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The SKIRT project
advanced radiative transfer for astrophysics
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The SKIRT project
advanced radiative transfer for astrophysics
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#include <GaussianGeometry.hpp>
Public Member Functions | |
| double | density (double r) const override |
| double | dispersion () const |
| double | randomRadius () const override |
| double | Sigmar () const override |
 Public Member Functions inherited from SpheGeometry | |
| virtual double | density (double r) const =0 |
| double | density (Position bfr) const override |
| int | dimension () const override |
| Position | generatePosition () const override |
| virtual double | randomRadius () const =0 |
| virtual double | Sigmar () const =0 |
| double | SigmaX () const override |
| double | SigmaY () const override |
| double | SigmaZ () const override |
| virtual double | density (Position bfr) const =0 |
| virtual int | dimension () const =0 |
| virtual Position | generatePosition () const =0 |
| virtual double | SigmaX () const =0 |
| virtual double | SigmaY () const =0 |
| virtual double | SigmaZ () const =0 |
| Public Member Functions inherited from SimulationItem | |
| template<class T > | |
| T * | find (bool setup=true) const |
| template<class T > | |
| T * | interface (int levels=-999999, bool setup=true) const |
| virtual string | itemName () const |
| void | setup () |
| string | typeAndName () const |
| Public Member Functions inherited from Item | |
| Item (const Item &)=delete | |
| virtual | ~Item () |
| void | addChild (Item *child) |
| const vector< Item * > & | children () const |
| virtual void | clearItemListProperty (const PropertyDef *property) |
| void | destroyChild (Item *child) |
| virtual bool | getBoolProperty (const PropertyDef *property) const |
| virtual vector< double > | getDoubleListProperty (const PropertyDef *property) const |
| virtual double | getDoubleProperty (const PropertyDef *property) const |
| virtual string | getEnumProperty (const PropertyDef *property) const |
| virtual int | getIntProperty (const PropertyDef *property) const |
| virtual vector< Item * > | getItemListProperty (const PropertyDef *property) const |
| virtual Item * | getItemProperty (const PropertyDef *property) const |
| virtual string | getStringProperty (const PropertyDef *property) const |
| int | getUtilityProperty (string name) const |
| virtual void | insertIntoItemListProperty (const PropertyDef *property, int index, Item *item) |
| Item & | operator= (const Item &)=delete |
| Item * | parent () const |
| virtual void | removeFromItemListProperty (const PropertyDef *property, int index) |
| virtual void | setBoolProperty (const PropertyDef *property, bool value) |
| virtual void | setDoubleListProperty (const PropertyDef *property, vector< double > value) |
| virtual void | setDoubleProperty (const PropertyDef *property, double value) |
| virtual void | setEnumProperty (const PropertyDef *property, string value) |
| virtual void | setIntProperty (const PropertyDef *property, int value) |
| virtual void | setItemProperty (const PropertyDef *property, Item *item) |
| virtual void | setStringProperty (const PropertyDef *property, string value) |
| void | setUtilityProperty (string name, int value) |
| virtual string | type () const |
Protected Member Functions | |
| GaussianGeometry () | |
| void | setupSelfBefore () override |
| Protected Member Functions inherited from SpheGeometry | |
| SpheGeometry () | |
| Protected Member Functions inherited from Geometry | |
| Geometry () | |
| Random * | random () const |
| void | setupSelfBefore () override |
| Protected Member Functions inherited from SimulationItem | |
| SimulationItem () | |
| virtual bool | offersInterface (const std::type_info &interfaceTypeInfo) const |
| virtual void | setupSelfAfter () |
| virtual void | setupSelfBefore () |
| Protected Member Functions inherited from Item | |
| Item () | |
Private Types | |
| using | BaseType = SpheGeometry |
| using | ItemType = GaussianGeometry |
Private Attributes | |
| double | _dispersion |
| double | _rho0 |
| Array | _rv |
| const double & | _sigma |
| Array | _Xv |
Friends | |
| class | ItemRegistry |
The GaussianGeometry class is a subclass of the SpheGeometry class, and describes spherical geometries characterized by a Gaussian density profile,
\[ \rho(r) = \rho_0\,\exp\left( -\frac{r^2}{2\sigma^2} \right) .\]
This geometry has one parameter, the radial dispersion \(\sigma\).
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inlineprotected |
Default constructor for concrete Item subclass GaussianGeometry : "a Gaussian geometry" .
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overridevirtual |
This function returns the density \(\rho(r)\) at the radius \(r\). It just implements the analytical formula.
Implements SpheGeometry.
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inline |
This function returns the value of the discoverable double property dispersion : "the scale length (dispersion) σ" .
This property represents a physical quantity of type "length" .
The minimum value for this property is "]0" .
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overridevirtual |
This function returns the radius \(r\) of a random position drawn from a spherical Gaussian density distribution. Such a value can be generated by picking a uniform deviate \({\cal{X}}\) and solving the equation
\[ {\cal{X}} = 4\pi \int_0^r \rho(r')\, r'^2\, {\text{d}}r' \]
for \(r\), where \(\rho(r)\) is the Gaussian radial density profile. This is done by interpolating from the precalculated table of the cumulative distribution.
Implements SpheGeometry.
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overrideprotectedvirtual |
This function calculates some frequently used values. The central density \(\rho_0\) is set by the normalization condition that the total mass equals one, which is straightforward for a Gaussian distribution,
\[ \rho_0 = \frac{1}{(2\pi)^{3/2}\,\sigma^3} .\]
This function also precalculates of a vector with the cumulative mass
\[ M(r) = 4\pi \int_0^r \rho(r')\, r'^2\, {\text{d}}r' \]
at a large number of radii. For the Gaussian distribution we find
\[ M(r) = \mathrm{erf}(t) - \frac{2}{\sqrt{\pi}} \,t \, \exp(-t^2) \quad\mathrm{with}\quad t = \frac{r}{\sqrt{2}\,\sigma} .\]
Reimplemented from SimulationItem.
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overridevirtual |
This function returns the surface mass density along a radial line starting at the centre of the coordinate system, i.e.
\[ \Sigma_r = \int_0^\infty \rho(r)\,{\text{d}}r. \]
For a Gaussian geometry we easily find
\[ \Sigma_r = \frac{1}{4\pi\,\sigma^2}. \]
Implements SpheGeometry.