A class to hold a critical point. This class holds a critical point in a 3D vector field It consists of a localtion $x_0 \in \mathbb{R}^3$ , Matrix $A \in \mathbb{R}^{3 \times 3}$ , and a magnitude $\gamma \in \mathbb{R}$ . It is used only as an intermidiate storage. More...

#include <mia/3d/critical_point.hh>

Public Types
typedef std::vector < C3DCriticalPoint >	List
	A list of critical points. More...

Public Member Functions
C3DFVector	at (const C3DFVector &x) const

C3DFVector	at_alt (const C3DFVector &x) const

	C3DCriticalPoint ()

	C3DCriticalPoint (const C3DFVector &x0_)

	C3DCriticalPoint (float x, float y, float z)

	C3DCriticalPoint (const C3DCriticalPoint &org)

const C3DFMatrix	get_a () const

C3DFMatrix &	get_a ()

float	get_gamma () const

const C3DFVector	get_point () const

C3DFVector &	get_point ()

bool	operator< (const C3DCriticalPoint &cp) const

C3DCriticalPoint &	operator= (const C3DCriticalPoint &org)

bool	operator== (const C3DCriticalPoint &cp) const

void	set_gamma (float gamma_)

Detailed Description

A class to hold a critical point. This class holds a critical point in a 3D vector field It consists of a localtion $x_0 \in \mathbb{R}^3$ , Matrix $A \in \mathbb{R}^{3 \times 3}$ , and a magnitude $\gamma \in \mathbb{R}$ . It is used only as an intermidiate storage.

Remarks: partially untested

Definition at line 44 of file critical_point.hh.

Member Typedef Documentation

typedef std::vector< C3DCriticalPoint > C3DCriticalPoint::List

A list of critical points.

Definition at line 48 of file critical_point.hh.

Constructor & Destructor Documentation

C3DCriticalPoint::C3DCriticalPoint ( )

The standart constructor. It created a critical point with a magintude of zero, at location (0,0,0) with the Zero - Matrix as phase portrait.

C3DCriticalPoint::C3DCriticalPoint ( const C3DFVector & x0_ )

Construct a critical point at a certain location. Magnitude and pahse portrait are set to zero.

Parameters

x0_	location of the new critical point

C3DCriticalPoint::C3DCriticalPoint	(	float	x,
		float	y,
		float	z
	)

Construct a critical point at a certain location. Magnitude and pahse portrait are set to zero.

Parameters

x	x-coordinate of the new critical point
y	y-coordinate of the new critical point
z	z-coordinate of the new critical point

C3DCriticalPoint::C3DCriticalPoint ( const C3DCriticalPoint & org )

Copy constructor.

Parameters

org	The critical point to be copied.

Member Function Documentation

C3DFVector C3DCriticalPoint::at ( const C3DFVector & x ) const

return the magniture of the critical point at location x according to

$\frac {\Gamma}{ \| \mathbf{x} - \mathbf{x_0} \| ^ 2} A \dot (x - x0)$

Parameters

x	location weher to evaluate the vector field

Return values

value of vector field created by this crtitical point at x

C3DFVector C3DCriticalPoint::at_alt ( const C3DFVector & x ) const

const C3DFMatrix C3DCriticalPoint::get_a ( ) const

inline

Return values

the	(read only) phase portrait of the critical point.

Definition at line 369 of file critical_point.hh.

C3DFMatrix & C3DCriticalPoint::get_a ( )

inline

Return values

the	phase portrait of the critical point writable

Definition at line 379 of file critical_point.hh.

float C3DCriticalPoint::get_gamma ( ) const

inline

Return values

the	magnitude of the critical point

Definition at line 384 of file critical_point.hh.

const C3DFVector C3DCriticalPoint::get_point ( ) const

inline

Return values

the	(read only) location of the critical point.

Definition at line 364 of file critical_point.hh.

C3DFVector & C3DCriticalPoint::get_point ( )

inline

Return values

the	location of the critical point writable

Definition at line 374 of file critical_point.hh.

bool C3DCriticalPoint::operator< ( const C3DCriticalPoint & cp ) const

inline

Definition at line 401 of file critical_point.hh.

C3DCriticalPoint& C3DCriticalPoint::operator= ( const C3DCriticalPoint & org )

Assignment operator.

Parameters

org	The critical point to be copied.

bool C3DCriticalPoint::operator== ( const C3DCriticalPoint & cp ) const

inline

compare two critical points

they are equal, if magnitude, phase portrait, and location are equal

Definition at line 395 of file critical_point.hh.

void C3DCriticalPoint::set_gamma ( float gamma_ )

inline

set the magnitude if the critical point

Parameters

gamma_ the new magnitude of the critical point

Definition at line 389 of file critical_point.hh.

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

critical_point.hh

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation