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<h1 class="chapter"> 48. draw </h1>
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<tr><td align="left" valign="top"><a href="#SEC240">48.1 Introduction to draw</a></td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top"><a href="#SEC241">48.2 Functions and Variables for draw</a></td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top"><a href="#SEC246">48.3 Functions and Variables for pictures</a></td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top"><a href="#SEC247">48.4 Functions and Variables for worldmap</a></td><td> </td><td align="left" valign="top">
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<p><a name="Item_003a-Introduction-to-draw"></a>
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<h2 class="section"> 48.1 Introduction to draw </h2>
<p><code>draw</code> is a Maxima-Gnuplot interface.
</p>
<p>There are three main functions to be used at Maxima level:
<code>draw2d</code>, <code>draw3d</code> and <code>draw</code>.
</p>
<p>Follow this link for more elaborated examples of this package:
</p>
<p><a href="http://riotorto.users.sourceforge.net/gnuplot">http://riotorto.users.sourceforge.net/gnuplot</a>
</p>
<p>You need Gnuplot 4.2 or newer to run this program.
</p>
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<p>@ref{Category: Plotting} ·
@ref{Category: Share packages} ·
@ref{Category: Package draw}
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<h2 class="section"> 48.2 Functions and Variables for draw </h2>
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<h3 class="subsection"> 48.2.1 Scenes </h3>
<p><a name="Item_003a-gr2d"></a>
</p><dl>
<dt><u>Scene constructor:</u> <b>gr2d</b><i> (<var>graphic option</var>, ..., <var>graphic object</var>, ...)</i>
<a name="IDX2010"></a>
</dt>
<dd><p>Function <code>gr2d</code> builds an object describing a 2D scene. Arguments are
<i>graphic options</i>, <i>graphic objects</i>, or lists containing both graphic options and objects.
This scene is interpreted sequentially: <i>graphic options</i> affect those <i>graphic objects</i>
placed on its right. Some <i>graphic options</i> affect the global appearence of the scene.
</p>
<p>This is the list of <i>graphic objects</i> available for scenes in two dimensions:
<code>bars</code>, <code>ellipse</code>, <code>explicit</code>, <code>image</code>, <code>implicit</code>, <code>label</code>,
<code>parametric</code>, <code>points</code>, <code>polar</code>, <code>polygon</code>, <code>quadrilateral</code>,
<code>rectangle</code>, <code>triangle</code>, <code>vector</code>, and <code>geomap</code>
(this one defined in package <code>worldmap</code>).
</p>
<p>See also <code>draw</code> and <code>draw2d</code>.
</p>
<p>To make use of this object, write first <code>load(draw)</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-gr3d"></a>
</p><dl>
<dt><u>Scene constructor:</u> <b>gr3d</b><i> (<var>graphic option</var>, ..., <var>graphic object</var>, ...)</i>
<a name="IDX2011"></a>
</dt>
<dd><p>Function <code>gr3d</code> builds an object describing a 3d scene. Arguments are
<i>graphic options</i>, <i>graphic objects</i>, or lists containing both graphic options
and objects. This scene is interpreted sequentially: <i>graphic options</i> affect those
<i>graphic objects</i> placed on its right. Some <i>graphic options</i> affect the global
appearence of the scene.
</p>
<p>This is the list of <i>graphic objects</i> available for scenes in three
dimensions:<br>
<code>cylindrical</code>, <code>elevation_grid</code>, <code>explicit</code>, <code>implicit</code>,
<code>label</code>, <code>mesh</code>, <code>parametric</code>,<br>
<code>parametric_surface</code>, <code>points</code>, <code>quadrilateral</code>,
<code>spherical</code>, <code>triangle</code>, <code>tube</code>,<br>
<code>vector</code>, and <code>geomap</code> (this one defined in package <code>worldmap</code>).
</p>
<p>See also <code>draw</code> and <code>draw3d</code>.
</p>
<p>To make use of this object, write first <code>load(draw)</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
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</tr></table>
<h3 class="subsection"> 48.2.2 Functions </h3>
<dl>
<dt><u>Function:</u> <b>draw</b><i> (<var>gr2d</var>, ..., <var>gr3d</var>, ..., <var>options</var>, ...)</i>
<a name="IDX2012"></a>
</dt>
<dd><p>Plots a series of scenes; its arguments are <code>gr2d</code> and/or <code>gr3d</code>
objects, together with some options, or lists of scenes and options.
By default, the scenes are put together
in one column.
</p>
<p>Function <code>draw</code> accepts the following global options: <code>terminal</code>,
<code>columns</code>, <code>dimensions</code>, <code>file_name</code> and <code>delay</code>.
</p>
<p>Functions <code>draw2d</code> and <code>draw3d</code> are short cuts to be used
when only one scene is required, in two or three dimensions, respectively.
</p>
<p>See also <code>gr2d</code> and <code>gr3d</code>.
</p>
<p>To make use of this function, write first <code>load(draw)</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) scene1: gr2d(title="Ellipse",
nticks=30,
parametric(2*cos(t),5*sin(t),t,0,2*%pi))$
(%i3) scene2: gr2d(title="Triangle",
polygon([4,5,7],[6,4,2]))$
(%i4) draw(scene1, scene2, columns = 2)$
</pre>
<p>The two draw sentences are equivalent:
</p><pre class="example">(%i1) load(draw)$
(%i2) draw(gr3d(explicit(x^2+y^2,x,-1,1,y,-1,1)));
(%o2) [gr3d(explicit)]
(%i3) draw3d(explicit(x^2+y^2,x,-1,1,y,-1,1));
(%o3) [gr3d(explicit)]
</pre>
<p>An animated gif file:
</p><pre class="example">(%i1) load(draw)$
(%i2) draw(
delay = 100,
file_name = "zzz",
terminal = 'animated_gif,
gr2d(explicit(x^2,x,-1,1)),
gr2d(explicit(x^3,x,-1,1)),
gr2d(explicit(x^4,x,-1,1)));
End of animation sequence
(%o2) [gr2d(explicit), gr2d(explicit), gr2d(explicit)]
</pre>
<p>See also <code>gr2d</code>, <code>gr3d</code>, <code>draw2d</code> and <code>draw3d</code>..
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw} ·
@ref{Category: File output}
</div>
</p></dd></dl>
<p><a name="Item_003a-draw2d"></a>
</p><dl>
<dt><u>Function:</u> <b>draw2d</b><i> (<var>option</var>, <var>graphic_object</var>, ...)</i>
<a name="IDX2013"></a>
</dt>
<dd><p>This function is a short cut for
<code>draw(gr2d(<var>options</var>, ..., <var>graphic_object</var>, ...))</code>.
</p>
<p>It can be used to plot a unique scene in 2d.
</p>
<p>To make use of this function, write first <code>load(draw)</code>.
</p>
<p>See also <code>draw</code> and <code>gr2d</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw} ·
@ref{Category: File output}
</div>
</p></dd></dl>
<p><a name="Item_003a-draw3d"></a>
</p><dl>
<dt><u>Function:</u> <b>draw3d</b><i> (<var>option</var>, <var>graphic_object</var>, ...)</i>
<a name="IDX2014"></a>
</dt>
<dd><p>This function is a short cut for
<code>draw(gr3d(<var>options</var>, ..., <var>graphic_object</var>, ...))</code>.
</p>
<p>It can be used to plot a unique scene in 3d.
</p>
<p>To make use of this function, write first <code>load(draw)</code>.
</p>
<p>See also <code>draw</code> and <code>gr3d</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw} ·
@ref{Category: File output}
</div>
</p></dd></dl>
<p><a name="Item_003a-draw_005ffile"></a>
</p><dl>
<dt><u>Function:</u> <b>draw_file</b><i> (<var>graphic option</var>, ..., <var>graphic object</var>, ...)</i>
<a name="IDX2015"></a>
</dt>
<dd><p>Saves the current plot into a file. Accepted graphics options are:
<code>terminal</code>, <code>dimensions</code>, <code>file_name</code> and <code>background_color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) /* screen plot */
draw(gr3d(explicit(x^2+y^2,x,-1,1,y,-1,1)))$
(%i3) /* same plot in eps format */
draw_file(terminal = eps,
dimensions = [5,5]) $
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw} ·
@ref{Category: File output}
</div>
</p></dd></dl>
<p><a name="Item_003a-multiplot_005fmode"></a>
</p><dl>
<dt><u>Function:</u> <b>multiplot_mode</b><i> (<var>term</var>)</i>
<a name="IDX2016"></a>
</dt>
<dd><p>This function enables Maxima to work in one-window multiplot mode with terminal
<var>term</var>; accepted arguments for this function are <code>screen</code>,
<code>wxt</code>, <code>aquaterm</code> and <code>none</code>.
</p>
<p>When multiplot mode is enabled, each call to <code>draw</code> sends a new plot to the
same window, without erasing the previous ones. To disable the multiplot mode,
write <code>multiplot_mode(none)</code>.
</p>
<p>When multiplot mode is enabled, global option <code>terminal</code> is blocked and you
have to disable this working mode before changing to another terminal.
</p>
<p>This feature does not work in Windows platforms.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) set_draw_defaults(
xrange = [-1,1],
yrange = [-1,1],
grid = true,
title = "Step by step plot" )$
(%i3) multiplot_mode(screen)$
(%i4) draw2d(color=blue, explicit(x^2,x,-1,1))$
(%i5) draw2d(color=red, explicit(x^3,x,-1,1))$
(%i6) draw2d(color=brown, explicit(x^4,x,-1,1))$
(%i7) multiplot_mode(none)$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw} ·
@ref{Category: File output}
</div>
</p></dd></dl>
<p><a name="Item_003a-set_005fdraw_005fdefaults"></a>
</p><dl>
<dt><u>Function:</u> <b>set_draw_defaults</b><i> (<var>graphic option</var>, ..., <var>graphic object</var>, ...)</i>
<a name="IDX2017"></a>
</dt>
<dd><p>Sets user graphics options. This function is useful for plotting a sequence
of graphics with common graphics options. Calling this function without
arguments removes user defaults.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) set_draw_defaults(
xrange = [-10,10],
yrange = [-2, 2],
color = blue,
grid = true)$
(%i3) /* plot with user defaults */
draw2d(explicit(((1+x)**2/(1+x*x))-1,x,-10,10))$
(%i4) set_draw_defaults()$
(%i5) /* plot with standard defaults */
draw2d(explicit(((1+x)**2/(1+x*x))-1,x,-10,10))$
</pre>
<p>To make use of this function, write first <code>load(draw)</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
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</tr></table>
<h3 class="subsection"> 48.2.3 Graphics options </h3>
<dl>
<dt><u>Graphic option:</u> <b>adapt_depth</b>
<a name="IDX2018"></a>
</dt>
<dd><p>Default value: 10
</p>
<p><code>adapt_depth</code> is the maximum number of splittings used by the adaptive plotting routine.
</p>
<p>This option is relevant only for 2d <code>explicit</code> functions.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-allocation"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>allocation</b>
<a name="IDX2019"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>With option <code>allocation</code> it is possible to place a scene in the
output window at will; this is of interest in multiplots. When <code>false</code>,
the scene is placed automatically, depending on the value assigned to option
<code>columns</code>. In any other case, <code>allocation</code> must be set to a list of
two pairs of numbers; the first corresponds to the position of the lower left
corner of the scene, and the second pair gives the width and height of the plot.
All quantities must be given in relative coordinates, between 0 and 1.
</p>
<p>Examples:
</p>
<p>In site graphics.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw(
gr2d(
explicit(x^2,x,-1,1)),
gr2d(
allocation = [[1/4, 1/4],[1/2, 1/2]],
explicit(x^3,x,-1,1),
grid = true) ) $
</pre>
<p>Multiplot with selected dimensions.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw(
terminal = wxt,
gr2d(
allocation = [[0, 0],[1, 1/4]],
explicit(x^2,x,-1,1)),
gr3d(
allocation = [[0, 1/4],[1, 3/4]],
explicit(x^2+y^2,x,-1,1,y,-1,1) ))$
</pre>
<p>See also option <code>columns</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-axis_005f3d"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>axis_3d</b>
<a name="IDX2020"></a>
</dt>
<dd><p>Default value: <code>true</code>
</p>
<p>If <code>axis_3d</code> is <code>true</code>, the <var>x</var>, <var>y</var> and <var>z</var> axis are shown in 3d scenes.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(axis_3d = false,
explicit(sin(x^2+y^2),x,-2,2,y,-2,2) )$
</pre>
<p>See also <code>axis_bottom</code>, <code>axis_left</code>, <code>axis_top</code>, and <code>axis_right</code> for axis in 2d.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-axis_005fbottom"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>axis_bottom</b>
<a name="IDX2021"></a>
</dt>
<dd><p>Default value: <code>true</code>
</p>
<p>If <code>axis_bottom</code> is <code>true</code>, the bottom axis is shown in 2d scenes.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(axis_bottom = false,
explicit(x^3,x,-1,1))$
</pre>
<p>See also <code>axis_left</code>, <code>axis_top</code>, <code>axis_right</code>, and <code>axis_3d</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-axis_005fleft"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>axis_left</b>
<a name="IDX2022"></a>
</dt>
<dd><p>Default value: <code>true</code>
</p>
<p>If <code>axis_left</code> is <code>true</code>, the left axis is shown in 2d scenes.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(axis_left = false,
explicit(x^3,x,-1,1))$
</pre>
<p>See also <code>axis_bottom</code>, <code>axis_top</code>, <code>axis_right</code>, and <code>axis_3d</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-axis_005fright"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>axis_right</b>
<a name="IDX2023"></a>
</dt>
<dd><p>Default value: <code>true</code>
</p>
<p>If <code>axis_right</code> is <code>true</code>, the right axis is shown in 2d scenes.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(axis_right = false,
explicit(x^3,x,-1,1))$
</pre>
<p>See also <code>axis_bottom</code>, <code>axis_left</code>, <code>axis_top</code>, and <code>axis_3d</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-axis_005ftop"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>axis_top</b>
<a name="IDX2024"></a>
</dt>
<dd><p>Default value: <code>true</code>
</p>
<p>If <code>axis_top</code> is <code>true</code>, the top axis is shown in 2d scenes.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(axis_top = false,
explicit(x^3,x,-1,1))$
</pre>
<p>See also <code>axis_bottom</code>, <code>axis_left</code>, <code>axis_right</code>, and <code>axis_3d</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-background_005fcolor"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>background_color</b>
<a name="IDX2025"></a>
</dt>
<dd><p>Default value: <code>white</code>
</p>
<p>Sets the background color for terminals. Default background color is white.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>This option das not work with terminals <code>epslatex</code> and <code>epslatex_standalone</code>.
</p>
<p>See also <code>color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-border"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>border</b>
<a name="IDX2026"></a>
</dt>
<dd><p>Default value: <code>true</code>
</p>
<p>If <code>border</code> is <code>true</code>, borders of polygons are painted
according to <code>line_type</code> and <code>line_width</code>.
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr2d</code>: <code>polygon</code>, <code>rectangle</code>, and <code>ellipse</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(color = brown,
line_width = 8,
polygon([[3,2],[7,2],[5,5]]),
border = false,
fill_color = blue,
polygon([[5,2],[9,2],[7,5]]) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-cbrange"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>cbrange</b>
<a name="IDX2027"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>If <code>cbrange</code> is <code>auto</code>, the range for the values which are
colored when <code>enhanced3d</code> is not <code>false</code> is computed
automatically. Values outside of the color range use color of the
nearest extreme.
</p>
<p>When <code>enhanced3d</code> or <code>colorbox</code> is <code>false</code>, option <code>cbrange</code> has
no effect.
</p>
<p>If the user wants a specific interval for the colored values, it must
be given as a Maxima list, as in <code>cbrange=[-2, 3]</code>.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d (
enhanced3d = true,
color = green,
cbrange = [-3,10],
explicit(x^2+y^2, x,-2,2,y,-2,2)) $
</pre>
<p>See also <code>enhanced3d</code>, <code>colorbox</code> and <code>cbtics</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p></dd></dl>
<p><a name="Item_003a-cbtics"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>cbtics</b>
<a name="IDX2028"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>This graphic option controls the way tic marks are drawn on the colorbox
when option <code>enhanced3d</code> is not <code>false</code>.
</p>
<p>When <code>enhanced3d</code> or <code>colorbox</code> is <code>false</code>, option <code>cbtics</code> has
no effect.
</p>
<p>See <code>xtics</code> for a complete description.
</p>
<p>Example :
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d (
enhanced3d = true,
color = green,
cbtics = {["High",10],["Medium",05],["Low",0]},
cbrange = [0, 10],
explicit(x^2+y^2, x,-2,2,y,-2,2)) $
</pre>
<p>See also <code>enhanced3d</code>, <code>colorbox</code> and <code>cbrange</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>color</b>
<a name="IDX2029"></a>
</dt>
<dd><p>Default value: <code>blue</code>
</p>
<p><code>color</code> specifies the color for plotting lines, points, borders of
polygons and labels.
</p>
<p>Colors can be given as names or in hexadecimal <i>rgb</i> code.
</p>
<p>Available color names are:
</p><pre class="verbatim">white black gray0 grey0
gray10 grey10 gray20 grey20
gray30 grey30 gray40 grey40
gray50 grey50 gray60 grey60
gray70 grey70 gray80 grey80
gray90 grey90 gray100 grey100
gray grey light_gray light_grey
dark_gray dark_grey red light_red
dark_red yellow light_yellow dark_yellow
green light_green dark_green spring_green
forest_green sea_green blue light_blue
dark_blue midnight_blue navy medium_blue
royalblue skyblue cyan light_cyan
dark_cyan magenta light_magenta dark_magenta
turquoise light_turquoise dark_turquoise pink
light_pink dark_pink coral light_coral
orange_red salmon light_salmon dark_salmon
aquamarine khaki dark_khaki goldenrod
light_goldenrod dark_goldenrod gold beige
brown orange dark_orange violet
dark_violet plum purple
</pre>
<p>Cromatic componentes in hexadecimal code are introduced in the form <code>"#rrggbb"</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^2,x,_1,1), /* default is black */
color = red,
explicit(0.5 + x^2,x,-1,1),
color = blue,
explicit(1 + x^2,x,-1,1),
color = light_blue,
explicit(1.5 + x^2,x,-1,1),
color = "#23ab0f",
label(["This is a label",0,1.2]) )$
</pre>
<p>See also <code>fill_color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-colorbox"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>colorbox</b>
<a name="IDX2030"></a>
</dt>
<dd><p>Default value: <code>true</code>
</p>
<p>If <code>colorbox</code> is <code>true</code>, a color scale without label is drawn together with
<code>image</code> 2D objects, or coloured 3d objects. If <code>colorbox</code> is <code>false</code>, no
color scale is shown. If <code>colorbox</code> is a string, a color scale with label is drawn.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<p>Color scale and images.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) im: apply('matrix,
makelist(makelist(random(200),i,1,30),i,1,30))$
(%i3) draw2d(image(im,0,0,30,30))$
(%i4) draw2d(colorbox = false, image(im,0,0,30,30))$
</pre>
<p>Color scale and 3D coloured object.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
colorbox = "Magnitude",
enhanced3d = true,
explicit(x^2+y^2,x,-1,1,y,-1,1))$
</pre>
<p>See also <code>palette</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-columns"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>columns</b>
<a name="IDX2031"></a>
</dt>
<dd><p>Default value: 1
</p>
<p><code>columns</code> is the number of columns in multiple plots.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter. It can be also used as an argument of function <code>draw</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) scene1: gr2d(title="Ellipse",
nticks=30,
parametric(2*cos(t),5*sin(t),t,0,2*%pi))$
(%i3) scene2: gr2d(title="Triangle",
polygon([4,5,7],[6,4,2]))$
(%i4) draw(scene1, scene2, columns = 2)$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-contour"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>contour</b>
<a name="IDX2032"></a>
</dt>
<dd><p>Default value: <code>none</code>
</p>
<p>Option <code>contour</code> enables the user to select where to plot contour lines.
