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< C3DCriticalPointList
 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
 
float get_gamma () const
 
const C3DFVector get_point () const
 
bool operator< (const C3DCriticalPoint &cp) const
 
C3DCriticalPointoperator= (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 48 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.

◆ 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
xx-coordinate of the new critical point
yy-coordinate of the new critical point
zz-coordinate of the new critical point

◆ C3DCriticalPoint() [4/4]

C3DCriticalPoint::C3DCriticalPoint ( const C3DCriticalPoint org)

Copy constructor.

Parameters
orgThe critical point to be copied.

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
xlocation weher to evaluate the vector field
Return values
valueof 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
xlocation weher to evaluate the vector field
Return values
valueof vector field created by this crtitical point at x

◆ get_a()

const C3DFMatrix C3DCriticalPoint::get_a ( ) const
inline
Return values
the(read only) phase portrait of the critical point.

Definition at line 357 of file critical_point.hh.

◆ get_gamma()

float C3DCriticalPoint::get_gamma ( ) const
inline
Return values
themagnitude of the critical point

Definition at line 374 of file critical_point.hh.

◆ get_point()

const C3DFVector C3DCriticalPoint::get_point ( ) const
inline
Return values
the(read only) location of the critical point.

Definition at line 352 of file critical_point.hh.

◆ operator<()

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

Definition at line 391 of file critical_point.hh.

References NS_MIA_END.

◆ operator=()

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

Assignment operator.

Parameters
orgThe critical point to be copied.

◆ 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 385 of file critical_point.hh.

◆ set_a()

void C3DCriticalPoint::set_a ( const C3DFMatrix a)
inline
Return values
thephase portrait of the critical point

Definition at line 368 of file critical_point.hh.

◆ 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 379 of file critical_point.hh.

◆ set_point()

void C3DCriticalPoint::set_point ( const C3DFVector x)
inline
Return values
thelocation of the critical point

Definition at line 363 of file critical_point.hh.


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