2D.h.

◆ fYNmin

double ROOT::Math::Delaunay2D::fYNmin

protected

Maximum value of fXN.

Definition at line 159 of file Delaunay2D.h.

◆ fZ

const double* ROOT::Math::Delaunay2D::fZ

protected

Pointer to Y array.

Definition at line 155 of file Delaunay2D.h.

◆ fZout

double ROOT::Math::Delaunay2D::fZout

protected

Normalization factor Y.

Definition at line 171 of file Delaunay2D.h.

Libraries for ROOT::Math::Delaunay2D:

[legend]

Classes

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Private Member Functions

Member Typedef Documentation

◆ Triangles

Constructor & Destructor Documentation

◆ Delaunay2D() [1/2]

◆ Delaunay2D() [2/2]

Member Function Documentation

◆ begin()

◆ Cell()

◆ CellX()

◆ CellY()

◆ DoFindTriangles()

◆ DoInterpolateNormalized()

◆ DoNormalizePoints()

◆ end()

◆ FindAllTriangles()

◆ Interpolate()

◆ Linear_transform()

◆ NumberOfTriangles()

◆ operator=()

◆ SetInputPoints()

◆ SetZOuterValue()

◆ XMax()

◆ XMin()

◆ YMax()

◆ YMin()

◆ ZOuterValue()

Member Data Documentation

◆ fCells

◆ fInit

◆ fNCells

◆ fNdt

◆ fNpoints

◆ fOffsetX

◆ fOffsetY

◆ fScaleFactorX

◆ fScaleFactorY

◆ fTriangles

◆ fX

◆ fXCellStep

◆ fXN

◆ fXNmax

◆ fXNmin

◆ fY

◆ fYCellStep

◆ fYN

◆ fYNmax

◆ fYNmin

◆ fZ

◆ fZout