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<h1>Coverage for <b>navipy/maths/coordinates.py</b> :
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<p id="t1" class="pln"><span class="str">"""</span><span class="strut"> </span></p>
<p id="t2" class="pln"><span class="str"> Conversion between coordinates systems</span><span class="strut"> </span></p>
<p id="t3" class="pln"><span class="str">"""</span><span class="strut"> </span></p>
<p id="t4" class="stm run hide_run"><span class="key">import</span> <span class="nam">numpy</span> <span class="key">as</span> <span class="nam">np</span><span class="strut"> </span></p>
<p id="t5" class="stm run hide_run"><span class="key">from</span> <span class="nam">navipy</span><span class="op">.</span><span class="nam">scene</span> <span class="key">import</span> <span class="nam">is_numeric_array</span><span class="strut"> </span></p>
<p id="t6" class="pln"><span class="strut"> </span></p>
<p id="t7" class="pln"><span class="strut"> </span></p>
<p id="t8" class="stm run hide_run"><span class="key">def</span> <span class="nam">cartesian_to_spherical</span><span class="op">(</span><span class="nam">x</span><span class="op">,</span> <span class="nam">y</span><span class="op">,</span> <span class="nam">z</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t9" class="pln"> <span class="str">""" Cartesian to spherical coordinates</span><span class="strut"> </span></p>
<p id="t10" class="pln"><span class="strut"> </span></p>
<p id="t11" class="pln"><span class="str"> :param x: position along x-axis</span><span class="strut"> </span></p>
<p id="t12" class="pln"><span class="str"> :param y: position along y-axis</span><span class="strut"> </span></p>
<p id="t13" class="pln"><span class="str"> :param z: position along z-axis</span><span class="strut"> </span></p>
<p id="t14" class="pln"><span class="str"> :returns: elevation,azimuth,radius</span><span class="strut"> </span></p>
<p id="t15" class="pln"><span class="strut"> </span></p>
<p id="t16" class="pln"><span class="str"> inverse transform of :</span><span class="strut"> </span></p>
<p id="t17" class="pln"><span class="str"> x = radius*cos(elevation) * cos(azimuth)</span><span class="strut"> </span></p>
<p id="t18" class="pln"><span class="str"> y = radius*cos(elevation) * sin(azimuth)</span><span class="strut"> </span></p>
<p id="t19" class="pln"><span class="str"> z = radius*sin(elevation)</span><span class="strut"> </span></p>
<p id="t20" class="pln"><span class="strut"> </span></p>
<p id="t21" class="pln"><span class="str"> """</span><span class="strut"> </span></p>
<p id="t22" class="stm mis"> <span class="nam">radius</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">sqrt</span><span class="op">(</span><span class="nam">x</span><span class="op">**</span><span class="num">2</span> <span class="op">+</span> <span class="nam">y</span><span class="op">**</span><span class="num">2</span> <span class="op">+</span> <span class="nam">z</span><span class="op">**</span><span class="num">2</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t23" class="stm mis"> <span class="nam">elevation</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">arctan2</span><span class="op">(</span><span class="nam">z</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">sqrt</span><span class="op">(</span><span class="nam">x</span><span class="op">**</span><span class="num">2</span> <span class="op">+</span> <span class="nam">y</span><span class="op">**</span><span class="num">2</span><span class="op">)</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t24" class="stm mis"> <span class="nam">azimuth</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">arctan2</span><span class="op">(</span><span class="nam">y</span><span class="op">,</span> <span class="nam">x</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t25" class="stm mis"> <span class="nam">spherical</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">zeros_like</span><span class="op">(</span><span class="nam">x</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t26" class="stm mis"> <span class="nam">spherical</span> <span class="op">=</span> <span class="nam">np</span><span class="op">.</span><span class="nam">tile</span><span class="op">(</span><span class="nam">spherical</span><span class="op">[</span><span class="op">...</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">newaxis</span><span class="op">]</span><span class="op">,</span> <span class="op">(</span><span class="num">3</span><span class="op">,</span><span class="op">)</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t27" class="stm mis"> <span class="key">return</span> <span class="nam">elevation</span><span class="op">,</span> <span class="nam">azimuth</span><span class="op">,</span> <span class="nam">radius</span><span class="strut"> </span></p>
<p id="t28" class="pln"><span class="strut"> </span></p>
<p id="t29" class="pln"><span class="strut"> </span></p>
