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<!DOCTYPE html>
<html lang="en-US">
<head>
<script async src="https://www.googletagmanager.com/gtag/js?id=UA-2029009-3"></script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag() { dataLayer.push(arguments); }
gtag('js', new Date());
gtag('config', 'UA-2029009-3');
</script>
<meta charset='utf-8'>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>I Hate Coordinate Systems!</title>
<link rel="icon" href="favicon16.svg" sizes="16x16" />
<link rel="icon" href="favicon32.svg" sizes="32x32" />
<link rel="stylesheet" type="text/css" media="screen" href="styles.css">
<script>
function lookupProjections() {
var lng = document.getElementById("lookup_lng").value;
var lat = document.getElementById("lookup_lat").value;
var x = document.getElementById("lookup_x").value;
var y = document.getElementById("lookup_y").value;
document.getElementById("projectionLoookupLoading").style.display = 'inherit';
if (![lng, lat, x, y].every((str) => { return !isNaN(str) && !isNaN(parseFloat(str)) })) {
document.getElementById("projectionLoookupLoadingText").innerHTML = "Please provide all four parameters.";
return false;
}
document.getElementById("projectionLookupButton").disabled = true;
document.getElementById("projectionLoookupLoadingText").innerHTML = "Searching for projections... (this can take up to 30 seconds)";
var url = `https://us-east1-ihatecoordinatesystems.cloudfunctions.net/projection_lookup_1?lng=${lng}&lat=${lat}&x=${x}&y=${y}`;
fetch(url)
.then(response => response.json())
.then(data => {
document.getElementById("projectionLookupButton").disabled = false;
if (data.error || data.projections.length == 0) {
document.getElementById("projectionLoookupLoadingText").innerHTML = "No results found!";
return;
}
document.getElementById("projectionLoookupLoading").style.display = 'none';
var table = document.getElementById("projectionLookupResults");
while (table.childElementCount > 1) {
table.removeChild(table.lastChild);
}
data.projections.forEach(element => {
var tr = document.createElement('tr');
tr.innerHTML = '<td style="padding-right:0.5em;">' + element.projection + '</td>' +
'<td style="padding-right:0.5em;">' + element.name + '</td>' +
'<td style="text-align:right;">' + element.distance.toFixed(2) + '</td>';
table.appendChild(tr);
});
table.style.display = 'inherit';
});
return false;
}
</script>
</head>
<body>
<div class="max-width">
<div id="header">
<h2 id="title" class="center"><a href="#">🤬 I Hate Coordinate Systems! 🤬</a></h2>
<p>
Coordinate reference systems (CRSs) are a thorn in the side of many geospatial professionals. It's easy
to get by when things are working, but if there's a problem it's hard to even know what to search for.
</p>
<p>
This is a <span class="bold">problem-based guide</span class="bold"> of common CRS issues, root
causes, and solutions.
</p>
</div>
<div id="contents">
<ul style="padding: 0;">
<li><a href="#mental-model">How do I wrap my head around these things?</a></li>
<li><a href="#null-island">My dataset is off the coast of Africa!</a></li>
<li><a href="#incorrectly-gcs">My dataset looks like it's bigger than the Earth!</a></li>
<li><a href="#wrong-crs">My dataset is not located where it should be!</a></li>
<li><a href="#correct-crs">What coordinate system should my dataset be in?</a></li>
<li><a href="#wrong-gcs">My dataset is slightly offset from where it should be!</a></li>
<li><a href="#redefine">How do I redefine a dataset's coordinate system?</a></li>
<li><a href="#not-equidistant">My measurements are bigger or smaller than they should be!</a></li>
<li><a href="#why-mercator">Why is Mercator used if it's so distorted?</a></li>
<li><a href="#why-project">Why don't we always use longitude/latitude?</a></li>
<li><a href="#ellipsoidal-vs-orthometric">My X- and Y-values are OK, but my Z-values (heights,
elevations) are off!</a></li>
<li><a href="#glossary">What do all these terms mean?</a></li>
</ul>
</div>
<div id="mental-model">
<h2><a href="#mental-model">I hate coordinate systems! How do I wrap my head around these things?</a></h2>
