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<title>MathGL 2.1.2: 4.14 Vector fields</title>
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<a name="Vector-fields"></a>
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<a name="Vector-fields-1"></a>
<h2 class="section">4.14 Vector fields</h2>
<a name="index-Traj"></a>
<a name="index-Vect"></a>
<a name="index-Dew"></a>
<a name="index-Flow"></a>
<a name="index-FlowP"></a>
<a name="index-Pipe"></a>
<p>These functions perform plotting of 2D and 3D vector fields. There are 5 generally different types of vector fields representations: simple vector field (Vect), vectors along the curve (Traj), vector field by dew-drops (Dew), flow threads (Flow, FlowP), flow pipes (Pipe). By default (if absent) values of <var>x</var>, <var>y</var>, <var>z</var> are equidistantly distributed in axis range. The minor dimensions of arrays <var>x</var>, <var>y</var>, <var>z</var>, <var>ax</var> should be equal. The size of <var>ax</var>, <var>ay</var> and <var>az</var> must be equal. Arrays <var>x</var>, <var>y</var>, <var>z</var> can be vectors (not matrices as <var>ax</var>). String <var>sch</var> sets the color scheme (see <a href="mathgl_en_24.html#Color-scheme">Color scheme</a>) for plot. String <var>opt</var> contain command options (see <a href="mathgl_en_27.html#Command-options">Command options</a>).
</p>
<p><a name="traj"></a>
</p><dl>
<dt><a name="index-traj"></a><u>MGL command:</u> <b>traj</b><i> xdat ydat udat vdat ['sch'='']</i></dt>
<dt><a name="index-traj-1"></a><u>MGL command:</u> <b>traj</b><i> xdat ydat zdat udat vdat wdat ['sch'='']</i></dt>
<dt><a name="index-Traj-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Traj</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Traj-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Traj</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005ftraj_005fxyz"></a><u>C function:</u> <code>void</code> <b>mgl_traj_xyz</b><i> (<code>HMGL</code> gr, <code>HCDT</code>x, <code>HCDT</code>y, <code>HCDT</code>z, <code>HCDT</code>ax, <code>HCDT</code>ay, <code>HCDT</code>az, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005ftraj_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_traj_xy</b><i> (<code>HMGL</code> gr, <code>HCDT</code>x, <code>HCDT</code>y, <code>HCDT</code>ax, <code>HCDT</code>ay, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws vectors {<var>ax</var>, <var>ay</var>, <var>az</var>} along a curve {<var>x</var>, <var>y</var>, <var>z</var>}. The length of arrows are proportional to <em>\sqrtax^2+ay^2+az^2</em>. String <var>pen</var> specifies the color (see <a href="mathgl_en_23.html#Line-styles">Line styles</a>). By default (<code>pen=""</code>) color from palette is used (see <a href="mathgl_en_31.html#Palette-and-colors">Palette and colors</a>). Option <var>value</var> set the vector length factor (if non-zero) or vector length to be proportional the distance between curve points (if <var>value</var>=0). The minor sizes of all arrays must be equal and large 2. The plots are drawn for each row if one of the data is the matrix. See also <a href="#vect">vect</a>. See section <a href="mathgl_en_17.html#Traj-sample">Traj sample</a>, for sample code and picture.
