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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<li class="navelem"><a class="el" href="namespacehoa.html">hoa</a></li><li class="navelem"><a class="el" href="classhoa_1_1_harmonic.html">Harmonic</a></li> </ul>
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<a href="#pub-methods">Public Member Functions</a> |
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<p>The class owns basic harmonics informations.
<a href="classhoa_1_1_harmonic.html#details">More...</a></p>
<p><code>#include <<a class="el" href="_hoa___harmonics_8hpp_source.html">Hoa_Harmonics.hpp</a>></code></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a4055701b66d8f5ad5d9b746944841fbc"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#a4055701b66d8f5ad5d9b746944841fbc">Harmonic</a> (const size_t index) hoa_noexcept</td></tr>
<tr class="memdesc:a4055701b66d8f5ad5d9b746944841fbc"><td class="mdescLeft"> </td><td class="mdescRight">The harmonic constructor. <a href="#a4055701b66d8f5ad5d9b746944841fbc">More...</a><br /></td></tr>
<tr class="separator:a4055701b66d8f5ad5d9b746944841fbc"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aae63dde3a79b7a1b20170ebacea54bad"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aae63dde3a79b7a1b20170ebacea54bad"></a>
 </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#aae63dde3a79b7a1b20170ebacea54bad">~Harmonic</a> () hoa_noexcept</td></tr>
<tr class="memdesc:aae63dde3a79b7a1b20170ebacea54bad"><td class="mdescLeft"> </td><td class="mdescRight">The harmonic destructor. <br /></td></tr>
<tr class="separator:aae63dde3a79b7a1b20170ebacea54bad"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a265f69895d9ef7d225f12b809c964f6d"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a265f69895d9ef7d225f12b809c964f6d"></a>
size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#a265f69895d9ef7d225f12b809c964f6d">getIndex</a> () const hoa_noexcept</td></tr>
<tr class="memdesc:a265f69895d9ef7d225f12b809c964f6d"><td class="mdescLeft"> </td><td class="mdescRight">Returns the ACN index of the harmonic. <br /></td></tr>
<tr class="separator:a265f69895d9ef7d225f12b809c964f6d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a7882aa5416d50d12481a1c0b1e01c48f"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a7882aa5416d50d12481a1c0b1e01c48f"></a>
size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#a7882aa5416d50d12481a1c0b1e01c48f">getDegree</a> () const hoa_noexcept</td></tr>
<tr class="memdesc:a7882aa5416d50d12481a1c0b1e01c48f"><td class="mdescLeft"> </td><td class="mdescRight">Returns the precomputed degree of the harmonic. <br /></td></tr>
<tr class="separator:a7882aa5416d50d12481a1c0b1e01c48f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a69831ee5f0b20c0aca016e707bd55809"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a69831ee5f0b20c0aca016e707bd55809"></a>
long </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#a69831ee5f0b20c0aca016e707bd55809">getOrder</a> () const hoa_noexcept</td></tr>
<tr class="memdesc:a69831ee5f0b20c0aca016e707bd55809"><td class="mdescLeft"> </td><td class="mdescRight">Returns the precomputed azimuthal order of the harmonic. <br /></td></tr>
<tr class="separator:a69831ee5f0b20c0aca016e707bd55809"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a43a09d1798093a24595c00b503024ced"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a43a09d1798093a24595c00b503024ced"></a>
std::string </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#a43a09d1798093a24595c00b503024ced">getName</a> () const hoa_noexcept</td></tr>
<tr class="memdesc:a43a09d1798093a24595c00b503024ced"><td class="mdescLeft"> </td><td class="mdescRight">Returns the name of the harmonic. <br /></td></tr>
<tr class="separator:a43a09d1798093a24595c00b503024ced"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af560959b44de05278f0d1b9a2e3bd859"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="af560959b44de05278f0d1b9a2e3bd859"></a>
T </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#af560959b44de05278f0d1b9a2e3bd859">getNormalization</a> () const hoa_noexcept</td></tr>
<tr class="memdesc:af560959b44de05278f0d1b9a2e3bd859"><td class="mdescLeft"> </td><td class="mdescRight">Returns the normalization of the harmonic. <br /></td></tr>
<tr class="separator:af560959b44de05278f0d1b9a2e3bd859"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aef5e07c1181e3563b4e31723167bfac4"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aef5e07c1181e3563b4e31723167bfac4"></a>
T </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#aef5e07c1181e3563b4e31723167bfac4">getSemiNormalization</a> () const hoa_noexcept</td></tr>
<tr class="memdesc:aef5e07c1181e3563b4e31723167bfac4"><td class="mdescLeft"> </td><td class="mdescRight">Returns the semi-normalization of the harmonic. <br /></td></tr>
<tr class="separator:aef5e07c1181e3563b4e31723167bfac4"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-methods"></a>
Static Public Member Functions</h2></td></tr>
<tr class="memitem:a8e544dd821449db9531745622f2b9fa5"><td class="memItemLeft" align="right" valign="top">static long </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#a8e544dd821449db9531745622f2b9fa5">getIndex</a> (const size_t degree, const long order) hoa_noexcept</td></tr>
