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<title>Coverage</title>
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<h1 id="Coverage">Data as coverage</h1>
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<p>
Images, or <dfn>rasters</dfn>, are a particular case of a data structure called a <dfn>coverage</dfn>.
A coverage is a function which returns attribute values from an input coordinate.
The set of valid input values is called the <dfn>domain</dfn>, while the set of possible output values is called the <dfn>range</dfn>.
The domain is often the spatio-temporal area covered by the data,
but <abbr>SIS</abbr> does not prevents coverages from extending to other dimensions.
For example, thermodynamic studies often use an area where the dimensions are temperature and pressure.
</p>
<div class="example"><p><b>Example:</b>
Digital Elevation Models (<abbr>DEM</abbr>) are often represented as images where pixel values are terrain elevation values.
This image can be used as the basis of an <var>h</var> = <var>f</var>(φ,λ) function providing
(eventually by interpolations between pixels) the elevation <var>h</var> at the geographic coordinate (φ,λ).
In that case, the <var>f</var> function is the <dfn>coverage</dfn>,
the geographic envelope of the image is the <dfn>domain</dfn>,
and the set of pixel values <var>h</var> that this function can return is the <dfn>range</dfn>.
</p></div>
<p>
Ranges may be finite or infinite, and are not necessarily numerical.
For example, the values returned by a coverage may come from an enumeration (“this is a forest”, “this is a lake”, <i>etc.</i>).
However in the enumeration case, interpolations are not allowed.
A coverage without interpolation is called a <dfn>discrete coverage</dfn>
while a coverage that allows interpolations is called a <dfn>continuous coverage</dfn>.
</p><p>
Different types of coverages may also be characterized by the geometry of their cells.
In particular, a coverage is not necessarily composed of quadrilateral cells.
However, given that quadrilateral cells are by far the most frequent (since this is the usual geometry of image pixels),
we use the <dfn>grid coverage</dfn> term to specify coverages composed of such cells.
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