Possible values are:
</p>
<ul>
<li>
<code>none</code>:
no contour lines are plotted.
</li><li>
<code>base</code>:
contour lines are projected on the xy plane.
</li><li>
<code>surface</code>:
contour lines are plotted on the surface.
</li><li>
<code>both</code>:
two contour lines are plotted: on the xy plane and on the surface.
</li><li>
<code>map</code>:
contour lines are projected on the xy plane, and the view point is
set just in the vertical.
</li></ul>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(explicit(20*exp(-x^2-y^2)-10,x,0,2,y,-3,3),
contour_levels = 15,
contour = both,
surface_hide = true) $
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-contour_005flevels"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>contour_levels</b>
<a name="IDX2033"></a>
</dt>
<dd><p>Default value: 5
</p>
<p>This graphic option controls the way contours are drawn.
<code>contour_levels</code> can be set to a positive integer number, a list of three
numbers or an arbitrary set of numbers:
</p>
<ul>
<li>
When option <code>contour_levels</code> is bounded to positive integer <var>n</var>,
<var>n</var> contour lines will be drawn at equal intervals. By default, five
equally spaced contours are plotted.
</li><li>
When option <code>contour_levels</code> is bounded to a list of length three of the
form <code>[lowest,s,highest]</code>, contour lines are plotted from <code>lowest</code>
to <code>highest</code> in steps of <code>s</code>.
</li><li>
When option <code>contour_levels</code> is bounded to a set of numbers of the
form <code>{n1, n2, ...}</code>, contour lines are plotted at values <code>n1</code>,
<code>n2</code>, ...
</li></ul>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Examples:
</p>
<p>Ten equally spaced contour lines. The actual number of
levels can be adjusted to give simple labels.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw3d(color = green,
explicit(20*exp(-x^2-y^2)-10,x,0,2,y,-3,3),
contour_levels = 10,
contour = both,
surface_hide = true) $
</pre>
<p>From -8 to 8 in steps of 4.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw3d(color = green,
explicit(20*exp(-x^2-y^2)-10,x,0,2,y,-3,3),
contour_levels = [-8,4,8],
contour = both,
surface_hide = true) $
</pre>
<p>Isolines at levels -7, -6, 0.8 and 5.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw3d(color = green,
explicit(20*exp(-x^2-y^2)-10,x,0,2,y,-3,3),
contour_levels = {-7, -6, 0.8, 5},
contour = both,
surface_hide = true) $
</pre>
<p>See also <code>contour</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-data_005ffile_005fname"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>data_file_name</b>
<a name="IDX2034"></a>
</dt>
<dd><p>Default value: <code>"data.gnuplot"</code>
</p>
<p>This is the name of the file with the numeric data needed
by Gnuplot to build the requested plot.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter. It can be also used as an argument of function <code>draw</code>.
</p>
<p>See example in <code>gnuplot_file_name</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-delay"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>delay</b>
<a name="IDX2035"></a>
</dt>
<dd><p>Default value: 5
</p>
<p>This is the delay in 1/100 seconds of frames in animated gif files.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter. It can be also used as an argument of function <code>draw</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw(
delay = 100,
file_name = "zzz",
terminal = 'animated_gif,
gr2d(explicit(x^2,x,-1,1)),
gr2d(explicit(x^3,x,-1,1)),
gr2d(explicit(x^4,x,-1,1)));
End of animation sequence
(%o2) [gr2d(explicit), gr2d(explicit), gr2d(explicit)]
</pre>
<p>Option <code>delay</code> is only active in animated gif's; it is ignored in
any other case.
</p>
<p>See also <code>terminal</code>, <code>dimensions</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-dimensions"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>dimensions</b>
<a name="IDX2036"></a>
</dt>
<dd><p>Default value: <code>[600,500]</code>
</p>
<p>Dimensions of the output terminal. Its value is a list formed by
the width and the height. The meaning of the two numbers depends on
the terminal you are working with.
</p>
<p>With terminals <code>gif</code>, <code>animated_gif</code>, <code>png</code>, <code>jpg</code>,
<code>svg</code>, <code>screen</code>, <code>wxt</code>, and <code>aquaterm</code>,
the integers represent the number of points in each direction. If they
are not intergers, they are rounded.
</p>
<p>With terminals <code>eps</code>, <code>eps_color</code>, <code>pdf</code>, and
<code>pdfcairo</code>, both numbers represent hundredths of cm, which
means that, by default, pictures in these formats are 6 cm in
width and 5 cm in height.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter. It can be also used as an argument of function <code>draw</code>.
</p>
<p>Examples:
</p>
<p>Option <code>dimensions</code> applied to file output
and to wxt canvas.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
dimensions = [300,300],
terminal = 'png,
explicit(x^4,x,-1,1)) $
(%i3) draw2d(
dimensions = [300,300],
terminal = 'wxt,
explicit(x^4,x,-1,1)) $
</pre>
<p>Option <code>dimensions</code> applied to eps output.
We want an eps file with A4 portrait dimensions.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) A4portrait: 100*[21, 29.7]$
(%i3) draw3d(
dimensions = A4portrait,
terminal = 'eps,
explicit(x^2-y^2,x,-2,2,y,-2,2)) $
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-draw_005frealpart"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>draw_realpart</b>
<a name="IDX2037"></a>
</dt>
<dd><p>Default value: <code>true</code>
</p>
<p>When <code>true</code>, functions to be drawn are considered as complex functions whose
real part value should be plotted; when <code>false</code>, nothing will be plotted when
the function does not give a real value.
</p>
<p>This option affects objects <code>explicit</code> and <code>parametric</code> in 2D and 3D, and
<code>parametric_surface</code>.
</p>
<p>Example:
</p>
<p>Option <code>draw_realpart</code> affects objects <code>explicit</code> and <code>parametric</code>.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
draw_realpart = false,
explicit(sqrt(x^2 - 4*x) - x, x, -1, 5),
color = red,
draw_realpart = true,
parametric(x,sqrt(x^2 - 4*x) - x + 1, x, -1, 5) );
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-enhanced3d"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>enhanced3d</b>
<a name="IDX2038"></a>
</dt>
<dd><p>Default value: <code>none</code>
</p>
<p>If <code>enhanced3d</code> is <code>none</code>, surfaces are not colored in 3D plots.
In order to get a colored surface, a list must be assigned to option
<code>enhanced3d</code>, where the first element is an expression and the rest
are the names of the variables or parameters used in that expression. A list such
<code>[f(x,y,z), x, y, z]</code> means that point <code>[x,y,z]</code> of the surface
is assigned number <code>f(x,y,z)</code>, which will be colored according to
the actual <code>palette</code>. For those 3D graphic objects defined in terms of
parameters, it is possible to define the color number in terms of
the parameters, as in <code>[f(u), u]</code>, as in objects <code>parametric</code> and
<code>tube</code>, or <code>[f(u,v), u, v]</code>, as in object <code>parametric_surface</code>.
While all 3D objects admit the model based on absolute coordinates,
<code>[f(x,y,z), x, y, z]</code>, only two of them, namely <code>explicit</code>
and <code>elevation_grid</code>, accept also models defined on the <code>[x,y]</code> coordinates,
<code>[f(x,y), x, y]</code>. 3D graphic object <code>implicit</code> accepts only the
<code>[f(x,y,z), x, y, z]</code> model. Object <code>points</code> accepts also the
<code>[f(x,y,z), x, y, z]</code> model, but when points have a chronological nature,
model <code>[f(k), k]</code> is also valid, being <code>k</code> an ordering parameter.
</p>
<p>When <code>enhanced3d</code> is assigned something different to <code>none</code>, options
<code>color</code> and <code>surface_hide</code> are ignored.
</p>
<p>The names of the variables defined in the lists may be different to those
used in the definitions of the graphic objects.
</p>
<p>In order to maintain back compatibility, <code>enhanced3d = false</code> is equivalent
to <code>enhanced3d = none</code>, and <code>enhanced3d = true</code> is equivalent to
<code>enhanced3d = [z, x, y, z]</code>. If an expression is given to <code>enhanced3d</code>,
its variables must be the same used in the surface definition. This is not
necessary when using lists.
</p>
<p>See option <code>palette</code> to learn how palettes are specified.
</p>
<p>Examples:
</p>
<p><code>explicit</code> object with coloring defined by the <code>[f(x,y,z), x, y, z]</code> model.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
enhanced3d = [x-z/10,x,y,z],
palette = gray,
explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3))$
</pre>
<p><code>explicit</code> object with coloring defined by the <code>[f(x,y), x, y]</code> model.
The names of the variables defined in the lists may be different to those
used in the definitions of the graphic objects; in this case, <code>r</code> corresponds
to <code>x</code>, and <code>s</code> to <code>y</code>.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
enhanced3d = [sin(r*s),r,s],
explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3))$
</pre>
<p><code>parametric</code> object with coloring defined by the <code>[f(x,y,z), x, y, z]</code> model.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
nticks = 100,
line_width = 2,
enhanced3d = [if y>= 0 then 1 else 0, x, y, z],
parametric(sin(u)^2,cos(u),u,u,0,4*%pi)) $
</pre>
<p><code>parametric</code> object with coloring defined by the <code>[f(u), u]</code> model.
In this case, <code>(u-1)^2</code> is a shortcut for <code>[(u-1)^2,u]</code>.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
nticks = 60,
line_width = 3,
enhanced3d = (u-1)^2,
parametric(cos(5*u)^2,sin(7*u),u-2,u,0,2))$
</pre>
<p><code>elevation_grid</code> object with coloring defined by the <code>[f(x,y), x, y]</code> model.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) m: apply(
matrix,
makelist(makelist(cos(i^2/80-k/30),k,1,30),i,1,20)) $
(%i3) draw3d(
enhanced3d = [cos(x*y*10),x,y],
elevation_grid(m,-1,-1,2,2),
xlabel = "x",
ylabel = "y");
</pre>
<p><code>tube</code> object with coloring defined by the <code>[f(x,y,z), x, y, z]</code> model.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
enhanced3d = [cos(x-y),x,y,z],
palette = gray,
xu_grid = 50,
tube(cos(a), a, 0, 1, a, 0, 4*%pi) )$
</pre>
<p><code>tube</code> object with coloring defined by the <code>[f(u), u]</code> model.
Here, <code>enhanced3d = -a</code> would be the shortcut for <code>enhanced3d = [-foo,foo]</code>.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
tube_extremes = [open, closed],
palette = [26,15,-2],
enhanced3d = [-foo, foo],
tube(a, a, a^2, 1, a, -2, 2) )$
</pre>
<p><code>implicit</code> and <code>points</code> objects with coloring defined by the <code>[f(x,y,z), x, y, z]</code> model.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
enhanced3d = [x-y,x,y,z],
implicit((x^2+y^2+z^2-1)*(x^2+(y-1.5)^2+z^2-0.5)=0.015,
x,-1,1,y,-1.2,2.3,z,-1,1)) $
(%i3) m: makelist([random(1.0),random(1.0),random(1.0)],k,1,2000)$
(%i4) draw3d(
point_type = filled_circle,
point_size = 2,
enhanced3d = [u+v-w,u,v,w],
points(m) ) $
</pre>
<p>When points have a chronological nature, model <code>[f(k), k]</code> is also valid,
being <code>k</code> an ordering parameter.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) m:makelist([random(1.0), random(1.0), random(1.0)],k,1,5)$
(%i3) draw3d(
enhanced3d = [sin(j), j],
point_size = 3,
point_type = filled_circle,
points_joined = true,
points(m)) $
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-error_005ftype"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>error_type</b>
<a name="IDX2039"></a>
</dt>
<dd><p>Default value: <code>y</code>
</p>
<p>Depending on its value, which can be <code>x</code>, <code>y</code>, or <code>xy</code>,
graphic object <code>errors</code> will draw points with horizontal, vertical,
or both, error bars. When <code>error_type=boxes</code>, boxes will be drawn
instead of crosses.
</p>
<p>See also <code>errors</code>.
</p></dd></dl>
<p><a name="Item_003a-file_005fname"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>file_name</b>
<a name="IDX2040"></a>
</dt>
<dd><p>Default value: <code>"maxima_out"</code>
</p>
<p>This is the name of the file where terminals <code>png</code>, <code>jpg</code>, <code>gif</code>,
<code>eps</code>, <code>eps_color</code>, <code>pdf</code>, <code>pdfcairo</code> and <code>svg</code>
will save the graphic.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter. It can be also used as an argument of function <code>draw</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(file_name = "myfile",
explicit(x^2,x,-1,1),
terminal = 'png)$
</pre>
<p>See also <code>terminal</code>, <code>dimensions</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-fill_005fcolor"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>fill_color</b>
<a name="IDX2041"></a>
</dt>
<dd><p>Default value: <code>"red"</code>
</p>
<p><code>fill_color</code> specifies the color for filling polygons and
2d <code>explicit</code> functions.
</p>
<p>See <code>color</code> to learn how colors are specified.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-fill_005fdensity"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>fill_density</b>
<a name="IDX2042"></a>
</dt>
<dd><p>Default value: 0
</p>
<p><code>fill_density</code> is a number between 0 and 1 that specifies
the intensity of the <code>fill_color</code> in <code>bars</code> objects.
</p>
<p>See <code>bars</code> for examples.
</p></dd></dl>
<p><a name="Item_003a-filled_005ffunc"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>filled_func</b>
<a name="IDX2043"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>Option <code>filled_func</code> controls how regions limited by functions
should be filled. When <code>filled_func</code> is <code>true</code>, the region
bounded by the function defined with object <code>explicit</code> and the
bottom of the graphic window is filled with <code>fill_color</code>. When
<code>filled_func</code> contains a function expression, then the region bounded
by this function and the function defined with object <code>explicit</code>
will be filled. By default, explicit functions are not filled.
</p>
<p>This option affects only the 2d graphic object <code>explicit</code>.
</p>
<p>Example:
</p>
<p>Region bounded by an <code>explicit</code> object and the bottom of the
graphic window.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(fill_color = red,
filled_func = true,
explicit(sin(x),x,0,10) )$
</pre>
<p>Region bounded by an <code>explicit</code> object and the function
defined by option <code>filled_func</code>. Note that the variable in
<code>filled_func</code> must be the same as that used in <code>explicit</code>.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(fill_color = grey,
filled_func = sin(x),
explicit(-sin(x),x,0,%pi));
</pre>
<p>See also <code>fill_color</code> and <code>explicit</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-font"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>font</b>
<a name="IDX2044"></a>
</dt>
<dd><p>Default value: <code>""</code> (empty string)
</p>
<p>This option can be used to set the font face to be used by the terminal.
Only one font face and size can be used throughout the plot.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>See also <code>font_size</code>.
</p>
<p>Gnuplot doesn't handle fonts by itself, it leaves this task to the
support libraries of the different terminals, each one with its own
philosophy about it. A brief summary follows:
</p>
<ul>
<li>
<i>x11</i>:
Uses the normal x11 font server mechanism.
<p>Example:
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(font = "Arial",
font_size = 20,
label(["Arial font, size 20",1,1]))$
</pre>
</li><li>
<i>windows</i>:
The windows terminal doesn't support changing of fonts from inside the plot.
Once the plot has been generated, the font can be changed right-clicking on
the menu of the graph window.
</li><li>
<i>png, jpeg, gif</i>:
The <i>libgd</i> library uses the font path stored in the environment
variable <code>GDFONTPATH</code>; in this case, it is only necessary to
set option <code>font</code> to the font's name. It is also possible to
give the complete path to the font file.
<p>Examples:
</p>
<p>Option <code>font</code> can be given the complete path to the font file:
</p><pre class="example">(%i1) load(draw)$
(%i2) path: "/usr/share/fonts/truetype/freefont/" $
(%i3) file: "FreeSerifBoldItalic.ttf" $
(%i4) draw2d(
font = concat(path, file),
font_size = 20,
color = red,
label(["FreeSerifBoldItalic font, size 20",1,1]),
terminal = png)$
</pre>
<p>If environment variable <code>GDFONTPATH</code> is set to the
path where font files are allocated, it is possible to
set graphic option <code>font</code> to the name of the font.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(
font = "FreeSerifBoldItalic",
font_size = 20,
color = red,
label(["FreeSerifBoldItalic font, size 20",1,1]),
terminal = png)$
</pre>
</li><li>
<i>Postscript</i>:
Standard Postscript fonts are:<br>
<code>"Times-Roman"</code>, <code>"Times-Italic"</code>, <code>"Times-Bold"</code>,
<code>"Times-BoldItalic"</code>,<br>
<code>"Helvetica"</code>, <code>"Helvetica-Oblique"</code>, <code>"Helvetica-Bold"</code>,<br>
<code>"Helvetic-BoldOblique"</code>, <code>"Courier"</code>,
<code>"Courier-Oblique"</code>, <code>"Courier-Bold"</code>,<br>
and <code>"Courier-BoldOblique"</code>.
<p>Example:
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(
font = "Courier-Oblique",
font_size = 15,
label(["Courier-Oblique font, size 15",1,1]),
terminal = eps)$
</pre>
</li><li>
<i>pdf</i>:
Uses same fonts as <i>Postscript</i>.
</li><li>
<i>pdfcairo</i>:
Uses same fonts as <i>wxt</i>.