<p><span class="bold">Apply this three-part mental model of geospatial datasets.</span> Many common problems
happen when one of these parts is missing or out of sync.</p>
<div class="partlist">
<p>
<span class="part1"><span class="bold">Attributes</span>: the meanings or labels of a data
point.</span>
</p>
<p>
<span class="part2"><span class="bold">Coordinates</span>: numbers describing the data
point's position in space.</span>
</p>
<p>
<span class="part3"><span class="bold">Coordinate (reference) system</span>: metadata
describing the space itself: origin, axes, units, etc.</span>
</p>
</div>
<p>For example:</p>
<div class="partlist">
<p>
<span class="part1"><span class="bold">Attributes</span>: "The White House" or "1600
Pennsylvania Avenue"</span>
</p>
<p>
<span class="part2"><span class="bold">Coordinates</span>: (-77.0367, 38.8976)</span>
</p>
<p>
<span class="part3"><span class="bold">Coordinate (reference) system</span>: WGS84
longitude,latitude</span>
</p>
</div>
</div>
<div id="null-island">
<h2><a href="#null-island">I hate coordinate systems! My dataset is off the coast of Africa!</a>
</h2>
<p>
<span class="bold">
Your dataset probably has some junk <span class="part2">coordinates</span>.
</span>
Many data formats store "null" as zeroes. If your software is assuming a longitude/latitude geographic
<span class="part3">coordinate system</span> (GCS), then the point with <span
class="part2">coordinates</span> (0, 0) is where the equator crosses the prime meridian off the
coast of Africa (humorously known as <a href="https://en.wikipedia.org/wiki/Null_Island"
target="_blank">Null Island</a>). This can sometimes happen when importing from Excel and empty rows
are not trimmed off.
</p>
<img src="images/null_island.png" width="100%">
<p>
<span class="bold">Solution:</span> Remove the data points from your dataset whose <span
class="part2">coordinates</span> are null.
</p>
</div>
<div id="incorrectly-gcs">
<h2><a href="#incorrectly-gcs">I hate coordinate systems! My dataset looks like it's bigger than
the Earth!</a></h2>
<p>
<span class="bold">
Your dataset probably has its <span class="part3">coordinate system</span> wrongly defined as a
longitude/latitude geographic coordinate system (GCS).
</span>
This can happen if the coordinate system is missing altogether, in which case GIS software often assumes
a GCS without telling you. A GCS only ranges from -180° west to +180° east in the X-axis and
-90° south to +90 north in the Y-axis. If the <span class="part2">coordinates</span> in your dataset are
out of this range then your dataset will look like it's off of the Earth.
</p>
<p>
<span class="bold">Solution:</span> <a href="#redefine">Redefine the coordinate system</a>, i.e. change
the <span class="part3">coordinate system</span> but not the <span class="part2">coordinates</span>,
from the GCS to the <a href="#correct-crs">correct coordinate system</a>.
</p>
</div>
<div id="wrong-crs">
<h2><a href="#wrong-crs">I hate coordinate systems! My dataset is not located where it should
be!</a>
</h2>
<p>
<span class="bold">
Your dataset probably has the wrong <span class="part3">coordinate system</span>.
</span> This is the more general case of the previous problem. This can happen if the coordinate system
is missing altogether, in which case GIS software often assumes that it is the same coordinate system as
a previously loaded dataset, or the coordinate system set in the "project" or "map document".
</p>
<p>
<span class="bold">Solution:</span> <a href="#redefine">Redefine the coordinate system</a>, i.e. change
the <span class="part3">coordinate system</span> but not the <span class="part2">coordinates</span>,
to the <a href="#correct-crs">correct coordinate system</a>.
</p>
</div>
<div id="correct-crs">
<h2><a href="#correct-crs">I hate coordinate systems! What coordinate system should my dataset be in?</a>
</h2>
<p>
<span class="bold">
Look at the two things you do know: the <span class="part1">attributes</span> and the <span
class="part2">coordinates</span>.
</span>
A data point's <span class="part1">attributes</span> gives context to where on the Earth it is located.
