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<a href="pearl-polar-coordinates_8ipf.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="preprocessor">#pragma TextEncoding = &quot;UTF-8&quot;</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="preprocessor">#pragma rtGlobals=3</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="preprocessor">#pragma version = 1.1</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="preprocessor">#pragma IgorVersion = 6.1</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="preprocessor">#pragma ModuleName = PearlPolarCoordinates</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span> </div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">// author: matthias.muntwiler@psi.ch</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Copyright (c) 2011-13 Paul Scherrer Institut</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// $Id$</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="foldopen" id="foldopen00011" data-start="{" data-end="}">
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"><a class="line" href="pearl-polar-coordinates_8ipf.html#aca0a5aaa4854d83ef667c53007312fb8"> 11</a></span>function <a class="code hl_function" href="pearl-polar-coordinates_8ipf.html#aca0a5aaa4854d83ef667c53007312fb8">cart2polar</a>(xx, yy, zz, radius, theta, phi)</div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// converts a 3-vector from Cartesian to polar coordinates</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> variable xx, yy, zz</div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> variable &amp;radius, &amp;theta, &amp;phi <span class="comment">// angles in degrees</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> radius = sqrt(xx^2 + yy^2 + zz^2)</div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> <span class="keywordflow">if</span> (radius &gt; 0)</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> theta = acos(zz / radius) * 180 / pi</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> theta = 0</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> endif</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordflow">if</span> (xx &gt; 0)</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> phi = atan(yy / xx) * 180 / pi</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> elseif (xx &lt; 0)</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> phi = atan(yy / xx) * 180 / pi + 180</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> else</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> if (yy &gt; 0)</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> phi = 90</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> else</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> phi = 270</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> endif</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> endif</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span>end</div>
</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="foldopen" id="foldopen00037" data-start="{" data-end="}">
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"><a class="line" href="pearl-polar-coordinates_8ipf.html#adfc1f0b3cddf672b0ccdb6a22b97ba9e"> 37</a></span>function <a class="code hl_function" href="pearl-polar-coordinates_8ipf.html#adfc1f0b3cddf672b0ccdb6a22b97ba9e">cart2polar_wave</a>(in, out)</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// converts a wave of 3-vectors from Cartesian to polar coordinates</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> wave in <span class="comment">// wave with dimensions (3, N), N &gt;= 1, (x, y, z)</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> wave out <span class="comment">// wave same dimensions as in, (radius, theta, phi)</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// angles in degrees</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> out[0][] = sqrt(in[0][q]^2 + in[1][q]^2 + in[2][q]^2)</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> out[1][] = acos(in[2][q] / out[0][q]) * 180 / pi</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> out[2][] = atan(in[1][q] / in[0][q]) * 180 / pi + 180 * (in[0][q] &lt; 0)</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> out[2][] = numtype(out[2][q]) == 0 ? out[2][q] : 90 + 180 * (in[1][q] &lt; 0)</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span>end</div>
</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="foldopen" id="foldopen00049" data-start="{" data-end="}">
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"><a class="line" href="pearl-polar-coordinates_8ipf.html#a94ccfa9cf52c55eb1f66c2704478c396"> 49</a></span>function <a class="code hl_function" href="pearl-polar-coordinates_8ipf.html#a94ccfa9cf52c55eb1f66c2704478c396">polar2cart</a>(radius, theta, phi, xx, yy, zz)</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// converts a 3-vector from Cartesian to polar coordinates</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> variable radius, theta, phi <span class="comment">// angles in degrees</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> variable &amp;xx, &amp;yy, &amp;zz</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> xx = radius * sin(theta * pi / 180) * cos(phi * pi / 180)</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> yy = radius * sin(theta * pi / 180) * sin(phi * pi / 180)</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> zz = radius * cos(theta * pi / 180)</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span>end</div>