</li><li>
<i>wxt</i>:
The <i>pango</i> library finds fonts via the <code>fontconfig</code> utility.
</li><li>
<i>aqua</i>:
Default is <code>"Times-Roman"</code>.
</li></ul>
<p>The gnuplot documentation is an important source of information about terminals and fonts.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-font_005fsize"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>font_size</b>
<a name="IDX2045"></a>
</dt>
<dd><p>Default value: 10
</p>
<p>This option can be used to set the font size to be used by the terminal.
Only one font face and size can be used throughout the plot. <code>font_size</code> is
active only when option <code>font</code> is not equal to the empty string.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>See also <code>font</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-gnuplot_005ffile_005fname"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>gnuplot_file_name</b>
<a name="IDX2046"></a>
</dt>
<dd><p>Default value: <code>"maxout.gnuplot"</code>
</p>
<p>This is the name of the file with the necessary commands to
be processed by Gnuplot.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter. It can be also used as an argument of function <code>draw</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
file_name = "my_file",
gnuplot_file_name = "my_commands_for_gnuplot",
data_file_name = "my_data_for_gnuplot",
terminal = png,
explicit(x^2,x,-1,1)) $
</pre>
<p>See also <code>data_file_name</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>grid</b>
<a name="IDX2047"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>grid</code> is <code>true</code>, a grid will be drawn on the <var>xy</var> plane.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(grid = true,
explicit(exp(u),u,-2,2))$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-head_005fangle"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>head_angle</b>
<a name="IDX2048"></a>
</dt>
<dd><p>Default value: 45
</p>
<p><code>head_angle</code> indicates the angle, in degrees, between the arrow heads and
the segment.
</p>
<p>This option is relevant only for <code>vector</code> objects.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [0,10],
yrange = [0,9],
head_length = 0.7,
head_angle = 10,
vector([1,1],[0,6]),
head_angle = 20,
vector([2,1],[0,6]),
head_angle = 30,
vector([3,1],[0,6]),
head_angle = 40,
vector([4,1],[0,6]),
head_angle = 60,
vector([5,1],[0,6]),
head_angle = 90,
vector([6,1],[0,6]),
head_angle = 120,
vector([7,1],[0,6]),
head_angle = 160,
vector([8,1],[0,6]),
head_angle = 180,
vector([9,1],[0,6]) )$
</pre>
<p>See also <code>head_both</code>, <code>head_length</code>, and <code>head_type</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-head_005fboth"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>head_both</b>
<a name="IDX2049"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>head_both</code> is <code>true</code>, vectors are plotted with two arrow heads.
If <code>false</code>, only one arrow is plotted.
</p>
<p>This option is relevant only for <code>vector</code> objects.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [0,8],
yrange = [0,8],
head_length = 0.7,
vector([1,1],[6,0]),
head_both = true,
vector([1,7],[6,0]) )$
</pre>
<p>See also <code>head_length</code>, <code>head_angle</code>, and <code>head_type</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-head_005flength"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>head_length</b>
<a name="IDX2050"></a>
</dt>
<dd><p>Default value: 2
</p>
<p><code>head_length</code> indicates, in <var>x</var>-axis units, the length of arrow heads.
</p>
<p>This option is relevant only for <code>vector</code> objects.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [0,12],
yrange = [0,8],
vector([0,1],[5,5]),
head_length = 1,
vector([2,1],[5,5]),
head_length = 0.5,
vector([4,1],[5,5]),
head_length = 0.25,
vector([6,1],[5,5]))$
</pre>
<p>See also <code>head_both</code>, <code>head_angle</code>, and <code>head_type</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-head_005ftype"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>head_type</b>
<a name="IDX2051"></a>
</dt>
<dd><p>Default value: <code>filled</code>
</p>
<p><code>head_type</code> is used to specify how arrow heads are plotted. Possible
values are: <code>filled</code> (closed and filled arrow heads), <code>empty</code>
(closed but not filled arrow heads), and <code>nofilled</code> (open arrow heads).
</p>
<p>This option is relevant only for <code>vector</code> objects.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [0,12],
yrange = [0,10],
head_length = 1,
vector([0,1],[5,5]), /* default type */
head_type = 'empty,
vector([3,1],[5,5]),
head_type = 'nofilled,
vector([6,1],[5,5]))$
</pre>
<p>See also <code>head_both</code>, <code>head_angle</code>, and <code>head_length</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-ip_005fgrid"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>ip_grid</b>
<a name="IDX2052"></a>
</dt>
<dd><p>Default value: <code>[50, 50]</code>
</p>
<p><code>ip_grid</code> sets the grid for the first sampling in implicit plots.
</p>
<p>This option is relevant only for <code>implicit</code> objects.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-ip_005fgrid_005fin"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>ip_grid_in</b>
<a name="IDX2053"></a>
</dt>
<dd><p>Default value: <code>[5, 5]</code>
</p>
<p><code>ip_grid_in</code> sets the grid for the second sampling in implicit plots.
</p>
<p>This option is relevant only for <code>implicit</code> objects.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-key"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>key</b>
<a name="IDX2054"></a>
</dt>
<dd><p>Default value: <code>""</code> (empty string)
</p>
<p><code>key</code> is the name of a function in the legend. If <code>key</code> is an
empty string, no key is assigned to the function.
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr2d</code>: <code>points</code>, <code>polygon</code>, <code>rectangle</code>,
<code>ellipse</code>, <code>vector</code>, <code>explicit</code>, <code>implicit</code>,
<code>parametric</code>, and <code>polar</code>.
</li><li>
<code>gr3d</code>: <code>points</code>, <code>explicit</code>, <code>parametric</code>,
and <code>parametric_surface</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(key = "Sinus",
explicit(sin(x),x,0,10),
key = "Cosinus",
color = red,
explicit(cos(x),x,0,10) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-label_005falignment"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>label_alignment</b>
<a name="IDX2055"></a>
</dt>
<dd><p>Default value: <code>center</code>
</p>
<p><code>label_alignment</code> is used to specify where to write labels with
respect to the given coordinates. Possible values are: <code>center</code>,
<code>left</code>, and <code>right</code>.
</p>
<p>This option is relevant only for <code>label</code> objects.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [0,10],
yrange = [0,10],
points_joined = true,
points([[5,0],[5,10]]),
color = blue,
label(["Centered alignment (default)",5,2]),
label_alignment = 'left,
label(["Left alignment",5,5]),
label_alignment = 'right,
label(["Right alignment",5,8]))$
</pre>
<p>See also <code>label_orientation</code>, and <code>color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-label_005forientation"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>label_orientation</b>
<a name="IDX2056"></a>
</dt>
<dd><p>Default value: <code>horizontal</code>
</p>
<p><code>label_orientation</code> is used to specify orientation of labels.
Possible values are: <code>horizontal</code>, and <code>vertical</code>.
</p>
<p>This option is relevant only for <code>label</code> objects.
</p>
<p>Example:
</p>
<p>In this example, a dummy point is added to get an image.
Package <code>draw</code> needs always data to draw an scene.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [0,10],
yrange = [0,10],
point_size = 0,
points([[5,5]]),
color = navy,
label(["Horizontal orientation (default)",5,2]),
label_orientation = 'vertical,
color = "#654321",
label(["Vertical orientation",1,5]))$
</pre>
<p>See also <code>label_alignment</code> and <code>color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-line_005ftype"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>line_type</b>
<a name="IDX2057"></a>
</dt>
<dd><p>Default value: <code>solid</code>
</p>
<p><code>line_type</code> indicates how lines are displayed; possible values are
<code>solid</code> and <code>dots</code>.
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr2d</code>: <code>points</code>, <code>polygon</code>, <code>rectangle</code>,
<code>ellipse</code>, <code>vector</code>, <code>explicit</code>, <code>implicit</code>,
<code>parametric</code> and <code>polar</code>.
</li><li>
<code>gr3d</code>: <code>points</code>, <code>explicit</code>, <code>parametric</code> and <code>parametric_surface</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(line_type = dots,
explicit(1 + x^2,x,-1,1),
line_type = solid, /* default */
explicit(2 + x^2,x,-1,1))$
</pre>
<p>See also <code>line_width</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-line_005fwidth"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>line_width</b>
<a name="IDX2058"></a>
</dt>
<dd><p>Default value: 1
</p>
<p><code>line_width</code> is the width of plotted lines.
Its value must be a positive number.
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr2d</code>: <code>points</code>, <code>polygon</code>, <code>rectangle</code>,
<code>ellipse</code>, <code>vector</code>, <code>explicit</code>, <code>implicit</code>,
<code>parametric</code> and <code>polar</code>.
</li><li>
<code>gr3d</code>: <code>points</code> and <code>parametric</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^2,x,-1,1), /* default width */
line_width = 5.5,
explicit(1 + x^2,x,-1,1),
line_width = 10,
explicit(2 + x^2,x,-1,1))$
</pre>
<p>See also <code>line_type</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-logcb"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>logcb</b>
<a name="IDX2059"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>logcb</code> is <code>true</code>, the tics in the colorbox will be drawn in the
logarithmic scale.
</p>
<p>When <code>enhanced3d</code> or <code>colorbox</code> is <code>false</code>, option <code>logcb</code> has
no effect.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d (
enhanced3d = true,
color = green,
logcb = true,
logz = true,
palette = [-15,24,-9],
explicit(exp(x^2-y^2), x,-2,2,y,-2,2)) $
</pre>
<p>See also <code>enhanced3d</code>, <code>colorbox</code> and <code>cbrange</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>logx</b>
<a name="IDX2060"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>logx</code> is <code>true</code>, the <var>x</var> axis will be drawn in the
logarithmic scale.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(log(x),x,0.01,5),
logx = true)$
</pre>
<p>See also <code>logy</code> and <code>logz</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>logy</b>
<a name="IDX2061"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>logy</code> is <code>true</code>, the <var>y</var> axis will be drawn in the
logarithmic scale.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(logy = true,
explicit(exp(x),x,0,5))$
</pre>
<p>See also <code>logx</code> and <code>logz</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-logz"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>logz</b>
<a name="IDX2062"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>logz</code> is <code>true</code>, the <var>z</var> axis will be drawn in the
logarithmic scale.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(logz = true,
explicit(exp(u^2+v^2),u,-2,2,v,-2,2))$
</pre>
<p>See also <code>logx</code> and <code>logy</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>nticks</b>
<a name="IDX2063"></a>
</dt>
<dd><p>Default value: 29
</p>
<p>In 2d, <code>nticks</code> gives the initial number of points used by the
adaptive plotting routine for explicit objects. It is also the
number of points that will be shown in parametric and polar curves.
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr2d</code>: <code>ellipse</code>, <code>explicit</code>, <code>parametric</code> and <code>polar</code>.
</li><li>
<code>gr3d</code>: <code>parametric</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(transparent = true,
ellipse(0,0,4,2,0,180),
nticks = 5,
ellipse(0,0,4,2,180,180) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>palette</b>
<a name="IDX2064"></a>
</dt>
<dd><p>Default value: <code>color</code>
</p>
<p><code>palette</code> indicates how to map gray levels onto color components.
It works together with option <code>enhanced3d</code> in 3D graphics,
who associates every point of a surfaces to a real number or gray level.
It also works with gray images. With <code>palette</code>, levels are transformed into colors.
</p>
<p>There are two ways for defining these transformations.
</p>
<p>First, <code>palette</code> can be a vector of length three with components
ranging from -36 to +36; each value is an index for a formula mapping the levels
onto red, green and blue colors, respectively:
</p><pre class="example"> 0: 0 1: 0.5 2: 1
3: x 4: x^2 5: x^3
6: x^4 7: sqrt(x) 8: sqrt(sqrt(x))
9: sin(90x) 10: cos(90x) 11: |x-0.5|
12: (2x-1)^2 13: sin(180x) 14: |cos(180x)|
15: sin(360x) 16: cos(360x) 17: |sin(360x)|
18: |cos(360x)| 19: |sin(720x)| 20: |cos(720x)|
21: 3x 22: 3x-1 23: 3x-2
24: |3x-1| 25: |3x-2| 26: (3x-1)/2
27: (3x-2)/2 28: |(3x-1)/2| 29: |(3x-2)/2|
30: x/0.32-0.78125 31: 2*x-0.84 32: 4x;1;-2x+1.84;x/0.08-11.5
33: |2*x - 0.5| 34: 2*x 35: 2*x - 0.5
36: 2*x - 1
</pre><p>negative numbers mean negative colour component.
<code>palette = gray</code> and <code>palette = color</code> are short cuts for
<code>palette = [3,3,3]</code> and <code>palette = [7,5,15]</code>, respectively.
</p>
<p>Second, <code>palette</code> can be a user defined lookup table. In this case,
the format for building a lookup table of length <code>n</code> is
<code>palette=[color_1, color_2, ..., color_n]</code>, where <code>color_i</code> is
a well formed color (see option <code>color</code>), such that <code>color_1</code> is
assigned to the lowest gray level and <code>color_n</code> to the highest. The rest
of colors are interpolated.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Examples:
</p>
<p>It works together with option <code>enhanced3d</code> in 3D graphics.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
enhanced3d = [z-x+2*y,x,y,z],
palette = [32, -8, 17],
explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3))$
</pre>
<p>It also works with gray images.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) im: apply(
'matrix,
makelist(makelist(random(200),i,1,30),i,1,30))$
(%i3) /* palette = color, default */
draw2d(image(im,0,0,30,30))$
(%i4) draw2d(palette = gray, image(im,0,0,30,30))$
(%i5) draw2d(palette = [15,20,-4],
colorbox=false,
image(im,0,0,30,30))$
</pre>
<p><code>palette</code> can be a user defined lookup table.
In this example, low values of <code>x</code> are colored
in red, and higher values in yellow.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
palette = [red, blue, yellow],
enhanced3d = x,
explicit(x^2+y^2,x,-1,1,y,-1,1)) $
</pre>
<p>See also <code>colorbox</code> and <code>enhanced3d</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-point_005fsize"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>point_size</b>
<a name="IDX2065"></a>
</dt>
<dd><p>Default value: 1
</p>
<p><code>point_size</code> sets the size for plotted points. It must be a
non negative number.
</p>
<p>This option has no effect when graphic option <code>point_type</code> is
set to <code>dot</code>.
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr2d</code>: <code>points</code>.
</li><li>
<code>gr3d</code>: <code>points</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(points(makelist([random(20),random(50)],k,1,10)),
point_size = 5,
points(makelist(k,k,1,20),makelist(random(30),k,1,20)))$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>point_type</b>
<a name="IDX2066"></a>
</dt>
<dd><p>Default value: 1
</p>
<p><code>point_type</code> indicates how isolated points are displayed; the value of this
option can be any integer index greater or equal than -1, or the name of
a point style: <code>$none</code> (-1), <code>dot</code> (0), <code>plus</code> (1), <code>multiply</code> (2),
<code>asterisk</code> (3), <code>square</code> (4), <code>filled_square</code> (5), <code>circle</code> (6),
<code>filled_circle</code> (7), <code>up_triangle</code> (8), <code>filled_up_triangle</code> (9),
<code>down_triangle</code> (10), <code>filled_down_triangle</code> (11), <code>diamant</code> (12) and
<code>filled_diamant</code> (13).
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr2d</code>: <code>points</code>.
</li><li>
<code>gr3d</code>: <code>points</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [0,10],
yrange = [0,10],
point_size = 3,
point_type = diamant,
points([[1,1],[5,1],[9,1]]),
point_type = filled_down_triangle,
points([[1,2],[5,2],[9,2]]),
point_type = asterisk,
points([[1,3],[5,3],[9,3]]),
point_type = filled_diamant,
points([[1,4],[5,4],[9,4]]),
point_type = 5,
points([[1,5],[5,5],[9,5]]),
point_type = 6,
points([[1,6],[5,6],[9,6]]),
point_type = filled_circle,
points([[1,7],[5,7],[9,7]]),
point_type = 8,
points([[1,8],[5,8],[9,8]]),
point_type = filled_diamant,
points([[1,9],[5,9],[9,9]]) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-points_005fjoined"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>points_joined</b>
<a name="IDX2067"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>When <code>points_joined</code> is <code>true</code>, points are joined by lines; when <code>false</code>,
isolated points are drawn. A third possible value for this graphic option is
<code>impulses</code>; in such case, vertical segments are drawn from points to the x-axis (2D)
or to the xy-plane (3D).
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr2d</code>: <code>points</code>.
</li><li>
<code>gr3d</code>: <code>points</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [0,10],
yrange = [0,4],
point_size = 3,
point_type = up_triangle,
color = blue,
points([[1,1],[5,1],[9,1]]),
points_joined = true,
point_type = square,
line_type = dots,
points([[1,2],[5,2],[9,2]]),
point_type = circle,
color = red,
line_width = 7,
points([[1,3],[5,3],[9,3]]) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-proportional_005faxes"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>proportional_axes</b>
<a name="IDX2068"></a>
</dt>
<dd><p>Default value: <code>none</code>
</p>
<p>When <code>proportional_axes</code> is equal to <code>xy</code> or <code>xyz</code>,
a 2D or 3D scene will be drawn with axes proportional to their relative
lengths.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>This option works with Gnuplot version 4.2.6 or greater.
</p>
<p>Examples:
</p>
<p>Single 2D plot.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
ellipse(0,0,1,1,0,360),
transparent=true,
color = blue,
line_width = 4,
ellipse(0,0,2,1/2,0,360),
proportional_axes = xy) $
</pre>
<p>Multiplot.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw(
terminal = wxt,
gr2d(proportional_axes = xy,
explicit(x^2,x,0,1)),
gr2d(explicit(x^2,x,0,1),
xrange = [0,1],
yrange = [0,2],
proportional_axes=xy),
gr2d(explicit(x^2,x,0,1)))$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-surface_005fhide"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>surface_hide</b>
<a name="IDX2069"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>surface_hide</code> is <code>true</code>, hidden parts are not plotted in 3d surfaces.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw(columns=2,
gr3d(explicit(exp(sin(x)+cos(x^2)),x,-3,3,y,-3,3)),
gr3d(surface_hide = true,
explicit(exp(sin(x)+cos(x^2)),x,-3,3,y,-3,3)) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-terminal"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>terminal</b>
<a name="IDX2070"></a>
</dt>
<dd><p>Default value: <code>screen</code>
</p>
<p>Selects the terminal to be used by Gnuplot; possible values are:
<code>screen</code> (default), <code>png</code>, <code>pngcairo</code>, <code>jpg</code>, <code>gif</code>,
<code>eps</code>, <code>eps_color</code>, <code>epslatex</code>, <code>epslatex_standalone</code>,
<code>svg</code>, <code>dumb</code>, <code>dumb_file</code>, <code>pdf</code>, <code>pdfcairo</code>,
<code>wxt</code>, <code>animated_gif</code>, <code>multipage_pdfcairo</code>, <code>multipage_pdf</code>,
<code>multipage_eps</code>, <code>multipage_eps_color</code>, and <code>aquaterm</code>.
