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