forked from Automating-GIS-processes/2016
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathLesson3-projections.html
470 lines (347 loc) · 24.3 KB
/
Lesson3-projections.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
<meta charset="utf-8">
<script type="text/javascript">
var _gaq = _gaq || [];
_gaq.push(['_setAccount', 'UA-88382509-1']);
_gaq.push(['_trackPageview']);
(function() {
var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
})();
</script>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Re-projecting data — GeoPython - AutoGIS 1 documentation</title>
<link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
<link rel="index" title="Index"
href="genindex.html"/>
<link rel="search" title="Search" href="search.html"/>
<link rel="top" title="GeoPython - AutoGIS 1 documentation" href="index.html"/>
<link rel="next" title="Point in Polygon & Intersect" href="Lesson3-point-in-polygon.html"/>
<link rel="prev" title="Table join" href="Lesson3-table-join.html"/>
<script src="_static/js/modernizr.min.js"></script>
</head>
<body class="wy-body-for-nav" role="document">
<div class="wy-grid-for-nav">
<nav data-toggle="wy-nav-shift" class="wy-nav-side">
<div class="wy-side-scroll">
<div class="wy-side-nav-search">
<a href="index.html" class="icon icon-home"> GeoPython - AutoGIS
<img src="_static/logo_hy_geo_135.png" class="logo" />
</a>
<div class="version">
2016 Autumn
</div>
<div role="search">
<form id="rtd-search-form" class="wy-form" action="search.html" method="get">
<input type="text" name="q" placeholder="Search docs" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
<p class="caption"><span class="caption-text">Course information</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="course-info.html">General info</a></li>
<li class="toctree-l1"><a class="reference internal" href="Installing_Anacondas_GIS.html">Installing Python + GIS</a></li>
<li class="toctree-l1"><a class="reference internal" href="License-terms.html">License and terms of usage</a></li>
</ul>
<p class="caption"><span class="caption-text">Lesson 1</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Lesson1-Intro-Python-GIS.html">Introduction to Python GIS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson1-Geometric-Objects.html">Geometric Objects - Spatial Data Model</a></li>
<li class="toctree-l1"><a class="reference internal" href="Exercise-1.html">Exercise 1</a></li>
</ul>
<p class="caption"><span class="caption-text">Lesson 2</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Lesson2-overview.html">Lesson 2 Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson2-download-data.html">Download datasets</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson2-overview-pandas-geopandas.html">Pandas and Geopandas -modules</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson2-pandas-intro.html">Introduction to Pandas</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson2-geopandas-basics.html">Introduction to Geopandas</a></li>
<li class="toctree-l1"><a class="reference internal" href="Exercise-2.html">Exercise 2</a></li>
</ul>
<p class="caption"><span class="caption-text">Lesson 3</span></p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="Lesson3-overview.html">Lesson 3 Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson3-geocoding.html">Geocoding</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson3-table-join.html">Table join</a></li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">Re-projecting data</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson3-point-in-polygon.html">Point in Polygon & Intersect</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson3-spatial-join.html">Spatial join</a></li>
<li class="toctree-l1"><a class="reference internal" href="Exercise-3.html">Exercise 3</a></li>
</ul>
<p class="caption"><span class="caption-text">Lesson 4</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Lesson4-overview.html">Lesson 4 Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson4-download-data.html">Download datasets</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson4-geometric-operations.html">Geometric operations</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson4-reclassify.html">Data reclassification</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson4-nearest-neighbour.html">Nearest Neighbour Analysis</a></li>
<li class="toctree-l1"><a class="reference internal" href="Exercise-4.html">Exercise 4</a></li>
</ul>
<p class="caption"><span class="caption-text">Lesson 5</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Lesson5-overview.html">Lesson 5 Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson5-download-data.html">Download datasets</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson5-static-maps.html">Static maps</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson5-interactive-map-bokeh.html">Interactive maps with Bokeh</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson5-share-on-github.html">Sharing interactive plots on GitHub</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson5-interactive-map-folium.html">Interactive maps on Leaflet</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson5-World-3D.html">Inspiration: World 3D</a></li>