<p id="t30" class="stm run hide_run"><span class="key">def</span> <span class="nam">spherical_to_cartesian</span><span class="op">(</span><span class="nam">elevation</span><span class="op">,</span> <span class="nam">azimuth</span><span class="op">,</span> <span class="nam">radius</span><span class="op">=</span><span class="num">1</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t31" class="pln"> <span class="str">"""Spherical to cartesian coordinates</span><span class="strut"> </span></p>
<p id="t32" class="pln"><span class="strut"> </span></p>
<p id="t33" class="pln"><span class="str"> :param elevation: elevation</span><span class="strut"> </span></p>
<p id="t34" class="pln"><span class="str"> :param azimuth: azimuth</span><span class="strut"> </span></p>
<p id="t35" class="pln"><span class="str"> :param radius: radius</span><span class="strut"> </span></p><p id="t36" class="pln"><span class="str"> :returns: x,y,z</span><span class="strut"> </span></p>
<p id="t37" class="pln"><span class="strut"> </span></p>
<p id="t38" class="pln"><span class="str"> transform :</span><span class="strut"> </span></p>
<p id="t39" class="pln"><span class="str"> x = radius*cos(elevation) * cos(azimuth)</span><span class="strut"> </span></p>
<p id="t40" class="pln"><span class="str"> y = radius*cos(elevation) * sin(azimuth)</span><span class="strut"> </span></p>
<p id="t41" class="pln"><span class="str"> z = radius*sin(elevation)</span><span class="strut"> </span></p>
<p id="t42" class="pln"><span class="str"> """</span><span class="strut"> </span></p>
<p id="t43" class="stm run hide_run"> <span class="nam">x</span> <span class="op">=</span> <span class="nam">radius</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">cos</span><span class="op">(</span><span class="nam">elevation</span><span class="op">)</span> <span class="op">*</span> <span class="nam">np</span><span class="op">.</span><span class="nam">cos</span><span class="op">(</span><span class="nam">azimuth</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t44" class="stm run hide_run"> <span class="nam">y</span> <span class="op">=</span> <span class="nam">radius</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">cos</span><span class="op">(</span><span class="nam">elevation</span><span class="op">)</span> <span class="op">*</span> <span class="nam">np</span><span class="op">.</span><span class="nam">sin</span><span class="op">(</span><span class="nam">azimuth</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t45" class="stm run hide_run"> <span class="nam">z</span> <span class="op">=</span> <span class="nam">radius</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">sin</span><span class="op">(</span><span class="nam">elevation</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t46" class="stm run hide_run"> <span class="key">return</span> <span class="nam">x</span><span class="op">,</span> <span class="nam">y</span><span class="op">,</span> <span class="nam">z</span><span class="strut"> </span></p>
<p id="t47" class="pln"><span class="strut"> </span></p>
<p id="t48" class="pln"><span class="strut"> </span></p>
<p id="t49" class="stm run hide_run"><span class="key">def</span> <span class="nam">cartesian_to_spherical_vectors</span><span class="op">(</span><span class="nam">cart_vec</span><span class="op">,</span> <span class="nam">viewing_direction</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t50" class="pln"> <span class="str">"""Now we need the cartesian vector as a spherical vecotr.</span><span class="strut"> </span></p>
<p id="t51" class="pln"><span class="str"> A vector in cartesian coordinates can be transform as one in</span><span class="strut"> </span></p>
<p id="t52" class="pln"><span class="str"> the spherical coordinates following the transformation:</span><span class="strut"> </span></p>
<p id="t53" class="pln"><span class="strut"> </span></p>
<p id="t54" class="pln"><span class="str"> A_rho =+A_x.*cos(epsilon).*cos(phi)</span><span class="strut"> </span></p>
<p id="t55" class="pln"><span class="str"> +A_y.*cos(epsilon).*sin(phi)</span><span class="strut"> </span></p>
<p id="t56" class="pln"><span class="str"> +A_z.*sin(epsilon)</span><span class="strut"> </span></p>
<p id="t57" class="pln"><span class="str"> A_epsilon=-A_x.*sin(epsilon).*cos(phi)</span><span class="strut"> </span></p>
<p id="t58" class="pln"><span class="str"> -A_y.*sin(epsilon).*sin(phi)</span><span class="strut"> </span></p>
<p id="t59" class="pln"><span class="str"> +A_z.*cos(epsilon)</span><span class="strut"> </span></p>
<p id="t60" class="pln"><span class="str"> A_phi =-A_x.*sin(phi)+A_y.*cos(phi)</span><span class="strut"> </span></p>
<p id="t61" class="pln"><span class="strut"> </span></p>
<p id="t62" class="pln"><span class="str"> for epsilon in [-pi/2 +pi/2] and phi in [0 2pi]</span><span class="strut"> </span></p>
<p id="t63" class="pln"><span class="str"> reverse tajectory, needed because the frame x,y,z is expressed in</span><span class="strut"> </span></p>