</p></dd></dl>
<p><a name="vect"></a>
</p><dl>
<dt><a name="index-vect"></a><u>MGL command:</u> <b>vect</b><i> udat vdat ['sch'='']</i></dt>
<dt><a name="index-vect-1"></a><u>MGL command:</u> <b>vect</b><i> xdat ydat udat vdat ['sch'='']</i></dt>
<dt><a name="index-Vect-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Vect</b><i> (<code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Vect-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Vect</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fvect_005f2d"></a><u>C function:</u> <code>void</code> <b>mgl_vect_2d</b><i> (<code>HMGL</code> gr, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fvect_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_vect_xy</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws plane vector field plot for the field {<var>ax</var>, <var>ay</var>} depending parametrically on coordinates <var>x</var>, <var>y</var> at level <var>z</var>=<var>Min</var>.z. The length and color of arrows are proportional to <em>\sqrtax^2+ay^2</em>. The number of arrows depend on <a href="mathgl_en_31.html#meshnum">meshnum</a>. The appearance of the hachures (arrows) can be changed by symbols:
</p><ul>
<li>
‘<samp>f</samp>’ for drawing arrows with fixed lengths,
</li><li>
‘<samp>></samp>’, ‘<samp><</samp>’ for drawing arrows to or from the cell point (default is centering),
</li><li>
‘<samp>.</samp>’ for drawing hachures with dots instead of arrows,
</li><li>
‘<samp>=</samp>’ for enabling color gradient along arrows.
</li></ul>
<p>See also <a href="#flow">flow</a>, <a href="#dew">dew</a>. See section <a href="mathgl_en_17.html#Vect-sample">Vect sample</a>, for sample code and picture.
</p></dd></dl>
<dl>
<dt><a name="index-vect-2"></a><u>MGL command:</u> <b>vect</b><i> udat vdat wdat ['sch'='']</i></dt>
<dt><a name="index-vect-3"></a><u>MGL command:</u> <b>vect</b><i> xdat ydat zdat udat vdat wdat ['sch'='']</i></dt>
<dt><a name="index-Vect-3"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Vect</b><i> (<code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Vect-4"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Vect</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fvect_005f3d"></a><u>C function:</u> <code>void</code> <b>mgl_vect_3d</b><i> (<code>HMGL</code> gr, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>HCDT</code> az, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fvect_005fxyz"></a><u>C function:</u> <code>void</code> <b>mgl_vect_xyz</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>HCDT</code> az, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>This is 3D version of the first functions. Here arrays <var>ax</var>, <var>ay</var>, <var>az</var> must be 3-ranged tensors with equal sizes and the length and color of arrows is proportional to <em>\sqrtax^2+ay^2+az^2</em>.
</p></dd></dl>
<p><a name="vect3"></a>
</p><dl>
<dt><a name="index-vect3"></a><u>MGL command:</u> <b>vect3</b><i> udat vdat wdat ['sch'='' sval]</i></dt>
<dt><a name="index-vect3-1"></a><u>MGL command:</u> <b>vect3</b><i> xdat ydat zdat udat vdat wdat ['sch'='' sval]</i></dt>
<dt><a name="index-Vect3"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Vect3</b><i> (<code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>mreal</code> sVal=<code>-1</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Vect3-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Vect3</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>mreal</code> sVal=<code>-1</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fvect3"></a><u>C function:</u> <code>void</code> <b>mgl_vect3</b><i> (<code>HMGL</code> gr, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>HCDT</code> az, <code>const char *</code>sch, <code>mreal</code> sVal, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fvect3_005fxyz"></a><u>C function:</u> <code>void</code> <b>mgl_vect3_xyz</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>HCDT</code> az, <code>const char *</code>sch, <code>mreal</code> sVal, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws 3D vector field plot for the field {<var>ax</var>, <var>ay</var>, <var>az</var>} depending parametrically on coordinates <var>x</var>, <var>y</var>, <var>z</var>. Vector field is drawn at slice <var>sVal</var> in direction {‘<samp>x</samp>’, ‘<samp>y</samp>’, ‘<samp>z</samp>’} if <var>sch</var> contain corresponding symbol (by default, ‘<samp>y</samp>’ direction is used). The length and color of arrows are proportional to <em>\sqrtax^2+ay^2+az^2</em>. The number of arrows depend on <a href="mathgl_en_31.html#meshnum">meshnum</a>. The appearance of the hachures (arrows) can be changed by symbols:
</p><ul>
<li>
‘<samp>f</samp>’ for drawing arrows with fixed lengths,
</li><li>
‘<samp>></samp>’, ‘<samp><</samp>’ for drawing arrows to or from the cell point (default is centering),
</li><li>
‘<samp>.</samp>’ for drawing hachures with dots instead of arrows,
</li><li>
‘<samp>=</samp>’ for enabling color gradient along arrows.