</p>
<p>Terminals <code>screen</code>, <code>wxt</code> and <code>aquaterm</code> can be also defined as a list
with two elements: the name of the terminal itself and a non negative integer number.
In this form, multiple windows can be opened at the same time, each with its
corresponding number. This feature does not work in Windows platforms.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter. It can be also used as an argument of function <code>draw</code>.
</p>
<p>N.B. pdfcairo requires Gnuplot 4.3 or newer.
<code>pdf</code> requires Gnuplot to be compiled with the option <code>--enable-pdf</code> and libpdf must
be installed. The pdf library is available from: <a href="http://www.pdflib.com/en/download/pdflib-family/pdflib-lite/">http://www.pdflib.com/en/download/pdflib-family/pdflib-lite/</a>
</p>
<p>Examples:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) /* screen terminal (default) */
draw2d(explicit(x^2,x,-1,1))$
(%i3) /* png file */
draw2d(terminal = 'png,
explicit(x^2,x,-1,1))$
(%i4) /* jpg file */
draw2d(terminal = 'jpg,
dimensions = [300,300],
explicit(x^2,x,-1,1))$
(%i5) /* eps file */
draw2d(file_name = "myfile",
explicit(x^2,x,-1,1),
terminal = 'eps)$
(%i6) /* pdf file */
draw2d(file_name = "mypdf",
dimensions = 100*[12.0,8.0],
explicit(x^2,x,-1,1),
terminal = 'pdf)$
(%i7) /* wxwidgets window */
draw2d(explicit(x^2,x,-1,1),
terminal = 'wxt)$
</pre>
<p>Multiple windows.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^5,x,-2,2), terminal=[screen, 3])$
(%i3) draw2d(explicit(x^2,x,-2,2), terminal=[screen, 0])$
</pre>
<p>An animated gif file.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw(
delay = 100,
file_name = "zzz",
terminal = 'animated_gif,
gr2d(explicit(x^2,x,-1,1)),
gr2d(explicit(x^3,x,-1,1)),
gr2d(explicit(x^4,x,-1,1)));
End of animation sequence
(%o2) [gr2d(explicit), gr2d(explicit), gr2d(explicit)]
</pre>
<p>Option <code>delay</code> is only active in animated gif's; it is ignored in
any other case.
</p>
<p>Multipage output in eps format.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw(
file_name = "parabol",
terminal = multipage_eps,
dimensions = 100*[10,10],
gr2d(explicit(x^2,x,-1,1)),
gr3d(explicit(x^2+y^2,x,-1,1,y,-1,1))) $
</pre>
<p>See also <code>file_name</code>, <code>dimensions</code> and <code>delay</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>title</b>
<a name="IDX2071"></a>
</dt>
<dd><p>Default value: <code>""</code> (empty string)
</p>
<p>Option <code>title</code>, a string, is the main title for the scene.
By default, no title is written.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(exp(u),u,-2,2),
title = "Exponential function")$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-transform"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>transform</b>
<a name="IDX2072"></a>
</dt>
<dd><p>Default value: <code>none</code>
</p>
<p>If <code>transform</code> is <code>none</code>, the space is not transformed and
graphic objects are drawn as defined. When a space transformation is
desired, a list must be assigned to option <code>transform</code>. In case of
a 2D scene, the list takes the form <code>[f1(x,y), f2(x,y), x, y]</code>.
In case of a 3D scene, the list is of the form
<code>[f1(x,y,z), f2(x,y,z), f3(x,y,z), x, y, z]</code>.
</p>
<p>The names of the variables defined in the lists may be different to those
used in the definitions of the graphic objects.
</p>
<p>Examples:
</p>
<p>Rotation in 2D.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) th : %pi / 4$
(%i3) draw2d(
color = "#e245f0",
proportional_axes = 'xy,
line_width = 8,
triangle([3,2],[7,2],[5,5]),
border = false,
fill_color = yellow,
transform = [cos(th)*x - sin(th)*y,
sin(th)*x + cos(th)*y, x, y],
triangle([3,2],[7,2],[5,5]) )$
</pre>
<p>Translation in 3D.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
color = "#a02c00",
explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3),
transform = [x+10,y+10,z+10,x,y,z],
color = blue,
explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p></dd></dl>
<p><a name="Item_003a-transparent"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>transparent</b>
<a name="IDX2073"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>transparent</code> is <code>false</code>, interior regions of polygons are
filled according to <code>fill_color</code>.
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr2d</code>: <code>polygon</code>, <code>rectangle</code>, and <code>ellipse</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(polygon([[3,2],[7,2],[5,5]]),
transparent = true,
color = blue,
polygon([[5,2],[9,2],[7,5]]) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-tube_005fextremes"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>tube_extremes</b>
<a name="IDX2074"></a>
</dt>
<dd><p>Default value: <code>[open, open]</code>
</p>
<p>A list with two possible elements, <code>open</code> and <code>closed</code>,
indicating whether the extremes of a graphic object <code>tube</code> remain open
or must be closed. By default, both extremes are left open.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
tube_extremes = [open, closed],
tube(0, 0, a, 1,
a, 0, 8) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-unit_005fvectors"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>unit_vectors</b>
<a name="IDX2075"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>unit_vectors</code> is <code>true</code>, vectors are plotted with module 1.
This is useful for plotting vector fields. If <code>unit_vectors</code> is <code>false</code>,
vectors are plotted with its original length.
</p>
<p>This option is relevant only for <code>vector</code> objects.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [-1,6],
yrange = [-1,6],
head_length = 0.1,
vector([0,0],[5,2]),
unit_vectors = true,
color = red,
vector([0,3],[5,2]))$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-user_005fpreamble"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>user_preamble</b>
<a name="IDX2076"></a>
</dt>
<dd><p>Default value: <code>""</code> (empty string)
</p>
<p>Expert Gnuplot users can make use of this option to fine tune Gnuplot's
behaviour by writing settings to be sent before the <code>plot</code> or <code>splot</code>
command.
</p>
<p>The value of this option must be a string or a list of strings (one per line).
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<p>The <i>dumb</i> terminal is not supported by package <code>draw</code>,
but it is possible to set it by making use of option <code>user_preamble</code>,
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(exp(x)-1,x,-1,1),
parametric(cos(u),sin(u),u,0,2*%pi),
user_preamble="set terminal dumb")$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-view"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>view</b>
<a name="IDX2077"></a>
</dt>
<dd><p>Default value: <code>[60,30]</code>
</p>
<p>A pair of angles, measured in degrees, indicating the view direction in a
3D scene. The first angle is the vertical rotation around the <var>x</var> axis, in
the range <em>[0, 360]</em>. The second one is the horizontal rotation around
the <var>z</var> axis, in the range <em>[0, 360]</em>.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(view = [170, 360],
explicit(sin(x^2+y^2),x,-2,2,y,-2,2) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-wired_005fsurface"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>wired_surface</b>
<a name="IDX2078"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>Indicates whether 3D surfaces in <code>enhanced3d</code> mode show the grid joinning
the points or not.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
enhanced3d = [sin(x),x,y],
wired_surface = true,
explicit(x^2+y^2,x,-1,1,y,-1,1)) $
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-x_005fvoxel"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>x_voxel</b>
<a name="IDX2079"></a>
</dt>
<dd><p>Default value: 10
</p>
<p><code>x_voxel</code> is the number of voxels in the x direction to
be used by the <i>marching cubes algorithm</i> implemented
by the 3d <code>implicit</code> object. It is also used by graphic
object <code>region</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xaxis"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xaxis</b>
<a name="IDX2080"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>xaxis</code> is <code>true</code>, the <var>x</var> axis is drawn.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
xaxis = true,
xaxis_color = blue)$
</pre>
<p>See also <code>xaxis_width</code>, <code>xaxis_type</code> and <code>xaxis_color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xaxis_005fcolor"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xaxis_color</b>
<a name="IDX2081"></a>
</dt>
<dd><p>Default value: <code>"black"</code>
</p>
<p><code>xaxis_color</code> specifies the color for the <var>x</var> axis. See
<code>color</code> to know how colors are defined.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
xaxis = true,
xaxis_color = red)$
</pre>
<p>See also <code>xaxis</code>, <code>xaxis_width</code> and <code>xaxis_type</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xaxis_005fsecondary"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xaxis_secondary</b>
<a name="IDX2082"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>xaxis_secondary</code> is <code>true</code>, function values can be plotted with
respect to the second <var>x</var> axis, which will be drawn on top of the scene.
</p>
<p>Note that this is a local graphics option which only affects to 2d plots.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
key = "Bottom x-axis",
explicit(x+1,x,1,2),
color = red,
key = "Above x-axis",
xtics_secondary = true,
xaxis_secondary = true,
explicit(x^2,x,-1,1)) $
</pre>
<p>See also <code>xrange_secondary</code>, <code>xtics_secondary</code>, <code>xtics_rotate_secondary</code>,
<code>xtics_axis_secondary</code> and <code>xaxis_secondary</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xaxis_005ftype"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xaxis_type</b>
<a name="IDX2083"></a>
</dt>
<dd><p>Default value: <code>dots</code>
</p>
<p><code>xaxis_type</code> indicates how the <var>x</var> axis is displayed;
possible values are <code>solid</code> and <code>dots</code>.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
xaxis = true,
xaxis_type = solid)$
</pre>
<p>See also <code>xaxis</code>, <code>xaxis_width</code> and <code>xaxis_color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xaxis_005fwidth"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xaxis_width</b>
<a name="IDX2084"></a>
</dt>
<dd><p>Default value: 1
</p>
<p><code>xaxis_width</code> is the width of the <var>x</var> axis.
Its value must be a positive number.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
xaxis = true,
xaxis_width = 3)$
</pre>
<p>See also <code>xaxis</code>, <code>xaxis_type</code> and <code>xaxis_color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>xlabel</b>
<a name="IDX2085"></a>
</dt>
<dd><p>Default value: <code>""</code> (empty string)
</p>
<p>Option <code>xlabel</code>, a string, is the label for the <var>x</var> axis.
By default, no label is written.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xlabel = "Time",
explicit(exp(u),u,-2,2),
ylabel = "Population")$
</pre>
<p>See also <code>ylabel</code>, and <code>zlabel</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xrange"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xrange</b>
<a name="IDX2086"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>If <code>xrange</code> is <code>auto</code>, the range for the <var>x</var> coordinate is
computed automatically.
</p>
<p>If the user wants a specific interval for <var>x</var>, it must be given as a
Maxima list, as in <code>xrange=[-2, 3]</code>.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [-3,5],
explicit(x^2,x,-1,1))$
</pre>
<p>See also <code>yrange</code> and <code>zrange</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xrange_005fsecondary"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xrange_secondary</b>
<a name="IDX2087"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>If <code>xrange_secondary</code> is <code>auto</code>, the range for the second <var>x</var> axis is
computed automatically.
</p>
<p>If the user wants a specific interval for the second <var>x</var> axis, it must be given as a
Maxima list, as in <code>xrange_secondary=[-2, 3]</code>.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>See also <code>xrange</code>, <code>yrange</code>, <code>zrange</code> and <code>yrange_secondary</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p></dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>xtics</b>
<a name="IDX2088"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>This graphic option controls the way tic marks are drawn on the <var>x</var> axis.
</p>
<ul>
<li>
When option <code>xtics</code> is bounded to symbol <var>auto</var>, tic marks are
drawn automatically.
</li><li>
When option <code>xtics</code> is bounded to symbol <var>none</var>, tic marks are
not drawn.
</li><li>
When option <code>xtics</code> is bounded to a positive number, this is the distance
between two consecutive tic marks.
</li><li>
When option <code>xtics</code> is bounded to a list of length three of the
form <code>[start,incr,end]</code>, tic marks are plotted from <code>start</code>
to <code>end</code> at intervals of length <code>incr</code>.
</li><li>
When option <code>xtics</code> is bounded to a set of numbers of the
form <code>{n1, n2, ...}</code>, tic marks are plotted at values <code>n1</code>,
<code>n2</code>, ...
</li><li>
When option <code>xtics</code> is bounded to a set of pairs of the
form <code>{["label1", n1], ["label2", n2], ...}</code>, tic marks corresponding to values <code>n1</code>,
<code>n2</code>, ... are labeled with <code>"label1"</code>, <code>"label2"</code>, ..., respectively.
</li></ul>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Examples:
</p>
<p>Disable tics.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(xtics = 'none,
explicit(x^3,x,-1,1) )$
</pre>
<p>Tics every 1/4 units.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(xtics = 1/4,
explicit(x^3,x,-1,1) )$
</pre>
<p>Tics from -3/4 to 3/4 in steps of 1/8.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(xtics = [-3/4,1/8,3/4],
explicit(x^3,x,-1,1) )$
</pre>
<p>Tics at points -1/2, -1/4 and 3/4.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(xtics = {-1/2,-1/4,3/4},
explicit(x^3,x,-1,1) )$
</pre>
<p>Labeled tics.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(xtics = {["High",0.75],["Medium",0],["Low",-0.75]},
explicit(x^3,x,-1,1) )$
</pre>
<p>See also <code>ytics</code>, and <code>ztics</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xtics_005faxis"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xtics_axis</b>
<a name="IDX2089"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>xtics_axis</code> is <code>true</code>, tic marks and their labels are plotted just
along the <var>x</var> axis, if it is <code>false</code> tics are plotted on the border.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xtics_005frotate"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xtics_rotate</b>
<a name="IDX2090"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>xtics_rotate</code> is <code>true</code>, tic marks on the <var>x</var> axis are rotated
90 degrees.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xtics_005frotate_005fsecondary"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xtics_rotate_secondary</b>
<a name="IDX2091"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>xtics_rotate_secondary</code> is <code>true</code>, tic marks on the secondary <var>x</var> axis are rotated
90 degrees.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xtics_005fsecondary"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xtics_secondary</b>
<a name="IDX2092"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>This graphic option controls the way tic marks are drawn on the second <var>x</var> axis.
</p>
<p>See <code>xtics</code> for a complete description.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xtics_005fsecondary_005faxis"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xtics_secondary_axis</b>
<a name="IDX2093"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>xtics_secondary_axis</code> is <code>true</code>, tic marks and their labels are plotted just
along the secondary <var>x</var> axis, if it is <code>false</code> tics are plotted on the border.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xu_005fgrid"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xu_grid</b>
<a name="IDX2094"></a>
</dt>
<dd><p>Default value: 30
</p>
<p><code>xu_grid</code> is the number of coordinates of the first variable
(<code>x</code> in explicit and <code>u</code> in parametric 3d surfaces) to
build the grid of sample points.
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr3d</code>: <code>explicit</code> and <code>parametric_surface</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(xu_grid = 10,
yv_grid = 50,
explicit(x^2+y^2,x,-3,3,y,-3,3) )$
</pre>
<p>See also <code>yv_grid</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xy_005ffile"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xy_file</b>
<a name="IDX2095"></a>
</dt>
<dd><p>Default value: <code>""</code> (empty string)
</p>
<p><code>xy_file</code> is the name of the file where the coordinates will be saved
after clicking with the mouse button and hitting the 'x' key. By default,
no coordinates are saved.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-xyplane"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>xyplane</b>
<a name="IDX2096"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>Allocates the xy-plane in 3D scenes. When <code>xyplane</code> is
<code>false</code>, the xy-plane is placed automatically; when it is
a real number, the xy-plane intersects the z-axis at this level.
This option has no effect in 2D scenes.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(xyplane = %e-2,
explicit(x^2+y^2,x,-1,1,y,-1,1))$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-y_005fvoxel"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>y_voxel</b>
<a name="IDX2097"></a>
</dt>
<dd><p>Default value: 10
</p>
<p><code>y_voxel</code> is the number of voxels in the y direction to
be used by the <i>marching cubes algorithm</i> implemented
by the 3d <code>implicit</code> object. It is also used by graphic
object <code>region</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-yaxis"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>yaxis</b>
<a name="IDX2098"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>yaxis</code> is <code>true</code>, the <var>y</var> axis is drawn.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
yaxis = true,
yaxis_color = blue)$
</pre>
<p>See also <code>yaxis_width</code>, <code>yaxis_type</code> and <code>yaxis_color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-yaxis_005fcolor"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>yaxis_color</b>
<a name="IDX2099"></a>
</dt>
<dd><p>Default value: <code>"black"</code>
</p>
<p><code>yaxis_color</code> specifies the color for the <var>y</var> axis. See
<code>color</code> to know how colors are defined.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
yaxis = true,
yaxis_color = red)$
</pre>
<p>See also <code>yaxis</code>, <code>yaxis_width</code> and <code>yaxis_type</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-yaxis_005fsecondary"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>yaxis_secondary</b>
<a name="IDX2100"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>yaxis_secondary</code> is <code>true</code>, function values can be plotted with
respect to the second <var>y</var> axis, which will be drawn on the right side of the
scene.
</p>
<p>Note that this is a local graphics option which only affects to 2d plots.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
explicit(sin(x),x,0,10),
yaxis_secondary = true,
ytics_secondary = true,
color = blue,
explicit(100*sin(x+0.1)+2,x,0,10));
</pre>
<p>See also <code>yrange_secondary</code>, <code>ytics_secondary</code>, <code>ytics_rotate_secondary</code>
and <code>ytics_axis_secondary</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-yaxis_005ftype"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>yaxis_type</b>
<a name="IDX2101"></a>
</dt>
<dd><p>Default value: <code>dots</code>
</p>
<p><code>yaxis_type</code> indicates how the <var>y</var> axis is displayed;
possible values are <code>solid</code> and <code>dots</code>.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
yaxis = true,
yaxis_type = solid)$
</pre>
<p>See also <code>yaxis</code>, <code>yaxis_width</code> and <code>yaxis_color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-yaxis_005fwidth"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>yaxis_width</b>
<a name="IDX2102"></a>
</dt>
<dd><p>Default value: 1
</p>
<p><code>yaxis_width</code> is the width of the <var>y</var> axis.
Its value must be a positive number.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(x^3,x,-1,1),
yaxis = true,
yaxis_width = 3)$
</pre>
<p>See also <code>yaxis</code>, <code>yaxis_type</code> and <code>yaxis_color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>ylabel</b>
<a name="IDX2103"></a>
</dt>
<dd><p>Default value: <code>""</code> (empty string)
</p>
<p>Option <code>ylabel</code>, a string, is the label for the <var>y</var> axis.
