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  <div class="navpath"><a class="el" href="namespacerbf.html">rbf</a>::<a class="el" href="classrbf_1_1thin__plate__spline.html">thin_plate_spline</a>
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<h1>rbf::thin_plate_spline Class Reference</h1><!-- doxytag: class="rbf::thin_plate_spline" --><!-- doxytag: inherits="rbf::piecewise_smooth_rbf" -->r^n log(r) with n even
<a href="#_details">More...</a>
<p>
<code>#include &lt;<a class="el" href="rbf_8hpp-source.html">rbf.hpp</a>&gt;</code>
<p>
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Inheritance diagram for rbf::thin_plate_spline:</div>
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Collaboration diagram for rbf::thin_plate_spline:</div>
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<p>
<a href="classrbf_1_1thin__plate__spline-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1thin__plate__spline.html#18e56f16510b1986809e13e06c57e603">thin_plate_spline</a> ()</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1thin__plate__spline.html#ca6f99af3f94dd490080bce202bea72b">thin_plate_spline</a> (const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;c)</td></tr>

<tr><td colspan="2"><br><h2>Static Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1thin__plate__spline.html#7db3860c7d6a9f48ae07853e32110ad6">set_n</a> (size_t new_n)</td></tr>

<tr><td colspan="2"><br><h2>Private Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1thin__plate__spline.html#bbdcc07f10356ae80eca1f2f789ef8cc">operator()</a> (double r) const </td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">The scalar functions defining each RBF.  <a href="#bbdcc07f10356ae80eca1f2f789ef8cc"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1thin__plate__spline.html#9033e98e17d9689d5815228089b7895c">d</a> (double r) const </td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">The scalar first derivative defining each RBF.  <a href="#9033e98e17d9689d5815228089b7895c"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1thin__plate__spline.html#e58fdc6d240f0146ef418507af2bc29d">d2</a> (double r) const </td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">The scalar second derivative defining each RBF.  <a href="#e58fdc6d240f0146ef418507af2bc29d"></a><br></td></tr>
<tr><td colspan="2"><br><h2>Static Private Attributes</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static size_t&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8">n</a> = 0</td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Shape parameter.  <a href="#758f6c4bbc04ff390006b47198429ca8"></a><br></td></tr>
</table>
<hr><a name="_details"></a><h2>Detailed Description</h2>
r^n log(r) with n even <hr><h2>Constructor &amp; Destructor Documentation</h2>
<a class="anchor" name="18e56f16510b1986809e13e06c57e603"></a><!-- doxytag: member="rbf::thin_plate_spline::thin_plate_spline" ref="18e56f16510b1986809e13e06c57e603" args="()" -->
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          <td class="memname">rbf::thin_plate_spline::thin_plate_spline           </td>
          <td>(</td>
          <td class="paramname">          </td>
          <td>&nbsp;)&nbsp;</td>
          <td><code> [inline]</code></td>
        </tr>
      </table>
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<p>
<div class="fragment"><pre class="fragment"><a name="l00145"></a>00145 {};
</pre></div>
<p>

</div>
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<a class="anchor" name="ca6f99af3f94dd490080bce202bea72b"></a><!-- doxytag: member="rbf::thin_plate_spline::thin_plate_spline" ref="ca6f99af3f94dd490080bce202bea72b" args="(const point &amp;c)" -->
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          <td class="memname">rbf::thin_plate_spline::thin_plate_spline           </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>c</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td><code> [inline]</code></td>
        </tr>
      </table>
</div>
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<p>
<div class="fragment"><pre class="fragment"><a name="l00146"></a>00146 : <a class="code" href="classrbf_1_1piecewise__smooth__rbf.html#ec3b67bc216c9846983953fdc1389da3">piecewise_smooth_rbf</a>(c){;};
</pre></div>
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</div>
</div><p>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="7db3860c7d6a9f48ae07853e32110ad6"></a><!-- doxytag: member="rbf::thin_plate_spline::set_n" ref="7db3860c7d6a9f48ae07853e32110ad6" args="(size_t new_n)" -->
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          <td class="memname">void rbf::thin_plate_spline::set_n           </td>
          <td>(</td>
          <td class="paramtype">size_t&nbsp;</td>
          <td class="paramname"> <em>new_n</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td><code> [static]</code></td>
        </tr>
      </table>
</div>
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<p>
<div class="fragment"><pre class="fragment"><a name="l00179"></a>00179                                            {
<a name="l00180"></a>00180     <span class="keywordflow">if</span>(n_new % 2 != 0){
<a name="l00181"></a>00181       badArgument exc;
<a name="l00182"></a>00182       exc.reason = <span class="stringliteral">"Cannot assign an odd n to a thin-plate spline RBF."</span>;
<a name="l00183"></a>00183       exc.line = __LINE__;
<a name="l00184"></a>00184       exc.file = __FILE__;
<a name="l00185"></a>00185       <span class="keywordflow">throw</span> exc;
<a name="l00186"></a>00186     }
<a name="l00187"></a>00187     <a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">thin_plate_spline::n</a> = n_new;
<a name="l00188"></a>00188   }
</pre></div>
<p>

