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<div class="section" id="point-in-polygon-intersect">
<h1>Point in Polygon & Intersect<a class="headerlink" href="#point-in-polygon-intersect" title="Permalink to this headline">¶</a></h1>
<p>Finding out if a certain point is located inside or outside of an area,
or finding out if a line intersects with another line or polygon are
fundamental geospatial operations that are often used e.g. to select
data based on location. Such spatial queries are one of the typical
first steps of the workflow when doing spatial analysis. Performing a
spatial join (will be introduced later) between two spatial datasets is
one of the most typical applications where Point in Polygon (PIP) query
is used.</p>
<p><strong>Sources</strong></p>
<p>Following materials are partly based on documentation of <a class="reference external" href="http://toblerity.org/shapely/manual.html">Shapely</a>, <a class="reference external" href="http://geopandas.org/geocoding.html">Geopandas</a> and <a class="reference external" href="https://www.packtpub.com/application-development/learning-geospatial-analysis-python">Lawhead, J. (2013), Chapters I and V</a>.</p>
<div class="section" id="how-to-check-if-point-is-inside-a-polygon">
<h2>How to check if point is inside a polygon?<a class="headerlink" href="#how-to-check-if-point-is-inside-a-polygon" title="Permalink to this headline">¶</a></h2>
<p>Computationally, detecting if a point is inside a polygon is most
commonly done using a specific formula called <a class="reference external" href="https://en.wikipedia.org/wiki/Point_in_polygon#Ray_casting_algorithm">Ray Casting
algorithm</a>.
Luckily, we do not need to create such a function ourselves for
conducting the Point in Polygon (PIP) query. Instead, we can take
advantage of <a class="reference external" href="http://toblerity.org/shapely/manual.html#binary-predicates">Shapely’s binary
predicates</a>
that can evaluate the topolocical relationships between geographical
objects, such as the PIP as we’re interested here.</p>
<p>There are basically two ways of conducting PIP in Shapely:</p>
<ol class="arabic simple">
<li>using a function called
<a class="reference external" href="http://toblerity.org/shapely/manual.html#object.within">.within()</a>
that checks if a point is within a polygon</li>
<li>using a function called
<a class="reference external" href="http://toblerity.org/shapely/manual.html#object.contains">.contains()</a>
that checks if a polygon contains a point</li>
</ol>
<p>Notice: even though we are talking here about <strong>Point</strong> in Polygon
operation, it is also possible to check if a LineString or Polygon is
inside another Polygon.</p>
<ul class="simple">
<li>Let’s first create a Polygon using a list of coordinate-tuples and a
couple of Point objects</li>
</ul>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">shapely.geometry</span> <span class="k">import</span> <span class="n">Point</span><span class="p">,</span> <span class="n">Polygon</span>
<span class="c1"># Create Point objects</span>
<span class="n">p1</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mf">24.952242</span><span class="p">,</span> <span class="mf">60.1696017</span><span class="p">)</span>
<span class="n">p2</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mf">24.976567</span><span class="p">,</span> <span class="mf">60.1612500</span><span class="p">)</span>
<span class="c1"># Create a Polygon</span>
<span class="n">coords</span> <span class="o">=</span> <span class="p">[(</span><span class="mf">24.950899</span><span class="p">,</span> <span class="mf">60.169158</span><span class="p">),</span> <span class="p">(</span><span class="mf">24.953492</span><span class="p">,</span> <span class="mf">60.169158</span><span class="p">),</span> <span class="p">(</span><span class="mf">24.953510</span><span class="p">,</span> <span class="mf">60.170104</span><span class="p">),</span> <span class="p">(</span><span class="mf">24.950958</span><span class="p">,</span> <span class="mf">60.169990</span><span class="p">)]</span>
<span class="n">poly</span> <span class="o">=</span> <span class="n">Polygon</span><span class="p">(</span><span class="n">coords</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="go"># Let's check what we have</span>
<span class="gp">In [1]: </span><span class="k">print</span><span class="p">(</span><span class="n">p1</span><span class="p">)</span>
<span class="go">POINT (24.952242 60.1696017)</span>
<span class="gp">In [2]: </span><span class="k">print</span><span class="p">(</span><span class="n">p2</span><span class="p">)</span>
<span class="go"> POINT (24.976567 60.16125)</span>
<span class="gp">In [3]: </span><span class="k">print</span><span class="p">(</span><span class="n">poly</span><span class="p">)</span>
<span class="go"> POLYGON ((24.950899 60.169158, 24.953492 60.169158, 24.95351 60.170104, 24.950958 60.16999, 24.950899 60.169158))</span>
</pre></div>
</div>
<ul class="simple">
<li>Let’s check if those points are <code class="docutils literal"><span class="pre">within</span></code> the polygon</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="go"># Check if p1 is within the polygon using the within function</span>
<span class="gp">In [4]: </span><span class="n">p1</span><span class="o">.</span><span class="n">within</span><span class="p">(</span><span class="n">poly</span><span class="p">)</span>
<span class="gh">Out[4]: </span><span class="go">True</span>
<span class="go"># Check if p2 is within the polygon</span>
<span class="gp">In [5]: </span><span class="n">p2</span><span class="o">.</span><span class="n">within</span><span class="p">(</span><span class="n">poly</span><span class="p">)</span>
<span class="go"> Out[5]: False</span>
</pre></div>
</div>
<p>Okey, so we can see that the first point seems to be inside that polygon
and the other one doesn’t.</p>
<ul class="simple">
<li>In fact, the first point is close to the center of the polygon as we
can see:</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="go"># Our point</span>
<span class="gp">In [6]: </span><span class="k">print</span><span class="p">(</span><span class="n">p1</span><span class="p">)</span>