</li></ul>
<p>See also <a href="#vect">vect</a>, <a href="#flow">flow</a>, <a href="#dew">dew</a>. See section <a href="mathgl_en_17.html#Vect3-sample">Vect3 sample</a>, for sample code and picture.
</p></dd></dl>
<p><a name="dew"></a>
</p><dl>
<dt><a name="index-dew"></a><u>MGL command:</u> <b>dew</b><i> udat vdat ['sch'='']</i></dt>
<dt><a name="index-dew-1"></a><u>MGL command:</u> <b>dew</b><i> xdat ydat udat vdat ['sch'='']</i></dt>
<dt><a name="index-Dew-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Dew</b><i> (<code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Dew-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Dew</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fdew"></a><u>C function:</u> <code>void</code> <b>mgl_dew</b><i> (<code>HMGL</code> gr, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fdew_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_dew_xy</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws dew-drops for plane vector field {<var>ax</var>, <var>ay</var>} depending parametrically on coordinates <var>x</var>, <var>y</var> at level <var>z</var>=<var>Min</var>.z. Note that this is very expensive plot in memory usage and creation time! The color of drops is proportional to <em>\sqrtax^2+ay^2</em>. The number of drops depend on <a href="mathgl_en_31.html#meshnum">meshnum</a>. See also <a href="#vect">vect</a>. See section <a href="mathgl_en_17.html#Dew-sample">Dew sample</a>, for sample code and picture.
</p></dd></dl>
<p><a name="flow"></a>
</p><dl>
<dt><a name="index-flow"></a><u>MGL command:</u> <b>flow</b><i> udat vdat ['sch'='']</i></dt>
<dt><a name="index-flow-1"></a><u>MGL command:</u> <b>flow</b><i> xdat ydat udat vdat ['sch'='']</i></dt>
<dt><a name="index-Flow-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Flow</b><i> (<code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Flow-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Flow</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fflow_005f2d"></a><u>C function:</u> <code>void</code> <b>mgl_flow_2d</b><i> (<code>HMGL</code> gr, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fflow_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_flow_xy</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws flow threads for the plane vector field {<var>ax</var>, <var>ay</var>} parametrically depending on coordinates <var>x</var>, <var>y</var> at level <var>z</var> = <var>Min</var>.z. Number of threads is proportional to <var>value</var> option (default is 5). String <var>sch</var> may contain:
</p><ul>
<li>
color scheme – up-half (warm) corresponds to normal flow (like attractor), bottom-half (cold) corresponds to inverse flow (like source);
</li><li>
‘<samp>#</samp>’ for starting threads from edges only;
</li><li>
‘<samp>v</samp>’ for drawing arrows on the threads;
</li><li>
‘<samp>x</samp>’, ‘<samp>z</samp>’ for drawing tapes of normals in x-y and y-z planes correspondingly.
</li></ul>
<p>See also <a href="#pipe">pipe</a>, <a href="#vect">vect</a>, <a href="mathgl_en_39.html#tape">tape</a>, <a href="mathgl_en_31.html#barwidth">barwidth</a>. See section <a href="mathgl_en_17.html#Flow-sample">Flow sample</a>, for sample code and picture.
</p></dd></dl>
<dl>
<dt><a name="index-flow-2"></a><u>MGL command:</u> <b>flow</b><i> udat vdat wdat ['sch'='']</i></dt>
<dt><a name="index-flow-3"></a><u>MGL command:</u> <b>flow</b><i> xdat ydat zdat udat vdat wdat ['sch'='']</i></dt>
<dt><a name="index-Flow-3"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Flow</b><i> (<code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Flow-4"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Flow</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fflow_005f3d"></a><u>C function:</u> <code>void</code> <b>mgl_flow_3d</b><i> (<code>HMGL</code> gr, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>HCDT</code> az, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fflow_005fxyz"></a><u>C function:</u> <code>void</code> <b>mgl_flow_xyz</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>HCDT</code> az, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>This is 3D version of the first functions. Here arrays <var>ax</var>, <var>ay</var>, <var>az</var> must be 3-ranged tensors with equal sizes and the color of line is proportional to <em>\sqrtax^2+ay^2+az^2</em>.
