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<h4 class="subsubsection" id="Two_002ddimensional-Function-Plotting-1"><span>15.2.1.2 Two-dimensional Function Plotting<a class="copiable-link" href="#Two_002ddimensional-Function-Plotting-1"> ¶</a></span></h4>
<a class="index-entry-id" id="index-plotting_002c-two_002ddimensional-functions"></a>
<p>Octave can plot a function from a function handle or string defining the
function without the user needing to explicitly create the data to be
plotted. The function <code class="code">fplot</code> also generates two-dimensional plots
with linear axes using a function name and limits for the range of the
x-coordinate instead of the x and y data. For example,
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">fplot (@sin, [-10, 10], 201);
</pre></div></div>
<p>produces a plot that is equivalent to the one above, but also includes a
legend displaying the name of the plotted function.
</p>
<a class="anchor" id="XREFfplot"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-fplot"><span><strong class="def-name">fplot</strong> <code class="def-code-arguments">(<var class="var">fcn</var>)</code><a class="copiable-link" href="#index-fplot"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-fplot-1"><span><strong class="def-name">fplot</strong> <code class="def-code-arguments">(<var class="var">fcn</var>, <var class="var">limits</var>)</code><a class="copiable-link" href="#index-fplot-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-fplot-2"><span><strong class="def-name">fplot</strong> <code class="def-code-arguments">(…, <var class="var">tol</var>)</code><a class="copiable-link" href="#index-fplot-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-fplot-3"><span><strong class="def-name">fplot</strong> <code class="def-code-arguments">(…, <var class="var">n</var>)</code><a class="copiable-link" href="#index-fplot-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-fplot-4"><span><strong class="def-name">fplot</strong> <code class="def-code-arguments">(…, <var class="var">fmt</var>)</code><a class="copiable-link" href="#index-fplot-4"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-fplot-5"><span><strong class="def-name">fplot</strong> <code class="def-code-arguments">(…, <var class="var">property</var>, <var class="var">value</var>, …)</code><a class="copiable-link" href="#index-fplot-5"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-fplot-6"><span><strong class="def-name">fplot</strong> <code class="def-code-arguments">(<var class="var">hax</var>, …)</code><a class="copiable-link" href="#index-fplot-6"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-fplot-7"><span><code class="def-type">[<var class="var">x</var>, <var class="var">y</var>] =</code> <strong class="def-name">fplot</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-fplot-7"> ¶</a></span></dt>
<dd><p>Plot a function <var class="var">fcn</var> within the range defined by <var class="var">limits</var>.
</p>
<p><var class="var">fcn</var> is a function handle, inline function, or string containing the
name of the function to evaluate.
</p>
<p>The limits of the plot are of the form <code class="code">[<var class="var">xlo</var>, <var class="var">xhi</var>]</code><!-- /@w --> or
<code class="code">[<var class="var">xlo</var>, <var class="var">xhi</var>, <var class="var">ylo</var>, <var class="var">yhi</var>]</code><!-- /@w -->. If no limits
are specified the default is <code class="code">[-5, 5]</code>.
</p>
<p>The next three arguments are all optional and any number of them may be
given in any order.
</p>
<p><var class="var">tol</var> is the relative tolerance to use for the plot and defaults
to 2e-3 (.2%).
</p>
<p><var class="var">n</var> is the minimum number of points to use. When <var class="var">n</var> is specified,
the maximum stepsize will be <code class="code">(<var class="var">xhi</var> - <var class="var">xlo</var>) / <var class="var">n</var></code>. More
than <var class="var">n</var> points may still be used in order to meet the relative
tolerance requirement.
</p>
<p>The <var class="var">fmt</var> argument specifies the linestyle to be used by the plot
command.
</p>
<p>Multiple property-value pairs may also be specified, but they must appear
in pairs. These arguments are applied to the line objects drawn by
<code class="code">plot</code>.
</p>
<p>The full list of line properties is documented at
<a class="ref" href="Line-Properties.html">Line Properties</a>.
</p>
<p>If the first argument <var class="var">hax</var> is an axes handle, then plot into this axes,
rather than the current axes returned by <code class="code">gca</code>.
</p>
<p>With no output arguments, the results are immediately plotted. With two
output arguments, the 2-D plot data is returned. The data can subsequently
be plotted manually with <code class="code">plot (<var class="var">x</var>, <var class="var">y</var>)</code>.
