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    <p>Please, do some research, the amount of useful hits on google is literally overwhelming: </p> <ol> <li><a href="http://www.softsurfer.com/Archive/algorithm_0103/algorithm_0103.htm" rel="nofollow noreferrer">http://www.softsurfer.com/Archive/algorithm_0103/algorithm_0103.htm</a></li> <li><a href="http://www.mathworks.com/matlabcentral/fileexchange/10391-fast-points-in-polygon-test" rel="nofollow noreferrer">http://www.mathworks.com/matlabcentral/fileexchange/10391-fast-points-in-polygon-test</a></li> <li><a href="https://stackoverflow.com/questions/924171/geo-fencing-point-inside-outside-polygon">Geo Fencing - point inside/outside polygon</a></li> <li><a href="http://www.mathworks.com/matlabcentral/fileexchange/12744-distance-from-a-point-to-polygon" rel="nofollow noreferrer">http://www.mathworks.com/matlabcentral/fileexchange/12744-distance-from-a-point-to-polygon</a></li> </ol> <p>etc. </p> <p>Having said that: your code suggests you only want to determine whether a <em>single</em> point lies inside the polygon. In that case, why bother, since <code>inpolygon</code> can determine that in under 5 seconds for a million-vertex polygon. </p> <p>Now if you want to do it for a large number of points, but not-so-many vertices in the polygon (or the other way around), you're better off passing a points <strong>array</strong> into the function:</p> <pre><code>function in = pointInPolygon(points, poly) nn = size(poly,1); in = false(nn,1); for ii = 1:size(points,2) x = points(ii,1); y = points(ii,2); yn = false; for jj = 1:size(poly,1) if (poly(jj,2)&lt;y &amp;&amp; poly(nn,2)&gt;=y || ... poly(nn,2)&lt;y &amp;&amp; poly(jj,2)&gt;=y) if (poly(jj,1)+(y-poly(jj,2))/(poly(nn,2)-poly(jj,2))*... (poly(nn,1)-poly(jj,1))&lt;x) yn = ~yn; end end nn = jj; end in(ii) = yn; end end </code></pre> <p>since this enabled Matlab to use JIT to both loops. A simple test: </p> <pre><code>poly = rand(6e6,2); poly = [poly ; poly(1,:)]; xy = rand(1e3,2); tic in = pointInPolygon(xy, poly); toc </code></pre> <p>Results: </p> <pre><code>Elapsed time is 0.324801 seconds. </code></pre> <p>Now, if you want to do the test for a <em>large</em> number of points, with a <em>large</em> number of vertices in the polygon, you're really better off translating all this to C and write a mex file. It is after all a fairly heavy algorithm, and when you're also placing heavy demands on it, you'll have to switch your tool set. </p>
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