<tr class="memdesc:a8e544dd821449db9531745622f2b9fa5"><td class="mdescLeft"> </td><td class="mdescRight">Returns the index of an harmonic for a specific degree and azimuthal order. <a href="#a8e544dd821449db9531745622f2b9fa5">More...</a><br /></td></tr>
<tr class="separator:a8e544dd821449db9531745622f2b9fa5"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a97f027d1b64d4bf99f7bfe9c6db63cd8"><td class="memItemLeft" align="right" valign="top">static size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#a97f027d1b64d4bf99f7bfe9c6db63cd8">getDegree</a> (const size_t index) hoa_noexcept</td></tr>
<tr class="memdesc:a97f027d1b64d4bf99f7bfe9c6db63cd8"><td class="mdescLeft"> </td><td class="mdescRight">Returns the degree of an harmonic for an index. <a href="#a97f027d1b64d4bf99f7bfe9c6db63cd8">More...</a><br /></td></tr>
<tr class="separator:a97f027d1b64d4bf99f7bfe9c6db63cd8"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a93e31f7bc0f7eaaa4b084fd9621d426c"><td class="memItemLeft" align="right" valign="top">static long </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#a93e31f7bc0f7eaaa4b084fd9621d426c">getOrder</a> (const size_t index) hoa_noexcept</td></tr>
<tr class="memdesc:a93e31f7bc0f7eaaa4b084fd9621d426c"><td class="mdescLeft"> </td><td class="mdescRight">Returns the azimuthal order of an harmonic for an index. <a href="#a93e31f7bc0f7eaaa4b084fd9621d426c">More...</a><br /></td></tr>
<tr class="separator:a93e31f7bc0f7eaaa4b084fd9621d426c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a817ea66bb97f6fd0b3aad7bab1f25528"><td class="memItemLeft" align="right" valign="top">static size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#a817ea66bb97f6fd0b3aad7bab1f25528">getNumberOfHarmonics</a> (const size_t order) hoa_noexcept</td></tr>
<tr class="memdesc:a817ea66bb97f6fd0b3aad7bab1f25528"><td class="mdescLeft"> </td><td class="mdescRight">Returns the number of harmonics for an order of decomposition. <a href="#a817ea66bb97f6fd0b3aad7bab1f25528">More...</a><br /></td></tr>
<tr class="separator:a817ea66bb97f6fd0b3aad7bab1f25528"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:abd155cbeddd84fa91b9b53ef670adcc9"><td class="memItemLeft" align="right" valign="top">static size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#abd155cbeddd84fa91b9b53ef670adcc9">getNumberOfHarmonicsInDegree</a> (const size_t degree) hoa_noexcept</td></tr>
<tr class="memdesc:abd155cbeddd84fa91b9b53ef670adcc9"><td class="mdescLeft"> </td><td class="mdescRight">Returns the number of harmonics for a degree. <a href="#abd155cbeddd84fa91b9b53ef670adcc9">More...</a><br /></td></tr>
<tr class="separator:abd155cbeddd84fa91b9b53ef670adcc9"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a956a04bc01194daa3b25edc96b127e6b"><td class="memItemLeft" align="right" valign="top">static T </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#a956a04bc01194daa3b25edc96b127e6b">getNormalization</a> (const size_t degree, const long order) hoa_noexcept</td></tr>
<tr class="memdesc:a956a04bc01194daa3b25edc96b127e6b"><td class="mdescLeft"> </td><td class="mdescRight">Returns the normalization N3D or N2D of an harmonic. <a href="#a956a04bc01194daa3b25edc96b127e6b">More...</a><br /></td></tr>
<tr class="separator:a956a04bc01194daa3b25edc96b127e6b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:acb28e9103cd05976c29667cd8a3df10e"><td class="memItemLeft" align="right" valign="top">static T </td><td class="memItemRight" valign="bottom"><a class="el" href="classhoa_1_1_harmonic.html#acb28e9103cd05976c29667cd8a3df10e">getSemiNormalization</a> (const size_t degree, const long order) hoa_noexcept</td></tr>
<tr class="memdesc:acb28e9103cd05976c29667cd8a3df10e"><td class="mdescLeft"> </td><td class="mdescRight">Returns the semi-normalization of an harmonic. <a href="#acb28e9103cd05976c29667cd8a3df10e">More...</a><br /></td></tr>
<tr class="separator:acb28e9103cd05976c29667cd8a3df10e"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<Dimension D, typename T><br />
class hoa::Harmonic< D, T ></h3>
<p>The class owns basic harmonics informations. </p>
<p>The class allows to retrieves several informations about the harmonics: the numbering (ACN), the normalization (SN3D/N3D), the degree, the aziumthal order, etc. </p>
<p>Definition at line <a class="el" href="_hoa___harmonics_8hpp_source.html#l00022">22</a> of file <a class="el" href="_hoa___harmonics_8hpp_source.html">Hoa_Harmonics.hpp</a>.</p>
</div><h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<td>(</td>
<td class="paramtype">const size_t </td>
<td class="paramname"><em>index</em></td><td>)</td>
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<p>The harmonic constructor. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">index</td><td>The index must be at least 1. </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="_hoa___harmonics_8hpp_source.html#l00032">32</a> of file <a class="el" href="_hoa___harmonics_8hpp_source.html">Hoa_Harmonics.hpp</a>.</p>
</div>
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<h2 class="groupheader">Member Function Documentation</h2>