<p id="t64" class="pln"><span class="str"> the orientation Yaw=pitch=roll=0"""</span><span class="strut"> </span></p>
<p id="t65" class="stm run hide_run"> <span class="key">if</span> <span class="nam">cart_vec</span> <span class="key">is</span> <span class="key">None</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t66" class="stm mis"> <span class="key">raise</span> <span class="nam">ValueError</span><span class="op">(</span><span class="str">"cartesian vector must not be None"</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t67" class="stm run hide_run"> <span class="key">if</span> <span class="nam">viewing_direction</span> <span class="key">is</span> <span class="key">None</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t68" class="stm mis"> <span class="key">raise</span> <span class="nam">ValueError</span><span class="op">(</span><span class="str">"viewing direction must not be None"</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t69" class="stm run hide_run"> <span class="key">if</span> <span class="op">(</span><span class="key">not</span> <span class="nam">isinstance</span><span class="op">(</span><span class="nam">cart_vec</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">ndarray</span><span class="op">)</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t70" class="stm mis"> <span class="key">raise</span> <span class="nam">TypeError</span><span class="op">(</span><span class="str">"vector must be of type np.ndarray"</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t71" class="stm run hide_run"> <span class="key">if</span> <span class="nam">cart_vec</span><span class="op">.</span><span class="nam">shape</span><span class="op">[</span><span class="num">0</span><span class="op">]</span> <span class="op">!=</span> <span class="num">3</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t72" class="stm mis"> <span class="key">raise</span> <span class="nam">Exception</span><span class="op">(</span><span class="str">"first dimension of cartesian vector\</span><span class="strut"> </span></p>
<p id="t73" class="pln"><span class="str"> must have size three"</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t74" class="stm run hide_run"> <span class="key">if</span> <span class="key">not</span> <span class="nam">is_numeric_array</span><span class="op">(</span><span class="nam">cart_vec</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t75" class="stm mis"> <span class="key">raise</span> <span class="nam">TypeError</span><span class="op">(</span><span class="str">"cartesian vector must be of numerical type"</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t76" class="stm run hide_run"> <span class="key">if</span> <span class="op">(</span><span class="key">not</span> <span class="nam">isinstance</span><span class="op">(</span><span class="nam">viewing_direction</span><span class="op">,</span> <span class="nam">list</span><span class="op">)</span><span class="op">)</span> <span class="key">and</span><span class="xx">\</span><span class="strut"> </span></p>
<p id="t77" class="pln"> <span class="op">(</span><span class="key">not</span> <span class="nam">isinstance</span><span class="op">(</span><span class="nam">viewing_direction</span><span class="op">,</span> <span class="nam">np</span><span class="op">.</span><span class="nam">ndarray</span><span class="op">)</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t78" class="stm mis"> <span class="key">raise</span> <span class="nam">TypeError</span><span class="op">(</span><span class="str">"angles must be list or np.ndarray"</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t79" class="stm run hide_run"> <span class="key">if</span> <span class="key">not</span> <span class="nam">is_numeric_array</span><span class="op">(</span><span class="nam">viewing_direction</span><span class="op">)</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t80" class="stm mis"> <span class="key">raise</span> <span class="nam">TypeError</span><span class="op">(</span><span class="str">"viewing_direction must be of numerical type"</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t81" class="stm run hide_run"> <span class="key">if</span> <span class="nam">len</span><span class="op">(</span><span class="nam">viewing_direction</span><span class="op">)</span> <span class="op">!=</span> <span class="num">2</span><span class="op">:</span><span class="strut"> </span></p>
<p id="t82" class="stm mis"> <span class="key">raise</span> <span class="nam">Exception</span><span class="op">(</span><span class="str">"first dimension of viewing\</span><span class="strut"> </span></p>
<p id="t83" class="pln"><span class="str"> direction must be of size two"</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t84" class="pln"><span class="strut"> </span></p>
<p id="t85" class="stm run hide_run"> <span class="nam">SPH_x</span> <span class="op">=</span> <span class="nam">cart_vec</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="strut"> </span></p>
