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<title>MathGL 2.1.2: 4.13 Dual plotting</title>
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<a name="Dual-plotting"></a>
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<a name="Dual-plotting-1"></a>
<h2 class="section">4.13 Dual plotting</h2>
<a name="index-SurfC"></a>
<a name="index-SurfA"></a>
<a name="index-Surf3C"></a>
<a name="index-Surf3A"></a>
<a name="index-TileS"></a>
<a name="index-Map"></a>
<a name="index-STFA"></a>
<p>These plotting functions draw <em>two matrix</em> simultaneously. There are 5 generally different types of data representations: surface or isosurface colored by other data (SurfC, Surf3C), surface or isosurface transpared by other data (SurfA, Surf3A), tiles with variable size (TileS), mapping diagram (Map), STFA diagram (STFA). 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>c</var> should be equal. Arrays <var>x</var>, <var>y</var> (and <var>z</var> for <code>Surf3C, Surf3A</code>) can be vectors (not matrices as <var>c</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="surfc"></a>
</p><dl>
<dt><a name="index-surfc"></a><u>MGL command:</u> <b>surfc</b><i> zdat cdat ['sch'='']</i></dt>
<dt><a name="index-surfc-1"></a><u>MGL command:</u> <b>surfc</b><i> xdat ydat zdat cdat ['sch'='']</i></dt>
<dt><a name="index-SurfC-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>SurfC</b><i> (<code>const mglDataA &</code>z, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-SurfC-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>SurfC</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fsurfc"></a><u>C function:</u> <code>void</code> <b>mgl_surfc</b><i> (<code>HMGL</code> gr, <code>HCDT</code> z, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fsurfc_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_surfc_xy</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws surface specified parametrically {<var>x</var>[i,j], <var>y</var>[i,j], <var>z</var>[i,j]} and color it by matrix <var>c</var>[i,j]. If string <var>sch</var> have symbol ‘<samp>#</samp>’ then grid lines are drawn. If string <var>sch</var> have symbol ‘<samp>.</samp>’ then plot by dots is produced. All dimensions of arrays <var>z</var> and <var>c</var> must be equal. Surface is plotted for each z slice of the data. See also <a href="mathgl_en_40.html#surf">surf</a>, <a href="#surfa">surfa</a>, <a href="#surf3c">surf3c</a>. See section <a href="mathgl_en_15.html#SurfC-sample">SurfC sample</a>, for sample code and picture.
</p></dd></dl>
<p><a name="surf3c"></a>
</p><dl>
<dt><a name="index-surf3c"></a><u>MGL command:</u> <b>surf3c</b><i> adat cdat <code>val</code> ['sch'='']</i></dt>
<dt><a name="index-surf3c-1"></a><u>MGL command:</u> <b>surf3c</b><i> xdat ydat zdat adat cdat <code>val</code> ['sch'='']</i></dt>
<dt><a name="index-Surf3C-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Surf3C</b><i> (<code>mreal</code> val, <code>const mglDataA &</code>a, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Surf3C-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Surf3C</b><i> (<code>mreal</code> val, <code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>a, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fsurf3c_005fval"></a><u>C function:</u> <code>void</code> <b>mgl_surf3c_val</b><i> (<code>HMGL</code> gr, <code>mreal</code> val, <code>HCDT</code> a, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fsurf3c_005fxyz_005fval"></a><u>C function:</u> <code>void</code> <b>mgl_surf3c_xyz_val</b><i> (<code>HMGL</code> gr, <code>mreal</code> val, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> a, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws isosurface plot for 3d array specified parametrically <var>a</var>[i,j,k](<var>x</var>[i,j,k], <var>y</var>[i,j,k], <var>z</var>[i,j,k]) at <var>a</var>(x,y,z)=<var>val</var>. It is mostly the same as <a href="mathgl_en_41.html#surf3">surf3</a> function but the color of isosurface depends on values of array <var>c</var>. If string <var>sch</var> contain ‘<samp>#</samp>’ then wire plot is produced. If string <var>sch</var> have symbol ‘<samp>.</samp>’ then plot by dots is produced. See also <a href="mathgl_en_41.html#surf3">surf3</a>, <a href="#surfc">surfc</a>, <a href="#surf3a">surf3a</a>. See section <a href="mathgl_en_16.html#Surf3C-sample">Surf3C sample</a>, for sample code and picture.
</p></dd></dl>
<dl>
<dt><a name="index-surf3c-2"></a><u>MGL command:</u> <b>surf3c</b><i> adat cdat ['sch'='']</i></dt>
<dt><a name="index-surf3c-3"></a><u>MGL command:</u> <b>surf3c</b><i> xdat ydat zdat adat cdat ['sch'='']</i></dt>
<dt><a name="index-Surf3C-3"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Surf3C</b><i> (<code>const mglDataA &</code>a, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Surf3C-4"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Surf3C</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>a, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fsurf3c"></a><u>C function:</u> <code>void</code> <b>mgl_surf3c</b><i> (<code>HMGL</code> gr, <code>HCDT</code> a, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fsurf3c_005fxyz"></a><u>C function:</u> <code>void</code> <b>mgl_surf3c_xyz</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> a, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>Draws <var>num</var>-th uniformly distributed in color range isosurfaces for 3d data. Here <var>num</var> is equal to parameter <var>value</var> in options <var>opt</var> (default is 3).