</div>
</div><p>
<a class="anchor" name="bbdcc07f10356ae80eca1f2f789ef8cc"></a><!-- doxytag: member="rbf::thin_plate_spline::operator()" ref="bbdcc07f10356ae80eca1f2f789ef8cc" args="(double r) const " -->
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          <td class="memname">double rbf::thin_plate_spline::operator()           </td>
          <td>(</td>
          <td class="paramtype">double&nbsp;</td>
          <td class="paramname"> <em>r</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td> const<code> [private, virtual]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>
The scalar functions defining each RBF.
<p>

<p>Implements <a class="el" href="classrbf_1_1radial__basis__function.html#ca1d152380fa43082c710a07f28080be">rbf::radial_basis_function</a>.</p>
<div class="fragment"><pre class="fragment"><a name="l00284"></a>00284                                                      {
<a name="l00285"></a>00285     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 0){
<a name="l00286"></a>00286       badArgument exc;
<a name="l00287"></a>00287       exc.reason =
<a name="l00288"></a>00288         <span class="stringliteral">"Parameter n not set for thin_plate_spline. \n"</span>
<a name="l00289"></a>00289         <span class="stringliteral">"Use thin_plate_spline::set_n before evaluating."</span>;
<a name="l00290"></a>00290       exc.line = __LINE__;
<a name="l00291"></a>00291       exc.file = __FILE__;
<a name="l00292"></a>00292       <span class="keywordflow">throw</span> exc;
<a name="l00293"></a>00293     }
<a name="l00294"></a>00294     r = fabs(r);
<a name="l00295"></a>00295     <span class="keywordflow">if</span>(r == 0)
<a name="l00296"></a>00296       <span class="keywordflow">return</span> 0;
<a name="l00297"></a>00297     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 2)
<a name="l00298"></a>00298       <span class="keywordflow">return</span> gsl_pow_2(r)*log(r);
<a name="l00299"></a>00299     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 4)
<a name="l00300"></a>00300       <span class="keywordflow">return</span> gsl_pow_4(r)*log(r);
<a name="l00301"></a>00301     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 6)
<a name="l00302"></a>00302       <span class="keywordflow">return</span> gsl_pow_6(r)*log(r);
<a name="l00303"></a>00303     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 8)
<a name="l00304"></a>00304       <span class="keywordflow">return</span> gsl_pow_8(r)*log(r);
<a name="l00305"></a>00305
<a name="l00306"></a>00306     <span class="keywordflow">return</span> pow(r,<span class="keywordtype">double</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a>))*log(r);
<a name="l00307"></a>00307   }
</pre></div>
<p>

</div>
</div><p>
<a class="anchor" name="9033e98e17d9689d5815228089b7895c"></a><!-- doxytag: member="rbf::thin_plate_spline::d" ref="9033e98e17d9689d5815228089b7895c" args="(double r) const " -->
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          <td class="memname">double rbf::thin_plate_spline::d           </td>
          <td>(</td>
          <td class="paramtype">double&nbsp;</td>
          <td class="paramname"> <em>r</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td> const<code> [private, virtual]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>
The scalar first derivative defining each RBF.
<p>

<p>Implements <a class="el" href="classrbf_1_1radial__basis__function.html#0aa55b82614330604e8ea63b8aef419a">rbf::radial_basis_function</a>.</p>
<div class="fragment"><pre class="fragment"><a name="l00310"></a>00310                                             {
<a name="l00311"></a>00311     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 0){
<a name="l00312"></a>00312       badArgument exc;
<a name="l00313"></a>00313       exc.reason =
<a name="l00314"></a>00314         <span class="stringliteral">"Parameter n not set for thin_plate_spline. \n"</span>
<a name="l00315"></a>00315         <span class="stringliteral">"Use thin_plate_spline::set_n before evaluating."</span>;
<a name="l00316"></a>00316       exc.line = __LINE__;
<a name="l00317"></a>00317       exc.file = __FILE__;
<a name="l00318"></a>00318       <span class="keywordflow">throw</span> exc;
<a name="l00319"></a>00319     }
<a name="l00320"></a>00320     r = fabs(r);
<a name="l00321"></a>00321     <span class="keywordflow">if</span>(r == 0)
<a name="l00322"></a>00322       <span class="keywordflow">return</span> 0;
<a name="l00323"></a>00323     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 2)
<a name="l00324"></a>00324       <span class="keywordflow">return</span> r*(2*log(r) + 1);
<a name="l00325"></a>00325     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 4)
<a name="l00326"></a>00326       <span class="keywordflow">return</span> gsl_pow_3(r)*(4*log(r) + 1);
<a name="l00327"></a>00327     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 6)
<a name="l00328"></a>00328       <span class="keywordflow">return</span> gsl_pow_5(r)*(6*log(r) + 1);
<a name="l00329"></a>00329     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 8)
<a name="l00330"></a>00330       <span class="keywordflow">return</span> gsl_pow_7(r)*(8*log(r) + 1);
<a name="l00331"></a>00331
<a name="l00332"></a>00332     <span class="keywordflow">return</span> pow(r,<span class="keywordtype">double</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a>-1))*(double(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a>)*log(r) + 1);
<a name="l00333"></a>00333   }
</pre></div>
<p>

