Georectified Image XXXX CRS GeorectifiedImageXXXXCRS Template for georectified 2D image coordinate reference system definition. In this CRS, the origin is at the center of the first pixel in the georectified image file. This CRS template can be used for any size georectified image, since no image size is specified. A CRS definition using this template is expected to be needed and thus created before the georectified image pixels are produced. The coordinate Conversion used by this CRS definition is expected to NOT closely approximate the reverse of the coordinate Transformation used to georectify this image. This CRS template is not expected to be useful for an ungeorectified image. Georectified image XXXX conversion Affine general parametric transformation 9624 XT = A0 + A1. XS + A2.YS; YT = B0 + B1. XS + B2.YS; where XT , YT are the coordinates of a point P in the target coordinate system; XS , YS are the coordinates of P in the source coordinate system. Reversibility: The parameter values for an affine transformation cannot be used for the reverse transformation. However, the reverse transformation is another affine transformation using the same formulas but with different parameter values. The reverse parameter values, indicated by a prime ('), can be calculated from those of the forward transformation as follows: D = A1 . B2 - A2 . B1; A0' = (A2 . B0 - B2 . A0) / D; B0' = (B1 . A0 - A1 . B0) / D; A1' = +B2 / D; A2' = - A2 / D; B1' = - B1 / D; B2' = +A1 / D. See Section 2.4.2.1 of EPSG Guidance Note 7. 2 2 A0 8623 A1 8624 A2 8625 B0 8639 B1 8640 B2 8641 9999 9999 9999 9999 9999 9999 #image 2D square-cell grid based coordinate system Grid2dSquareCS A 2D grid-based coordinate system for use by an image or other continuous grid coverage. It can be used for a grid of any size, since no grid size is defined. This coordinate system specifies that each row coordinate value shall be listed before the column coordinate value. The grid cells are assumed to be square, with the same grid spacing or pixel spacing in each direction. In a grid coverage file, the "row" axis shall be the first axis by which grid points are sequenced, and the "column" axis shall be the second axis, as could be specified by the "scanDirection : Sequence(CharacterString)" attribute of the CV_SequenceRule class in Clause 8 of ISO 19123. With linear sequencing, the grid points in the first row shall be listed first, followed by other rows, with the grid points in each row listed in column number order. This relationship between the "row" and "column" names and the first grid points shall apply whether this Grid2dSquareCS is associated with a grid file before or after that file is recorded. The "row" and "column" axis names are used here although the "scanDirection : Sequence(CharacterString)" attribute may provide other axis names. Use of other axis names would require defining different CartesianCSs for other names, or adding other names as additional axisID values. The following XML includes the axis names "line" and "sample" as additional axisID values. If not otherwise identified in an image file, the "row" axis shall be the first axis whose number of pixels is identified, and the "column" axis shall be the second axis, as could be specified by the "extent[0..1] : CV_GridEnvelope" attribute of the CV_Grid class in Clause 8 of ISO 19123. In either case, the first point in the grid coverage file is assumed to be numbered (1, 1), meaning row 1, column 1. The first row in a grid is sometimes called the "top" row, the first column is sometimes called the "left" column, and the first grid point is then called the "upperLeft" point. If desired, those names can be used with this Grid2dSquareCS. However other names can also be used, since this Grid2dSquareCS has been defined so that it does not depend on such left/right, top/bottom, and up/down names. Grid row axis Row For this grid axis, row coordinate values match grid row numbers, but allow fractional coordinate values between grid points. The first row in a grid is sometimes called the "top" row, so the direction of this axis is "down", but these terms are not required. R urn:ogc:def:axisDirection:OGC:1.0:rowPositive Grid column axis Column For this grid axis, column coordinate values match grid column numbers, but allow fractional coordinate values between grid points. The first column is sometimes called the "left" column, so the direction of this axis is "right", but these terms are not required. C urn:ogc:def:axisDirection:OGC:1.0:columnPositive