= Index CRSs 

This page describes how to use and interpret Index Coordinate Reference Systems (CRSs), and how they differs from other linear coordinate systems and especially how it differs from the ''internal'' grid CRS, known as `CRS:1`.

GML definitions for [http://kahlua.eecs.jacobs-university.de:8080/def/crs/OGC/0/Index1D Index1D], [http://kahlua.eecs.jacobs-university.de:8080/def/crs/OGC/0/Index2D Index2D] and [http://kahlua.eecs.jacobs-university.de:8080/def/crs/OGC/0/Index3D Index3D] are already embedded in our [SecoreDevGuide SECORE] resolver and their official acknowledgment is on OGC table.

== Definition

As you can verify by looking at the "extra" (non-EPSG) CRS definitions [http://kahlua.eecs.jacobs-university.de:8080/def/crs/OGC/0/ provided] by SECORE, among others there are three new Index CRSs, namely [http://kahlua.eecs.jacobs-university.de:8080/def/crs/OGC/0/Index1D 1D], [http://kahlua.eecs.jacobs-university.de:8080/def/crs/OGC/0/Index2D 2D] and [http://kahlua.eecs.jacobs-university.de:8080/def/crs/OGC/0/Index3D 3D] reference systems.

The ''index'' prefix refers to the fact that ''integral'' coordinates shall be used in the geometric (cartesian) space. The n-dimensional Coordinate System (CS) is supposed to be bound to an multidimensional array (marray) of cells: the origin of the CS is placed in the centre of the 0-cell. This represents the datum and completes the picture to define the CRS.

[[Image(indexCrs.png, center, 70%)]]

Using index CRSs can be useful especially when using `rasdaman` for applications not related to the geo-referenced world of satellite products, or more generally to remote-sensing imagery. For instance, `rasdaman` could be used to process [http://link.springer.com/article/10.1134/S105466181304007X large bio-medical images], which do not need a geo-reference.

The previous case is out of scope in the OGC services, and it is probably better handled via direct `rasql` requests (also via [PetascopeUserGuide Petascope] `rasql` web interface). However, more interestingly, index CRSs could also be used to access "pixel" coordinates from an image, or to access layers of height/time via their ordinal position in the stack (this requires CRS extensions [Features available]).

Index CRSs exploit indexed cartesian CSs by defining the Unit of Measure (Uom) of each of its axes to be an integral. The specific terminology that is used is [http://www.opengis.net/def/uom/OGC/1.0/GridSpacing GridSpacing], defined by OGC in the context of the [http://www.opengeospatial.org/standards/deprecated deprecated] (2D) Image CRS. Indeed index CRSs are considered the n-dimensional extension/generalization of the previously defined [http://schemas.opengis.net/ImageCRSs/ Image CRSs]: this means replacing the typically-2D terminology of ''pixels'', ''rows'' and ''columns'' with the more general ''cells'' and ''axis''.

The following picture clarifies what is the space of coordinates covered by a standard 2D (linear) cartesian CS, and an indexed one:

[[Image(IndexVsCartesianCRS.png, center, 90%)]]

The 2D space is fully covered on a geometric space with no additional constraints, whereas limiting the coordinates to integrals confines the address space to a grid of 0D points. While this is easily understandable, it has some important consequences: '''sample sizes''' (footprints) of coverages' points are confined to be 0D on an index CRSs since the areas between CRS points is not reachable and hence loses its meaning. 

In the regular 2D case, usually a pixel represents its extent/area (though [http://trac.osgeo.org/gdal/wiki/rfc33_gtiff_pixelispoint not always] of course), while a coverage point is always a 0D point: on an index CRS the point is on integral coordinates, and the footprint would be half-pixel away from it, over unreachable spaces `0.5 GridSpacing` away from it. Truncating this footprint to the legal index space, the footprints/pixels reduce to the point itself.

== Grid origin and offset vectors

TBD

[[Image(IndexAndGrids.png, center, 50%)]]

== Change label of the axes

TBD
Parametrized