</div>
</div><p>
<a class="anchor" name="e58fdc6d240f0146ef418507af2bc29d"></a><!-- doxytag: member="rbf::thin_plate_spline::d2" ref="e58fdc6d240f0146ef418507af2bc29d" args="(double r) const " -->
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          <td class="memname">double rbf::thin_plate_spline::d2           </td>
          <td>(</td>
          <td class="paramtype">double&nbsp;</td>
          <td class="paramname"> <em>r</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td> const<code> [private, virtual]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>
The scalar second derivative defining each RBF.
<p>

<p>Implements <a class="el" href="classrbf_1_1radial__basis__function.html#97c9b2a2a93d7133d57cbecf7c3996ac">rbf::radial_basis_function</a>.</p>
<div class="fragment"><pre class="fragment"><a name="l00335"></a>00335                                              {
<a name="l00336"></a>00336     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 0){
<a name="l00337"></a>00337       badArgument exc;
<a name="l00338"></a>00338       exc.reason =
<a name="l00339"></a>00339         <span class="stringliteral">"Parameter n not set for thin_plate_spline. \n"</span>
<a name="l00340"></a>00340         <span class="stringliteral">"Use thin_plate_spline::set_n before evaluating."</span>;
<a name="l00341"></a>00341       exc.line = __LINE__;
<a name="l00342"></a>00342       exc.file = __FILE__;
<a name="l00343"></a>00343       <span class="keywordflow">throw</span> exc;
<a name="l00344"></a>00344     }
<a name="l00345"></a>00345     <span class="keywordflow">if</span> (<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 2 and r == 0){
<a name="l00346"></a>00346       badDomain exc;
<a name="l00347"></a>00347       exc.reason =
<a name="l00348"></a>00348         <span class="stringliteral">"For n = 2, thin-plate splines do no have a derivative at zero."</span>;
<a name="l00349"></a>00349       exc.line = __LINE__;
<a name="l00350"></a>00350       exc.file = __FILE__;
<a name="l00351"></a>00351       <span class="keywordflow">throw</span> exc;
<a name="l00352"></a>00352     }
<a name="l00353"></a>00353     <span class="keywordflow">if</span>(r == 0)
<a name="l00354"></a>00354       <span class="keywordflow">return</span> 0;
<a name="l00355"></a>00355
<a name="l00356"></a>00356     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 2)
<a name="l00357"></a>00357       <span class="keywordflow">return</span> 2*log(r) + 3;
<a name="l00358"></a>00358     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 4)
<a name="l00359"></a>00359       <span class="keywordflow">return</span> gsl_pow_2(r)*(12*log(r) + 7);
<a name="l00360"></a>00360     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 6)
<a name="l00361"></a>00361       <span class="keywordflow">return</span> gsl_pow_4(r)*(30*log(r) + 11);
<a name="l00362"></a>00362     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> == 8)
<a name="l00363"></a>00363       <span class="keywordflow">return</span> gsl_pow_6(r)*(56*log(r) + 15);
<a name="l00364"></a>00364
<a name="l00365"></a>00365     <span class="keywordflow">return</span> pow(r,<span class="keywordtype">double</span>(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a>-2))*(double(<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a>*<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> - <a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a>)*log(r) + double(2*<a class="code" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8" title="Shape parameter.">n</a> - 1));
<a name="l00366"></a>00366   }
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<hr><h2>Member Data Documentation</h2>
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          <td class="memname">size_t <a class="el" href="classrbf_1_1thin__plate__spline.html#758f6c4bbc04ff390006b47198429ca8">rbf::thin_plate_spline::n</a> = 0<code> [static, private]</code>          </td>
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<p>
Shape parameter.
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<hr>The documentation for this class was generated from the following files:<ul>
<li>include/<a class="el" href="rbf_8hpp-source.html">rbf.hpp</a><li><a class="el" href="rbf_8cpp.html">rbf.cpp</a></ul>
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<hr size="1"><address style="text-align: right;"><small>Generated on Sat Jun 28 00:33:26 2008 by&nbsp;
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author	Jordi Guitérrez Hermoso <jordigh@gmail.com>
date	Sun, 29 Jun 2008 04:06:48 -0500
parents	4fa56dc7e271
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