</p></dd></dl>
<p><a name="surfa"></a>
</p><dl>
<dt><a name="index-surfa"></a><u>MGL command:</u> <b>surfa</b><i> zdat cdat ['sch'='']</i></dt>
<dt><a name="index-surfa-1"></a><u>MGL command:</u> <b>surfa</b><i> xdat ydat zdat cdat ['sch'='']</i></dt>
<dt><a name="index-SurfA-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>SurfA</b><i> (<code>const mglDataA &</code>z, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-SurfA-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>SurfA</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fsurfa"></a><u>C function:</u> <code>void</code> <b>mgl_surfa</b><i> (<code>HMGL</code> gr, <code>HCDT</code> z, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fsurfa_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_surfa_xy</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws surface specified parametrically {<var>x</var>[i,j], <var>y</var>[i,j], <var>z</var>[i,j]} and transparent it by matrix <var>c</var>[i,j]. If string <var>sch</var> have symbol ‘<samp>#</samp>’ then grid lines are drawn. If string <var>sch</var> have symbol ‘<samp>.</samp>’ then plot by dots is produced. All dimensions of arrays <var>z</var> and <var>c</var> must be equal. Surface is plotted for each z slice of the data. See also <a href="mathgl_en_40.html#surf">surf</a>, <a href="#surfc">surfc</a>, <a href="#surf3a">surf3a</a>. See section <a href="mathgl_en_15.html#SurfA-sample">SurfA sample</a>, for sample code and picture.
</p></dd></dl>
<p><a name="surf3a"></a>
</p><dl>
<dt><a name="index-surf3a"></a><u>MGL command:</u> <b>surf3a</b><i> adat cdat <code>val</code> ['sch'='']</i></dt>
<dt><a name="index-surf3a-1"></a><u>MGL command:</u> <b>surf3a</b><i> xdat ydat zdat adat cdat <code>val</code> ['sch'='']</i></dt>
<dt><a name="index-Surf3A-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Surf3A</b><i> (<code>mreal</code> val, <code>const mglDataA &</code>a, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Surf3A-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Surf3A</b><i> (<code>mreal</code> val, <code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>a, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fsurf3a_005fval"></a><u>C function:</u> <code>void</code> <b>mgl_surf3a_val</b><i> (<code>HMGL</code> gr, <code>mreal</code> val, <code>HCDT</code> a, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fsurf3a_005fxyz_005fval"></a><u>C function:</u> <code>void</code> <b>mgl_surf3a_xyz_val</b><i> (<code>HMGL</code> gr, <code>mreal</code> val, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> a, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws isosurface plot for 3d array specified parametrically <var>a</var>[i,j,k](<var>x</var>[i,j,k], <var>y</var>[i,j,k], <var>z</var>[i,j,k]) at <var>a</var>(x,y,z)=<var>val</var>. It is mostly the same as <a href="mathgl_en_41.html#surf3">surf3</a> function but the color of isosurface depends on values of array <var>c</var>. If string <var>sch</var> contain ‘<samp>#</samp>’ then wire plot is produced. If string <var>sch</var> have symbol ‘<samp>.</samp>’ then plot by dots is produced. See also <a href="mathgl_en_41.html#surf3">surf3</a>, <a href="#surfc">surfc</a>, <a href="#surf3a">surf3a</a>. See section <a href="mathgl_en_16.html#Surf3A-sample">Surf3A sample</a>, for sample code and picture.
</p></dd></dl>
<dl>
<dt><a name="index-surf3a-2"></a><u>MGL command:</u> <b>surf3a</b><i> adat cdat ['sch'='']</i></dt>
<dt><a name="index-surf3a-3"></a><u>MGL command:</u> <b>surf3a</b><i> xdat ydat zdat adat cdat ['sch'='']</i></dt>
<dt><a name="index-Surf3A-3"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Surf3A</b><i> (<code>const mglDataA &</code>a, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-Surf3A-4"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Surf3A</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>a, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fsurf3a"></a><u>C function:</u> <code>void</code> <b>mgl_surf3a</b><i> (<code>HMGL</code> gr, <code>HCDT</code> a, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fsurf3a_005fxyz"></a><u>C function:</u> <code>void</code> <b>mgl_surf3a_xyz</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> a, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>Draws <var>num</var>-th uniformly distributed in color range isosurfaces for 3d data. At this array <var>c</var> can be vector with values of transparency and <var>num</var>=<var>c</var>.nx. In opposite case <var>num</var> is equal to parameter <var>value</var> in options <var>opt</var> (default is 3).
