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<div class="sphx-glr-example-title section" id="parametric-curve">
<span id="sphx-glr-gallery-mplot3d-lines3d-py"></span><h1>Parametric Curve<a class="headerlink" href="#parametric-curve" title="Permalink to this headline">¶</a></h1>
<p>This example demonstrates plotting a parametric curve in 3D.</p>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<a href="../../api/matplotlib_configuration_api.html#matplotlib.RcParams" title="matplotlib.RcParams" class="sphx-glr-backref-module-matplotlib sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="../../api/matplotlib_configuration_api.html#matplotlib.RcParams" title="matplotlib.RcParams" class="sphx-glr-backref-module-matplotlib sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="../../api/matplotlib_configuration_api.html#matplotlib.RcParams" title="matplotlib.RcParams" class="sphx-glr-backref-module-matplotlib sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">plt</span><span class="o">.</span><span class="n">rcParams</span></a></a></a><span class="p">[</span><span class="s1">'legend.fontsize'</span><span class="p">]</span> <span class="o">=</span> <span class="mi">10</span>
<a href="../../api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="../../api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="../../api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a></a></a> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><a href="../../api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><a href="../../api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a></a></a><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <a href="../../api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure.gca" title="matplotlib.figure.Figure.gca" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-method"><a href="../../api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure.gca" title="matplotlib.figure.Figure.gca" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-method"><a href="../../api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure.gca" title="matplotlib.figure.Figure.gca" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-method"><span class="n">fig</span><span class="o">.</span><span class="n">gca</span></a></a></a><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
<span class="c1"># Prepare arrays x, y, z</span>
<a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">theta</span></a></a></a> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a></a></a><span class="p">(</span><span class="o">-</span><span class="mi">4</span> <span class="o">*</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a></a></a><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a></a></a><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">z</span></a></a></a> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a></a></a><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">r</span></a></a></a> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">z</span></a></a></a><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span>
<a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a></a></a> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">r</span></a></a></a> <span class="o">*</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html#numpy.sin" title="numpy.sin" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html#numpy.sin" title="numpy.sin" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html#numpy.sin" title="numpy.sin" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a></a></a><span class="p">(</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">theta</span></a></a></a><span class="p">)</span>
<a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a></a></a> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">r</span></a></a></a> <span class="o">*</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.cos.html#numpy.cos" title="numpy.cos" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.cos.html#numpy.cos" title="numpy.cos" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.cos.html#numpy.cos" title="numpy.cos" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">cos</span></a></a></a><span class="p">(</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">theta</span></a></a></a><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><a href="../../api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="matplotlib.axes.Axes.plot" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">plot</span></a></a></a><span class="p">(</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x</span></a></a></a><span class="p">,</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a></a></a><span class="p">,</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">z</span></a></a></a><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'parametric curve'</span><span class="p">)</span>
<a href="../../api/_as_gen/matplotlib.axes.Axes.legend.html#matplotlib.axes.Axes.legend" title="matplotlib.axes.Axes.legend" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><a href="../../api/_as_gen/matplotlib.axes.Axes.legend.html#matplotlib.axes.Axes.legend" title="matplotlib.axes.Axes.legend" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><a href="../../api/_as_gen/matplotlib.axes.Axes.legend.html#matplotlib.axes.Axes.legend" title="matplotlib.axes.Axes.legend" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">legend</span></a></a></a><span class="p">()</span>
<a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><a href="../../api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a></a></a><span class="p">()</span>
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