Most GIS software will display the minimum and maximum <span class="part2">coordinates</span> in the
layer's properties as "extent" or "bounding box". From these, do some detective work on the <span
class="part3">coordinate system</span> which you should use when <a href="#redefine">redefining</a>
your dataset.
</p>
<p class="solutions"><span class="bold">Solutions:</span></p>
<ul class="solutions">
<li>
If the <span class="part1">attributes</span> indicate the approximate longitude,latitude where the
<span class="part2">coordinates</span> <span class="italic">should</span> be located, try doing a
reverse lookup. This iterates over every well-defined <span class="part3">coordinate system</span>,
unprojects the X,Y <span class="part2">coordinates</span> to WGS84, and measures the error to the
known longitude,latitude. Errors less than a few hundred meters denote a reasonable projection,
though this isn't precise enough to <a href="#wrong-gcs">determine the GCS</a>. You can run
<a href="https://github.com/dmahr1/ihatecoordinatesystems/blob/master/lookup.py">this sample
code</a> yourself, or use this form:
</li>
<form onsubmit="return lookupProjections()" action="javascript:void(0);">
<table style="padding: 0.5em;width:100%;font-size:90%;">
<colgroup>
<col span="1" style="width: 18%;">
<col span="1" style="width: 20%;">
<col span="1" style="width: 18%;">
<col span="1" style="width: 20%;">
<col span="1" style="width: 20%;">
</colgroup>
<tbody>
<tr>
<td style="text-align:right;"><label for="lookup_lng">Longitude:</label></td>
<td><input style="width:90%;" type="number" step="any" id="lookup_lng"
name="lookup_lng"></td>
<td style="text-align:right;"><label for="lookup_lat">Latitude:</label></td>
<td><input style="width:90%;" type="number" step="any" id="lookup_lat"
name="lookup_lat"><br></td>
<td></td>
</tr>
<tr>
<td style="text-align:right;"><label for="lookup_x">X-coordinate:</label></td>
<td><input style="width:90%;" type="number" step="any" id="lookup_x" name="lookup_x">
</td>
<td style="text-align:right;"><label for="lookup_y">Y-coordinate:</label></td>
<td><input style="width:90%;" type="number" step="any" id="lookup_y" name="lookup_y">
</td>
<td><input style="width:70%;" id="projectionLookupButton" type="submit" value="Submit">
</td>
</tr>
</tbody>
</table>
</form>
<p id="projectionLoookupLoading" style="display:none;text-align:center;">
<span id="projectionLoookupLoadingText" class="bold italic"></span>
</p>
<table id="projectionLookupResults" style="display:none;padding:0.5em;font-size:80%;">
<tr>
<td><span class="bold">Code</span></td>
<td><span class="bold">Name</span></td>
<td style="text-align:right;"><span class="bold">Error (meters)</span></td>
</tr>
</table>
<li>
If the <span class="part2">coordinates</span> have X-values between -180 and 180, and Y-values
between -90 and 90, then you probably want to <a href="#redefine">redefine</a> to a
longitude,latitude geographic <span class="part3">coordinate system</span> (GCS) like WGS84.
</li>
<li>
If the <span class="part2">coordinates</span> have large absolute values, try <a
href="#redefine">redefining</a> to a local <span class="part3">coordinate system</span> like
UTM, Gauss-Krüger, State Plane, or a national grid. Also consider trying neighboring zones, e.g. if
UTM Zone 19N is wrong, try UTM Zone 18N.
</li>
<li>
If the <span class="part1">attributes</span> suggest the dataset is in the USA, then there might a
problem converting to/from <img src="images/flag-usa.png" class="flag"> Freedom Units <img
src="images/flag-usa.png" class="flag">. Try multiplying/dividing a data point's <span
class="part2">coordinates</span> by 3.28084 to convert feet to meters/meters to feet and see if
that places it in the proper location.
</li>
<li>
If the minimum X/Y <span class="part2">coordinates</span> are both zero and the maxmimum X/Y <span
class="part2">coordinates</span> are both positive, then the dataset may have been exported from
non-geospatial software like Photoshop or Illustrator or Inkscape. This is especially likely if the
dataset is flipped vertically since those editors typically have the Y-axis increasing going down.