</p></dd></dl>
<p><a name="tiles"></a>
</p><dl>
<dt><a name="index-tiles"></a><u>MGL command:</u> <b>tiles</b><i> zdat rdat ['sch'='']</i></dt>
<dt><a name="index-tiles-1"></a><u>MGL command:</u> <b>tiles</b><i> xdat ydat zdat rdat ['sch'='']</i></dt>
<dt><a name="index-TileS-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>TileS</b><i> (<code>const mglDataA &</code>z, <code>const mglDataA &</code>c, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-TileS-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>TileS</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>z, <code>const mglDataA &</code>r, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005ftiles"></a><u>C function:</u> <code>void</code> <b>mgl_tiles</b><i> (<code>HMGL</code> gr, <code>HCDT</code> z, <code>HCDT</code> c, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005ftiles_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_tiles_xy</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> z, <code>HCDT</code> r, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>The function draws horizontal tiles for surface specified parametrically {<var>x</var>[i,j], <var>y</var>[i,j], <var>z</var>[i,j]}. It is mostly the same as <a href="mathgl_en_40.html#tile">tile</a> but the size of tiles is determined by <var>r</var> array. This is some kind of “transparency” useful for exporting to EPS files. Tiles is plotted for each z slice of the data. See also <a href="#surfa">surfa</a>, <a href="mathgl_en_40.html#tile">tile</a>. See section <a href="mathgl_en_15.html#TileS-sample">TileS sample</a>, for sample code and picture.
</p></dd></dl>
<p><a name="map"></a>
</p><dl>
<dt><a name="index-map"></a><u>MGL command:</u> <b>map</b><i> udat vdat ['sch'='']</i></dt>
<dt><a name="index-map-1"></a><u>MGL command:</u> <b>map</b><i> xdat ydat udat vdat ['sch'='']</i></dt>
<dt><a name="index-Map-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Map</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-Map-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>Map</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_005fmap"></a><u>C function:</u> <code>void</code> <b>mgl_map</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_005fmap_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_map_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 mapping plot for matrices {<var>ax</var>, <var>ay</var> } which parametrically depend on coordinates <var>x</var>, <var>y</var>. The initial position of the cell (point) is marked by color. Height is proportional to Jacobian(ax,ay). This plot is like Arnold diagram ??? If string <var>sch</var> contain symbol ‘<samp>.</samp>’ then the color ball at matrix knots are drawn otherwise face is drawn. See section <a href="mathgl_en_18.html#Mapping-visualization">Mapping visualization</a>, for sample code and picture.
</p></dd></dl>
<p><a name="stfa"></a>
</p><dl>
<dt><a name="index-stfa"></a><u>MGL command:</u> <b>stfa</b><i> re im <code>dn</code> ['sch'='']</i></dt>
<dt><a name="index-stfa-1"></a><u>MGL command:</u> <b>stfa</b><i> xdat ydat re im <code>dn</code> ['sch'='']</i></dt>
<dt><a name="index-STFA-1"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>STFA</b><i> (<code>const mglDataA &</code>re, <code>const mglDataA &</code>im, <code>int</code> dn, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-STFA-2"></a><u>Method on <code>mglGraph</code>:</u> <code>void</code> <b>STFA</b><i> (<code>const mglDataA &</code>x, <code>const mglDataA &</code>y, <code>const mglDataA &</code>re, <code>const mglDataA &</code>im, <code>int</code> dn, <code>const char *</code>sch=<code>""</code>, <code>const char *</code>opt=<code>""</code>)</i></dt>
<dt><a name="index-mgl_005fstfa"></a><u>C function:</u> <code>void</code> <b>mgl_stfa</b><i> (<code>HMGL</code> gr, <code>HCDT</code> re, <code>HCDT</code> im, <code>int</code> dn, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dt><a name="index-mgl_005fstfa_005fxy"></a><u>C function:</u> <code>void</code> <b>mgl_stfa_xy</b><i> (<code>HMGL</code> gr, <code>HCDT</code> x, <code>HCDT</code> y, <code>HCDT</code> re, <code>HCDT</code> im, <code>int</code> dn, <code>const char *</code>sch, <code>const char *</code>opt)</i></dt>
<dd><p>Draws spectrogram of complex array <var>re</var>+i*<var>im</var> for Fourier size of <var>dn</var> points at plane <var>z</var>=<var>Min</var>.z. For example in 1D case, result is density plot of data <em>res[i,j]=|\sum_d^dn exp(I*j*d)*(re[i*dn+d]+I*im[i*dn+d])|/dn</em> with size {int(nx/dn), dn, ny}. At this array <var>re</var>, <var>im</var> parametrically depend on coordinates <var>x</var>, <var>y</var>. The size of <var>re</var> and <var>im</var> must be the same. The minor dimensions of arrays <var>x</var>, <var>y</var>, <var>re</var> should be equal. Arrays <var>x</var>, <var>y</var> can be vectors (not matrix as <var>re</var>). See section <a href="mathgl_en_18.html#STFA-sample">STFA sample</a>, for sample code and picture.
</p></dd></dl>
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