<span class="go">POINT (24.952242 60.1696017)</span>
<span class="go"># The centroid</span>
<span class="gp">In [7]: </span><span class="k">print</span><span class="p">(</span><span class="n">poly</span><span class="o">.</span><span class="n">centroid</span><span class="p">)</span>
<span class="go"> POINT (24.95224242849236 60.16960179038188)</span>
</pre></div>
</div>
<ul class="simple">
<li>It is also possible to do PIP other way around, i.e. to check if
polygon contains a point:</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="go"># Does polygon contain p1?</span>
<span class="gp">In [8]: </span><span class="n">poly</span><span class="o">.</span><span class="n">contains</span><span class="p">(</span><span class="n">p1</span><span class="p">)</span>
<span class="gh">Out[8]: </span><span class="go">True</span>
<span class="go"># Does polygon contain p2?</span>
<span class="gp">In [9]: </span><span class="n">poly</span><span class="o">.</span><span class="n">contains</span><span class="p">(</span><span class="n">p2</span><span class="p">)</span>
<span class="go"> Out[9]: False</span>
</pre></div>
</div>
<p>Thus, both ways of checking the spatial relationship results in the same way.</p>
<p>Which one should you use then? Well, it depends:</p>
<ul>
<li><p class="first">if you have many points and just one polygon and you try to find out
which one of them is inside the polygon:</p>
<ul class="simple">
<li>you need to iterate over the points and check one at a time if it
is <strong>within()</strong> the polygon specified</li>
</ul>
</li>
<li><p class="first">if you have many polygons and just one point and you want to find out
which polygon contains the point</p>
<blockquote>
<div><ul class="simple">
<li>you need to iterate over the polygons until you find a polygon that
<strong>contains()</strong> the point specified (assuming there are no overlapping
polygons)</li>
</ul>
</div></blockquote>
</li>
</ul>
</div>
<div class="section" id="intersect">
<h2>Intersect<a class="headerlink" href="#intersect" title="Permalink to this headline">¶</a></h2>
<p>Another typical geospatial operation is to see if a geometry
<a class="reference external" href="http://toblerity.org/shapely/manual.html#object.intersects">intersect</a>
or <a class="reference external" href="http://toblerity.org/shapely/manual.html#object.touches">touches</a>
another one. The difference between these two is that:</p>
<ul class="simple">
<li>if objects intersect, the boundary and interior of an object needs to
intersect in any way with those of the other.</li>
<li>If an object touches the other one, it is only necessary to have (at
least) a single point of their boundaries in common but their
interiors shoud NOT intersect.</li>
</ul>
<p>Let’s try these out.</p>
<ul class="simple">
<li>Let’s create two LineStrings</li>
</ul>
<div class="code python highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">shapely.geometry</span> <span class="k">import</span> <span class="n">LineString</span><span class="p">,</span> <span class="n">MultiLineString</span>
<span class="c1"># Create two lines</span>
<span class="n">line_a</span> <span class="o">=</span> <span class="n">LineString</span><span class="p">([(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)])</span>
<span class="n">line_b</span> <span class="o">=</span> <span class="n">LineString</span><span class="p">([(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">)])</span>
</pre></div>
</div>
<ul class="simple">
<li>Let’s see if they intersect</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="gp">In [10]: </span><span class="n">line_a</span><span class="o">.</span><span class="n">intersects</span><span class="p">(</span><span class="n">line_b</span><span class="p">)</span>
<span class="gh">Out[10]: </span><span class="go">True</span>
</pre></div>
</div>
<ul class="simple">
<li>Do they also touch each other?</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="gp">In [11]: </span><span class="n">line_a</span><span class="o">.</span><span class="n">touches</span><span class="p">(</span><span class="n">line_b</span><span class="p">)</span>
<span class="gh">Out[11]: </span><span class="go">True</span>
</pre></div>
</div>
<p>Indeed, they do and we can see this by plotting the features together</p>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="go"># Create a MultiLineString</span>
<span class="gp">In [12]: </span><span class="n">multi_line</span> <span class="o">=</span> <span class="n">MultiLineString</span><span class="p">([</span><span class="n">line_a</span><span class="p">,</span> <span class="n">line_b</span><span class="p">])</span>
<span class="gp">In [13]: </span><span class="n">multi_line</span><span class="p">;</span>
</pre></div>
</div>
<img alt="_images/Lesson3-point-in-polygon_16_0.svg" src="_images/Lesson3-point-in-polygon_16_0.svg" /><p>Thus, the <code class="docutils literal"><span class="pre">line_b</span></code> continues from the same node ( (1,1) ) where <code class="docutils literal"><span class="pre">line_a</span></code> ends.</p>
<p>However, if the lines overlap fully, they don’t touch due to the spatial relationship rule, as we can see:</p>
<ul class="simple">
<li>Check if line_a touches itself</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="go"># Does the line touch with itself?</span>
<span class="gp">In [14]: </span><span class="n">line_a</span><span class="o">.</span><span class="n">touches</span><span class="p">(</span><span class="n">line_a</span><span class="p">)</span>
<span class="gh">Out[14]: </span><span class="go">False</span>
</pre></div>
</div>
<ul class="simple">
<li>It does not. However, it does intersect</li>
</ul>
<div class="highlight-ipython"><div class="highlight"><pre><span></span><span class="go"># Does the line intersect with itself?</span>
<span class="gp">In [15]: </span><span class="n">line_a</span><span class="o">.</span><span class="n">intersects</span><span class="p">(</span><span class="n">line_a</span><span class="p">)</span>
<span class="gh">Out[15]: </span><span class="go">True</span>
</pre></div>
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