You will need to manually georeference the dataset to use it, which changes both the <span
class="part2">coordinates</span> and the <span class="part3">coordinate system</span>.
</li>
</ul>
</div>
<div id="wrong-gcs">
<h2><a href="#wrong-gcs">I hate coordinate systems! My dataset is slightly offset from where it
should be!</a></h2>
<p>
<span class="bold">Your dataset probably has the wrong longitude/latitude geographic <span
class="part3">coordinate system</span> (GCS)</span>. Different GCSs define slightly different
sizes/shapes of the Earth (their ellipsoids) and different positionings on the Earth (their
datums). As a result, the same longitude/latitude <span class="part2">coordinates</span> in two
different GCSs can appear offset, although typically within tens of meters of each other. This can
happen even if you are using a projected coordinate system (PCS) whose units are not degrees of
longitude/latitude since PCSs have a GCS embedded within them. <img src="images/wrong-gcs.png"
width="100%">
<p class="solutions"><span class="bold">Solution:</span><a href="#redefine"> Redefine the coordinate
system</a>, i.e. change the <span class="part3">coordinate system</span> but not the <span
class="part2">coordinates</span>, to one of the following
</p>
<ul class="solutions">
<li>Try redefining to the WGS84 GCS.</li>
<li>If your dataset was collected with GPS <img src="images/flag-usa.png" class="flag">, try redefining
to WGS84.</li>
<li>If your dataset was collected with GLONASS <img src="images/flag-ru.png" class="flag">, try
redefining to PZ-90.</li>
<li>If your dataset was collected with Galileo <img src="images/flag-eu.png" class="flag">, try
redefining to ITRF.</li>
<li>If your dataset is in the USA <img src="images/flag-usa.png" class="flag">, try redefining to NAD27,
NAD83, or WGS84.</li>
<li>If your dataset is in Europe <img src="images/flag-eu.png" class="flag">, try redefining to ED50,
ETRS89, or WGS84.</li>
<li>If your dataset is in Australia <img src="images/flag-au.png" class="flag">, try redefining to GDA94
or GDA2020.</li>
<li>If your dataset is in China <img src="images/flag-cn.png" class="flag"> and/or collected with
BeiDou, <a
href="https://en.wikipedia.org/wiki/Restrictions_on_geographic_data_in_China#Coordinate_systems"
target="_blank">good
luck</a>.</li>
</ul>
</div>
<div id="redefine">
<h2><a href="#redefine">I hate coordinate systems! How do I redefine a dataset's coordinate system?</a></h2>
<p>
<span class="bold">
It depends on your software.
</span>
Remember, redefining means the metadata about the <span class="part3">coordinate system</span> is
modified but the
<span class="part2">coordinates</span> are not. This contrasts with reprojections and transformations,
which modify both the <span class="part3">coordinate system</span> and the <span
class="part2">coordinates</span>.
</p>
<p class="solutions"><span class="bold">Solutions:</span></p>
<ul class="solutions">
<li>In ArcGIS Pro, use the <a
href="https://pro.arcgis.com/en/pro-app/tool-reference/data-management/define-projection.htm"
target="_blank">Define
Projection tool</a>, <span class="italic">not</span> the Project tool.</li>
<li>In ArcMap, use the <a
href="https://desktop.arcgis.com/en/arcmap/latest/tools/data-management-toolbox/define-projection.htm"
target="_blank">Define
Projection tool</a>, <span class="italic">not</span> the Project tool.</li>
<li>In QGIS, for vector datasets, use the <a
href="https://docs.qgis.org/latest/en/docs/user_manual/processing_algs/qgis/vectorgeneral.html#assign-projection"
target="_blank">Assign
Projection tool</a> in the Vector General toolset, <span class="italic">not</span> the
Reproject Layer tool.</li>
<li>In QGIS, for raster datasets, use the <a
href="https://docs.qgis.org/latest/en/docs/user_manual/processing_algs/gdal/rasterprojections.html#assign-projection"
target="_blank">Assign
Projection</a> tool in the "GDAL" toolset, <span class="italic">not</span> the Warp (Reproject)
tool.</li>
<li>From the command line, for vector datasets, use <a
href="https://gdal.org/programs/ogr2ogr.html#cmdoption-ogr2ogr-a_srs" target="_blank"><span
class="mono">ogr2ogr</span> with the <span class="mono">-a_srs</span>
parameter</a>, <span class="italic">not</span> the <span class="mono">-t_srs</span> parameter.
