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<a name="Functions-and-Variables-for-worldmap"></a>
<div class="header">
<p>
Previous: <a href="maxima_251.html#Functions-and-Variables-for-pictures" accesskey="p" rel="previous">Functions and Variables for pictures</a>, Up: <a href="maxima_248.html#draw_002dpkg" accesskey="u" rel="up">draw-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Functions-and-Variables-for-worldmap-1"></a>
<h3 class="section">53.4 Functions and Variables for worldmap</h3>
<a name="Variables-and-Functions"></a>
<h4 class="subsection">53.4.1 Variables and Functions</h4>
<a name="boundaries_005farray"></a><a name="Item_003a-draw_002fdefvr_002fboundaries_005farray"></a><dl>
<dt><a name="index-boundaries_005farray"></a>Global variable: <strong>boundaries_array</strong></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><a href="#geomap">geomap</a></code>.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-draw">Package draw</a>
·</div>
</dd></dl>
<a name="numbered_005fboundaries"></a><a name="Item_003a-draw_002fdeffn_002fnumbered_005fboundaries"></a><dl>
<dt><a name="index-numbered_005fboundaries"></a>Function: <strong>numbered_boundaries</strong> <em>(<var>nlist</var>)</em></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><div class="example">
<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>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-draw">Package draw</a>
·</div>
</dd></dl>
<a name="make_005fpoly_005fcontinent"></a><a name="Item_003a-draw_002fdeffn_002fmake_005fpoly_005fcontinent"></a><dl>
<dt><a name="index-make_005fpoly_005fcontinent"></a>Function: <strong>make_poly_continent</strong> <em><br> <tt>make_poly_continent</tt> (<var>continent_name</var>) <br> <tt>make_poly_continent</tt> (<var>country_list</var>)</em></dt>
<dd>
<p>Makes the necessary polygons to draw a colored continent
or a list of countries.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) load("worldmap")$
(%i2) /* A continent */
make_poly_continent(Africa)$
(%i3) apply(draw2d, %)$
</pre></div>
<img src="./figures/worldmap_make_poly_continent.png" alt="./figures/worldmap_make_poly_continent">
<div class="example">
<pre class="example">(%i4) /* A list of countries */
make_poly_continent([Germany,Denmark,Poland])$
(%i5) apply(draw2d, %)$
</pre></div>
<img src="./figures/worldmap_make_poly_continent2.png" alt="./figures/worldmap_make_poly_continent2">
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-draw">Package draw</a>
·</div>
</dd></dl>
<a name="make_005fpoly_005fcountry"></a><a name="Item_003a-draw_002fdeffn_002fmake_005fpoly_005fcountry"></a><dl>
<dt><a name="index-make_005fpoly_005fcountry"></a>Function: <strong>make_poly_country</strong> <em>(<var>country_name</var>)</em></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>
<div class="example">
<pre class="example">(%i1) load("worldmap")$
(%i2) make_poly_country(India)$
(%i3) apply(draw2d, %)$
</pre></div>
<img src="./figures/worldmap_make_poly_country.png" alt="./figures/worldmap_make_poly_country">
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-draw">Package draw</a>
·</div>
</dd></dl>
<a name="make_005fpolygon"></a><a name="Item_003a-draw_002fdeffn_002fmake_005fpolygon"></a><dl>
<dt><a name="index-make_005fpolygon"></a>Function: <strong>make_polygon</strong> <em>(<var>nlist</var>)</em></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 conclusion, boundary numbers
171, 173 and 1143 (in this order) are compatible and the colored
polygon can be drawn.
</p><div class="example">
<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>
<img src="./figures/worldmap_make_polygon.png" alt="./figures/worldmap_make_polygon">
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-draw">Package draw</a>
·</div>
</dd></dl>
<a name="region_005fboundaries"></a><a name="Item_003a-draw_002fdeffn_002fregion_005fboundaries"></a><dl>
<dt><a name="index-region_005fboundaries"></a>Function: <strong>region_boundaries</strong> <em>(<var>x1</var>,<var>y1</var>,<var>x2</var>,<var>y2</var>)</em></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><div class="example">
<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>
<img src="./figures/worldmap_region_boundaries.png" alt="./figures/worldmap_region_boundaries">
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-draw">Package draw</a>
·</div>
</dd></dl>
<a name="region_005fboundaries_005fplus"></a><a name="Item_003a-draw_002fdeffn_002fregion_005fboundaries_005fplus"></a><dl>
<dt><a name="index-region_005fboundaries_005fplus"></a>Function: <strong>region_boundaries_plus</strong> <em>(<var>x1</var>,<var>y1</var>,<var>x2</var>,<var>y2</var>)</em></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>
<div class="example">
<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>
<img src="./figures/worldmap_region_boundaries_plus.png" alt="./figures/worldmap_region_boundaries_plus">
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-draw">Package draw</a>
·</div>
</dd></dl>
<a name="Graphic-objects"></a>
<h4 class="subsection">53.4.2 Graphic objects</h4>
<a name="geomap"></a><a name="Item_003a-draw_002fdeffn_002fgeomap"></a><dl>
<dt><a name="index-geomap"></a>Graphic object: <strong>geomap</strong> <em><br> <tt>geomap</tt> (<var>numlist</var>) <br> <tt>geomap</tt> (<var>numlist</var>,<var>3Dprojection</var>)</em></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><a href="maxima_250.html#line_005fwidth">line_width</a></code>,
<code><a href="maxima_250.html#line_005ftype">line_type</a></code> and <code>color</code>.
</p>
<p>Examples:
</p>
<p>A simple map defined by hand:
</p><div class="example">
<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></div>
<img src="./figures/worldmap_geomap.png" alt="./figures/worldmap_geomap">
<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="https://web.archive.org/web/20100310124019/http://www-cger.nies.go.jp/grid-e/gridtxt/grid19.html">https://web.archive.org/web/20100310124019/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><div class="example">
<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></div>
<img src="./figures/worldmap_geomap2.png" alt="./figures/worldmap_geomap2">
<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><a href="#make_005fpoly_005fcountry">make_poly_country</a></code>
and <code><a href="#make_005fpoly_005fcontinent">make_poly_continent</a></code> to understand the following code.
</p><div class="example">
<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></div>
<img src="./figures/worldmap_geomap3.png" alt="./figures/worldmap_geomap3">
<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>).
<div class="example">
<pre class="example">(%i1) load("worldmap")$
(%i2) draw3d(geomap(Australia), /* default projection */
geomap(Australia,
[spherical_projection,2,2,2,3]))$
</pre></div>
<img src="./figures/worldmap_geomap4.png" alt="./figures/worldmap_geomap4">
</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>).
<div class="example">
<pre class="example">(%i1) load("worldmap")$
(%i2) draw3d(geomap([America_coastlines,Eurasia_coastlines],
[cylindrical_projection,2,2,2,3,4]))$
</pre></div>
<img src="./figures/worldmap_geomap5.png" alt="./figures/worldmap_geomap5">
</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.
<div class="example">
<pre class="example">(%i1) load("worldmap")$
(%i2) draw3d(geomap(World_coastlines,
[conic_projection,0,0,0,1,90]))$
</pre></div>
</li></ul>
<img src="./figures/worldmap_geomap6.png" alt="./figures/worldmap_geomap6">
<p>See also <a href="http://riotorto.users.sf.net/gnuplot/geomap">http://riotorto.users.sf.net/gnuplot/geomap</a>
for more elaborated examples.
</p>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-draw">Package draw</a>
·</div>
</dd></dl>
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