By default, no label is written.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xlabel = "Time",
ylabel = "Population",
explicit(exp(u),u,-2,2) )$
</pre>
<p>See also <code>xlabel</code>, and <code>zlabel</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-yrange"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>yrange</b>
<a name="IDX2104"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>If <code>yrange</code> is <code>auto</code>, the range for the <var>y</var> coordinate is
computed automatically.
</p>
<p>If the user wants a specific interval for <var>y</var>, it must be given as a
Maxima list, as in <code>yrange=[-2, 3]</code>.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(yrange = [-2,3],
explicit(x^2,x,-1,1),
xrange = [-3,3])$
</pre>
<p>See also <code>xrange</code>, <code>yrange_secondary</code> and <code>zrange</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-yrange_005fsecondary"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>yrange_secondary</b>
<a name="IDX2105"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>If <code>yrange_secondary</code> is <code>auto</code>, the range for the second <var>y</var> axis is
computed automatically.
</p>
<p>If the user wants a specific interval for the second <var>y</var> axis, it must be given as a
Maxima list, as in <code>yrange_secondary=[-2, 3]</code>.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
explicit(sin(x),x,0,10),
yaxis_secondary = true,
ytics_secondary = true,
yrange = [-3, 3],
yrange_secondary = [-20, 20],
color = blue,
explicit(100*sin(x+0.1)+2,x,0,10)) $
</pre>
<p>See also <code>xrange</code>, <code>yrange</code> and <code>zrange</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p></dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>ytics</b>
<a name="IDX2106"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>This graphic option controls the way tic marks are drawn on the <var>y</var> axis.
</p>
<p>See <code>xtics</code> for a complete description.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-ytics_005faxis"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>ytics_axis</b>
<a name="IDX2107"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>ytics_axis</code> is <code>true</code>, tic marks and their labels are plotted just
along the <var>y</var> axis, if it is <code>false</code> tics are plotted on the border.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-ytics_005frotate"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>ytics_rotate</b>
<a name="IDX2108"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>ytics_rotate</code> is <code>true</code>, tic marks on the <var>y</var> axis are rotated
90 degrees.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-ytics_005frotate_005fsecondary"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>ytics_rotate_secondary</b>
<a name="IDX2109"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>ytics_rotate_secondary</code> is <code>true</code>, tic marks on the secondary <var>y</var> axis are rotated
90 degrees.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-ytics_005fsecondary"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>ytics_secondary</b>
<a name="IDX2110"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>This graphic option controls the way tic marks are drawn on the second <var>y</var> axis.
</p>
<p>See <code>xtics</code> for a complete description.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-ytics_005fsecondary_005faxis"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>ytics_secondary_axis</b>
<a name="IDX2111"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>ytics_secondary_axis</code> is <code>true</code>, tic marks and their labels are plotted just
along the secondary <var>y</var> axis, if it is <code>false</code> tics are plotted on the border.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-yv_005fgrid"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>yv_grid</b>
<a name="IDX2112"></a>
</dt>
<dd><p>Default value: 30
</p>
<p><code>yv_grid</code> is the number of coordinates of the second variable
(<code>y</code> in explicit and <code>v</code> in parametric 3d surfaces) to
build the grid of sample points.
</p>
<p>This option affects the following graphic objects:
</p><ul>
<li>
<code>gr3d</code>: <code>explicit</code> and <code>parametric_surface</code>.
</li></ul>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(xu_grid = 10,
yv_grid = 50,
explicit(x^2+y^2,x,-3,3,y,-3,3) )$
</pre>
<p>See also <code>xu_grid</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-z_005fvoxel"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>z_voxel</b>
<a name="IDX2113"></a>
</dt>
<dd><p>Default value: 10
</p>
<p><code>z_voxel</code> is the number of voxels in the z direction to
be used by the <i>marching cubes algorithm</i> implemented
by the 3d <code>implicit</code> object.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-zaxis"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>zaxis</b>
<a name="IDX2114"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>zaxis</code> is <code>true</code>, the <var>z</var> axis is drawn in 3D plots.
This option has no effect in 2D scenes.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(explicit(x^2+y^2,x,-1,1,y,-1,1),
zaxis = true,
zaxis_type = solid,
zaxis_color = blue)$
</pre>
<p>See also <code>zaxis_width</code>, <code>zaxis_type</code> and <code>zaxis_color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-zaxis_005fcolor"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>zaxis_color</b>
<a name="IDX2115"></a>
</dt>
<dd><p>Default value: <code>"black"</code>
</p>
<p><code>zaxis_color</code> specifies the color for the <var>z</var> axis. See
<code>color</code> to know how colors are defined.
This option has no effect in 2D scenes.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(explicit(x^2+y^2,x,-1,1,y,-1,1),
zaxis = true,
zaxis_type = solid,
zaxis_color = red)$
</pre>
<p>See also <code>zaxis</code>, <code>zaxis_width</code> and <code>zaxis_type</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-zaxis_005ftype"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>zaxis_type</b>
<a name="IDX2116"></a>
</dt>
<dd><p>Default value: <code>dots</code>
</p>
<p><code>zaxis_type</code> indicates how the <var>z</var> axis is displayed;
possible values are <code>solid</code> and <code>dots</code>.
This option has no effect in 2D scenes.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(explicit(x^2+y^2,x,-1,1,y,-1,1),
zaxis = true,
zaxis_type = solid)$
</pre>
<p>See also <code>zaxis</code>, <code>zaxis_width</code> and <code>zaxis_color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-zaxis_005fwidth"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>zaxis_width</b>
<a name="IDX2117"></a>
</dt>
<dd><p>Default value: 1
</p>
<p><code>zaxis_width</code> is the width of the <var>z</var> axis.
Its value must be a positive number. This option has no effect in 2D scenes.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(explicit(x^2+y^2,x,-1,1,y,-1,1),
zaxis = true,
zaxis_type = solid,
zaxis_width = 3)$
</pre>
<p>See also <code>zaxis</code>, <code>zaxis_type</code> and <code>zaxis_color</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<dl>
<dt><u>Graphic option:</u> <b>zlabel</b>
<a name="IDX2118"></a>
</dt>
<dd><p>Default value: <code>""</code> (empty string)
</p>
<p>Option <code>zlabel</code>, a string, is the label for the <var>z</var> axis.
By default, no label is written.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(zlabel = "Z variable",
ylabel = "Y variable",
explicit(sin(x^2+y^2),x,-2,2,y,-2,2),
xlabel = "X variable" )$
</pre>
<p>See also <code>xlabel</code>, and <code>ylabel</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-zrange"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>zrange</b>
<a name="IDX2119"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>If <code>zrange</code> is <code>auto</code>, the range for the <var>z</var> coordinate is
computed automatically.
</p>
<p>If the user wants a specific interval for <var>z</var>, it must be given as a
Maxima list, as in <code>zrange=[-2, 3]</code>.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(yrange = [-3,3],
zrange = [-2,5],
explicit(x^2+y^2,x,-1,1,y,-1,1),
xrange = [-3,3])$
</pre>
<p>See also <code>xrange</code> and <code>yrange</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p></dd></dl>
<p><a name="Item_003a-ztics"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>ztics</b>
<a name="IDX2120"></a>
</dt>
<dd><p>Default value: <code>auto</code>
</p>
<p>This graphic option controls the way tic marks are drawn on the <var>z</var> axis.
</p>
<p>See <code>xtics</code> for a complete description.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-ztics_005faxis"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>ztics_axis</b>
<a name="IDX2121"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>ztics_axis</code> is <code>true</code>, tic marks and their labels are plotted just
along the <var>z</var> axis, if it is <code>false</code> tics are plotted on the border.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-ztics_005frotate"></a>
</p><dl>
<dt><u>Graphic option:</u> <b>ztics_rotate</b>
<a name="IDX2122"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>If <code>ztics_rotate</code> is <code>true</code>, tic marks on the <var>z</var> axis are rotated
90 degrees.
</p>
<p>Since this is a global graphics option, its position in the scene description
does not matter.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
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<h3 class="subsection"> 48.2.4 Graphics objects </h3>
<p><a name="Item_003a-bars"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>bars</b><i> ([<var>x1</var>,<var>h1</var>,<var>w1</var>], [<var>x2</var>,<var>h2</var>,<var>w2</var>, ...])</i>
<a name="IDX2123"></a>
</dt>
<dd><p>Draws vertical bars in 2D.
</p>
<p><b>2D</b>
</p>
<p><code>bars ([<var>x1</var>,<var>h1</var>,<var>w1</var>], [<var>x2</var>,<var>h2</var>,<var>w2</var>, ...])</code>
draws bars centered at values <var>x1</var>, <var>x2</var>, ... with heights <var>h1</var>, <var>h2</var>, ...
and widths <var>w1</var>, <var>w2</var>, ...
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>key</code>,
<code>fill_color</code>, <code>fill_density</code> and <code>line_width</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
key = "Group A",
fill_color = blue,
fill_density = 0.2,
bars([0.8,5,0.4],[1.8,7,0.4],[2.8,-4,0.4]),
key = "Group B",
fill_color = red,
fill_density = 0.6,
line_width = 4,
bars([1.2,4,0.4],[2.2,-2,0.4],[3.2,5,0.4]),
xaxis = true);
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-cylindrical"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>cylindrical</b><i> (<var>radius</var>, <var>z</var>, <var>minz</var>, <var>maxz</var>, <var>azi</var>, <var>minazi</var>, <var>maxazi</var>)</i>
<a name="IDX2124"></a>
</dt>
<dd><p>Draws 3D functions defined in cylindrical coordinates.
</p>
<p><b>3D</b>
</p>
<p><code>cylindrical(<var>radius</var>, <var>z</var>, <var>minz</var>, <var>maxz</var>, <var>azi</var>,
<var>minazi</var>, <var>maxazi</var>)</code> plots the function <code><var>radius</var>(<var>z</var>,
<var>azi</var>)</code> defined in cylindrical coordinates, with variable <var>z</var> taking
values from <var>minz</var> to <var>maxz</var> and <i>azimuth</i> <var>azi</var> taking values
from <var>minazi</var> to <var>maxazi</var>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>xu_grid</code>,
<code>yv_grid</code>, <code>line_type</code>, <code>key</code>, <code>wired_surface</code>, <code>enhanced3d</code> and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(cylindrical(1,z,-2,2,az,0,2*%pi))$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-elevation_005fgrid"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>elevation_grid</b><i> (<var>mat</var>,<var>x0</var>,<var>y0</var>,<var>width</var>,<var>height</var>)</i>
<a name="IDX2125"></a>
</dt>
<dd><p>Draws matrix <var>mat</var> in 3D space. <var>z</var> values are taken from <var>mat</var>,
the abscissas range from <var>x0</var> to <em><var>x0</var> + <var>width</var></em>
and ordinates from <var>y0</var> to <em><var>y0</var> + <var>height</var></em>. Element <em>a(1,1)</em>
is projected on point <em>(x0,y0+height)</em>, <em>a(1,n)</em> on <em>(x0+width,y0+height)</em>,
<em>a(m,1)</em> on <em>(x0,y0)</em>, and <em>a(m,n)</em> on <em>(x0+width,y0)</em>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>line_type</code>,
<code>line_width</code>, <code>key</code>, <code>wired_surface</code>, <code>enhanced3d</code>, and <code>color</code>.
</p>
<p>In older versions of Maxima, <code>elevation_grid</code> was called <code>mesh</code>.
See also <code>mesh</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) m: apply(
matrix,
makelist(makelist(random(10.0),k,1,30),i,1,20)) $
(%i3) draw3d(
color = blue,
elevation_grid(m,0,0,3,2),
xlabel = "x",
ylabel = "y",
surface_hide = true);
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-ellipse"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>ellipse</b><i> (<var>xc</var>, <var>yc</var>, <var>a</var>, <var>b</var>, <var>ang1</var>, <var>ang2</var>)</i>
<a name="IDX2126"></a>
</dt>
<dd><p>Draws ellipses and circles in 2D.
</p>
<p><b>2D</b>
</p>
<p><code>ellipse (<var>xc</var>, <var>yc</var>, <var>a</var>, <var>b</var>, <var>ang1</var>, <var>ang2</var>)</code>
plots an ellipse centered at <code>[<var>xc</var>, <var>yc</var>]</code> with horizontal and vertical
semi axis <var>a</var> and <var>b</var>, respectively, starting at angle <var>ang1</var> with an amplitude
equal to angle <var>ang2</var>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>nticks</code>,
<code>transparent</code>, <code>fill_color</code>, <code>border</code>, <code>line_width</code>,
<code>line_type</code>, <code>key</code> and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(transparent = false,
fill_color = red,
color = gray30,
transparent = false,
line_width = 5,
ellipse(0,6,3,2,270,-270),
/* center (x,y), a, b, start & end in degrees */
transparent = true,
color = blue,
line_width = 3,
ellipse(2.5,6,2,3,30,-90),
xrange = [-3,6],
yrange = [2,9] )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-errors"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>errors</b><i> ([<var>x1</var>, <var>x2</var>, …], [<var>y1</var>, <var>y2</var>, …])</i>
<a name="IDX2127"></a>
</dt>
<dd><p>Draws points with error bars, horizontally, vertically or both, depending on the
value of option <code>error_type</code>.
</p>
<p><b>2D</b>
</p>
<p>If <code>error_type = x</code>, arguments to <code>errors</code> must be of the form
<code>[x, y, xdelta]</code> or <code>[x, y, xlow, xhigh]</code>. If <code>error_type = y</code>,
arguments must be of the form <code>[x, y, ydelta]</code> or
<code>[x, y, ylow, yhigh]</code>. If <code>error_type = xy</code> or
<code>error_type = boxes</code>, arguments to <code>errors</code> must be of the form
<code>[x, y, xdelta, ydelta]</code> or <code>[x, y, xlow, xhigh, ylow, yhigh]</code>.
</p>
<p>See also <code>error_type</code>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>error_type</code>,
<code>points_joined</code>, <code>line_width</code>, <code>key</code>, <code>line_type</code>,
<code>color</code>, <code>fill_density</code>, <code>xaxis_secondary</code>, and <code>yaxis_secondary</code>.
</p>
<p>Option <code>fill_density</code> is only relevant when <code>error_type=boxes</code>.
</p>
<p>Examples:
</p>
<p>Horizontal error bars.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
error_type = y,
errors([[1,2,1], [3,5,3], [10,3,1], [17,6,2]]))$
</pre>
<p>Vertical and horizontal error bars.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
error_type = xy,
points_joined = true,
color = blue,
errors([[1,2,1,2], [3,5,2,1], [10,3,1,1], [17,6,1/2,2]]));
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-explicit"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>explicit</b><i> (<var>fcn</var>,<var>var</var>,<var>minval</var>,<var>maxval</var>)</i>
<a name="IDX2128"></a>
</dt>
<dt><u>Graphic object:</u> <b>explicit</b><i> (<var>fcn</var>,<var>var1</var>,<var>minval1</var>,<var>maxval1</var>,<var>var2</var>,<var>minval2</var>,<var>maxval2</var>)</i>
<a name="IDX2129"></a>
</dt>
<dd><p>Draws explicit functions in 2D and 3D.
</p>
<p><b>2D</b>
</p>
<p><code>explicit(<var>fcn</var>,<var>var</var>,<var>minval</var>,<var>maxval</var>)</code> plots explicit function <var>fcn</var>,
with variable <var>var</var> taking values from <var>minval</var> to <var>maxval</var>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>nticks</code>,
<code>adapt_depth</code>, <code>draw_realpart</code>, <code>line_width</code>, <code>line_type</code>, <code>key</code>,
<code>filled_func</code>, <code>fill_color</code> and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(line_width = 3,
color = blue,
explicit(x^2,x,-3,3) )$
(%i3) draw2d(fill_color = brown,
filled_func = true,
explicit(x^2,x,-3,3) )$
</pre>
<p><b>3D</b>
</p>
<p><code>explicit(<var>fcn</var>, <var>var1</var>, <var>minval1</var>, <var>maxval1</var>, <var>var2</var>,
<var>minval2</var>, <var>maxval2</var>)</code> plots the explicit function <var>fcn</var>, with
variable <var>var1</var> taking values from <var>minval1</var> to <var>maxval1</var> and
variable <var>var2</var> taking values from <var>minval2</var> to <var>maxval2</var>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>draw_realpart</code>, <code>xu_grid</code>,
<code>yv_grid</code>, <code>line_type</code>, <code>line_width</code>, <code>key</code>, <code>wired_surface</code>,
<code>enhanced3d</code>, and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(key = "Gauss",
color = "#a02c00",
explicit(20*exp(-x^2-y^2)-10,x,-3,3,y,-3,3),
yv_grid = 10,
color = blue,
key = "Plane",
explicit(x+y,x,-5,5,y,-5,5),
surface_hide = true)$
</pre>
<p>See also <code>filled_func</code> for filled functions.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-image"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>image</b><i> (<var>im</var>,<var>x0</var>,<var>y0</var>,<var>width</var>,<var>height</var>)</i>
<a name="IDX2130"></a>
</dt>
<dd><p>Renders images in 2D.
</p>
<p><b>2D</b>
</p>
<p><code>image (<var>im</var>,<var>x0</var>,<var>y0</var>,<var>width</var>,<var>height</var>)</code> plots image <var>im</var> in the rectangular
region from vertex <code>(<var>x0</var>,<var>y0</var>)</code> to <code>(x0+<var>width</var>,y0+<var>height</var>)</code> on the real
plane. Argument <var>im</var> must be a matrix of real numbers, a matrix of
vectors of length three or a <var>picture</var> object.
</p>
<p>If <var>im</var> is a matrix of real numbers or a <var>levels picture</var> object,
pixel values are interpreted according to graphic option <code>palette</code>,
which is a vector of length three with components
ranging from -36 to +36; each value is an index for a formula mapping the levels
onto red, green and blue colors, respectively:
</p><pre class="example"> 0: 0 1: 0.5 2: 1
3: x 4: x^2 5: x^3
6: x^4 7: sqrt(x) 8: sqrt(sqrt(x))
9: sin(90x) 10: cos(90x) 11: |x-0.5|
12: (2x-1)^2 13: sin(180x) 14: |cos(180x)|
15: sin(360x) 16: cos(360x) 17: |sin(360x)|
18: |cos(360x)| 19: |sin(720x)| 20: |cos(720x)|
21: 3x 22: 3x-1 23: 3x-2
24: |3x-1| 25: |3x-2| 26: (3x-1)/2
27: (3x-2)/2 28: |(3x-1)/2| 29: |(3x-2)/2|
30: x/0.32-0.78125 31: 2*x-0.84
32: 4x;1;-2x+1.84;x/0.08-11.5
33: |2*x - 0.5| 34: 2*x 35: 2*x - 0.5
36: 2*x - 1
</pre><p>negative numbers mean negative colour component.