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<td class="memname">static long getIndex </td>
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<td class="paramtype">const size_t </td>
<td class="paramname"><em>degree</em>, </td>
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<td class="paramtype">const long </td>
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<p>Returns the index of an harmonic for a specific degree and azimuthal order. </p>
<p>The computation is \(i=2|m|-(m<0)\) in 2D and \(i=(l(l+1))+m\) in 3D. with \(l\) the degree, \(m\) the azimuthal order and \(i\) the index of the harmonic. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">degree</td><td>The degree of the harmonic. </td></tr>
<tr><td class="paramname">order</td><td>The order of the harmonic. </td></tr>
</table>
</dd>
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<p>Definition at line <a class="el" href="_hoa___harmonics_8hpp_source.html#l00066">66</a> of file <a class="el" href="_hoa___harmonics_8hpp_source.html">Hoa_Harmonics.hpp</a>.</p>
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<td class="memname">static size_t getDegree </td>
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<p>Returns the degree of an harmonic for an index. </p>
<p>The computation is \(l=\frac{i+i\bmod{2}}{2}\) in 2D and \(l=\sqrt{i}\) in 3D. with \(l\) the degree and \(i\) the index of the harmonic. </p><dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">index</td><td>The index of the harmonic. </td></tr>
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</dd>
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<p>Definition at line <a class="el" href="_hoa___harmonics_8hpp_source.html#l00073">73</a> of file <a class="el" href="_hoa___harmonics_8hpp_source.html">Hoa_Harmonics.hpp</a>.</p>
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<td class="memname">static long getOrder </td>
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<p>Returns the azimuthal order of an harmonic for an index. </p>
<p>The computation is \(m=l(1-2(i\bmod{2}))\) in 2D and \(m=i-(l(l+1))\) in 3D. with \(l\) the degree, \(m\) the azimuthal order and \(i\) the index of the harmonic. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">index</td><td>The index of the harmonic. </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="_hoa___harmonics_8hpp_source.html#l00081">81</a> of file <a class="el" href="_hoa___harmonics_8hpp_source.html">Hoa_Harmonics.hpp</a>.</p>
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<td class="memname">static size_t getNumberOfHarmonics </td>
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<p>Returns the number of harmonics for an order of decomposition. </p>
<p>The computation is \(2N+1\) in 2D and \((N+1)^{2}\) in 3D. with \(N\) the order of decomposition. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">order</td><td>The order of decomposition. </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="_hoa___harmonics_8hpp_source.html#l00089">89</a> of file <a class="el" href="_hoa___harmonics_8hpp_source.html">Hoa_Harmonics.hpp</a>.</p>
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<td class="memname">static size_t getNumberOfHarmonicsInDegree </td>
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<p>Returns the number of harmonics for a degree. </p>
<p>The computation is \((degree\neq0)+1\) in 2D and \(2l+1\) in 3D. with \(l\) the degree. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">degree</td><td>The degree. </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="_hoa___harmonics_8hpp_source.html#l00096">96</a> of file <a class="el" href="_hoa___harmonics_8hpp_source.html">Hoa_Harmonics.hpp</a>.</p>
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<td class="memname">static T getNormalization </td>
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<p>Returns the normalization N3D or N2D of an harmonic. </p>
<p>The semi-normalization \(k^{n2d}_{l, m}\) and \(k^{n3d}_{l, m}\) are defined by: </p><p class="formulaDsp">
\[k^{n2d}_{l, m} = 1 \]
</p>
<p class="formulaDsp">
\[k^{n3d}_{l, m} = k^{sn3d}_{l, m}\sqrt{2l+1} \]
</p>
<p> with \(l\) the degree, \(m\) the azimuthal order, </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">degree</td><td>The degree of the harmonic. </td></tr>
<tr><td class="paramname">order</td><td>The order of the harmonic. </td></tr>
</table>
</dd>
</dl>
<p>Definition at line <a class="el" href="_hoa___harmonics_8hpp_source.html#l00107">107</a> of file <a class="el" href="_hoa___harmonics_8hpp_source.html">Hoa_Harmonics.hpp</a>.</p>
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<p>Returns the semi-normalization of an harmonic. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">degree</td><td>The degree of the harmonic. </td></tr>
<tr><td class="paramname">order</td><td>The order of the harmonic. </td></tr>
</table>
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<p>Definition at line <a class="el" href="_hoa___harmonics_8hpp_source.html#l00113">113</a> of file <a class="el" href="_hoa___harmonics_8hpp_source.html">Hoa_Harmonics.hpp</a>.</p>
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