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<title>Coordinate Transformations - GNU Octave</title>
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Next: <a rel="next" accesskey="n" href="Mathematical-Constants.html#Mathematical-Constants">Mathematical Constants</a>,
Previous: <a rel="previous" accesskey="p" href="Rational-Approximations.html#Rational-Approximations">Rational Approximations</a>,
Up: <a rel="up" accesskey="u" href="Arithmetic.html#Arithmetic">Arithmetic</a>
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<h3 class="section">17.8 Coordinate Transformations</h3>
<!-- cart2pol scripts/general/cart2pol.m -->
<p><a name="doc_002dcart2pol"></a>
<div class="defun">
— Function File: [<var>theta</var>, <var>r</var>] = <b>cart2pol</b> (<var>x, y</var>)<var><a name="index-cart2pol-1940"></a></var><br>
— Function File: [<var>theta</var>, <var>r</var>, <var>z</var>] = <b>cart2pol</b> (<var>x, y, z</var>)<var><a name="index-cart2pol-1941"></a></var><br>
— Function File: [<var>theta</var>, <var>r</var>] = <b>cart2pol</b> (<var>c</var>)<var><a name="index-cart2pol-1942"></a></var><br>
— Function File: [<var>theta</var>, <var>r</var>, <var>z</var>] = <b>cart2pol</b> (<var>c</var>)<var><a name="index-cart2pol-1943"></a></var><br>
— Function File: <var>p</var> = <b>cart2pol</b> (<var><small class="dots">...</small></var>)<var><a name="index-cart2pol-1944"></a></var><br>
<blockquote>
<p>Transform Cartesian to polar or cylindrical coordinates.
<p><var>theta</var> describes the angle relative to the positive x-axis.
<var>r</var> is the distance to the z-axis (0, 0, z)<!-- /@w -->.
<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>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>)).
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dpol2cart.html#doc_002dpol2cart">pol2cart</a>, <a href="doc_002dcart2sph.html#doc_002dcart2sph">cart2sph</a>, <a href="doc_002dsph2cart.html#doc_002dsph2cart">sph2cart</a>.
</p></blockquote></div>
<!-- pol2cart scripts/general/pol2cart.m -->
<p><a name="doc_002dpol2cart"></a>
<div class="defun">
— Function File: [<var>x</var>, <var>y</var>] = <b>pol2cart</b> (<var>theta, r</var>)<var><a name="index-pol2cart-1945"></a></var><br>
— Function File: [<var>x</var>, <var>y</var>, <var>z</var>] = <b>pol2cart</b> (<var>theta, r, z</var>)<var><a name="index-pol2cart-1946"></a></var><br>
— Function File: [<var>x</var>, <var>y</var>] = <b>pol2cart</b> (<var>p</var>)<var><a name="index-pol2cart-1947"></a></var><br>
— Function File: [<var>x</var>, <var>y</var>, <var>z</var>] = <b>pol2cart</b> (<var>p</var>)<var><a name="index-pol2cart-1948"></a></var><br>
— Function File: <var>C</var> = <b>pol2cart</b> (<var><small class="dots">...</small></var>)<var><a name="index-pol2cart-1949"></a></var><br>
<blockquote><p>Transform polar or cylindrical to Cartesian coordinates.
<p><var>theta</var>, <var>r</var>, (and <var>z</var>) must be the same shape, or scalar.
<var>theta</var> describes the angle relative to the positive x-axis.
<var>r</var> is the distance to the z-axis (0, 0, z).
If called with a single matrix argument then each row of <var>p</var>
represents the polar/(cylindrical) coordinate (<var>x</var>, <var>y</var> (, <var>z</var>)).
<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>)).
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dcart2pol.html#doc_002dcart2pol">cart2pol</a>, <a href="doc_002dsph2cart.html#doc_002dsph2cart">sph2cart</a>, <a href="doc_002dcart2sph.html#doc_002dcart2sph">cart2sph</a>.
</p></blockquote></div>
<!-- cart2sph scripts/general/cart2sph.m -->
<p><a name="doc_002dcart2sph"></a>
<div class="defun">
— Function File: [<var>theta</var>, <var>phi</var>, <var>r</var>] = <b>cart2sph</b> (<var>x, y, z</var>)<var><a name="index-cart2sph-1950"></a></var><br>
— Function File: [<var>theta</var>, <var>phi</var>, <var>r</var>] = <b>cart2sph</b> (<var>C</var>)<var><a name="index-cart2sph-1951"></a></var><br>
— Function File: <var>S</var> = <b>cart2sph</b> (<var><small class="dots">...</small></var>)<var><a name="index-cart2sph-1952"></a></var><br>
<blockquote><p>Transform Cartesian to spherical coordinates.
<p><var>theta</var> describes the angle relative to the positive x-axis.
<var>phi</var> is the angle relative to the xy-plane.
<var>r</var> is the distance to the origin (0, 0, 0)<!-- /@w -->.
<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>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>).
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dsph2cart.html#doc_002dsph2cart">sph2cart</a>, <a href="doc_002dcart2pol.html#doc_002dcart2pol">cart2pol</a>, <a href="doc_002dpol2cart.html#doc_002dpol2cart">pol2cart</a>.
</p></blockquote></div>
<!-- sph2cart scripts/general/sph2cart.m -->
<p><a name="doc_002dsph2cart"></a>
<div class="defun">
— Function File: [<var>x</var>, <var>y</var>, <var>z</var>] = <b>sph2cart</b> (<var>theta, phi, r</var>)<var><a name="index-sph2cart-1953"></a></var><br>
— Function File: [<var>x</var>, <var>y</var>, <var>z</var>] = <b>sph2cart</b> (<var>S</var>)<var><a name="index-sph2cart-1954"></a></var><br>
— Function File: C = <b>sph2cart</b> (<var><small class="dots">...</small></var>)<var><a name="index-sph2cart-1955"></a></var><br>
<blockquote><p>Transform spherical to Cartesian coordinates.
<p><var>theta</var> describes the angle relative to the positive x-axis.
<var>phi</var> is the angle relative to the xy-plane.
<var>r</var> is the distance to the origin (0, 0, 0)<!-- /@w -->.
<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>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>).
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dcart2sph.html#doc_002dcart2sph">cart2sph</a>, <a href="doc_002dpol2cart.html#doc_002dpol2cart">pol2cart</a>, <a href="doc_002dcart2pol.html#doc_002dcart2pol">cart2pol</a>.
</p></blockquote></div>
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