#include <TPZProjectEllipse.h>

Collaboration diagram for TPZProjectEllipse:

Public Types
enum	EType { EVerySimple2D, ESimple2D, E3D, E2D }

Public Member Functions
	TPZProjectEllipse (EType project, TPZFMatrix< REAL > &Points)

	TPZProjectEllipse (std::multimap< REAL, REAL > &Points)

void	Getcoefficients (TPZVec< REAL > &coef)

void	PrintingAsSimpleEquation (TPZVec< REAL > &Center, TPZVec< REAL > &Ratios, std::ostream &out)

bool	StandardFormatForSimpleEllipse (TPZVec< REAL > &Center, TPZVec< REAL > &Ratios)

Private Member Functions
bool	LeastSquaresToGetVerySimpleEllipse ()

bool	AdjustingWithSimpleEllipse ()

bool	AdjustingWithVerySimpleEllipse ()

bool	AdjustingWithEllipse ()

bool	DiagonalizingQuadraticForm (int dim, TPZFMatrix< REAL > &Coeffs, TPZFMatrix< REAL > &NewCoeffs)

void	AlmostZeroToZero (TPZFMatrix< REAL > &mat)

void	AlmostZeroToZero (TPZVec< REAL > &mat)

bool	LeastSquaresToGetSimpleEllipse ()

bool	LeastSquaresToGetEllipse ()

void	PrintAxes (TPZFMatrix< REAL > &P, std::ostream &out)

Private Attributes
TPZFMatrix< REAL >	fPoints
	Points which determine the projection. More...

int	fType
	Projection type. More...

TPZManVector< REAL, 6 >	fcoefficients
	coefficients determined by the least squares problem More...

REAL	fTol
	Tolerance to project the coefficients to zero value. More...

Detailed Description

Definition at line 17 of file TPZProjectEllipse.h.

Member Enumeration Documentation

◆ EType

enum TPZProjectEllipse::EType

Enumerator
EVerySimple2D
ESimple2D
E3D
E2D

Definition at line 31 of file TPZProjectEllipse.h.

Constructor & Destructor Documentation

◆ TPZProjectEllipse() [1/2]

TPZProjectEllipse::TPZProjectEllipse	(	EType	project,
		TPZFMatrix< REAL > &	Points
	)

inline

Definition at line 33 of file TPZProjectEllipse.h.

References DebugStop, ESimple2D, EVerySimple2D, LeastSquaresToGetSimpleEllipse(), LeastSquaresToGetVerySimpleEllipse(), and TPZVec< T >::resize().

◆ TPZProjectEllipse() [2/2]

TPZProjectEllipse::TPZProjectEllipse ( std::multimap< REAL, REAL > & Points )

inline

Definition at line 55 of file TPZProjectEllipse.h.

References EVerySimple2D, fPoints, LeastSquaresToGetVerySimpleEllipse(), TPZVec< T >::resize(), and TPZFMatrix< TVar >::Resize().

Member Function Documentation

◆ AdjustingWithEllipse()

bool TPZProjectEllipse::AdjustingWithEllipse ( )

private

Process to get the ellipse by least square method from a set of points. First: Find coefficients of the quadratic form (with mixed terms) from a set of points using least square method. Second: Apply diagonalization to transform quadratic form with mixed terms to quadratic form with only quadratic terms of the variables. Third: From new coefficients get the center and axes of the ellipse adjusted Fourth: Print the result and standard form into saida.

Definition at line 402 of file TPZProjectEllipse.cpp.

References TPZMatrix< TVar >::Cols(), DebugStop, fcoefficients, fPoints, IsZero(), LeastSquaresToGetEllipse(), PrintingAsSimpleEquation(), StandardFormatForSimpleEllipse(), and ZeroTolerance().

Referenced by Getcoefficients().

◆ AdjustingWithSimpleEllipse()

bool TPZProjectEllipse::AdjustingWithSimpleEllipse ( )

private

Process to get the ellipse by least square method from a set of points. First: Find coefficients of the simple quadratic form from a set of points using least square method. Second: From coefficients get the center and axes of the ellipse adjusted Third: Print the result and standard form into saida.

Definition at line 351 of file TPZProjectEllipse.cpp.

References TPZMatrix< TVar >::Cols(), fPoints, LeastSquaresToGetSimpleEllipse(), PrintingAsSimpleEquation(), StandardFormatForSimpleEllipse(), and ZeroTolerance().

Referenced by Getcoefficients().