</li>
<li>From the command line, for raster datasets, use <a
href="https://gdal.org/programs/gdal_edit.html#cmdoption-a_srs" target="_blank"><span
class="mono">gdal_edit.py</span> with the <span class="mono">-a_srs</span>
parameter</a>.
</li>
</ul>
</div>
<div id="not-equidistant">
<h2><a href="#not-equidistant">I hate coordinate systems! My measurements are bigger or smaller than they
should be!</a></h2>
<p>
<span class="bold">
Your dataset is probably in a non-equidistant <span class="part3">coordinate system</span>.
</span> Most GIS software stupidly calculates distances, areas, and volumes using Euclidean math in
the dataset's or data frame's <span class="part3">coordinate system</span>, <span
class="italic">regardless</span> of whether it is
equidistant. Depending on the amount of distortion associated with the projection, this can lead to
(wildly) incorrect measurements without you realizing. In the common case of the Mercator projection,
distances are enlarged by about <span class="mono">1/cos(latitude)</span>.
</p>
<p class="solutions"><span class="bold">Solutions:</span></p>
<ul class="solutions">
<li>Reproject your dataset (changing both the <span class="part2">coordinates</span> and <span
class="part3">coordinate system</span>) to an appropriate "local" <span class="part3">coordinate
system</span>. A local coordinate system is tuned to offer very accurate Euclidean measurements
for a constrained region of the Earth. Examples include UTM, Gauss-Krüger, State Plane, and
equidistant national grids like the Equidistant Conic.</li>
<li>Perform geodesic measurements. This unprojects the <span class="part2">coordinates</span> to
longitude/latitude (if projected) and then calculates precise distance along the GCS's ellipsoid.
But beware: each calculation is slower than the Euclidean version, and the improvement in accuracy
is marginal versus a local <span class="part3">coordinate </span> (the previous solution) unless you
require sub-centimeter accuracy. This is done by default in <a
href="https://docs.qgis.org/latest/en/docs/user_manual/introduction/general_tools.html#measuring"
target="_blank">QGIS</a>, can be enabled in <a
href="https://pro.arcgis.com/en/pro-app/help/mapping/navigation/measure.htm"
target="_blank">ArcGIS Pro</a> and <a
href="https://desktop.arcgis.com/en/arcmap/latest/map/working-with-layers/measuring-distances-and-areas.htm"
target="_blank">ArcMap</a>, and can be performed programmatically with open-source libraries
like <a href="https://geographiclib.sourceforge.io/" target="_blank">GeographicLib</a>.
</li>
</ul>
</div>
<div id="why-mercator">
<h2><a href="#why-mercator">I hate coordinate systems! Why is Mercator ever used if it's so distorted?</a>
</h2>
<p>
<span class="bold">Mercator is the only <span class="italic">conformal</span> cylindrical map
projection.</span> Cylindrical map projections mean the whole Earth fits into a rectangle,
which is very convenient for data processing algorithms that are used to working with rectangular
images. Conformal means that angles and shapes are always preserved: north is always up, squares are
always square, etc. Using a non-conformal projection would make things look stretched, squashed, and/or
rotated when zooming in.