<li class="toctree-l1"><a class="reference internal" href="Exercise-5.html">Exercise 5</a></li>
</ul>
<p class="caption"><span class="caption-text">Lesson 6</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Lesson6-overview.html">Lesson 6 Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson6-arcpy.html">Python in ArcGIS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson6-toolbox.html">ArcGIS Toolbox</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson6-arcpy-script.html">Writing arcpy scripts</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson6-run-the-tool.html">Running the Python script from ArcGIS</a></li>
</ul>
<p class="caption"><span class="caption-text">Lesson 7</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Lesson7-overview.html">Lesson 7 Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson7-download.html">Download data</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson7-read-raster.html">Reading raster files with GDAL</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson7-read-raster-array.html">Reading raster as a numerical array</a></li>
<li class="toctree-l1"><a class="reference internal" href="Lesson7-gdal-utilities.html">GDAL command line tools</a></li>
<li class="toctree-l1"><a class="reference internal" href="Exercise-7.html">Exercise 7</a></li>
</ul>
<p class="caption"><span class="caption-text">Lesson 8</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Lesson8-network-analysis.html">Network analysis in Python</a></li>
</ul>
<p class="caption"><span class="caption-text">Final Assignment</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Final-assignment.html">Final assignment</a></li>
</ul>
<p class="caption"><span class="caption-text">Map Challenge 2016</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="map-challenge.html">Map Challenge 2016</a></li>
</ul>
</div>
</div>
</nav>
<section data-toggle="wy-nav-shift" class="wy-nav-content-wrap">
<nav class="wy-nav-top" role="navigation" aria-label="top navigation">
<i data-toggle="wy-nav-top" class="fa fa-bars"></i>
<a href="index.html">GeoPython - AutoGIS</a>
</nav>
<div class="wy-nav-content">
<div class="rst-content">
<div role="navigation" aria-label="breadcrumbs navigation">
<ul class="wy-breadcrumbs">
<li><a href="index.html">Docs</a> »</li>
<li>Re-projecting data</li>
<li class="wy-breadcrumbs-aside">
<a href="https://github.com/Automating-GIS-processes/2016/blob/master/source/Lesson3-projections.rst" class="fa fa-github"> Edit on GitHub</a>
</li>
</ul>
<hr/>
</div>
<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
<div itemprop="articleBody">
<div class="section" id="re-projecting-data">
<h1>Re-projecting data<a class="headerlink" href="#re-projecting-data" title="Permalink to this headline">¶</a></h1>
<p>A map projection is a systematic transformation of the latitudes and
longitudes into a plain surface. As map projections of gis-layers are
fairly often defined differently (i.e. they do not match), it is a
common procedure to redefine the map projections to be identical in both
layers. It is important that the layers have the same projection as it
makes it possible to analyze the spatial relationships between layer,
such as conduct the Point in Polygon spatial query (which we will try
next).</p>
<p>Defining a projection and changing it is easy in Geopandas. Let’s
continue working with our <a class="reference external" href="Lesson3-geocoding.html">address points</a>, and change the
Coordinate Reference System (CRS) from WGS84 into a projection called
<a class="reference external" href="http://www.maanmittauslaitos.fi/ammattilaisille/maastotiedot/koordinaatti-korkeusjarjestelmat/karttaprojektiot-tasokoordinaatistot/tasokoordinaatistot/etrs-gkn">ETRS GK-25</a>
(EPSG:3879) which uses a Gauss-Krüger projection that is (sometimes)
used in Finland.</p>
<ul class="simple">
<li>Let’s first read the data from the Shapefile that we <a class="reference external" href="Lesson3-table-join.html">created previously</a></li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="gp">In [1]: </span><span class="kn">import</span> <span class="nn">geopandas</span> <span class="kn">as</span> <span class="nn">gpd</span>
<span class="go"># Filepath to the addresses Shapefile</span>
<span class="gp">In [2]: </span><span class="n">fp</span> <span class="o">=</span> <span class="s2">"/home/geo/addresses.shp"</span>
<span class="go"># Read data</span>
<span class="gp">In [3]: </span><span class="n">data</span> <span class="o">=</span> <span class="n">gpd</span><span class="o">.</span><span class="n">read_file</span><span class="p">(</span><span class="n">fp</span><span class="p">)</span>
</pre></div>
</div>
<ul class="simple">
<li>Let’s check what is the current CRS of our layer</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="gp">In [4]: </span><span class="n">data</span><span class="o">.</span><span class="n">crs</span>
<span class="gh">Out[4]: </span><span class="go">{'init': 'epsg:4326'}</span>
</pre></div>
</div>
<p>Okey, so it is WGS84 (i.e. EPSG: 4326).</p>
<ul class="simple">