◆ AdjustingWithVerySimpleEllipse()

bool TPZProjectEllipse::AdjustingWithVerySimpleEllipse ( )

private

Definition at line 374 of file TPZProjectEllipse.cpp.

References LeastSquaresToGetVerySimpleEllipse(), PrintingAsSimpleEquation(), StandardFormatForSimpleEllipse(), and ZeroTolerance().

Referenced by Getcoefficients().

◆ AlmostZeroToZero() [1/2]

void TPZProjectEllipse::AlmostZeroToZero ( TPZFMatrix< REAL > & mat )

private

Definition at line 233 of file TPZProjectEllipse.cpp.

References TPZMatrix< TVar >::Cols(), fabs, fTol, TPZFMatrix< TVar >::GetVal(), TPZFMatrix< TVar >::PutVal(), and TPZMatrix< TVar >::Rows().

Referenced by Getcoefficients(), and PrintAxes().

◆ AlmostZeroToZero() [2/2]

void TPZProjectEllipse::AlmostZeroToZero ( TPZVec< REAL > & mat )

private

Definition at line 242 of file TPZProjectEllipse.cpp.

References fabs, fTol, and TPZVec< T >::NElements().

◆ DiagonalizingQuadraticForm()

bool TPZProjectEllipse::DiagonalizingQuadraticForm	(	int	dim,
		TPZFMatrix< REAL > &	Coeffs,
		TPZFMatrix< REAL > &	NewCoeffs
	)

private

Referenced by Getcoefficients().

◆ Getcoefficients()

void TPZProjectEllipse::Getcoefficients ( TPZVec< REAL > & coef )

inline

Definition at line 70 of file TPZProjectEllipse.h.

References AdjustingWithEllipse(), AdjustingWithSimpleEllipse(), AdjustingWithVerySimpleEllipse(), AlmostZeroToZero(), DiagonalizingQuadraticForm(), fcoefficients, LeastSquaresToGetEllipse(), LeastSquaresToGetSimpleEllipse(), LeastSquaresToGetVerySimpleEllipse(), PrintAxes(), PrintingAsSimpleEquation(), and StandardFormatForSimpleEllipse().

◆ LeastSquaresToGetEllipse()

bool TPZProjectEllipse::LeastSquaresToGetEllipse ( )

private

Find coefficients of the quadratic equation (Quadratic form) with best adjust to points given y^2 = a x^2 + b x + c xy + d y + e z^2 = a x^2 + b x + c y^2 + d y + e xy + f z + g yz + h xz + i using the least square method.

Definition at line 90 of file TPZProjectEllipse.cpp.

References TPZMatrix< TVar >::Cols(), ELU, fcoefficients, TPZVec< T >::Fill(), fPoints, TPZFMatrix< TVar >::PutVal(), TPZFMatrix< TVar >::Redim(), TPZManVector< T, NumExtAlloc >::Resize(), TPZMatrix< TVar >::Rows(), TPZMatrix< TVar >::SolveDirect(), TPZFMatrix< TVar >::Transpose(), and TPZFMatrix< TVar >::Zero().

Referenced by AdjustingWithEllipse(), and Getcoefficients().

◆ LeastSquaresToGetSimpleEllipse()

bool TPZProjectEllipse::LeastSquaresToGetSimpleEllipse ( )

private

Find coefficients of the quadratic equation with best adjust to points given y^2 = a x^2 + b x + c y + d z^2 = a x^2 + b x + c y^2 + d y + e z + f using the least square method.

Definition at line 16 of file TPZProjectEllipse.cpp.

References TPZMatrix< TVar >::Cols(), ELU, fcoefficients, TPZVec< T >::Fill(), fPoints, TPZFMatrix< TVar >::PutVal(), TPZFMatrix< TVar >::Redim(), TPZManVector< T, NumExtAlloc >::Resize(), TPZMatrix< TVar >::Rows(), TPZMatrix< TVar >::SolveDirect(), TPZFMatrix< TVar >::Transpose(), and TPZFMatrix< TVar >::Zero().

Referenced by AdjustingWithSimpleEllipse(), Getcoefficients(), and TPZProjectEllipse().

◆ LeastSquaresToGetVerySimpleEllipse()

bool TPZProjectEllipse::LeastSquaresToGetVerySimpleEllipse ( )

private

Definition at line 178 of file TPZProjectEllipse.cpp.