</p>
<p>Example:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">fplot (@cos, [0, 2*pi])
fplot ("[cos(x), sin(x)]", [0, 2*pi])
</pre></div></div>
<p>Programming Notes:
</p>
<p><code class="code">fplot</code> works best with continuous functions. Functions with
discontinuities are unlikely to plot well. This restriction may be removed
in the future.
</p>
<p><code class="code">fplot</code> performance is better when the function accepts and returns a
vector argument. Consider this when writing user-defined functions and use
element-by-element operators such as <code class="code">.*</code>, <code class="code">./</code>, etc.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFezplot">ezplot</a>, <a class="ref" href="Two_002dDimensional-Plots.html#XREFplot">plot</a>.
</p></dd></dl>
<p>Other functions that can create two-dimensional plots directly from a
function include <code class="code">ezplot</code>, <code class="code">ezcontour</code>, <code class="code">ezcontourf</code> and
<code class="code">ezpolar</code>.
</p>
<a class="anchor" id="XREFezplot"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-ezplot"><span><strong class="def-name">ezplot</strong> <code class="def-code-arguments">(<var class="var">f</var>)</code><a class="copiable-link" href="#index-ezplot"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezplot-1"><span><strong class="def-name">ezplot</strong> <code class="def-code-arguments">(<var class="var">f2v</var>)</code><a class="copiable-link" href="#index-ezplot-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezplot-2"><span><strong class="def-name">ezplot</strong> <code class="def-code-arguments">(<var class="var">fx</var>, <var class="var">fy</var>)</code><a class="copiable-link" href="#index-ezplot-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezplot-3"><span><strong class="def-name">ezplot</strong> <code class="def-code-arguments">(…, <var class="var">dom</var>)</code><a class="copiable-link" href="#index-ezplot-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezplot-4"><span><strong class="def-name">ezplot</strong> <code class="def-code-arguments">(…, <var class="var">n</var>)</code><a class="copiable-link" href="#index-ezplot-4"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezplot-5"><span><strong class="def-name">ezplot</strong> <code class="def-code-arguments">(<var class="var">hax</var>, …)</code><a class="copiable-link" href="#index-ezplot-5"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezplot-6"><span><code class="def-type"><var class="var">h</var> =</code> <strong class="def-name">ezplot</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-ezplot-6"> ¶</a></span></dt>
<dd>
<p>Plot the 2-D curve defined by the function <var class="var">f</var>.
</p>
<p>The function <var class="var">f</var> may be a string, inline function, or function handle
and can have either one or two variables. If <var class="var">f</var> has one variable, then
the function is plotted over the domain <code class="code">-2*pi < <var class="var">x</var> < 2*pi</code>
with 500 points.
</p>
<p>If <var class="var">f2v</var> is a function of two variables then the implicit function
<code class="code"><var class="var">f</var>(<var class="var">x</var>,<var class="var">y</var>) = 0</code> is calculated over the meshed domain
<code class="code">-2*pi <= <var class="var">x</var> | <var class="var">y</var> <= 2*pi</code> with 60 points in each dimension.
</p>
<p>For example:
</p>
<div class="example">
<pre class="example-preformatted">ezplot (@(<var class="var">x</var>, <var class="var">y</var>) <var class="var">x</var>.^2 - <var class="var">y</var>.^2 - 1)
</pre></div>
<p>If two functions are passed as inputs then the parametric function
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"><var class="var">x</var> = <var class="var">fx</var> (<var class="var">t</var>)
<var class="var">y</var> = <var class="var">fy</var> (<var class="var">t</var>)
</pre></div></div>
<p>is plotted over the domain <code class="code">-2*pi <= <var class="var">t</var> <= 2*pi</code> with 500 points.
</p>
<p>If <var class="var">dom</var> is a two element vector, it represents the minimum and maximum
values of both <var class="var">x</var> and <var class="var">y</var>, or <var class="var">t</var> for a parametric plot. If
<var class="var">dom</var> is a four element vector, then the minimum and maximum values are
<code class="code">[xmin xmax ymin ymax]</code>.
</p>
<p><var class="var">n</var> is a scalar defining the number of points to use in plotting
the function.
