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<span id="Coordinate-Transformations-1"></span><h3 class="section">17.8 Coordinate Transformations</h3>
<span id="XREFcart2pol"></span><dl class="def">
<dt id="index-cart2pol"><span class="category">: </span><span><em>[<var>theta</var>, <var>r</var>] =</em> <strong>cart2pol</strong> <em>(<var>x</var>, <var>y</var>)</em><a href='#index-cart2pol' class='copiable-anchor'> ¶</a></span></dt>
<dt id="index-cart2pol-1"><span class="category">: </span><span><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><a href='#index-cart2pol-1' class='copiable-anchor'> ¶</a></span></dt>
<dt id="index-cart2pol-2"><span class="category">: </span><span><em>[<var>theta</var>, <var>r</var>] =</em> <strong>cart2pol</strong> <em>(<var>C</var>)</em><a href='#index-cart2pol-2' class='copiable-anchor'> ¶</a></span></dt>
<dt id="index-cart2pol-3"><span class="category">: </span><span><em>[<var>theta</var>, <var>r</var>, <var>z</var>] =</em> <strong>cart2pol</strong> <em>(<var>C</var>)</em><a href='#index-cart2pol-3' class='copiable-anchor'> ¶</a></span></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 pair (<var>x</var>, <var>y</var>) or triplet
(<var>x</var>, <var>y</var>, <var>z</var>).
</p>
<p>The outputs <var>theta</var>, <var>r</var> (, and <var>z</var>) match the shape of the
inputs. For a matrix input <var>C</var> the outputs will be column vectors with
rows corresponding to the rows of the input matrix.
</p>
<p><var>theta</var> describes the angle relative to the positive x-axis measured in
the xy-plane.
</p>
<p><var>r</var> is the distance to the z-axis (0, 0, z)<!-- /@w -->.
</p>
<p><var>z</var>, if present, is unchanged by the transformation.
</p>
<p>The coordinate transformation is computed using:
</p>
<div class="example">
<pre class="example"><var>theta</var> = arctan (<var>y</var> / <var>x</var>)
<var>r</var> = sqrt (<var>x</var>^2 + <var>y</var>^2)
<var>z</var> = <var>z</var>
</pre></div>
<p>Note: For <small>MATLAB</small> compatibility, this function no longer returns a full
coordinate matrix when called with a single return argument.
</p>
<p><strong>See also:</strong> <a href="#XREFpol2cart">pol2cart</a>, <a href="#XREFcart2sph">cart2sph</a>, <a href="#XREFsph2cart">sph2cart</a>.
</p></dd></dl>
<span id="XREFpol2cart"></span><dl class="def">
<dt id="index-pol2cart"><span class="category">: </span><span><em>[<var>x</var>, <var>y</var>] =</em> <strong>pol2cart</strong> <em>(<var>theta</var>, <var>r</var>)</em><a href='#index-pol2cart' class='copiable-anchor'> ¶</a></span></dt>
<dt id="index-pol2cart-1"><span class="category">: </span><span><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><a href='#index-pol2cart-1' class='copiable-anchor'> ¶</a></span></dt>
<dt id="index-pol2cart-2"><span class="category">: </span><span><em>[<var>x</var>, <var>y</var>] =</em> <strong>pol2cart</strong> <em>(<var>P</var>)</em><a href='#index-pol2cart-2' class='copiable-anchor'> ¶</a></span></dt>
<dt id="index-pol2cart-3"><span class="category">: </span><span><em>[<var>x</var>, <var>y</var>, <var>z</var>] =</em> <strong>pol2cart</strong> <em>(<var>P</var>)</em><a href='#index-pol2cart-3' class='copiable-anchor'> ¶</a></span></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 coordinate pair (<var>theta</var>, <var>r</var>) or the
cylindrical triplet (<var>theta</var>, <var>r</var>, <var>z</var>).
</p>
<p>The outputs <var>x</var>, <var>y</var> (, and <var>z</var>) match the shape of the inputs.
For a matrix input <var>P</var> the outputs will be column vectors with rows
corresponding to the rows of the input matrix.
</p>
<p><var>theta</var> describes the angle relative to the positive x-axis measured in
the xy-plane.
</p>
<p><var>r</var> is the distance to the z-axis (0, 0, z)<!-- /@w -->.
</p>
<p><var>z</var>, if present, is unchanged by the transformation.