<p id="t86" class="stm run hide_run"> <span class="nam">SPH_y</span> <span class="op">=</span> <span class="nam">cart_vec</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="strut"> </span></p>
<p id="t87" class="stm run hide_run"> <span class="nam">SPH_z</span> <span class="op">=</span> <span class="nam">cart_vec</span><span class="op">[</span><span class="num">2</span><span class="op">]</span><span class="strut"> </span></p>
<p id="t88" class="pln"><span class="strut"> </span></p>
<p id="t89" class="stm run hide_run"> <span class="nam">epsilon</span> <span class="op">=</span> <span class="nam">viewing_direction</span><span class="op">[</span><span class="num">1</span><span class="op">]</span><span class="strut"> </span></p>
<p id="t90" class="stm run hide_run"> <span class="nam">phi</span> <span class="op">=</span> <span class="nam">viewing_direction</span><span class="op">[</span><span class="num">0</span><span class="op">]</span><span class="strut"> </span></p>
<p id="t91" class="pln"><span class="strut"> </span></p>
<p id="t92" class="stm run hide_run"> <span class="nam">rofterm1</span> <span class="op">=</span> <span class="op">+</span><span class="nam">SPH_x</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">cos</span><span class="op">(</span><span class="nam">epsilon</span><span class="op">)</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">cos</span><span class="op">(</span><span class="nam">phi</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t93" class="stm run hide_run"> <span class="nam">rofterm2</span> <span class="op">=</span> <span class="op">+</span><span class="nam">SPH_y</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">cos</span><span class="op">(</span><span class="nam">epsilon</span><span class="op">)</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">sin</span><span class="op">(</span><span class="nam">phi</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t94" class="stm run hide_run"> <span class="nam">rofterm3</span> <span class="op">=</span> <span class="op">+</span><span class="nam">SPH_z</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">sin</span><span class="op">(</span><span class="nam">epsilon</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t95" class="stm run hide_run"> <span class="nam">sph_x</span> <span class="op">=</span> <span class="nam">rofterm1</span><span class="op">+</span><span class="nam">rofterm2</span><span class="op">+</span><span class="nam">rofterm3</span><span class="strut"> </span></p>
<p id="t96" class="pln"><span class="strut"> </span></p>
<p id="t97" class="stm run hide_run"> <span class="nam">vofterm1</span> <span class="op">=</span> <span class="op">-</span><span class="nam">SPH_x</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">sin</span><span class="op">(</span><span class="nam">epsilon</span><span class="op">)</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">cos</span><span class="op">(</span><span class="nam">phi</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t98" class="stm run hide_run"> <span class="nam">vofterm2</span> <span class="op">=</span> <span class="op">-</span><span class="nam">SPH_y</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">sin</span><span class="op">(</span><span class="nam">epsilon</span><span class="op">)</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">sin</span><span class="op">(</span><span class="nam">phi</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t99" class="stm run hide_run"> <span class="nam">vofterm3</span> <span class="op">=</span> <span class="nam">SPH_z</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">cos</span><span class="op">(</span><span class="nam">epsilon</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t100" class="stm run hide_run"> <span class="nam">sph_z</span> <span class="op">=</span> <span class="nam">vofterm1</span><span class="op">+</span><span class="nam">vofterm2</span><span class="op">+</span><span class="nam">vofterm3</span><span class="strut"> </span></p>
<p id="t101" class="stm run hide_run"> <span class="nam">sph_y</span> <span class="op">=</span> <span class="op">-</span><span class="nam">SPH_x</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">sin</span><span class="op">(</span><span class="nam">phi</span><span class="op">)</span> <span class="op">+</span> <span class="nam">SPH_y</span><span class="op">*</span><span class="nam">np</span><span class="op">.</span><span class="nam">cos</span><span class="op">(</span><span class="nam">phi</span><span class="op">)</span><span class="strut"> </span></p>
<p id="t102" class="pln"><span class="strut"> </span></p>
<p id="t103" class="stm run hide_run"> <span class="key">return</span> <span class="op">[</span><span class="nam">sph_x</span><span class="op">,</span> <span class="nam">sph_y</span><span class="op">,</span> <span class="nam">sph_z</span><span class="op">]</span><span class="strut"> </span></p>
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