<li>Let’s also check the values in our <code class="docutils literal"><span class="pre">geometry</span></code> column</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="gp">In [5]: </span><span class="n">data</span><span class="p">[</span><span class="s1">'geometry'</span><span class="p">]</span><span class="o">.</span><span class="n">head</span><span class="p">()</span>
<span class="gh">Out[5]: </span><span class="go"></span>
<span class="go">0 POINT (24.9301701 60.1683731)</span>
<span class="go">1 POINT (24.9418933 60.1698665)</span>
<span class="go">2 POINT (24.9774004 60.18735880000001)</span>
<span class="go">3 POINT (25.0919641 60.21448089999999)</span>
<span class="go">4 POINT (24.9214846 60.1565781)</span>
<span class="go">Name: geometry, dtype: object</span>
</pre></div>
</div>
<p>Okey, so they indeed look like lat-lon values.</p>
<ul class="simple">
<li>Let’s convert those geometries into ETRS GK-25 projection (EPSG:
3879). Changing the projection is really easy to <a class="reference external" href="http://geopandas.org/projections.html#re-projecting">do in
Geopandas</a>
with <code class="docutils literal"><span class="pre">.to_crs()</span></code> -function. As an input for the function, you
should define the column containing the geometries, i.e. <code class="docutils literal"><span class="pre">geometry</span></code>
in this case, and a <code class="docutils literal"><span class="pre">epgs</span></code> value of the projection that you want to
use.</li>
<li>Note: there is also possibility to pass the projection information as
proj4 strings or dictionaries, see more
<a class="reference external" href="http://geopandas.org/projections.html#coordinate-reference-systems">here</a></li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="go"># Let's take a copy of our layer</span>
<span class="gp">In [6]: </span><span class="n">data_proj</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="go"># Reproject the geometries by replacing the values with projected ones</span>
<span class="gp">In [7]: </span><span class="n">data_proj</span><span class="p">[</span><span class="s1">'geometry'</span><span class="p">]</span> <span class="o">=</span> <span class="n">data_proj</span><span class="p">[</span><span class="s1">'geometry'</span><span class="p">]</span><span class="o">.</span><span class="n">to_crs</span><span class="p">(</span><span class="n">epsg</span><span class="o">=</span><span class="mi">3879</span><span class="p">)</span>
</pre></div>
</div>
<ul class="simple">
<li>Let’s see how they look now</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="gp">In [8]: </span><span class="n">data_proj</span><span class="p">[</span><span class="s1">'geometry'</span><span class="p">]</span><span class="o">.</span><span class="n">head</span><span class="p">()</span>
<span class="gh">Out[8]: </span><span class="go"></span>
<span class="go">0 POINT (25496123.30852197 6672833.941567578)</span>
<span class="go">1 POINT (25496774.28242895 6672999.698581985)</span>
<span class="go">2 POINT (25498746.0795546 6674947.404346379)</span>
<span class="go">3 POINT (25505098.34340289 6677972.568484426)</span>
<span class="go">4 POINT (25495639.56049686 6671520.343245601)</span>
<span class="go">Name: geometry, dtype: object</span>
</pre></div>
</div>
<p>And here we go, the numbers have changed! Now we have successfully
changed the projection of our layer into a new one.</p>
<ul class="simple">
<li>Let’s still compare the layers visually</li>
</ul>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="c1"># Plot the WGS84</span>
<span class="n">data</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">markersize</span><span class="o">=</span><span class="mi">6</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"red"</span><span class="p">);</span>
<span class="c1"># Add title</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"WGS84 projection"</span><span class="p">);</span>
<span class="c1"># Remove empty white space around the plot</span>
<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="c1"># Plot the one with ETRS GK-25 projection</span>
<span class="n">data_proj</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">markersize</span><span class="o">=</span><span class="mi">6</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"blue"</span><span class="p">);</span>
<span class="c1"># Add title</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"ETRS GK-25 projection"</span><span class="p">);</span>
<span class="c1"># Remove empty white space around the plot</span>
<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
</pre></div>
</div>
<div class="highlight-ipython"><div class="highlight"><pre><span></span>
</pre></div>
</div>
<a class="reference internal image-reference" href="_images/wgs84.png"><img alt="_images/wgs84.png" src="_images/wgs84.png" style="width: 3.5in;" /></a>
<a class="reference internal image-reference" href="_images/projected.png"><img alt="_images/projected.png" src="_images/projected.png" style="width: 3.5in;" /></a>
<p>Indeed, they look different and our re-projected one looks much better
in Finland (not so stretced as in WGS84).</p>
<ul class="simple">
<li>Now we still need to change the crs of our GeoDataFrame into EPSG
3879 as now we only modified the values of the <code class="docutils literal"><span class="pre">geometry</span></code> column.
