C3DCriticalPoint Class Reference

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.

Public Member Functions
C3DFVector	at (const C3DFVector &x) const
C3DFVector	at_alt (const C3DFVector &x) const
	C3DCriticalPoint ()
	C3DCriticalPoint (const C3DCriticalPoint &org)
	C3DCriticalPoint (const C3DFVector &x0_)
	C3DCriticalPoint (float x, float y, float z)
const C3DFMatrix	get_a () const
float	get_gamma () const
const C3DFVector	get_point () const
C3DCriticalPoint &	operator= (const C3DCriticalPoint &org)
bool	operator== (const C3DCriticalPoint &cp) const
void	set_a (const C3DFMatrix &)
void	set_gamma (float gamma_)
void	set_point (const C3DFVector &)

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

List

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

A list of critical points.

Definition at line 49 of file critical_point.hh.

Constructor & Destructor Documentation

C3DCriticalPoint() [1/4]

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.

Referenced by at_alt(), C3DCriticalPoint(), operator=(), and operator==().

C3DCriticalPoint() [2/4]

C3DCriticalPoint::C3DCriticalPoint

(

const C3DFVector &

x0_

)

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

Parameters

x0_	location of the new critical point

C3DCriticalPoint() [3/4]

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() [4/4]

C3DCriticalPoint::C3DCriticalPoint

(

const C3DCriticalPoint &

org

)

Copy constructor.

Parameters

org	The critical point to be copied.

References C3DCriticalPoint().

Member Function Documentation

at()

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

at_alt()

C3DFVector C3DCriticalPoint::at_alt

(

const C3DFVector &

x

)

const

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

\[ \frac {A \dot (x - x0)}{ | \| \mathbf{x} - \mathbf{x_0} \|_2 - gamma |} \]

Parameters

x	location weher to evaluate the vector field

Return values

value

of vector field created by this crtitical point at x

References C3DCriticalPoint().

get_a()

const C3DFMatrix C3DCriticalPoint::get_a ( ) const

inline

Return values

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

Definition at line 360 of file critical_point.hh.

Referenced by operator=().

get_gamma()

float C3DCriticalPoint::get_gamma ( ) const

inline

Return values

the	magnitude of the critical point

Definition at line 377 of file critical_point.hh.

Referenced by operator=().

get_point()

const C3DFVector C3DCriticalPoint::get_point ( ) const

inline

Return values

the	(read only) location of the critical point.

Definition at line 355 of file critical_point.hh.

Referenced by operator=().

operator=()

C3DCriticalPoint & C3DCriticalPoint::operator=

(

const C3DCriticalPoint &

org

)

Assignment operator.

Parameters

org	The critical point to be copied.

References C3DCriticalPoint(), get_a(), get_gamma(), get_point(), set_a(), set_gamma(), and set_point().

operator==()

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 388 of file critical_point.hh.

References C3DCriticalPoint().

set_a()

void C3DCriticalPoint::set_a ( const C3DFMatrix & a )

inline

Return values

the	phase portrait of the critical point

Definition at line 371 of file critical_point.hh.

Referenced by operator=().

set_gamma()

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 382 of file critical_point.hh.

Referenced by operator=().

set_point()

void C3DCriticalPoint::set_point ( const C3DFVector & x )

inline

Return values

the	location of the critical point

Definition at line 366 of file critical_point.hh.

Referenced by operator=().

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

• critical_point.hh