</p></dd></dl>
<dl>
<dt><a name="index-flow-4"></a><u>MGL command:</u> <b>flow</b><i> <code>x0 y0</code> udat vdat ['sch'='']</i></dt>
<dt><a name="index-flow-5"></a><u>MGL command:</u> <b>flow</b><i> <code>x0 y0</code> xdat ydat udat vdat ['sch'='']</i></dt>
<dt><a name="index-FlowP-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>FlowP</b><i> (<code>mglPoint</code> p0, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-FlowP-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>FlowP</b><i> (<code>mglPoint</code> p0, <code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fflowp_005f2d"></a><u>C function:</u> <code>void</code> <b>mgl_flowp_2d</b><i> (<code>HMGL</code> gr, <code>mreal</code> x0, <code>mreal</code> y0, <code>mreal</code> z0, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fflowp_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_flowp_xy</b><i> (<code>HMGL</code> gr, <code>mreal</code> x0, <code>mreal</code> y0, <code>mreal</code> z0, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The same as first one (<a href="#flow">flow</a>) but draws single flow thread starting from point <var>p0</var>={<var>x0</var>,<var>y0</var>,<var>z0</var>}.
</p></dd></dl>
<dl>
<dt><a name="index-flow-6"></a><u>MGL command:</u> <b>flow</b><i> <code>x0 y0 z0</code> udat vdat wdat ['sch'='']</i></dt>
<dt><a name="index-flow-7"></a><u>MGL command:</u> <b>flow</b><i> <code>x0 y0 z0</code> xdat ydat zdat udat vdat wdat ['sch'='']</i></dt>
<dt><a name="index-FlowP-3"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>FlowP</b><i> (<code>mglPoint</code> p0, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-FlowP-4"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>FlowP</b><i> (<code>mglPoint</code> p0, <code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fflowp_005f3d"></a><u>C function:</u> <code>void</code> <b>mgl_flowp_3d</b><i> (<code>HMGL</code> gr, <code>mreal</code> x0, <code>mreal</code> y0, <code>mreal</code> z0, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>HCDT</code> az, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fflowp_005fxyz"></a><u>C function:</u> <code>void</code> <b>mgl_flowp_xyz</b><i> (<code>HMGL</code> gr, <code>mreal</code> x0, <code>mreal</code> y0, <code>mreal</code> z0, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>HCDT</code> az, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>This is 3D version of the previous functions.
</p></dd></dl>
<p><a name="grad"></a>
</p><dl>
<dt><a name="index-grad"></a><u>MGL command:</u> <b>grad</b><i> pdat ['sch'='']</i></dt>
<dt><a name="index-grad-1"></a><u>MGL command:</u> <b>grad</b><i> xdat ydat pdat ['sch'='']</i></dt>
<dt><a name="index-grad-2"></a><u>MGL command:</u> <b>grad</b><i> xdat ydat zdat pdat ['sch'='']</i></dt>
<dt><a name="index-Grad-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Grad</b><i> (<code>const mglDataA &</code>phi, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Grad-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Grad</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>phi, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Grad-3"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Grad</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>phi, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fgrad"></a><u>C function:</u> <code>void</code> <b>mgl_grad</b><i> (<code>HMGL</code> gr, <code>HCDT</code> phi, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fgrad_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_grad_xy</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> phi, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fgrad_005fxyz"></a><u>C function:</u> <code>void</code> <b>mgl_grad_xyz</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> phi, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws gradient lines for scalar field <var>phi</var>[i,j] (or <var>phi</var>[i,j,k] in 3d case) specified parametrically {<var>x</var>[i,j,k], <var>y</var>[i,j,k], <var>z</var>[i,j,k]}. Number of lines is proportional to <var>value</var> option (default is 5). See also <a href="mathgl_en_40.html#dens">dens</a>, <a href="mathgl_en_40.html#cont">cont</a>, <a href="#flow">flow</a>.