</p>
<p>If the first argument <var class="var">hax</var> is an axes handle, then plot into this axes,
rather than the current axes returned by <code class="code">gca</code>.
</p>
<p>The optional return value <var class="var">h</var> is a vector of graphics handles to
the created line objects.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="Two_002dDimensional-Plots.html#XREFplot">plot</a>, <a class="ref" href="Three_002ddimensional-Function-Plotting.html#XREFezplot3">ezplot3</a>, <a class="ref" href="#XREFezpolar">ezpolar</a>, <a class="ref" href="#XREFezcontour">ezcontour</a>, <a class="ref" href="#XREFezcontourf">ezcontourf</a>, <a class="ref" href="Three_002ddimensional-Function-Plotting.html#XREFezmesh">ezmesh</a>, <a class="ref" href="Three_002ddimensional-Function-Plotting.html#XREFezmeshc">ezmeshc</a>, <a class="ref" href="Three_002ddimensional-Function-Plotting.html#XREFezsurf">ezsurf</a>, <a class="ref" href="Three_002ddimensional-Function-Plotting.html#XREFezsurfc">ezsurfc</a>.
</p></dd></dl>
<a class="anchor" id="XREFezcontour"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-ezcontour"><span><strong class="def-name">ezcontour</strong> <code class="def-code-arguments">(<var class="var">f</var>)</code><a class="copiable-link" href="#index-ezcontour"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezcontour-1"><span><strong class="def-name">ezcontour</strong> <code class="def-code-arguments">(…, <var class="var">dom</var>)</code><a class="copiable-link" href="#index-ezcontour-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezcontour-2"><span><strong class="def-name">ezcontour</strong> <code class="def-code-arguments">(…, <var class="var">n</var>)</code><a class="copiable-link" href="#index-ezcontour-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezcontour-3"><span><strong class="def-name">ezcontour</strong> <code class="def-code-arguments">(<var class="var">hax</var>, …)</code><a class="copiable-link" href="#index-ezcontour-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezcontour-4"><span><code class="def-type"><var class="var">h</var> =</code> <strong class="def-name">ezcontour</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-ezcontour-4"> ¶</a></span></dt>
<dd>
<p>Plot the contour lines of a function.
</p>
<p><var class="var">f</var> is a string, inline function, or function handle with two arguments
defining the function. By default the plot is over the meshed domain
<code class="code">-2*pi <= <var class="var">x</var> | <var class="var">y</var> <= 2*pi</code> with 60 points in each dimension.
</p>
<p>If <var class="var">dom</var> is a two element vector, it represents the minimum and maximum
values of both <var class="var">x</var> and <var class="var">y</var>. If <var class="var">dom</var> is a four element vector,
then the minimum and maximum values are <code class="code">[xmin xmax ymin ymax]</code>.
</p>
<p><var class="var">n</var> is a scalar defining the number of points to use in each dimension.
</p>
<p>If the first argument <var class="var">hax</var> is an axes handle, then plot into this axes,
rather than the current axes returned by <code class="code">gca</code>.
</p>
<p>The optional return value <var class="var">h</var> is a graphics handle to the created plot.
</p>
<p>Example:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">f = @(x,y) sqrt (abs (x .* y)) ./ (1 + x.^2 + y.^2);
ezcontour (f, [-3, 3]);
</pre></div></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="Two_002dDimensional-Plots.html#XREFcontour">contour</a>, <a class="ref" href="#XREFezcontourf">ezcontourf</a>, <a class="ref" href="#XREFezplot">ezplot</a>, <a class="ref" href="Three_002ddimensional-Function-Plotting.html#XREFezmeshc">ezmeshc</a>, <a class="ref" href="Three_002ddimensional-Function-Plotting.html#XREFezsurfc">ezsurfc</a>.
</p></dd></dl>
<a class="anchor" id="XREFezcontourf"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-ezcontourf"><span><strong class="def-name">ezcontourf</strong> <code class="def-code-arguments">(<var class="var">f</var>)</code><a class="copiable-link" href="#index-ezcontourf"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezcontourf-1"><span><strong class="def-name">ezcontourf</strong> <code class="def-code-arguments">(…, <var class="var">dom</var>)</code><a class="copiable-link" href="#index-ezcontourf-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezcontourf-2"><span><strong class="def-name">ezcontourf</strong> <code class="def-code-arguments">(…, <var class="var">n</var>)</code><a class="copiable-link" href="#index-ezcontourf-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezcontourf-3"><span><strong class="def-name">ezcontourf</strong> <code class="def-code-arguments">(<var class="var">hax</var>, …)</code><a class="copiable-link" href="#index-ezcontourf-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezcontourf-4"><span><code class="def-type"><var class="var">h</var> =</code> <strong class="def-name">ezcontourf</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-ezcontourf-4"> ¶</a></span></dt>
<dd>
<p>Plot the filled contour lines of a function.
