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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 <CubicSplineSmoothingKernel.hpp>
Public Member Functions | |
| double | columnDensity (double q) const override |
| double | density (double u) const override |
| double | generateRadius () const override |
| 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 | |
| CubicSplineSmoothingKernel () | |
| void | setupSelfBefore () override |
| Protected Member Functions inherited from SmoothingKernel | |
| SmoothingKernel () | |
| 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 () |
| Protected Member Functions inherited from Item | |
| Item () | |
Private Types | |
| using | BaseType |
| using | ItemType |
Private Attributes | |
| Array | _Xv |
Friends | |
| class | ItemRegistry |
The CubicSpineSmoothingKernel class is a subclass of the abstract SmoothingKernel class, and describes smoothing kernels defined by the standard cubic spline density,
\[ W(u) = \begin{cases}\; \dfrac{8\,(1-6\,u^2+6\,u^3)}{\pi} & \quad\text{if }0\leq u \leq \tfrac12, \\ \; \dfrac{16\,(1-u)^3}{\pi} & \quad \text{if }\tfrac12 \leq u \leq 1, \\ \; 0 & \quad \text{else}. \end{cases} \]
It can be checked that this function is continuous at \(u=\tfrac12\) and that it satisfies the required normalization
\[ 4\pi \int_0^\infty W(u)\, u^2\, {\text{d}}u = 1. \]
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inlineprotected |
Default constructor for concrete Item subclass CubicSplineSmoothingKernel: "a cubic spline smoothing kernel".
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overridevirtual |
This function returns the column density \(\Sigma(q) = 2 \int_{q}^1 \frac{W(u)\,u \,{\text{d}}u} {\sqrt{u^2-q^2}}\) of the smoothing kernel as a function of the normalized impact radius \(q=r_\text{i}/h\). For the cubic spline smoothing kernel, we obtain
\[\Sigma(q) = \begin{cases} \; \dfrac{2}{\pi}\left[(4+26\,q^2)\sqrt{1-q^2} - (1+26\,q^2)\sqrt{1-4\,q^2} \right. \\ \left. \qquad\quad-18\,q^4\ln \left(\dfrac{2\,q} {1+\sqrt{1-4\,q^2}}\right) -6\,q^2(4+q^2) \ln\left(\dfrac{2+2\sqrt{1-q^2}} {1+\sqrt{1-4\,q^2}}\right) \right] & \quad{\text{if }}0\leq q\leq \tfrac12, \\[1em] \; \dfrac{4}{\pi}\left[(2+13\,q^2)\sqrt{1-q^2} + 3\,q^2(4+q^2)\ln\left(\dfrac{q} {1+\sqrt{1-q^2}}\right)\right] & \quad{\text{if }}\tfrac12\leq q\leq 1, \\ \; 0 & \quad{\text{else}}. \end{cases} \]
Implements SmoothingKernel.
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overridevirtual |
This function returns the density \(W(u)\) of the smoothing kernel as a function of the normalized radius \(u\). It just implements the analytical formula given in the class header.
Implements SmoothingKernel.
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overridevirtual |
This function generates a random normalized radius \(u\) from the smoothing kernel. This is accomplished by generating a uniform deviate \({\cal{X}}\), and solving the equation
\[ {\cal{X}} = \int_0^u 4\pi\,W(u')\,u'^2\, {\text{d}}u' \]
for \(u\). For the cubic spline smoothing kernel, we obtain
\[ \int_0^u 4\pi\,W(u')\,u'^2\, {\text{d}}u' = \begin{cases} \; 32 u^{6}-\dfrac{192}{5} u^{5}+\dfrac{32}{3} u^{3} & \quad\text{if }0\leq u \leq \tfrac12, \\ \; -\dfrac{32}{3} u^{6}+\dfrac{192}{5} u^{5}-48 u^{4}+\dfrac{64}{3} u^{3}-\dfrac{1}{15} & \quad \text{if }\tfrac12 \leq u \leq 1. \end{cases} \]
We precompute a tabulation of this cumulative distribution function on which we interpolate to solve this equation.
Implements SmoothingKernel.
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overrideprotectedvirtual |
This function sets up a grid that will be used to sample random radii from the smoothing kernel.
Reimplemented from SimulationItem.