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.
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#include <mia/3d/critical_point.hh>
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.
Definition at line 44 of file critical_point.hh.
◆ List
◆ C3DCriticalPoint() [1/4]
| C3DCriticalPoint::C3DCriticalPoint |
( |
| ) |
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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, |
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|
float |
z |
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) |
| |
Construct a critical point at a certain location. Magnitude and pahse portrait are set to zero.
- Parameters
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| 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]
Copy constructor.
- Parameters
-
| org | The critical point to be copied. |
◆ at()
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()
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 |
◆ get_a()
| const C3DFMatrix C3DCriticalPoint::get_a |
( |
| ) |
const |
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inline |
- Return values
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| 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 |
◆ 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<()
◆ operator=()
Assignment operator.
- Parameters
-
| org | The critical point to be copied. |
◆ operator==()
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 | ) |
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|
inline |
- Return values
-
| the | phase 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 | ) |
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|
inline |
The documentation for this class was generated from the following file:
1.8.13