References ELU, fcoefficients, fPoints, TPZFMatrix< TVar >::PutVal(), TPZFMatrix< TVar >::Redim(), TPZMatrix< TVar >::Rows(), TPZMatrix< TVar >::SolveDirect(), TPZFMatrix< TVar >::Transpose(), and TPZFMatrix< TVar >::Zero().

Referenced by AdjustingWithVerySimpleEllipse(), Getcoefficients(), and TPZProjectEllipse().

◆ PrintAxes()

void TPZProjectEllipse::PrintAxes	(	TPZFMatrix< REAL > &	P,
		std::ostream &	out
	)

private

Print the unitary vectors for rotated axes to ellipse

Definition at line 251 of file TPZProjectEllipse.cpp.

References AlmostZeroToZero(), TPZMatrix< TVar >::Cols(), TPZFMatrix< TVar >::GetVal(), and TPZMatrix< TVar >::Rows().

Referenced by Getcoefficients().

◆ PrintingAsSimpleEquation()

void TPZProjectEllipse::PrintingAsSimpleEquation	(	TPZVec< REAL > &	Center,
		TPZVec< REAL > &	Ratios,
		std::ostream &	out
	)

Definition at line 325 of file TPZProjectEllipse.cpp.

References fcoefficients, and TPZVec< T >::size().

Referenced by AdjustingWithEllipse(), AdjustingWithSimpleEllipse(), AdjustingWithVerySimpleEllipse(), and Getcoefficients().

◆ StandardFormatForSimpleEllipse()

bool TPZProjectEllipse::StandardFormatForSimpleEllipse	(	TPZVec< REAL > &	Center,
		TPZVec< REAL > &	Ratios
	)

From quadratic equation (Quadratic form) y^2 = a x^2 + b x + c xy + d y + e z^2 = a x^2 + b x + c y^2 + d y + e xy + f z + g yz + h xz + i compute the coordinates of the center and axes of the ellipse. Print in the standard equation.

Definition at line 274 of file TPZProjectEllipse.cpp.

References fcoefficients, IsZero(), TPZVec< T >::size(), and sqrt.

Referenced by AdjustingWithEllipse(), AdjustingWithSimpleEllipse(), AdjustingWithVerySimpleEllipse(), and Getcoefficients().

Member Data Documentation

◆ fcoefficients

TPZManVector<REAL,6> TPZProjectEllipse::fcoefficients

private

coefficients determined by the least squares problem

Definition at line 24 of file TPZProjectEllipse.h.

Referenced by AdjustingWithEllipse(), Getcoefficients(), LeastSquaresToGetEllipse(), LeastSquaresToGetSimpleEllipse(), LeastSquaresToGetVerySimpleEllipse(), PrintingAsSimpleEquation(), and StandardFormatForSimpleEllipse().

◆ fPoints

TPZFMatrix<REAL> TPZProjectEllipse::fPoints

private

Points which determine the projection.

Definition at line 20 of file TPZProjectEllipse.h.

Referenced by AdjustingWithEllipse(), AdjustingWithSimpleEllipse(), LeastSquaresToGetEllipse(), LeastSquaresToGetSimpleEllipse(), LeastSquaresToGetVerySimpleEllipse(), and TPZProjectEllipse().

◆ fTol

REAL TPZProjectEllipse::fTol

private

Tolerance to project the coefficients to zero value.

Definition at line 27 of file TPZProjectEllipse.h.

Referenced by AlmostZeroToZero().

◆ fType

int TPZProjectEllipse::fType

private

Projection type.

Definition at line 22 of file TPZProjectEllipse.h.

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

Post/TPZProjectEllipse.h
Post/TPZProjectEllipse.cpp

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Enumeration Documentation

◆ EType

Constructor & Destructor Documentation

◆ TPZProjectEllipse() [1/2]

◆ TPZProjectEllipse() [2/2]

Member Function Documentation

◆ AdjustingWithEllipse()

◆ AdjustingWithSimpleEllipse()

◆ AdjustingWithVerySimpleEllipse()

◆ AlmostZeroToZero() [1/2]

◆ AlmostZeroToZero() [2/2]

◆ DiagonalizingQuadraticForm()

◆ Getcoefficients()

◆ LeastSquaresToGetEllipse()

◆ LeastSquaresToGetSimpleEllipse()

◆ LeastSquaresToGetVerySimpleEllipse()

◆ PrintAxes()

◆ PrintingAsSimpleEquation()

◆ StandardFormatForSimpleEllipse()

Member Data Documentation

◆ fcoefficients

◆ fPoints

◆ fTol

◆ fType