<story><title>What&apos;s the Most Concave State in the U.S.? Using R to Solve a Geography Puzzle</title><url>http://news.rapgenius.com/Atodd-whats-the-most-concave-state-in-the-us-using-r-to-solve-a-geography-puzzle-lyrics</url><text></text></story><parent_chain><item><author>epi8</author><text>Any idea whether this depends on the projection used to get the map in the first place? I mean, the &amp;quot;straight lines&amp;quot; are really curves that lie in the boundary of the Earth&amp;#x27;s surface,  unless I&amp;#x27;m missing something major.</text></item></parent_chain><comment><author>homeomorphic</author><text>It doesn&amp;#x27;t matter. He&amp;#x27;s counting the number of times a continuous curve C on the surface of the Earth crosses other continuous curves (state boundaries). A crossing is a property of the curve and its embedding onto the Earth&amp;#x27;s surface. While a (continuous) map projection can deform both C and the state boundaries, it cannot create or destroy crossings.&lt;p&gt;To &lt;i&gt;draw&lt;/i&gt; the crossings, however, he needs to pick a projection and project both C and the state boundaries, which I guess is why he included some PROJ.4 calls.</text></comment>
<story><title>What&apos;s the Most Concave State in the U.S.? Using R to Solve a Geography Puzzle</title><url>http://news.rapgenius.com/Atodd-whats-the-most-concave-state-in-the-us-using-r-to-solve-a-geography-puzzle-lyrics</url><text></text></story><parent_chain><item><author>epi8</author><text>Any idea whether this depends on the projection used to get the map in the first place? I mean, the &amp;quot;straight lines&amp;quot; are really curves that lie in the boundary of the Earth&amp;#x27;s surface,  unless I&amp;#x27;m missing something major.</text></item></parent_chain><comment><author>adolgert</author><text>That&amp;#x27;s an excellent question. Latitude and longitude are straight in the projection he is most likely using, but great circle arcs are what we consider straight on the globe. The kicker is that most political boundaries are neither. They are Rhumb lines, aka loxodromes, which mean that someone started walking in a direction and kept going.&lt;p&gt;The standard solution for this is to put lots of little points into the state GIS definition, so that the points get transformed correctly. That way short line segments don&amp;#x27;t differ by more than a few meters. That means you have to watch out for simplified state representations, but not much else, unless you&amp;#x27;re being a stickler.</text></comment>