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<div><h1 id="sec:threedim">1.14 Three-Dimensional Plotting</h1>
<p>Three-dimensional graphs may be produced by placing the modifier <tt class="tt">3d</tt> immediately after the <tt class="tt">plot</tt> command, as demonstrated by the following simple example which draws a helix: </p><p> <tt class="tt">set key below</tt><br /><tt class="tt">set size 8 ratio 0.6 zratio 0.6</tt><br /><tt class="tt">set grid</tt><br /><tt class="tt">plot 3d sin(x):cos(x) with lw 3 col hsb(x/20+0.5):0.9:0.8</tt> </p><p> <center>
<img src="images/img-0541.png" alt="\includegraphics[width=10cm]{examples/eps/ex_3d_helix}" style="width:10cm" /></center> </p><p>Many plot styles take additional columns of data when used on three-dimensional plots, reading in three values for the <img src="images/img-0019.png" alt="$x$" style="vertical-align:0px;
width:10px;
height:8px" class="math gen" />, <img src="images/img-0020.png" alt="$y$" style="vertical-align:-4px;
width:9px;
height:12px" class="math gen" /> and <img src="images/img-0101.png" alt="$z$" style="vertical-align:0px;
width:9px;
height:8px" class="math gen" /> coordinates of each datapoint, where previously only <img src="images/img-0019.png" alt="$x$" style="vertical-align:0px;
width:10px;
height:8px" class="math gen" /> and <img src="images/img-0020.png" alt="$y$" style="vertical-align:-4px;
width:9px;
height:12px" class="math gen" /> coordinates were required. In the above example, the <tt class="tt">lines</tt> plot style is used, which takes three columns of input data when used on three-dimensional plots, as compared to two on two-dimensional plots. The descriptions of each plot style in Section <a href="sec-list_of_plotstyles.html">1.2</a> includes information on the number of columns of data required for two- and three-dimensional plots. </p><p>The example above also demonstrates that the <tt class="tt">set size</tt> command<a name="a0000000858" id="a0000000858"></a> takes an additional aspect ratio <tt class="tt">zratio</tt> which affects three-dimensional plots; whereas the aspect ratio <tt class="tt">ratio</tt> determines the ratio of the lengths of the <img src="images/img-0020.png" alt="$y$" style="vertical-align:-4px;
width:9px;
height:12px" class="math gen" />-axes of plots to their <img src="images/img-0019.png" alt="$x$" style="vertical-align:0px;
width:10px;
height:8px" class="math gen" />-axes, the aspect ratio <tt class="tt">zratio</tt> determines the ratio of the lengths of the <img src="images/img-0101.png" alt="$z$" style="vertical-align:0px;
width:9px;
height:8px" class="math gen" />-axes of plots to their <img src="images/img-0019.png" alt="$x$" style="vertical-align:0px;
width:10px;
height:8px" class="math gen" />-axes. </p><p>The angle from which three-dimensional plots are viewed can be set using the <tt class="tt">set view</tt> command<a name="a0000000859" id="a0000000859"></a>. This should be followed by two angles, which can either be expressed in degrees, as dimensionless numbers, or as quantities with physical units of angle: </p><pre>
set view 60,30
set unit angle nodimensionless
set view unit(0.1*rev),unit(2*rad)
</pre><p> The orientation <img src="images/img-0543.png" alt="$(0,0)$" style="vertical-align:-4px;
width:38px;
height:18px" class="math gen" /> corresponds to having the <img src="images/img-0019.png" alt="$x$" style="vertical-align:0px;
width:10px;
height:8px" class="math gen" />-axis horizontal, the <img src="images/img-0101.png" alt="$z$" style="vertical-align:0px;
width:9px;
height:8px" class="math gen" />-axis vertical, and the <img src="images/img-0020.png" alt="$y$" style="vertical-align:-4px;
width:9px;
height:12px" class="math gen" />-axis directed into the page. The first angle supplied to the <tt class="tt">set view</tt> command rotates the plot in the <img src="images/img-0188.png" alt="$(x,y)$" style="vertical-align:-4px;
width:40px;
height:18px" class="math gen" /> plane, and the second angle tips the plot up in the plane containing the <img src="images/img-0101.png" alt="$z$" style="vertical-align:0px;
width:9px;
height:8px" class="math gen" />-axis and the normal to the user’s two-dimensional display. </p><p>The <tt class="tt">replot</tt> command<a name="a0000000860" id="a0000000860"></a> command may be used to add additional datasets to three-dimensional plots in an entirely analogous fashion to two-dimensional plots. </p></div>
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