</p>
<p><code>palette = gray</code> and <code>palette = color</code> are short cuts for
<code>palette = [3,3,3]</code> and <code>palette = [7,5,15]</code>, respectively.
</p>
<p>If <var>im</var> is a matrix of vectors of length three or an <var>rgb picture</var> object,
they are interpreted as red, green and blue color components.
</p>
<p>Examples:
</p>
<p>If <var>im</var> is a matrix of real numbers, pixel values are interpreted according
to graphic option <code>palette</code>.
</p><pre class="example">(%i1) load(draw)$
(%i2) im: apply(
'matrix,
makelist(makelist(random(200),i,1,30),i,1,30))$
(%i3) /* palette = color, default */
draw2d(image(im,0,0,30,30))$
(%i4) draw2d(palette = gray, image(im,0,0,30,30))$
(%i5) draw2d(palette = [15,20,-4],
colorbox=false,
image(im,0,0,30,30))$
</pre>
<p>See also <code>colorbox</code>.
</p>
<p>If <var>im</var> is a matrix of vectors of length three, they are interpreted
as red, green and blue color components.
</p><pre class="example">(%i1) load(draw)$
(%i2) im: apply(
'matrix,
makelist(
makelist([random(300),
random(300),
random(300)],i,1,30),i,1,30))$
(%i3) draw2d(image(im,0,0,30,30))$
</pre>
<p>Package <code>draw</code> automatically loads package <code>picture</code>. In this
example, a level picture object is built by hand and then rendered.
</p><pre class="example">(%i1) load(draw)$
(%i2) im: make_level_picture([45,87,2,134,204,16],3,2);
(%o2) picture(level, 3, 2, {Array: #(45 87 2 134 204 16)})
(%i3) /* default color palette */
draw2d(image(im,0,0,30,30))$
(%i4) /* gray palette */
draw2d(palette = gray,
image(im,0,0,30,30))$
</pre>
<p>An xpm file is read and then rendered.
</p><pre class="example">(%i1) load(draw)$
(%i2) im: read_xpm("myfile.xpm")$
(%i3) draw2d(image(im,0,0,10,7))$
</pre>
<p>See also <code>make_level_picture</code>, <code>make_rgb_picture</code> and <code>read_xpm</code>.
</p>
<p><a href="http://www.telefonica.net/web2/biomates/maxima/gpdraw/image">http://www.telefonica.net/web2/biomates/maxima/gpdraw/image</a><br>
contains more elaborated examples.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-implicit"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>implicit</b><i> (<var>fcn</var>,<var>x</var>,<var>xmin</var>,<var>xmax</var>,<var>y</var>,<var>ymin</var>,<var>ymax</var>)</i>
<a name="IDX2131"></a>
</dt>
<dt><u>Graphic object:</u> <b>implicit</b><i> (<var>fcn</var>,<var>x</var>,<var>xmin</var>,<var>xmax</var>,<var>y</var>,<var>ymin</var>,<var>ymax</var>,<var>z</var>,<var>zmin</var>,<var>zmax</var>)</i>
<a name="IDX2132"></a>
</dt>
<dd><p>Draws implicit functions in 2D and 3D.
</p>
<p><b>2D</b>
</p>
<p><code>implicit(<var>fcn</var>,<var>x</var>,<var>xmin</var>,<var>xmax</var>,<var>y</var>,<var>ymin</var>,<var>ymax</var>)</code>
plots the implicit function defined by <var>fcn</var>, with variable <var>x</var> taking values
from <var>xmin</var> to <var>xmax</var>, and variable <var>y</var> taking values
from <var>ymin</var> to <var>ymax</var>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>ip_grid</code>,
<code>ip_grid_in</code>, <code>line_width</code>, <code>line_type</code>, <code>key</code> and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(terminal = eps,
grid = true,
line_type = solid,
key = "y^2=x^3-2*x+1",
implicit(y^2=x^3-2*x+1, x, -4,4, y, -4,4),
line_type = dots,
key = "x^3+y^3 = 3*x*y^2-x-1",
implicit(x^3+y^3 = 3*x*y^2-x-1, x,-4,4, y,-4,4),
title = "Two implicit functions" )$
</pre>
<p><b>3D</b>
</p>
<p><code>implicit (<var>fcn</var>,<var>x</var>,<var>xmin</var>,<var>xmax</var>, <var>y</var>,<var>ymin</var>,<var>ymax</var>, <var>z</var>,<var>zmin</var>,<var>zmax</var>)</code>
plots the implicit surface defined by <var>fcn</var>, with variable <var>x</var> taking values
from <var>xmin</var> to <var>xmax</var>, variable <var>y</var> taking values
from <var>ymin</var> to <var>ymax</var> and variable <var>z</var> taking values
from <var>zmin</var> to <var>zmax</var>. This object implements the <i>marching cubes algorithm</i>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>x_voxel</code>,
<code>y_voxel</code>, <code>z_voxel</code>, <code>line_width</code>, <code>line_type</code>, <code>key</code>,
<code>wired_surface</code>, <code>enhanced3d</code>,and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
color=blue,
implicit((x^2+y^2+z^2-1)*(x^2+(y-1.5)^2+z^2-0.5)=0.015,
x,-1,1,y,-1.2,2.3,z,-1,1),
surface_hide=true);
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p></dd></dl>
<dl>
<dt><u>Graphic object:</u> <b>label</b><i> ([<var>string</var>,<var>x</var>,<var>y</var>],...)</i>
<a name="IDX2133"></a>
</dt>
<dt><u>Graphic object:</u> <b>label</b><i> ([<var>string</var>,<var>x</var>,<var>y</var>,<var>z</var>],...)</i>
<a name="IDX2134"></a>
</dt>
<dd><p>Writes labels in 2D and 3D.
</p>
<p>Colored labels work only with Gnuplot 4.3. This is a known bug in package <code>draw</code>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>label_alignment</code>,
<code>label_orientation</code> and <code>color</code>.
</p>
<p><b>2D</b>
</p>
<p><code>label([<var>string</var>,<var>x</var>,<var>y</var>])</code> writes the <var>string</var> at point
<code>[<var>x</var>,<var>y</var>]</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(yrange = [0.1,1.4],
color = red,
label(["Label in red",0,0.3]),
color = "#0000ff",
label(["Label in blue",0,0.6]),
color = light_blue,
label(["Label in light-blue",0,0.9],
["Another light-blue",0,1.2]) )$
</pre>
<p><b>3D</b>
</p>
<p><code>label([<var>string</var>,<var>x</var>,<var>y</var>,<var>z</var>])</code> writes the <var>string</var> at point
<code>[<var>x</var>,<var>y</var>,<var>z</var>]</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(explicit(exp(sin(x)+cos(x^2)),x,-3,3,y,-3,3),
color = red,
label(["UP 1",-2,0,3], ["UP 2",1.5,0,4]),
color = blue,
label(["DOWN 1",2,0,-3]) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-mesh"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>mesh</b><i> (<var>row_1</var>,<var>row_2</var>,...)</i>
<a name="IDX2135"></a>
</dt>
<dd><p>Draws a quadrangular mesh in 3D.
</p>
<p><b>3D</b>
</p>
<p>Argument <var>row_i</var> is a list of <var>n</var> 3D points of the form
<code>[[x_i1,y_i1,z_i1], ...,[x_in,y_in,z_in]]</code>, and all rows are
of equal length. All these points define an arbitrary surface in 3D and
in some sense it's a generalization of the <code>elevation_grid</code> object.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>line_type</code>,
<code>line_width</code>, <code>color</code>, <code>key</code>, <code>wired_surface</code>, <code>enhanced3d</code>, and <code>transform</code>.
</p>
<p>Examples:
</p>
<p>A simple example.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
mesh([[1,1,3], [7,3,1],[12,-2,4],[15,0,5]],
[[2,7,8], [4,3,1],[10,5,8], [12,7,1]],
[[-2,11,10],[6,9,5],[6,15,1], [20,15,2]])) $
</pre>
<p>Plotting a triangle in 3D.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
line_width = 2,
mesh([[1,0,0],[0,1,0]],
[[0,0,1],[0,0,1]])) $
</pre>
<p>Two quadrilaterals.
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
surface_hide = true,
line_width = 3,
color = red,
mesh([[0,0,0], [0,1,0]],
[[2,0,2], [2,2,2]]),
color = blue,
mesh([[0,0,2], [0,1,2]],
[[2,0,4], [2,2,4]])) $
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-parametric"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>parametric</b><i> (<var>xfun</var>,<var>yfun</var>,<var>par</var>,<var>parmin</var>,<var>parmax</var>)</i>
<a name="IDX2136"></a>
</dt>
<dt><u>Graphic object:</u> <b>parametric</b><i> (<var>xfun</var>,<var>yfun</var>,<var>zfun</var>,<var>par</var>,<var>parmin</var>,<var>parmax</var>)</i>
<a name="IDX2137"></a>
</dt>
<dd><p>Draws parametric functions in 2D and 3D.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>nticks</code>,
<code>line_width</code>, <code>line_type</code>, <code>key</code>, <code>color</code> and <code>enhanced3d</code>.
</p>
<p><b>2D</b>
</p>
<p>The command <code>parametric(<var>xfun</var>, <var>yfun</var>, <var>par</var>, <var>parmin</var>,
<var>parmax</var>)</code> plots the parametric function <code>[<var>xfun</var>, <var>yfun</var>]</code>,
with parameter <var>par</var> taking values from <var>parmin</var> to <var>parmax</var>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(explicit(exp(x),x,-1,3),
color = red,
key = "This is the parametric one!!",
parametric(2*cos(rrr),rrr^2,rrr,0,2*%pi))$
</pre>
<p><b>3D</b>
</p>
<p><code>parametric(<var>xfun</var>, <var>yfun</var>, <var>zfun</var>, <var>par</var>, <var>parmin</var>,
<var>parmax</var>)</code> plots the parametric curve <code>[<var>xfun</var>, <var>yfun</var>,
<var>zfun</var>]</code>, with parameter <var>par</var> taking values from <var>parmin</var> to
<var>parmax</var>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(explicit(exp(sin(x)+cos(x^2)),x,-3,3,y,-3,3),
color = royalblue,
parametric(cos(5*u)^2,sin(7*u),u-2,u,0,2),
color = turquoise,
line_width = 2,
parametric(t^2,sin(t),2+t,t,0,2),
surface_hide = true,
title = "Surface & curves" )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-parametric_005fsurface"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>parametric_surface</b><i> (<var>xfun</var>, <var>yfun</var>, <var>zfun</var>, <var>par1</var>, <var>par1min</var>, <var>par1max</var>, <var>par2</var>, <var>par2min</var>, <var>par2max</var>)</i>
<a name="IDX2138"></a>
</dt>
<dd><p>Draws parametric surfaces in 3D.
</p>
<p><b>3D</b>
</p>
<p>The command <code>parametric_surface(<var>xfun</var>, <var>yfun</var>, <var>zfun</var>,
<var>par1</var>, <var>par1min</var>, <var>par1max</var>, <var>par2</var>, <var>par2min</var>,
<var>par2max</var>)</code> plots the parametric surface <code>[<var>xfun</var>, <var>yfun</var>,
<var>zfun</var>]</code>, with parameter <var>par1</var> taking values from <var>par1min</var> to
<var>par1max</var> and parameter <var>par2</var> taking values from <var>par2min</var> to
<var>par2max</var>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>draw_realpart</code>, <code>xu_grid</code>,
<code>yv_grid</code>, <code>line_type</code>, <code>line_width</code>, <code>key</code>, <code>wired_surface</code>, <code>enhanced3d</code>,
and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(title = "Sea shell",
xu_grid = 100,
yv_grid = 25,
view = [100,20],
surface_hide = true,
parametric_surface(0.5*u*cos(u)*(cos(v)+1),
0.5*u*sin(u)*(cos(v)+1),
u*sin(v) - ((u+3)/8*%pi)^2 - 20,
u, 0, 13*%pi, v, -%pi, %pi) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-points"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>points</b><i> ([[<var>x1</var>,<var>y1</var>], [<var>x2</var>,<var>y2</var>],...])</i>
<a name="IDX2139"></a>
</dt>
<dt><u>Graphic object:</u> <b>points</b><i> ([<var>x1</var>,<var>x2</var>,...], [<var>y1</var>,<var>y2</var>,...])</i>
<a name="IDX2140"></a>
</dt>
<dt><u>Graphic object:</u> <b>points</b><i> ([<var>y1</var>,<var>y2</var>,...])</i>
<a name="IDX2141"></a>
</dt>
<dt><u>Graphic object:</u> <b>points</b><i> ([[<var>x1</var>,<var>y1</var>,<var>z1</var>], [<var>x2</var>,<var>y2</var>,<var>z2</var>],...])</i>
<a name="IDX2142"></a>
</dt>
<dt><u>Graphic object:</u> <b>points</b><i> ([<var>x1</var>,<var>x2</var>,...], [<var>y1</var>,<var>y2</var>,...], [<var>z1</var>,<var>z2</var>,...])</i>
<a name="IDX2143"></a>
</dt>
<dt><u>Graphic object:</u> <b>points</b><i> (<var>matrix</var>)</i>
<a name="IDX2144"></a>
</dt>
<dt><u>Graphic object:</u> <b>points</b><i> (<var>1d_y_array</var>)</i>
<a name="IDX2145"></a>
</dt>
<dt><u>Graphic object:</u> <b>points</b><i> (<var>1d_x_array</var>, <var>1d_y_array</var>)</i>
<a name="IDX2146"></a>
</dt>
<dt><u>Graphic object:</u> <b>points</b><i> (<var>1d_x_array</var>, <var>1d_y_array</var>, <var>1d_z_array</var>)</i>
<a name="IDX2147"></a>
</dt>
<dt><u>Graphic object:</u> <b>points</b><i> (<var>2d_xy_array</var>)</i>
<a name="IDX2148"></a>
</dt>
<dt><u>Graphic object:</u> <b>points</b><i> (<var>2d_xyz_array</var>)</i>
<a name="IDX2149"></a>
</dt>
<dd><p>Draws points in 2D and 3D.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>point_size</code>,
<code>point_type</code>, <code>points_joined</code>, <code>line_width</code>, <code>key</code>,
<code>line_type</code> and <code>color</code>. In 3D mode, it is also affected by <code>enhanced3d</code>.
</p>
<p><b>2D</b>
</p>
<p><code>points ([[<var>x1</var>,<var>y1</var>], [<var>x2</var>,<var>y2</var>],...])</code> or
<code>points ([<var>x1</var>,<var>x2</var>,...], [<var>y1</var>,<var>y2</var>,...])</code>
plots points <code>[x1,y1]</code>, <code>[x2,y2]</code>, etc. If abscissas
are not given, they are set to consecutive positive integers, so that
<code>points ([<var>y1</var>,<var>y2</var>,...])</code> draws points <code>[1,<var>y1</var>]</code>, <code>[2,<var>y2</var>]</code>, etc.
If <var>matrix</var> is a two-column or two-row matrix, <code>points (<var>matrix</var>)</code>
draws the associated points. If <var>matrix</var> is a one-column or one-row matrix,
abscissas are assigned automatically.
</p>
<p>If <var>1d_y_array</var> is a 1D lisp array of numbers, <code>points (<var>1d_y_array</var>)</code> plots them
setting abscissas to consecutive positive integers. <code>points (<var>1d_x_array</var>, <var>1d_y_array</var>)</code>
plots points with their coordinates taken from the two arrays passed as arguments. If
<var>2d_xy_array</var> is a 2D array with two columns, or with two rows, <code>points (<var>2d_xy_array</var>)</code>
plots the corresponding points on the plane.
</p>
<p>Examples:
</p>
<p>Two types of arguments for <code>points</code>, a list of pairs and two lists
of separate coordinates.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(
key = "Small points",
points(makelist([random(20),random(50)],k,1,10)),
point_type = circle,
point_size = 3,
points_joined = true,
key = "Great points",
points(makelist(k,k,1,20),makelist(random(30),k,1,20)),
point_type = filled_down_triangle,
key = "Automatic abscissas",
color = red,
points([2,12,8]))$
</pre>
<p>Drawing impulses.
</p><pre class="example">(%i1) load(draw)$
(%i2) draw2d(
points_joined = impulses,
line_width = 2,
color = red,
points(makelist([random(20),random(50)],k,1,10)))$
</pre>
<p>Array with ordinates.
</p><pre class="example">(%i1) load(draw)$
(%i2) a: make_array (flonum, 100) $
(%i3) for i:0 thru 99 do a[i]: random(1.0) $
(%i4) draw2d(points(a)) $
</pre>
<p>Two arrays with separate coordinates.
</p><pre class="example">(%i1) load(draw)$
(%i2) x: make_array (flonum, 100) $
(%i3) y: make_array (fixnum, 100) $
(%i4) for i:0 thru 99 do (
x[i]: float(i/100),
y[i]: random(10) ) $
(%i5) draw2d(points(x, y)) $
</pre>
<p>A two-column 2D array.
</p><pre class="example">(%i1) load(draw)$
(%i2) xy: make_array(flonum, 100, 2) $
(%i3) for i:0 thru 99 do (
xy[i, 0]: float(i/100),
xy[i, 1]: random(10) ) $
(%i4) draw2d(points(xy)) $
</pre>
<p>Drawing an array filled with function <code>read_array</code>.
</p><pre class="example">(%i1) load(draw)$
(%i2) a: make_array(flonum,100) $
(%i3) read_array (file_search ("pidigits.data"), a) $
(%i4) draw2d(points(a)) $
</pre>
<p><b>3D</b>
</p>
<p><code>points([[<var>x1</var>, <var>y1</var>, <var>z1</var>], [<var>x2</var>, <var>y2</var>, <var>z2</var>],
...])</code> or <code>points([<var>x1</var>, <var>x2</var>, ...], [<var>y1</var>, <var>y2</var>, ...],
[<var>z1</var>, <var>z2</var>,...])</code> plots points <code>[<var>x1</var>, <var>y1</var>, <var>z1</var>]</code>,
<code>[<var>x2</var>, <var>y2</var>, <var>z2</var>]</code>, etc. If <var>matrix</var> is a three-column
or three-row matrix, <code>points (<var>matrix</var>)</code> draws the associated points.
