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## Pixel Indices, Pixel Co-ordinates, and Grid Co-ordinates

In this sub-section we will look at the definition of the four basic co-ordinate systems available in all NDFs--pixel indices, pixel co-ordinates, grid co-ordinates, and normalised co-ordinates.

Pixel indices are integer values that are used to count the pixels along each axis of an NDF. The first pixel can be given any arbitrary pixel index, and this value is known as the pixel origin. When a section is extracted from an NDF, the pixel origin in the extracted section is set so that each pixel retains its original pixel indices (see Figure 10).

Figure 10: Pixel indices

Pixel co-ordinates are floating-point values that allow positions to be specified with sub-pixel accuracy. They are related to pixel indices as indicated in Figure 11).

Figure 11: Pixel co-ordinates.

Grid co-ordinates are floating-point values that are similar to pixel co-ordinates except that the origin is fixed so that the first pixel on an axis is centred at a grid co-ordinate value of 1.0, no matter what the pixel origin is. This corresponds to the FITS idea of `pixel co-ordinates' (FITS makes no provision for an arbitrary pixel origin). When a section is extracted from an array, the grid co-ordinates of the extracted section include no knowledge of where the section was located in the original array. See Figure 12).

Figure 12: Grid co-ordinates.

Fraction co-ordinates are floating-point values that are normalised pixel or grid co-ordinates such that each axis extends from zero to one. Thus in Figure 13 pixel co-ordinate 2.0 or grid co-ordinate 0.5 becomes 0.0 in fraction co-ordinates, and pixel co-ordinate 7.0 or grid co-ordinate 5.5 becomes 1.0 in fraction co-ordinates.

Figure 13: Fraction co-ordinates.

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KAPPA --- Kernel Application Package
Starlink User Note 95
Malcolm J. Currie & David S. Berry
2013 February 14