</p>
<img src="images/mercator.jpg" width="100%" style="border: 0; display: block; opacity: 0.9;">
<table
style="width: 100%; text-align: center; border: 2px solid #4e4e4e;margin: 0; border-top: 0; padding: 0; border-spacing: 0;">
<colgroup>
<col style="width: 33%">
<col style="width: 34%">
<col style="width: 33%">
</colgroup>
<tbody>
<tr>
<td><span class="bold">Mercator (cylindrical)</span></td>
<td style="border-left: 2px solid #4e4e4e; border-right: 2px solid #4e4e4e"><span
class="bold">Lambert Cylindrical</span></td>
<td><span class="bold">Albers Conic</span></td>
</tr>
<tr>
<td>✅ Shape</td>
<td style="border-left: 2px solid #4e4e4e; border-right: 2px solid #4e4e4e">❌ Shape</td>
<td>✅ Shape</td>
</tr>
<tr>
<td>✅ Rotation</td>
<td style="border-left: 2px solid #4e4e4e; border-right: 2px solid #4e4e4e">✅ Rotation</td>
<td>❌ Rotation</td>
</tr>
<tr>
<td>❌ Area</td>
<td style="border-left: 2px solid #4e4e4e; border-right: 2px solid #4e4e4e">✅ Area</td>
<td>✅ Area</td>
</tr>
</tbody>
</table>
<p>
Mercator does enlarge <span class="italic">areas</span> farther from the equator, but at least this
distortion is the same horizontally and vertically. And it's trivial to calculate a <a
href="https://en.wikipedia.org/wiki/Mercator_projection#Scale_factor" target="_blank">scale
factor</a> to correct measurements. The only time the distortion is problematic is when viewing a
global-scale map with a range of different scale factors, but most maps are not global-scale and there
are plenty of better projections to use for this case.
</p>
</div>
<div id="why-project">
<h2><a href="#why-project">I hate coordinate systems! Why don't we always use longitude/latitude?</a></h2>
<p class="solutions">Good question. There are a bunch of reasons we use planar projected <span
class="part3">coordinate systems</span> rather than just sticking with latitude,longitude geographic
<span class="part3">coordinate systems</span> all the time:</p>
<ul class="solutions">
<li><span class="bold">Planar measurements are ubiquitous.</span> Common GIS features like
property boundaries, road centerlines, forests, lakes, etc. are all reckoned in
Euclidean distances, areas, and volumes - not in terms of angles.</li>
<li><span class="bold">Planar measurements are easier to calculate.</span> Measuring distances on a
plane with the Pythagorean theorem is easier than along a sphere with the <a
href="https://en.wikipedia.org/wiki/Haversine_formula" target="_blank">Haversine formula</a> and
<span class="italic">way</span> easier than along an ellipsoid with the <a
href="https://en.wikipedia.org/wiki/Vincenty%27s_formulae" target="_blank">Vincenty's
formulae</a>, to say nothing of areas or volumes.</li>
<li><span class="bold">Planar measurements can be more accurate.</span> Tectonic drift is not
negligible; Australia is drifting around 7 cm per year. Referencing locations in terms of meters
from a fixed monument on the same tectonic plate can avoid errors that accumulate over time when
referencing against a global datum. Temporal datums try to solve this, but they have limited
software support.</li>
<li><span class="bold">Longitude was hard to figure out before GNSS.</span> Reliable means of
determining longitude are <a href="https://en.wikipedia.org/wiki/History_of_longitude"
target="_blank">only a couple hundred years old</a>, and GPS only a couple decades old. There
is a lot of inertia in surveying and geodesy using Cartesian distances from fixed monuments.</li>
</ul>
</div>
<div id="ellipsoidal-vs-orthometric">
<h2><a href="#ellipsoidal-vs-orthometric">I hate coordinate systems! My X- and Y-values are OK, but my
Z-values (heights, elevations) are off!</a></h2>
<p>
<span class="bold">
Your dataset is probably measuring height above the ellipsoid instead of above sea level (geoid), or
vice-versa.
</span>
Sea level follows the geoid, a surface which is lumpy because of minute regional variations in gravity.
GNSS like GPS do not measure the height above the geoid but rather the idealized mathematical
representation called the ellipsoid. Some GPS devices automatically convert ellipsoidal height to height
above sea level (aka orthometric height aka geoidal height), but many do not.
</p>
<img src="images/ellipsoid-vs-geoid.png" width="100%">
<p>
<span class="bold">Solution:</span> Use <a href="https://proj.org/apps/cs2cs.html" target="_blank"><span
class="mono">cs2cs</span> in PROJ</a>, or alternatively an older tool like <a
href="https://vdatum.noaa.gov/" target="_blank">VDatum</a>, to convert between ellipsoidal and
orthometric (above sea level) heights. For a reasonably small dataset, a constant offset can be applied
to all Z-coordinates.