We can take use of fiona’s <code class="docutils literal"><span class="pre">from_epsg</span></code> -function.</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="gp">In [9]: </span><span class="kn">from</span> <span class="nn">fiona.crs</span> <span class="kn">import</span> <span class="n">from_epsg</span>
<span class="go"># Determine the CRS of the GeoDataFrame</span>
<span class="gp">In [10]: </span><span class="n">data_proj</span><span class="o">.</span><span class="n">crs</span> <span class="o">=</span> <span class="n">from_epsg</span><span class="p">(</span><span class="mi">3879</span><span class="p">)</span>
<span class="go"># Let's see what we have</span>
<span class="gp">In [11]: </span><span class="n">data_proj</span><span class="o">.</span><span class="n">crs</span>
<span class="gh">Out[11]: </span><span class="go">{'init': 'epsg:3879', 'no_defs': True}</span>
</pre></div>
</div>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">The above works for most EPSG codes but as ETRS GK-25
projection is a rather rare one, we still need to make sure
that .prj file is having correct coordinate system information. We do that by
passing a proj4 dictionary (below) into it (otherwise the <code class="docutils literal"><span class="pre">.prj</span></code> file of the Shapefile
might be empty):</p>
</div>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="go"># Pass the coordinate information</span>
<span class="gp">In [12]: </span><span class="n">data_proj</span><span class="o">.</span><span class="n">crs</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'y_0'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s1">'no_defs'</span><span class="p">:</span> <span class="bp">True</span><span class="p">,</span> <span class="s1">'x_0'</span><span class="p">:</span> <span class="mi">25500000</span><span class="p">,</span> <span class="s1">'k'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s1">'lat_0'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s1">'units'</span><span class="p">:</span> <span class="s1">'m'</span><span class="p">,</span> <span class="s1">'lon_0'</span><span class="p">:</span> <span class="mi">25</span><span class="p">,</span> <span class="s1">'ellps'</span><span class="p">:</span> <span class="s1">'GRS80'</span><span class="p">,</span> <span class="s1">'proj'</span><span class="p">:</span> <span class="s1">'tmerc'</span><span class="p">}</span>
<span class="go"># Check that it changed</span>
<span class="gp">In [13]: </span><span class="n">data_proj</span><span class="o">.</span><span class="n">crs</span>
<span class="gh">Out[13]: </span><span class="go"></span>
<span class="go">{'ellps': 'GRS80',</span>
<span class="go"> 'k': 1,</span>
<span class="go"> 'lat_0': 0,</span>
<span class="go"> 'lon_0': 25,</span>
<span class="go"> 'no_defs': True,</span>
<span class="go"> 'proj': 'tmerc',</span>
<span class="go"> 'units': 'm',</span>
<span class="go"> 'x_0': 25500000,</span>
<span class="go"> 'y_0': 0}</span>
</pre></div>
</div>
<ul class="simple">
<li>Finally, let’s save our projected layer into a Shapefile so that we
can use it later.</li>
</ul>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Ouput file path</span>
<span class="n">outfp</span> <span class="o">=</span> <span class="s2">r"/home/geo/addresses_epsg3879.shp"</span>
<span class="c1"># Save to disk</span>
<span class="n">data_proj</span><span class="o">.</span><span class="n">to_file</span><span class="p">(</span><span class="n">outfp</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
<footer>
<div class="rst-footer-buttons" role="navigation" aria-label="footer navigation">
<a href="Lesson3-point-in-polygon.html" class="btn btn-neutral float-right" title="Point in Polygon & Intersect" accesskey="n">Next <span class="fa fa-arrow-circle-right"></span></a>
<a href="Lesson3-table-join.html" class="btn btn-neutral" title="Table join" accesskey="p"><span class="fa fa-arrow-circle-left"></span> Previous</a>
</div>
<hr/>
<div role="contentinfo">
<p>
© Copyright 2016, Henrikki Tenkanen.
Last updated on Feb 20, 2017.
</p>
</div>
Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/snide/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>.
</footer>
</div>
</div>
</section>
</div>
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT:'./',
VERSION:'1',
COLLAPSE_INDEX:false,
FILE_SUFFIX:'.html',
HAS_SOURCE: true
};
</script>
<script type="text/javascript" src="_static/jquery.js"></script>
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/javascript" src="_static/js/theme.js"></script>
<script type="text/javascript">
jQuery(function () {
SphinxRtdTheme.StickyNav.enable();
});
</script>
<li><a href="http://project.invalid/">Project Homepage</a> »</li>
<div class="footer">
<img src="../img/GPLv3_Logo.svg">
</div>
</body>
</html>