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<a name="Coordinate-Transformations"></a>
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<a name="Coordinate-Transformations-1"></a>
<h3 class="section">17.8 Coordinate Transformations</h3>

<a name="XREFcart2pol"></a><dl>
<dt><a name="index-cart2pol"></a><em>[<var>theta</var>, <var>r</var>] =</em> <strong>cart2pol</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dt><a name="index-cart2pol-1"></a><em>[<var>theta</var>, <var>r</var>, <var>z</var>] =</em> <strong>cart2pol</strong> <em>(<var>x</var>, <var>y</var>, <var>z</var>)</em></dt>
<dt><a name="index-cart2pol-2"></a><em>[<var>theta</var>, <var>r</var>] =</em> <strong>cart2pol</strong> <em>(<var>C</var>)</em></dt>
<dt><a name="index-cart2pol-3"></a><em>[<var>theta</var>, <var>r</var>, <var>z</var>] =</em> <strong>cart2pol</strong> <em>(<var>C</var>)</em></dt>
<dt><a name="index-cart2pol-4"></a><em><var>P</var> =</em> <strong>cart2pol</strong> <em>(&hellip;)</em></dt>
<dd>
<p>Transform Cartesian coordinates to polar or cylindrical coordinates.
</p>
<p>The inputs <var>x</var>, <var>y</var> (, and <var>z</var>) must be the same shape, or
scalar.  If called with a single matrix argument then each row of <var>C</var>
represents the Cartesian coordinate (<var>x</var>, <var>y</var> (, <var>z</var>)).
</p>
<p><var>theta</var> describes the angle relative to the positive x-axis.
</p>
<p><var>r</var> is the distance to the z-axis (0,&nbsp;0,&nbsp;z)<!-- /@w -->.
</p>
<p>If only a single return argument is requested then return a matrix <var>P</var>
where each row represents one polar/(cylindrical) coordinate
(<var>theta</var>, <var>phi</var> (, <var>z</var>)).
</p>
<p><strong>See also:</strong> <a href="#XREFpol2cart">pol2cart</a>, <a href="#XREFcart2sph">cart2sph</a>, <a href="#XREFsph2cart">sph2cart</a>.
</p></dd></dl>


<a name="XREFpol2cart"></a><dl>
<dt><a name="index-pol2cart"></a><em>[<var>x</var>, <var>y</var>] =</em> <strong>pol2cart</strong> <em>(<var>theta</var>, <var>r</var>)</em></dt>
<dt><a name="index-pol2cart-1"></a><em>[<var>x</var>, <var>y</var>, <var>z</var>] =</em> <strong>pol2cart</strong> <em>(<var>theta</var>, <var>r</var>, <var>z</var>)</em></dt>
<dt><a name="index-pol2cart-2"></a><em>[<var>x</var>, <var>y</var>] =</em> <strong>pol2cart</strong> <em>(<var>P</var>)</em></dt>
<dt><a name="index-pol2cart-3"></a><em>[<var>x</var>, <var>y</var>, <var>z</var>] =</em> <strong>pol2cart</strong> <em>(<var>P</var>)</em></dt>
<dt><a name="index-pol2cart-4"></a><em><var>C</var> =</em> <strong>pol2cart</strong> <em>(&hellip;)</em></dt>
<dd><p>Transform polar or cylindrical coordinates to Cartesian coordinates.
</p>
<p>The inputs <var>theta</var>, <var>r</var>, (and <var>z</var>) must be the same shape, or
scalar.  If called with a single matrix argument then each row of <var>P</var>
represents the polar/(cylindrical) coordinate (<var>theta</var>, <var>r</var>
(, <var>z</var>)).
</p>
<p><var>theta</var> describes the angle relative to the positive x-axis.
</p>
<p><var>r</var> is the distance to the z-axis (0, 0, z).
</p>
<p>If only a single return argument is requested then return a matrix <var>C</var>
where each row represents one Cartesian coordinate
(<var>x</var>, <var>y</var> (, <var>z</var>)).
</p>
<p><strong>See also:</strong> <a href="#XREFcart2pol">cart2pol</a>, <a href="#XREFsph2cart">sph2cart</a>, <a href="#XREFcart2sph">cart2sph</a>.
</p></dd></dl>


<a name="XREFcart2sph"></a><dl>
<dt><a name="index-cart2sph"></a><em>[<var>theta</var>, <var>phi</var>, <var>r</var>] =</em> <strong>cart2sph</strong> <em>(<var>x</var>, <var>y</var>, <var>z</var>)</em></dt>
<dt><a name="index-cart2sph-1"></a><em>[<var>theta</var>, <var>phi</var>, <var>r</var>] =</em> <strong>cart2sph</strong> <em>(<var>C</var>)</em></dt>
<dt><a name="index-cart2sph-2"></a><em><var>S</var> =</em> <strong>cart2sph</strong> <em>(&hellip;)</em></dt>
<dd><p>Transform Cartesian coordinates to spherical coordinates.
</p>
<p>The inputs <var>x</var>, <var>y</var>, and <var>z</var> must be the same shape, or scalar.
If called with a single matrix argument then each row of <var>C</var> represents
the Cartesian coordinate (<var>x</var>, <var>y</var>, <var>z</var>).
</p>
<p><var>theta</var> describes the angle relative to the positive x-axis.
</p>
<p><var>phi</var> is the angle relative to the xy-plane.
</p>
<p><var>r</var> is the distance to the origin (0,&nbsp;0,&nbsp;0)<!-- /@w -->.
</p>
<p>If only a single return argument is requested then return a matrix <var>S</var>
where each row represents one spherical coordinate
(<var>theta</var>, <var>phi</var>, <var>r</var>).
</p>
<p><strong>See also:</strong> <a href="#XREFsph2cart">sph2cart</a>, <a href="#XREFcart2pol">cart2pol</a>, <a href="#XREFpol2cart">pol2cart</a>.
</p></dd></dl>


<a name="XREFsph2cart"></a><dl>
<dt><a name="index-sph2cart"></a><em>[<var>x</var>, <var>y</var>, <var>z</var>] =</em> <strong>sph2cart</strong> <em>(<var>theta</var>, <var>phi</var>, <var>r</var>)</em></dt>
<dt><a name="index-sph2cart-1"></a><em>[<var>x</var>, <var>y</var>, <var>z</var>] =</em> <strong>sph2cart</strong> <em>(<var>S</var>)</em></dt>
<dt><a name="index-sph2cart-2"></a><em><var>C</var> =</em> <strong>sph2cart</strong> <em>(&hellip;)</em></dt>
<dd><p>Transform spherical coordinates to Cartesian coordinates.
</p>
<p>The inputs <var>theta</var>, <var>phi</var>, and <var>r</var> must be the same shape, or
scalar.  If called with a single matrix argument then each row of <var>S</var>
represents the spherical coordinate (<var>theta</var>, <var>phi</var>, <var>r</var>).
</p>
<p><var>theta</var> describes the angle relative to the positive x-axis.
</p>
<p><var>phi</var> is the angle relative to the xy-plane.
</p>
<p><var>r</var> is the distance to the origin (0,&nbsp;0,&nbsp;0)<!-- /@w -->.
</p>
<p>If only a single return argument is requested then return a matrix <var>C</var>
where each row represents one Cartesian coordinate
(<var>x</var>, <var>y</var>, <var>z</var>).
</p>
<p><strong>See also:</strong> <a href="#XREFcart2sph">cart2sph</a>, <a href="#XREFpol2cart">pol2cart</a>, <a href="#XREFcart2pol">cart2pol</a>.
</p></dd></dl>


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