</p></dd></dl>
<p><a name="pipe"></a>
</p><dl>
<dt><a name="index-pipe"></a><u>MGL command:</u> <b>pipe</b><i> udat vdat ['sch'='' <code>r0=0.05</code>]</i></dt>
<dt><a name="index-pipe-1"></a><u>MGL command:</u> <b>pipe</b><i> xdat ydat udat vdat ['sch'='' <code>r0=0.05</code>]</i></dt>
<dt><a name="index-Pipe-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Pipe</b><i> (<code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>mreal</code> r0=<code>0.05</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Pipe-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Pipe</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const char *</code>sch=<code>""</code>, <code>mreal</code> r0=<code>0.05</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fpipe_005f2d"></a><u>C function:</u> <code>void</code> <b>mgl_pipe_2d</b><i> (<code>HMGL</code> gr, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>const char *</code>sch, <code>mreal</code> r0, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fpipe_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_pipe_xy</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>const char *</code>sch, <code>mreal</code> r0, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws flow pipes for the plane vector field {<var>ax</var>, <var>ay</var>} parametrically depending on coordinates <var>x</var>, <var>y</var> at level <var>z</var> = <var>Min</var>.z. Number of pipes is proportional to <var>value</var> option (default is 5). If ‘<samp>#</samp>’ symbol is specified then pipes start only from edges of axis range. The color of lines is proportional to <em>\sqrtax^2+ay^2</em>. Warm color corresponds to normal flow (like attractor). Cold one corresponds to inverse flow (like source). Parameter <var>r0</var> set the base pipe radius. If <var>r0</var><0 or symbol ‘<samp>i</samp>’ is specified then pipe radius is inverse proportional to amplitude. The vector field is plotted for each z slice of <var>ax</var>, <var>ay</var>. See also <a href="#flow">flow</a>, <a href="#vect">vect</a>. See section <a href="mathgl_en_17.html#Pipe-sample">Pipe sample</a>, for sample code and picture.
</p></dd></dl>
<dl>
<dt><a name="index-pipe-2"></a><u>MGL command:</u> <b>pipe</b><i> udat vdat wdat ['sch'='' <code>r0=0.05</code>]</i></dt>
<dt><a name="index-pipe-3"></a><u>MGL command:</u> <b>pipe</b><i> xdat ydat zdat udat vdat wdat ['sch'='' <code>r0=0.05</code>]</i></dt>
<dt><a name="index-Pipe-3"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Pipe</b><i> (<code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>mreal</code> r0=<code>0.05</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Pipe-4"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Pipe</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>ax, <code>const mglDataA &</code>ay, <code>const mglDataA &</code>az, <code>const char *</code>sch=<code>""</code>, <code>mreal</code> r0=<code>0.05</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fpipe_005f3d"></a><u>C function:</u> <code>void</code> <b>mgl_pipe_3d</b><i> (<code>HMGL</code> gr, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>HCDT</code> az, <code>const char *</code>sch, <code>mreal</code> r0, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fpipe_005fxyz"></a><u>C function:</u> <code>void</code> <b>mgl_pipe_xyz</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> ax, <code>HCDT</code> ay, <code>HCDT</code> az, <code>const char *</code>sch, <code>mreal</code> r0, <code>const char *</code>opt)</i></dt>
<dd><p>This is 3D version of the first functions. Here arrays <var>ax</var>, <var>ay</var>, <var>az</var> must be 3-ranged tensors with equal sizes and the color of line is proportional to <em>\sqrtax^2+ay^2+az^2</em>.
</p></dd></dl>
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