</p>
<p><var class="var">f</var> is a string, inline function, or function handle with two arguments
defining the function. By default the plot is over the meshed domain
<code class="code">-2*pi <= <var class="var">x</var> | <var class="var">y</var> <= 2*pi</code> with 60 points in each dimension.
</p>
<p>If <var class="var">dom</var> is a two element vector, it represents the minimum and maximum
values of both <var class="var">x</var> and <var class="var">y</var>. If <var class="var">dom</var> is a four element vector,
then the minimum and maximum values are <code class="code">[xmin xmax ymin ymax]</code>.
</p>
<p><var class="var">n</var> is a scalar defining the number of points to use in each dimension.
</p>
<p>If the first argument <var class="var">hax</var> is an axes handle, then plot into this axes,
rather than the current axes returned by <code class="code">gca</code>.
</p>
<p>The optional return value <var class="var">h</var> is a graphics handle to the created plot.
</p>
<p>Example:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">f = @(x,y) sqrt (abs (x .* y)) ./ (1 + x.^2 + y.^2);
ezcontourf (f, [-3, 3]);
</pre></div></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="Two_002dDimensional-Plots.html#XREFcontourf">contourf</a>, <a class="ref" href="#XREFezcontour">ezcontour</a>, <a class="ref" href="#XREFezplot">ezplot</a>, <a class="ref" href="Three_002ddimensional-Function-Plotting.html#XREFezmeshc">ezmeshc</a>, <a class="ref" href="Three_002ddimensional-Function-Plotting.html#XREFezsurfc">ezsurfc</a>.
</p></dd></dl>
<a class="anchor" id="XREFezpolar"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-ezpolar"><span><strong class="def-name">ezpolar</strong> <code class="def-code-arguments">(<var class="var">f</var>)</code><a class="copiable-link" href="#index-ezpolar"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezpolar-1"><span><strong class="def-name">ezpolar</strong> <code class="def-code-arguments">(…, <var class="var">dom</var>)</code><a class="copiable-link" href="#index-ezpolar-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezpolar-2"><span><strong class="def-name">ezpolar</strong> <code class="def-code-arguments">(…, <var class="var">n</var>)</code><a class="copiable-link" href="#index-ezpolar-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezpolar-3"><span><strong class="def-name">ezpolar</strong> <code class="def-code-arguments">(<var class="var">hax</var>, …)</code><a class="copiable-link" href="#index-ezpolar-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-ezpolar-4"><span><code class="def-type"><var class="var">h</var> =</code> <strong class="def-name">ezpolar</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-ezpolar-4"> ¶</a></span></dt>
<dd>
<p>Plot a 2-D function in polar coordinates.
</p>
<p>The function <var class="var">f</var> is a string, inline function, or function handle with
a single argument. The expected form of the function is
<code class="code"><var class="var">rho</var> = <var class="var">f</var>(<var class="var">theta</var>)</code>.
By default the plot is over the domain <code class="code">0 <= <var class="var">theta</var> <= 2*pi</code>
with 500 points.
</p>
<p>If <var class="var">dom</var> is a two element vector, it represents the minimum and maximum
values of <var class="var">theta</var>.
</p>
<p><var class="var">n</var> is a scalar defining the number of points to use in plotting
the function.
</p>
<p>If the first argument <var class="var">hax</var> is an axes handle, then plot into this axes,
rather than the current axes returned by <code class="code">gca</code>.
</p>
<p>The optional return value <var class="var">h</var> is a graphics handle to the created plot.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example-preformatted">ezpolar (@(t) sin (5/4 * t), [0, 8*pi]);
</pre></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="Two_002dDimensional-Plots.html#XREFpolar">polar</a>, <a class="ref" href="#XREFezplot">ezplot</a>.
</p></dd></dl>
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