</p>
<p>The coordinate transformation is computed using:
</p>
<div class="example">
<pre class="example"><var>x</var> = <var>r</var> * cos (<var>theta</var>)
<var>y</var> = <var>r</var> * sin (<var>theta</var>)
<var>z</var> = <var>z</var>
</pre></div>
<p>Note: For <small>MATLAB</small> compatibility, this function no longer returns a full
coordinate matrix when called with a single return argument.
</p>
<p><strong>See also:</strong> <a href="#XREFcart2pol">cart2pol</a>, <a href="#XREFsph2cart">sph2cart</a>, <a href="#XREFcart2sph">cart2sph</a>.
</p></dd></dl>
<span id="XREFcart2sph"></span><dl class="def">
<dt id="index-cart2sph"><span class="category">: </span><span><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><a href='#index-cart2sph' class='copiable-anchor'> ¶</a></span></dt>
<dt id="index-cart2sph-1"><span class="category">: </span><span><em>[<var>theta</var>, <var>phi</var>, <var>r</var>] =</em> <strong>cart2sph</strong> <em>(<var>C</var>)</em><a href='#index-cart2sph-1' class='copiable-anchor'> ¶</a></span></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> must
represent a Cartesian coordinate triplet (<var>x</var>, <var>y</var>, <var>z</var>).
</p>
<p>The outputs <var>theta</var>, <var>phi</var>, <var>r</var> match the shape of the inputs.
For a matrix input <var>C</var> the outputs will be column vectors with rows
corresponding to the rows of the input matrix.
</p>
<p><var>theta</var> describes the azimuth angle relative to the positive x-axis
measured in the xy-plane.
</p>
<p><var>phi</var> is the elevation angle measured relative to the xy-plane.
</p>
<p><var>r</var> is the distance to the origin (0, 0, 0)<!-- /@w -->.
</p>
<p>The coordinate transformation is computed using:
</p>
<div class="example">
<pre class="example"><var>theta</var> = arctan (<var>y</var> / <var>x</var>)
<var>phi</var> = arctan (<var>z</var> / sqrt (<var>x</var>^2 + <var>y</var>^2))
<var>r</var> = sqrt (<var>x</var>^2 + <var>y</var>^2 + <var>z</var>^2)
</pre></div>
<p>Note: For <small>MATLAB</small> compatibility, this function no longer returns a full
coordinate matrix when called with a single return argument.
</p>
<p><strong>See also:</strong> <a href="#XREFsph2cart">sph2cart</a>, <a href="#XREFcart2pol">cart2pol</a>, <a href="#XREFpol2cart">pol2cart</a>.
</p></dd></dl>
<span id="XREFsph2cart"></span><dl class="def">
<dt id="index-sph2cart"><span class="category">: </span><span><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><a href='#index-sph2cart' class='copiable-anchor'> ¶</a></span></dt>
<dt id="index-sph2cart-1"><span class="category">: </span><span><em>[<var>x</var>, <var>y</var>, <var>z</var>] =</em> <strong>sph2cart</strong> <em>(<var>S</var>)</em><a href='#index-sph2cart-1' class='copiable-anchor'> ¶</a></span></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>
must represent a spherical coordinate triplet (<var>theta</var>, <var>phi</var>,
<var>r</var>).
</p>
<p>The outputs <var>x</var>, <var>y</var>, <var>z</var> match the shape of the inputs. For a
matrix input <var>S</var> the outputs are column vectors with rows corresponding
to the rows of the input matrix.
</p>
<p><var>theta</var> describes the azimuth angle relative to the positive x-axis
measured in the xy-plane.
</p>
<p><var>phi</var> is the elevation angle measured relative to the xy-plane.
</p>
<p><var>r</var> is the distance to the origin (0, 0, 0)<!-- /@w -->.
</p>
<p>The coordinate transformation is computed using:
</p>
<div class="example">
<pre class="example"><var>x</var> = r * cos (<var>phi</var>) * cos (<var>theta</var>)
<var>y</var> = r * cos (<var>phi</var>) * sin (<var>theta</var>)
<var>z</var> = r * sin (<var>phi</var>)
</pre></div>
<p>Note: For <small>MATLAB</small> compatibility, this function no longer returns a full
coordinate matrix when called with a single return argument.
</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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Next: <a href="Mathematical-Constants.html">Mathematical Constants</a>, Previous: <a href="Rational-Approximations.html">Rational Approximations</a>, Up: <a href="Arithmetic.html">Arithmetic</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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