</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> </div>
<div class="foldopen" id="foldopen00059" data-start="{" data-end="}">
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"><a class="line" href="pearl-polar-coordinates_8ipf.html#a6a0ffb6b9160413d9694b1fd8e10c858"> 59</a></span>function <a class="code hl_function" href="pearl-polar-coordinates_8ipf.html#a6a0ffb6b9160413d9694b1fd8e10c858">polar2cart_wave</a>(in, out)</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// converts a wave of 3-vectors from polar to Cartesian coordinates</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> wave in <span class="comment">// wave with dimensions (3, N), N &gt;= 1, (radius, theta, phi)</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// angles in degrees</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> wave out <span class="comment">// wave same dimensions as in, (x, y, z)</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> out[0][] = in[0][q] * sin(in[1][q] * pi / 180) * cos(in[2][q] * pi / 180)</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> out[1][] = in[0][q] * sin(in[1][q] * pi / 180) * sin(in[2][q] * pi / 180)</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> out[2][] = in[0][q] * cos(in[1][q] * pi / 180)</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span>end</div>
</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="foldopen" id="foldopen00070" data-start="{" data-end="}">
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"><a class="line" href="pearl-polar-coordinates_8ipf.html#a58139e6ebfba242b6b2ba3533b865a9a"> 70</a></span>function <a class="code hl_function" href="pearl-polar-coordinates_8ipf.html#a58139e6ebfba242b6b2ba3533b865a9a">polar_distance</a>(polar1, azim1, polar2, azim2)</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// returns the angle between two spherical coordinates</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> variable polar1, azim1</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// angles in degrees</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> variable polar2, azim2</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// angles in degrees</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> variable xx1, yy1, zz1</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> variable xx2, yy2, zz2</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <a class="code hl_function" href="pearl-polar-coordinates_8ipf.html#a94ccfa9cf52c55eb1f66c2704478c396">polar2cart</a>(1, polar1, azim1, xx1, yy1, zz1)</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <a class="code hl_function" href="pearl-polar-coordinates_8ipf.html#a94ccfa9cf52c55eb1f66c2704478c396">polar2cart</a>(1, polar2, azim2, xx2, yy2, zz2)</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> variable vv</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> vv = (xx1 * xx2 + yy1 * yy2 + zz1 * zz2) / sqrt(xx1^2 + yy1^2 + zz1^2) / sqrt(xx2^2 + yy2^2 + zz2^2)</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> return acos(vv) * 180 / pi</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span>end</div>
</div>
<div class="ttc" id="apearl-polar-coordinates_8ipf_html_a58139e6ebfba242b6b2ba3533b865a9a"><div class="ttname"><a href="pearl-polar-coordinates_8ipf.html#a58139e6ebfba242b6b2ba3533b865a9a">polar_distance</a></div><div class="ttdeci">variable polar_distance(variable polar1, variable azim1, variable polar2, variable azim2)</div><div class="ttdef"><b>Definition</b> <a href="pearl-polar-coordinates_8ipf_source.html#l00070">pearl-polar-coordinates.ipf:70</a></div></div>
<div class="ttc" id="apearl-polar-coordinates_8ipf_html_a6a0ffb6b9160413d9694b1fd8e10c858"><div class="ttname"><a href="pearl-polar-coordinates_8ipf.html#a6a0ffb6b9160413d9694b1fd8e10c858">polar2cart_wave</a></div><div class="ttdeci">variable polar2cart_wave(wave in, wave out)</div><div class="ttdef"><b>Definition</b> <a href="pearl-polar-coordinates_8ipf_source.html#l00059">pearl-polar-coordinates.ipf:59</a></div></div>
<div class="ttc" id="apearl-polar-coordinates_8ipf_html_a94ccfa9cf52c55eb1f66c2704478c396"><div class="ttname"><a href="pearl-polar-coordinates_8ipf.html#a94ccfa9cf52c55eb1f66c2704478c396">polar2cart</a></div><div class="ttdeci">variable polar2cart(variable radius, variable theta, variable phi, variable *xx, variable *yy, variable *zz)</div><div class="ttdef"><b>Definition</b> <a href="pearl-polar-coordinates_8ipf_source.html#l00049">pearl-polar-coordinates.ipf:49</a></div></div>
<div class="ttc" id="apearl-polar-coordinates_8ipf_html_aca0a5aaa4854d83ef667c53007312fb8"><div class="ttname"><a href="pearl-polar-coordinates_8ipf.html#aca0a5aaa4854d83ef667c53007312fb8">cart2polar</a></div><div class="ttdeci">variable cart2polar(variable xx, variable yy, variable zz, variable *radius, variable *theta, variable *phi)</div><div class="ttdef"><b>Definition</b> <a href="pearl-polar-coordinates_8ipf_source.html#l00011">pearl-polar-coordinates.ipf:11</a></div></div>
<div class="ttc" id="apearl-polar-coordinates_8ipf_html_adfc1f0b3cddf672b0ccdb6a22b97ba9e"><div class="ttname"><a href="pearl-polar-coordinates_8ipf.html#adfc1f0b3cddf672b0ccdb6a22b97ba9e">cart2polar_wave</a></div><div class="ttdeci">variable cart2polar_wave(wave in, wave out)</div><div class="ttdef"><b>Definition</b> <a href="pearl-polar-coordinates_8ipf_source.html#l00037">pearl-polar-coordinates.ipf:37</a></div></div>
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