</p>
<p>When arguments are lisp arrays, <code>points (<var>1d_x_array</var>, <var>1d_y_array</var>, <var>1d_z_array</var>)</code>
takes coordinates from the three 1D arrays. If <var>2d_xyz_array</var> is a 2D array with three columns,
or with three rows, <code>points (<var>2d_xyz_array</var>)</code> plots the corresponding points.
</p>
<p>Examples:
</p>
<p>One tridimensional sample,
</p><pre class="example">(%i1) load(draw)$
(%i2) load (numericalio)$
(%i3) s2 : read_matrix (file_search ("wind.data"))$
(%i4) draw3d(title = "Daily average wind speeds",
point_size = 2,
points(args(submatrix (s2, 4, 5))) )$
</pre>
<p>Two tridimensional samples,
</p><pre class="example">(%i1) load(draw)$
(%i2) load (numericalio)$
(%i3) s2 : read_matrix (file_search ("wind.data"))$
(%i4) draw3d(
title = "Daily average wind speeds. Two data sets",
point_size = 2,
key = "Sample from stations 1, 2 and 3",
points(args(submatrix (s2, 4, 5))),
point_type = 4,
key = "Sample from stations 1, 4 and 5",
points(args(submatrix (s2, 2, 3))) )$
</pre>
<p>Unidimensional arrays,
</p><pre class="example">(%i1) load(draw)$
(%i2) x: make_array (fixnum, 10) $
(%i3) y: make_array (fixnum, 10) $
(%i4) z: make_array (fixnum, 10) $
(%i5) for i:0 thru 9 do (
x[i]: random(10),
y[i]: random(10),
z[i]: random(10) ) $
(%i6) draw3d(points(x,y,z)) $
</pre>
<p>Bidimensional colored array,
</p><pre class="example">(%i1) load(draw)$
(%i2) xyz: make_array(fixnum, 10, 3) $
(%i3) for i:0 thru 9 do (
xyz[i, 0]: random(10),
xyz[i, 1]: random(10),
xyz[i, 2]: random(10) ) $
(%i4) draw3d(
enhanced3d = true,
points_joined = true,
points(xyz)) $
</pre>
<p>Color numbers explicitly specified by the user.
</p><pre class="example">(%i1) load(draw)$
(%i2) pts: makelist([t,t^2,cos(t)], t, 0, 15)$
(%i3) col_num: makelist(k, k, 1, length(pts))$
(%i4) draw3d(
enhanced3d = ['part(col_num,k),k],
point_size = 3,
point_type = filled_circle,
points(pts))$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-polar"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>polar</b><i> (<var>radius</var>,<var>ang</var>,<var>minang</var>,<var>maxang</var>)</i>
<a name="IDX2150"></a>
</dt>
<dd><p>Draws 2D functions defined in polar coordinates.
</p>
<p><b>2D</b>
</p>
<p><code>polar (<var>radius</var>,<var>ang</var>,<var>minang</var>,<var>maxang</var>)</code> plots function
<code><var>radius</var>(<var>ang</var>)</code> defined in polar coordinates, with variable
<var>ang</var> taking values from
<var>minang</var> to <var>maxang</var>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>nticks</code>,
<code>line_width</code>, <code>line_type</code>, <code>key</code> and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(user_preamble = "set grid polar",
nticks = 200,
xrange = [-5,5],
yrange = [-5,5],
color = blue,
line_width = 3,
title = "Hyperbolic Spiral",
polar(10/theta,theta,1,10*%pi) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-polygon"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>polygon</b><i> ([[<var>x1</var>, <var>y1</var>], [<var>x2</var>, <var>y2</var>], …])</i>
<a name="IDX2151"></a>
</dt>
<dt><u>Graphic object:</u> <b>polygon</b><i> ([<var>x1</var>, <var>x2</var>, …], [<var>y1</var>, <var>y2</var>, …])</i>
<a name="IDX2152"></a>
</dt>
<dd><p>Draws polygons in 2D.
</p>
<p><b>2D</b>
</p>
<p>The commands <code>polygon([[<var>x1</var>, <var>y1</var>], [<var>x2</var>, <var>y2</var>], ...])</code>
or <code>polygon([<var>x1</var>, <var>x2</var>, ...], [<var>y1</var>, <var>y2</var>, ...])</code> plot on
the plane a polygon with vertices <code>[<var>x1</var>, <var>y1</var>]</code>, <code>[<var>x2</var>,
<var>y2</var>]</code>, etc.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>transparent</code>,
<code>fill_color</code>, <code>border</code>, <code>line_width</code>, <code>key</code>,
<code>line_type</code> and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(color = "#e245f0",
line_width = 8,
polygon([[3,2],[7,2],[5,5]]),
border = false,
fill_color = yellow,
polygon([[5,2],[9,2],[7,5]]) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-quadrilateral"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>quadrilateral</b><i> (<var>point_1</var>, <var>point_2</var>, <var>point_3</var>, <var>point_4</var>)</i>
<a name="IDX2153"></a>
</dt>
<dd><p>Draws a quadrilateral.
</p>
<p><b>2D</b>
</p>
<p><code>quadrilateral([<var>x1</var>, <var>y1</var>], [<var>x2</var>, <var>y2</var>],
[<var>x3</var>, <var>y3</var>], [<var>x4</var>, <var>y4</var>])</code> draws a quadrilateral with vertices
<code>[<var>x1</var>, <var>y1</var>]</code>, <code>[<var>x2</var>, <var>y2</var>]</code>,
<code>[<var>x3</var>, <var>y3</var>]</code>, and <code>[<var>x4</var>, <var>y4</var>]</code>.
</p>
<p>This object is affected by the following <i>graphic options</i>:<br>
<code>transparent</code>, <code>fill_color</code>, <code>border</code>, <code>line_width</code>,
<code>key</code>, <code>xaxis_secondary</code>, <code>yaxis_secondary</code>, <code>line_type</code>,
<code>transform</code> and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
quadrilateral([1,1],[2,2],[3,-1],[2,-2]))$
</pre>
<p><b>3D</b>
</p>
<p><code>quadrilateral([<var>x1</var>, <var>y1</var>, <var>z1</var>], [<var>x2</var>, <var>y2</var>,
<var>z2</var>], [<var>x3</var>, <var>y3</var>, <var>z3</var>], [<var>x4</var>, <var>y4</var>, <var>z4</var>])</code>
draws a quadrilateral with vertices <code>[<var>x1</var>, <var>y1</var>, <var>z1</var>]</code>,
<code>[<var>x2</var>, <var>y2</var>, <var>z2</var>]</code>, <code>[<var>x3</var>, <var>y3</var>, <var>z3</var>]</code>,
and <code>[<var>x4</var>, <var>y4</var>, <var>z4</var>]</code>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>line_type</code>,
<code>line_width</code>, <code>color</code>, <code>key</code>, <code>enhanced3d</code>, and
<code>transform</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p></dd></dl>
<p><a name="Item_003a-rectangle"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>rectangle</b><i> ([<var>x1</var>,<var>y1</var>], [<var>x2</var>,<var>y2</var>])</i>
<a name="IDX2154"></a>
</dt>
<dd><p>Draws rectangles in 2D.
</p>
<p><b>2D</b>
</p>
<p><code>rectangle ([<var>x1</var>,<var>y1</var>], [<var>x2</var>,<var>y2</var>])</code> draws a rectangle with opposite vertices
<code>[<var>x1</var>,<var>y1</var>]</code> and <code>[<var>x2</var>,<var>y2</var>]</code>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>transparent</code>,
<code>fill_color</code>, <code>border</code>, <code>line_width</code>, <code>key</code>,
<code>line_type</code> and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(fill_color = red,
line_width = 6,
line_type = dots,
transparent = false,
fill_color = blue,
rectangle([-2,-2],[8,-1]), /* opposite vertices */
transparent = true,
line_type = solid,
line_width = 1,
rectangle([9,4],[2,-1.5]),
xrange = [-3,10],
yrange = [-3,4.5] )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-region"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>region</b><i> (<var>expr</var>,<var>var1</var>,<var>minval1</var>,<var>maxval1</var>,<var>var2</var>,<var>minval2</var>,<var>maxval2</var>)</i>
<a name="IDX2155"></a>
</dt>
<dd><p>Plots a region on the plane defined by inequalities.
</p>
<p><b>2D</b>
<var>expr</var> is an expression formed by inequalities and boolean operators
<code>and</code>, <code>or</code>, and <code>not</code>. The region is bounded by the rectangle
defined by <em>[<var>minval1</var>, <var>maxval1</var>]</em> and <em>[<var>minval2</var>, <var>maxval2</var>]</em>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>fill_color</code>,
<code>key</code>, <code>x_voxel</code>, and <code>y_voxel</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
x_voxel = 30,
y_voxel = 30,
region(x^2+y^2<1 and x^2+y^2 > 1/2,
x, -1.5, 1.5, y, -1.5, 1.5));
</pre></dd></dl>
<p><a name="Item_003a-spherical"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>spherical</b><i> (<var>radius</var>, <var>azi</var>, <var>minazi</var>, <var>maxazi</var>, <var>zen</var>, <var>minzen</var>, <var>maxzen</var>)</i>
<a name="IDX2156"></a>
</dt>
<dd><p>Draws 3D functions defined in spherical coordinates.
</p>
<p><b>3D</b>
</p>
<p><code>spherical(<var>radius</var>, <var>azi</var>, <var>minazi</var>, <var>maxazi</var>, <var>zen</var>,
<var>minzen</var>, <var>maxzen</var>)</code> plots the function <code><var>radius</var>(<var>azi</var>,
<var>zen</var>)</code> defined in spherical coordinates, with <i>azimuth</i> <var>azi</var> taking
values from <var>minazi</var> to <var>maxazi</var> and <i>zenith</i> <var>zen</var> taking values
from <var>minzen</var> to <var>maxzen</var>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>xu_grid</code>,
<code>yv_grid</code>, <code>line_type</code>, <code>key</code>, <code>wired_surface</code>, <code>enhanced3d</code> and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(spherical(1,a,0,2*%pi,z,0,%pi))$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-triangle"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>triangle</b><i> (<var>point_1</var>, <var>point_2</var>, <var>point_3</var>)</i>
<a name="IDX2157"></a>
</dt>
<dd><p>Draws a triangle.
</p>
<p><b>2D</b>
</p>
<p><code>triangle ([<var>x1</var>,<var>y1</var>], [<var>x2</var>,<var>y2</var>], [<var>x3</var>,<var>y3</var>])</code> draws a triangle with vertices <code>[<var>x1</var>,<var>y1</var>]</code>, <code>[<var>x2</var>,<var>y2</var>]</code>,
and <code>[<var>x3</var>,<var>y3</var>]</code>.
</p>
<p>This object is affected by the following <i>graphic options</i>:<br>
<code>transparent</code>, <code>fill_color</code>, <code>border</code>, <code>line_width</code>,
<code>key</code>, <code>xaxis_secondary</code>, <code>yaxis_secondary</code>, <code>line_type</code>,
<code>transform</code>, and <code>color</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(
triangle([1,1],[2,2],[3,-1]))$
</pre>
<p><b>3D</b>
</p>
<p><code>triangle ([<var>x1</var>,<var>y1</var>,<var>z1</var>], [<var>x2</var>,<var>y2</var>,<var>z2</var>], [<var>x3</var>,<var>y3</var>,<var>z3</var>])</code> draws a triangle with vertices <code>[<var>x1</var>,<var>y1</var>,<var>z1</var>]</code>,
<code>[<var>x2</var>,<var>y2</var>,<var>z2</var>]</code>, and <code>[<var>x3</var>,<var>y3</var>,<var>z3</var>]</code>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>line_type</code>,
<code>line_width</code>, <code>color</code>, <code>key</code>, <code>enhanced3d</code>, and <code>transform</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-tube"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>tube</b><i> (<var>xfun</var>,<var>yfun</var>,<var>zfun</var>,<var>rfun</var>,<var>p</var>,<var>pmin</var>,<var>pmax</var>)</i>
<a name="IDX2158"></a>
</dt>
<dd><p>Draws a tube in 3D with varying diameter.
</p>
<p><b>3D</b>
</p>
<p><code>[<var>xfun</var>,<var>yfun</var>,<var>zfun</var>]</code>
is the parametric curve with parameter <var>p</var> taking values from <var>pmin</var>
to <var>pmax</var>. Circles of radius <var>rfun</var> are placed with their centers on
the parametric curve and perpendicular to it.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>xu_grid</code>,
<code>yv_grid</code>, <code>line_type</code>, <code>line_width</code>, <code>key</code>, <code>wired_surface</code>, <code>enhanced3d</code>,
<code>color</code>, and <code>tube_extremes</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(
enhanced3d = true,
xu_grid = 50,
tube(cos(a), a, 0, cos(a/10)^2,
a, 0, 4*%pi) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-vector"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>vector</b><i> ([<var>x</var>,<var>y</var>], [<var>dx</var>,<var>dy</var>])</i>
<a name="IDX2159"></a>
</dt>
<dt><u>Graphic object:</u> <b>vector</b><i> ([<var>x</var>,<var>y</var>,<var>z</var>], [<var>dx</var>,<var>dy</var>,<var>dz</var>])</i>
<a name="IDX2160"></a>
</dt>
<dd><p>Draws vectors in 2D and 3D.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>head_both</code>,
<code>head_length</code>, <code>head_angle</code>, <code>head_type</code>, <code>line_width</code>,
<code>line_type</code>, <code>key</code> and <code>color</code>.
</p>
<p><b>2D</b>
</p>
<p><code>vector([<var>x</var>,<var>y</var>], [<var>dx</var>,<var>dy</var>])</code> plots vector
<code>[<var>dx</var>,<var>dy</var>]</code> with origin in <code>[<var>x</var>,<var>y</var>]</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw2d(xrange = [0,12],
yrange = [0,10],
head_length = 1,
vector([0,1],[5,5]), /* default type */
head_type = 'empty,
vector([3,1],[5,5]),
head_both = true,
head_type = 'nofilled,
line_type = dots,
vector([6,1],[5,5]))$
</pre>
<p><b>3D</b>
</p>
<p><code>vector([<var>x</var>,<var>y</var>,<var>z</var>], [<var>dx</var>,<var>dy</var>,<var>dz</var>])</code>
plots vector <code>[<var>dx</var>,<var>dy</var>,<var>dz</var>]</code> with
origin in <code>[<var>x</var>,<var>y</var>,<var>z</var>]</code>.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) draw3d(color = cyan,
vector([0,0,0],[1,1,1]/sqrt(3)),
vector([0,0,0],[1,-1,0]/sqrt(2)),
vector([0,0,0],[1,1,-2]/sqrt(6)) )$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-Functions-and-Variables-for-pictures"></a>
</p><hr size="6">
<a name="Functions-and-Variables-for-pictures"></a>
<a name="SEC246"></a>
<table cellpadding="1" cellspacing="1" border="0">
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<td valign="middle" align="left">[<a href="maxima_abt.html#SEC_About" title="About (help)"> ? </a>]</td>
</tr></table>
<h2 class="section"> 48.3 Functions and Variables for pictures </h2>
<p><a name="Item_003a-get_005fpixel"></a>
</p><dl>
<dt><u>Function:</u> <b>get_pixel</b><i> (<var>pic</var>,<var>x</var>,<var>y</var>)</i>
<a name="IDX2161"></a>
</dt>
<dd><p>Returns pixel from picture. Coordinates <var>x</var> and <var>y</var> range from 0 to
<code>width-1</code> and <code>height-1</code>, respectively.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-make_005flevel_005fpicture"></a>
</p><dl>
<dt><u>Function:</u> <b>make_level_picture</b><i> (<var>data</var>)</i>
<a name="IDX2162"></a>
</dt>
<dt><u>Function:</u> <b>make_level_picture</b><i> (<var>data</var>,<var>width</var>,<var>height</var>)</i>
<a name="IDX2163"></a>
</dt>
<dd><p>Returns a levels <var>picture</var> object. <code>make_level_picture (<var>data</var>)</code>
builds the <var>picture</var> object from matrix <var>data</var>.
<code>make_level_picture (<var>data</var>,<var>width</var>,<var>height</var>)</code>
builds the object from a list of numbers; in this case, both the
<var>width</var> and the <var>height</var> must be given.
</p>
<p>The returned <var>picture</var> object contains the following
four parts:
</p>
<ol>
<li> symbol <code>level</code>
</li><li> image width
</li><li> image height
</li><li> an integer array with pixel data ranging from 0 to 255.
Argument <var>data</var> must contain only numbers ranged from 0 to 255;
negative numbers are substituted by 0, and those which are
greater than 255 are set to 255.
</li></ol>
<p>Example:
</p>
<p>Level picture from matrix.
</p><pre class="example">(%i1) load(draw)$
(%i2) make_level_picture(matrix([3,2,5],[7,-9,3000]));
(%o2) picture(level, 3, 2, {Array: #(3 2 5 7 0 255)})
</pre>
<p>Level picture from numeric list.
</p><pre class="example">(%i1) load(draw)$
(%i2) make_level_picture([-2,0,54,%pi],2,2);
(%o2) picture(level, 2, 2, {Array: #(0 0 54 3)})
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-make_005frgb_005fpicture"></a>
</p><dl>
<dt><u>Function:</u> <b>make_rgb_picture</b><i> (<var>redlevel</var>,<var>greenlevel</var>,<var>bluelevel</var>)</i>
<a name="IDX2164"></a>
</dt>
<dd><p>Returns an rgb-coloured <var>picture</var> object. All three arguments must
be levels picture; with red, green and blue levels.
</p>
<p>The returned <var>picture</var> object contains the following
four parts:
</p>
<ol>
<li> symbol <code>rgb</code>
</li><li> image width
</li><li> image height
</li><li> an integer array of length <var>3*width*height</var> with pixel data ranging
from 0 to 255. Each pixel is represented by three consecutive numbers
(red, green, blue).