</p>
</div>
<div id="glossary">
<h2><a href="#glossary">I hate coordinate systems! What do all these terms mean?</a></h2>
<p class="solutions"><span class="bold">Here's a glossary:</span></p>
<ul class="solutions">
<li><span class="part1"><span class="bold">Attributes</span>:
the meanings or labels of a data point</li></span>
<li><span class="part3"><span class="bold">Coordinate (reference) system (CRS)</span>:
metadata describing the space in which coordinates exist, e.g. origin, axes, units, etc.</span>
</li>
<li><span class="part2"><span class="bold">Coordinates</span>:
numbers describing a data point's position within a CRS.</span>
</li>
<li><span class="bold">Datum</span>:
a precise reference frame calculated from a collection of known reference points; one part of a GCS.
</li>
<li><span class="bold">Ellipsoid</span>:
a mathematical approximation of the size and shape of the earth; one part of a GCS.
</li>
<li><span class="bold">Extent</span>:
the minimum and maximum values of the <span class="part2">coordinates</span>.
</li>
<li><span class="bold">Geographic <span class="part3">coordinate system</span> (GCS)</span>:
a <span class="part3">coordinate system</span> with angular longitude,latitude units in degrees;
composed of a datum and an ellipsoid.
</li>
<li><span class="bold">Geoid</span>:
an imaginary surface similar to sea level if landmasses were "cut away"; unlike the smooth
ellipsoid, the geoid is lumpy due to regional variations in gravity.
</li>
<li><span class="bold">GNSS</span>:
global navigation satellite system for precisely global positioning; the most common are GPS <img
src="images/flag-usa.png" class="flag">, GLONASS <img src="images/flag-ru.png" class="flag">,
BeiDou <img src="images/flag-cn.png" class="flag">, and Galileo <img src="images/flag-eu.png"
class="flag">.
</li>
<li><span class="bold">Project</span>:
the act of converting <span class="part2">coordinates</span> from a ellipsoidal longitude,latitude
<span class="part3">GCS</span> to a planar x,y <span class="part3">PCS</span> using a projection.
</li>
<li><span class="bold">Projected <span class="part3">coordinate system</span> (PCS)</span>:
a planar <span class="part3">coordinate system</span> with Euclidean x,y units (not angles);
composed of a GCS and a projection.
</li>
<li><span class="bold">Projection</span>:
an algorithm for converting angular longitude,latitude <span class="part2">coordinates</span> in a
<span class="part3">GCS</span> to a plane (a <span class="part3">PCS</span>) on/near the Earth's
surface, e.g. Mercator, Equidistant Conic, Stereographic, Dymaxion. Different zones (e.g. UTM) are
the same fundamental projection with different parameters.
</li>
<li><span class="bold">Redefine projection</span>:
the act of changing the <span class="part3">coordinate system</span> <span
class="italic">without</span> changing the <span class="part2">coordinates</span>.
</li>
<li><span class="bold">Reproject</span>:
the act of changing the <span class="part3">coordinate system</span> <span class="italic">and</span>
changing the <span class="part2">coordinates</span>. Typically done by unprojecting from the PCS to
the old GCS, transforming to new GCS (if different), and projecting to the new PCS.
</li>
<li><span class="bold">Transform</span>:
the act of changing between two <span class="part3">GCSs</span>. There are often multiple
transformation algorithms for a given pair of <span class="part3">GCSs</span>; the best choice
depends on the location of your data within the GCS.
</li>
<li><span class="bold">Unproject</span>:
the act of converting <span class="part2">coordinates</span> from a planar x,y <span
class="part3">PCS</span> to an ellipsoidal longitude,latitude <span class="part3">GCS</span>;
the inverse of project.
</li>
</ul>
</div>
<!--
<div id="desc">
<h2><a href="#desc">I hate coordinate systems! [PROBLEM]</a></h2>
<p>
<span class="bold">
[ROOT CAUSE]
</span>
[EXPLANATION]
</p>
<p>
<span class="bold">Solution:</span> [SINGLE SOLUTION].
</p>
<p class="solutions"><span class="bold">Solutions:</span></p>
<ul class="solutions">
<li>MULTIPLE</li>
<li>SOLUTIONS</li>
</ul>
</div>
-->
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