</li></ol>
<p>Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) red: make_level_picture(matrix([3,2],[7,260]));
(%o2) picture(level, 2, 2, {Array: #(3 2 7 255)})
(%i3) green: make_level_picture(matrix([54,23],[73,-9]));
(%o3) picture(level, 2, 2, {Array: #(54 23 73 0)})
(%i4) blue: make_level_picture(matrix([123,82],[45,32.5698]));
(%o4) picture(level, 2, 2, {Array: #(123 82 45 33)})
(%i5) make_rgb_picture(red,green,blue);
(%o5) picture(rgb, 2, 2,
{Array: #(3 54 123 2 23 82 7 73 45 255 0 33)})
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-negative_005fpicture"></a>
</p><dl>
<dt><u>Function:</u> <b>negative_picture</b><i> (<var>pic</var>)</i>
<a name="IDX2165"></a>
</dt>
<dd><p>Returns the negative of a (<var>level</var> or <var>rgb</var>) picture.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p></dd></dl>
<p><a name="Item_003a-picture_005fequalp"></a>
</p><dl>
<dt><u>Function:</u> <b>picture_equalp</b><i> (<var>x</var>,<var>y</var>)</i>
<a name="IDX2166"></a>
</dt>
<dd><p>Returns <code>true</code> in case of equal pictures, and <code>false</code> otherwise.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw} ·
@ref{Category: Predicate functions}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-picturep"></a>
</p><dl>
<dt><u>Function:</u> <b>picturep</b><i> (<var>x</var>)</i>
<a name="IDX2167"></a>
</dt>
<dd><p>Returns <code>true</code> if the argument is a well formed image,
and <code>false</code> otherwise.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw} ·
@ref{Category: Predicate functions}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-read_005fxpm"></a>
</p><dl>
<dt><u>Function:</u> <b>read_xpm</b><i> (<var>xpm_file</var>)</i>
<a name="IDX2168"></a>
</dt>
<dd><p>Reads a file in xpm and returns a picture object.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-rgb2level"></a>
</p><dl>
<dt><u>Function:</u> <b>rgb2level</b><i> (<var>pic</var>)</i>
<a name="IDX2169"></a>
</dt>
<dd><p>Transforms an <var>rgb</var> picture into a <var>level</var> one by
averaging the red, green and blue channels.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-take_005fchannel"></a>
</p><dl>
<dt><u>Function:</u> <b>take_channel</b><i> (<var>im</var>,<var>color</var>)</i>
<a name="IDX2170"></a>
</dt>
<dd><p>If argument <var>color</var> is <code>red</code>, <code>green</code> or <code>blue</code>,
function <code>take_channel</code> returns the corresponding color channel of
picture <var>im</var>.
Example:
</p>
<pre class="example">(%i1) load(draw)$
(%i2) red: make_level_picture(matrix([3,2],[7,260]));
(%o2) picture(level, 2, 2, {Array: #(3 2 7 255)})
(%i3) green: make_level_picture(matrix([54,23],[73,-9]));
(%o3) picture(level, 2, 2, {Array: #(54 23 73 0)})
(%i4) blue: make_level_picture(matrix([123,82],[45,32.5698]));
(%o4) picture(level, 2, 2, {Array: #(123 82 45 33)})
(%i5) make_rgb_picture(red,green,blue);
(%o5) picture(rgb, 2, 2,
{Array: #(3 54 123 2 23 82 7 73 45 255 0 33)})
(%i6) take_channel(%,'green); /* simple quote!!! */
(%o6) picture(level, 2, 2, {Array: #(54 23 73 0)})
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-Functions-and-Variables-for-worldmap"></a>
</p><hr size="6">
<a name="Functions-and-Variables-for-worldmap"></a>
<a name="SEC247"></a>
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<td valign="middle" align="left">[<a href="maxima_abt.html#SEC_About" title="About (help)"> ? </a>]</td>
</tr></table>
<h2 class="section"> 48.4 Functions and Variables for worldmap </h2>
<p>This package automatically loads package <code>draw</code>.
</p>
<hr size="6">
<a name="SEC248"></a>
<table cellpadding="1" cellspacing="1" border="0">
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<td valign="middle" align="left">[<a href="maxima.html#SEC_Top" title="Cover (top) of document">Top</a>]</td>
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<td valign="middle" align="left">[<a href="maxima_82.html#SEC380" title="Index">Index</a>]</td>
<td valign="middle" align="left">[<a href="maxima_abt.html#SEC_About" title="About (help)"> ? </a>]</td>
</tr></table>
<h3 class="subsection"> 48.4.1 Variables and Functions </h3>
<p><a name="Item_003a-boundaries_005farray"></a>
</p><dl>
<dt><u>Global variable:</u> <b>boundaries_array</b>
<a name="IDX2171"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p><code>boundaries_array</code> is where the graphic object <code>geomap</code> looks
for boundaries coordinates.
</p>
<p>Each component of <code>boundaries_array</code> is an array of floating
point quantities, the coordinates of a polygonal segment or map boundary.
</p>
<p>See also <code>geomap</code>.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-numbered_005fboundaries"></a>
</p><dl>
<dt><u>Function:</u> <b>numbered_boundaries</b><i> (<var>nlist</var>)</i>
<a name="IDX2172"></a>
</dt>
<dd><p>Draws a list of polygonal segments (boundaries), labeled by
its numbers (<code>boundaries_array</code> coordinates). This is of great
help when building new geographical entities.
</p>
<p>Example:
</p>
<p>Map of Europe labeling borders with their component number in
<code>boundaries_array</code>.
</p><pre class="example">(%i1) load(worldmap)$
(%i2) european_borders:
region_boundaries(-31.81,74.92,49.84,32.06)$
(%i3) numbered_boundaries(european_borders)$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-make_005fpoly_005fcontinent"></a>
</p><dl>
<dt><u>Function:</u> <b>make_poly_continent</b><i> (<var>continent_name</var>)</i>
<a name="IDX2173"></a>
</dt>
<dt><u>Function:</u> <b>make_poly_continent</b><i> (<var>country_list</var>)</i>
<a name="IDX2174"></a>
</dt>
<dd><p>Makes the necessary polygons to draw a colored continent
or a list of countries.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(worldmap)$
(%i2) /* A continent */
make_poly_continent(Africa)$
(%i3) apply(draw2d, %)$
(%i4) /* A list of countries */
make_poly_continent([Germany,Denmark,Poland])$
(%i5) apply(draw2d, %)$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-make_005fpoly_005fcountry"></a>
</p><dl>
<dt><u>Function:</u> <b>make_poly_country</b><i> (<var>country_name</var>)</i>
<a name="IDX2175"></a>
</dt>
<dd><p>Makes the necessary polygons to draw a colored country.
If islands exist, one country can be defined with more than
just one polygon.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(worldmap)$
(%i2) make_poly_country(India)$
(%i3) apply(draw2d, %)$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-make_005fpolygon"></a>
</p><dl>
<dt><u>Function:</u> <b>make_polygon</b><i> (<var>nlist</var>)</i>
<a name="IDX2176"></a>
</dt>
<dd><p>Returns a <code>polygon</code> object from boundary indices. Argument
<var>nlist</var> is a list of components of <code>boundaries_array</code>.
</p>
<p>Example:
</p>
<p>Bhutan is defined by boundary numbers 171, 173
and 1143, so that <code>make_polygon([171,173,1143])</code>
appends arrays of coordinates <code>boundaries_array[171]</code>,
<code>boundaries_array[173]</code> and <code>boundaries_array[1143]</code> and
returns a <code>polygon</code> object suited to be plotted by
<code>draw</code>. To avoid an error message, arrays must be
compatible in the sense that any two consecutive
arrays have two coordinates in the extremes in common. In this
example, the two first components of <code>boundaries_array[171]</code> are
equal to the last two coordinates of <code>boundaries_array[173]</code>, and
the two first of <code>boundaries_array[173]</code> are equal to the two first
of <code>boundaries_array[1143]</code>; in conclussion, boundary numbers
171, 173 and 1143 (in this order) are compatible and the colored
polygon can be drawn.
</p><pre class="example">(%i1) load(worldmap)$
(%i2) Bhutan;
(%o2) [[171, 173, 1143]]
(%i3) boundaries_array[171];
(%o3) {Array:
#(88.750549 27.14727 88.806351 27.25305 88.901367 27.282221
88.917877 27.321039)}
(%i4) boundaries_array[173];
(%o4) {Array:
#(91.659554 27.76511 91.6008 27.66666 91.598022 27.62499
91.631348 27.536381 91.765533 27.45694 91.775253 27.4161
92.007751 27.471939 92.11441 27.28583 92.015259 27.168051
92.015533 27.08083 92.083313 27.02277 92.112183 26.920271
92.069977 26.86194 91.997192 26.85194 91.915253 26.893881
91.916924 26.85416 91.8358 26.863331 91.712479 26.799999
91.542191 26.80444 91.492188 26.87472 91.418854 26.873329
91.371353 26.800831 91.307457 26.778049 90.682457 26.77417
90.392197 26.903601 90.344131 26.894159 90.143044 26.75333
89.98996 26.73583 89.841919 26.70138 89.618301 26.72694
89.636093 26.771111 89.360786 26.859989 89.22081 26.81472
89.110237 26.829161 88.921631 26.98777 88.873016 26.95499
88.867737 27.080549 88.843307 27.108601 88.750549
27.14727)}
(%i5) boundaries_array[1143];
(%o5) {Array:
#(91.659554 27.76511 91.666924 27.88888 91.65831 27.94805
91.338028 28.05249 91.314972 28.096661 91.108856 27.971109
91.015808 27.97777 90.896927 28.05055 90.382462 28.07972
90.396088 28.23555 90.366074 28.257771 89.996353 28.32333
89.83165 28.24888 89.58609 28.139999 89.35997 27.87166
89.225517 27.795 89.125793 27.56749 88.971077 27.47361
88.917877 27.321039)}
(%i6) Bhutan_polygon: make_polygon([171,173,1143])$
(%i7) draw2d(Bhutan_polygon)$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-region_005fboundaries"></a>
</p><dl>
<dt><u>Function:</u> <b>region_boundaries</b><i> (<var>x1</var>,<var>y1</var>,<var>x2</var>,<var>y2</var>)</i>
<a name="IDX2177"></a>
</dt>
<dd><p>Detects polygonal segments of global variable <code>boundaries_array</code>
fully contained in the rectangle with vertices (<var>x1</var>,<var>y1</var>) -upper left-
and (<var>x2</var>,<var>y2</var>) -bottom right-.
</p>
<p>Example:
</p>
<p>Returns segment numbers for plotting southern Italy.
</p><pre class="example">(%i1) load(worldmap)$
(%i2) region_boundaries(10.4,41.5,20.7,35.4);
(%o2) [1846, 1863, 1864, 1881, 1888, 1894]
(%i3) draw2d(geomap(%))$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-region_005fboundaries_005fplus"></a>
</p><dl>
<dt><u>Function:</u> <b>region_boundaries_plus</b><i> (<var>x1</var>,<var>y1</var>,<var>x2</var>,<var>y2</var>)</i>
<a name="IDX2178"></a>
</dt>
<dd><p>Detects polygonal segments of global variable <code>boundaries_array</code>
containing at least one vertex in the rectangle defined by vertices (<var>x1</var>,<var>y1</var>)
-upper left- and (<var>x2</var>,<var>y2</var>) -bottom right-.
</p>
<p>Example:
</p>
<pre class="example">(%i1) load(worldmap)$
(%i2) region_boundaries_plus(10.4,41.5,20.7,35.4);
(%o2) [1060, 1062, 1076, 1835, 1839, 1844, 1846, 1858,
1861, 1863, 1864, 1871, 1881, 1888, 1894, 1897]
(%i3) draw2d(geomap(%))$
</pre>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<hr size="6">
<a name="SEC249"></a>
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<h3 class="subsection"> 48.4.2 Graphic objects </h3>
<p><a name="Item_003a-geomap"></a>
</p><dl>
<dt><u>Graphic object:</u> <b>geomap</b><i> (<var>numlist</var>)</i>
<a name="IDX2179"></a>
</dt>
<dt><u>Graphic object:</u> <b>geomap</b><i> (<var>numlist</var>,<var>3Dprojection</var>)</i>
<a name="IDX2180"></a>
</dt>
<dd><p>Draws cartographic maps in 2D and 3D.
</p>
<p><b>2D</b>
</p>
<p>This function works together with global variable <code>boundaries_array</code>.
</p>
<p>Argument <var>numlist</var> is a list containing numbers or lists of numbers.
All these numbers must be integers greater or equal than zero,
representing the components of global array <code>boundaries_array</code>.
</p>
<p>Each component of <code>boundaries_array</code> is an array of floating
point quantities, the coordinates of a polygonal segment or map boundary.
</p>
<p><code>geomap (<var>numlist</var>)</code> flattens its arguments and draws the
associated boundaries in <code>boundaries_array</code>.
</p>
<p>This object is affected by the following <i>graphic options</i>: <code>line_width</code>,
<code>line_type</code> and <code>color</code>.
</p>
<p>Examples:
</p>
<p>A simple map defined by hand:
</p><pre class="example">(%i1) load(worldmap)$
(%i2) /* Vertices of boundary #0: {(1,1),(2,5),(4,3)} */
( bnd0: make_array(flonum,6),
bnd0[0]:1.0, bnd0[1]:1.0, bnd0[2]:2.0,
bnd0[3]:5.0, bnd0[4]:4.0, bnd0[5]:3.0 )$
(%i3) /* Vertices of boundary #1: {(4,3),(5,4),(6,4),(5,1)} */
( bnd1: make_array(flonum,8),
bnd1[0]:4.0, bnd1[1]:3.0, bnd1[2]:5.0, bnd1[3]:4.0,
bnd1[4]:6.0, bnd1[5]:4.0, bnd1[6]:5.0, bnd1[7]:1.0)$
(%i4) /* Vertices of boundary #2: {(5,1), (3,0), (1,1)} */
( bnd2: make_array(flonum,6),
bnd2[0]:5.0, bnd2[1]:1.0, bnd2[2]:3.0,
bnd2[3]:0.0, bnd2[4]:1.0, bnd2[5]:1.0 )$
(%i5) /* Vertices of boundary #3: {(1,1), (4,3)} */
( bnd3: make_array(flonum,4),
bnd3[0]:1.0, bnd3[1]:1.0, bnd3[2]:4.0, bnd3[3]:3.0)$
(%i6) /* Vertices of boundary #4: {(4,3), (5,1)} */
( bnd4: make_array(flonum,4),
bnd4[0]:4.0, bnd4[1]:3.0, bnd4[2]:5.0, bnd4[3]:1.0)$
(%i7) /* Pack all together in boundaries_array */
( boundaries_array: make_array(any,5),
boundaries_array[0]: bnd0, boundaries_array[1]: bnd1,
boundaries_array[2]: bnd2, boundaries_array[3]: bnd3,
boundaries_array[4]: bnd4 )$
(%i8) draw2d(geomap([0,1,2,3,4]))$
</pre>
<p>The auxiliary package <code>worldmap</code> sets the global variable
<code>boundaries_array</code> to real world boundaries in
(longitude, latitude) coordinates. These data are in the
public domain and come from
<a href="http://www-cger.nies.go.jp/grid-e/gridtxt/grid19.html">http://www-cger.nies.go.jp/grid-e/gridtxt/grid19.html</a>.
Package <code>worldmap</code> defines also boundaries for countries,
continents and coastlines as lists with the necessary components of
<code>boundaries_array</code> (see file <code>share/draw/worldmap.mac</code>
for more information). Package <code>worldmap</code> automatically loads
package <code>worldmap</code>.
</p><pre class="example">(%i1) load(worldmap)$
(%i2) c1: gr2d(geomap(Canada,United_States,
Mexico,Cuba))$
(%i3) c2: gr2d(geomap(Africa))$
(%i4) c3: gr2d(geomap(Oceania,China,Japan))$
(%i5) c4: gr2d(geomap(France,Portugal,Spain,
Morocco,Western_Sahara))$
(%i6) draw(columns = 2,
c1,c2,c3,c4)$
</pre>
<p>Package <code>worldmap</code> is also useful for plotting
countries as polygons. In this case, graphic object
<code>geomap</code> is no longer necessary and the <code>polygon</code>
object is used instead. Since lists are now used and not
arrays, maps rendering will be slower. See also <code>make_poly_country</code>
and <code>make_poly_continent</code> to understand the following code.
</p><pre class="example">(%i1) load(worldmap)$
(%i2) mymap: append(
[color = white], /* borders are white */
[fill_color = red], make_poly_country(Bolivia),
[fill_color = cyan], make_poly_country(Paraguay),
[fill_color = green], make_poly_country(Colombia),
[fill_color = blue], make_poly_country(Chile),
[fill_color = "#23ab0f"], make_poly_country(Brazil),
[fill_color = goldenrod], make_poly_country(Argentina),
[fill_color = "midnight-blue"], make_poly_country(Uruguay))$
(%i3) apply(draw2d, mymap)$
</pre>
<p><b>3D</b>
</p>
<p><code>geomap (<var>numlist</var>)</code> projects map boundaries on the sphere of radius 1
centered at (0,0,0). It is possible to change the sphere or the projection type
by using <code>geomap (<var>numlist</var>,<var>3Dprojection</var>)</code>.
</p>
<p>Available 3D projections:
</p>
<ul>
<li>
<code>[spherical_projection,<var>x</var>,<var>y</var>,<var>z</var>,<var>r</var>]</code>: projects map boundaries on the sphere of
radius <var>r</var> centered at (<var>x</var>,<var>y</var>,<var>z</var>).
<pre class="example">(%i1) load(worldmap)$
(%i2) draw3d(geomap(Australia), /* default projection */
geomap(Australia,
[spherical_projection,2,2,2,3]))$
</pre>
</li><li>
<code>[cylindrical_projection,<var>x</var>,<var>y</var>,<var>z</var>,<var>r</var>,<var>rc</var>]</code>: re-projects spherical map boundaries on the cylinder of radius
<var>rc</var> and axis passing through the poles of the globe of radius <var>r</var> centered at (<var>x</var>,<var>y</var>,<var>z</var>).
<pre class="example">(%i1) load(worldmap)$
(%i2) draw3d(geomap([America_coastlines,Eurasia_coastlines],
[cylindrical_projection,2,2,2,3,4]))$
</pre>
</li><li>
<code>[conic_projection,<var>x</var>,<var>y</var>,<var>z</var>,<var>r</var>,<var>alpha</var>]</code>: re-projects spherical map boundaries on the cones of angle <var>alpha</var>,
with axis passing through the poles of the globe of radius <var>r</var> centered at (<var>x</var>,<var>y</var>,<var>z</var>). Both
the northern and southern cones are tangent to sphere.
<pre class="example">(%i1) load(worldmap)$
(%i2) draw3d(geomap(World_coastlines,
[conic_projection,0,0,0,1,90]))$
</pre></li></ul>
<p>See also <a href="http://www.telefonica.net/web2/biomates/maxima/gpdraw/geomap">http://www.telefonica.net/web2/biomates/maxima/gpdraw/geomap</a>
for more elaborated examples.
</p>
<div class=categorybox>
·
<p>@ref{Category: Package draw}
</div>
</p>
</dd></dl>
<p><a name="Item_003a-drawdf"></a>
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