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Construct affine spatial-referencing matrix

`R = makerefmat(x11, y11, dx, dy)`

R = makerefmat(lon11, lat11, dlon, dlat)

R = makerefmat(param1, val1, param2, val2, ...)

`R = makerefmat(x11, y11, dx, dy)`

,
with scalars `dx`

and `dy`

, constructs
a referencing matrix that aligns image or data grid rows to map *x* and
columns to map *y*. Scalars `x11`

and `y11`

specify
the map location of the center of the first (1,1) pixel in the image
or the first element of the data grid, so that

[x11 y11] = pix2map(R,1,1)

`dx`

is the difference in *x* (or
longitude) between pixels in successive columns, and `dy`

is
the difference in *y* (or latitude) between pixels
in successive rows. More abstractly, `R`

is defined
such that

[x11 + (col-1) * dx, y11 + (row-1) * dy] = pix2map(R, row, col)

Pixels cover squares on the map when `abs(dx) = abs(dy)`

.
To achieve the most typical kind of alignment, where *x* increases
from column to column and *y* decreases from row
to row, make `dx`

positive and `dy`

negative.
In order to specify such an alignment along with square pixels, make `dx`

positive
and make `dy`

equal to `-dx`

:

R = makerefmat(x11, y11, dx, -dx)

`R = makerefmat(x11, y11, dx, dy)`

, with two-element
vectors `dx`

and `dy`

, constructs
the most general possible kind of referencing matrix, for which

[x11 + ([row col]-1) * dx(:), y11 + ([row col]-1) * dy(:)] ... = pix2map(R, row, col)

In this general case, each pixel can become a parallelogram
on the map, with neither edge necessarily aligned to map *x* or *y*.
The vector `[dx(1) dy(1)]`

is the difference in map
location between a pixel in one row and its neighbor in the preceding
row. Likewise, `[dx(2) dy(2)]`

is the difference
in map location between a pixel in one column and its neighbor in
the preceding column.

To specify pixels that are rectangular or square (but possibly
rotated), choose `dx`

and `dy`

such
that `prod(dx) + prod(dy) = 0`

. To specify square
(but possibly rotated) pixels, choose `dx`

and `dy`

such
that the 2-by-2 matrix `[dx(:) dy(:)]`

is a scalar
multiple of an orthogonal matrix (that is, its two eigenvalues are
real, nonzero, and equal in absolute value). This amounts to either
rotation, a mirror image, or a combination of both. Note that for
scalars `dx`

and `dy`

,

R = makerefmat(x11, y11, [0 dx], [dy 0])

is equivalent to

R = makerefmat(x11, y11, dx, dy)

`R = makerefmat(lon11, lat11, dlon, dlat)`

,
with longitude preceding latitude, constructs a referencing matrix
for use with geographic coordinates. In this case,

[lat11,lon11] = pix2latlon(R,1,1), [lat11+(row-1)*dlat,lon11+(col-1)*dlon] = pix2latlon(R,row,col)

for scalar `dlat`

and `dlon`

,
and

[lat11+[row col]-1)*dlat,lon11+([row col]-1)*dlon] = ... pix2latlon(R, row,col)

for vector `dlat`

and `dlon`

.
Images or data grids aligned with latitude and longitude might already
have referencing vectors. In this case you can use function `refvec2mat`

to convert to a referencing matrix.

`R = makerefmat(param1, val1, param2, val2, ...)`

uses
parameter name-value pairs to construct a referencing matrix for an
image or raster grid that is referenced to and aligned with a geographic
coordinate system. There can be no rotation or skew: each column must
fall along a meridian, and each row must fall along a parallel. Each
parameter name must be specified exactly as shown, including case.

Parameter Name | Data Type | Value |
---|---|---|

`RasterSize` | Two-element size vector `[M N]` | The number of rows ( With R = makerefmat('RasterSize', ... size(RGB), ...) `RGB` is `M-by-N-by-3` .
However, in cases like this, only the first two elements of the size
vector will actually be used. The higher (non-spatial) dimensions
will be ignored. The default value is [1 1]. |

`LatitudeLimits` | Two-element row vector of the form: ```
[southern_limit,
northern_limit]
``` , in units of degrees. | The limits in latitude of the geographic quadrangle bounding the georeferenced raster. The default value is [0 1]. |

`LongitudeLimits` | Two-element row vector of the form: ```
[western_limit,
eastern_limit]
``` , in units of degrees. | The limits in longitude of the geographic quadrangle bounding
the georeferenced raster. The elements of the `'LongitudeLimits'` vector
must be ascending in value. In other words, the limits must be unwrapped.
The default value is [0 1]. |

`ColumnsStartFrom` | Character vector | Indicates the column direction of the raster (south-to-north
vs. north-to-south) in terms of the edge from which row indexing starts.
Values are `'south'` or `'north'` and
they can be shortened, and are case-insensitive. In a typical terrain
grid, row indexing starts at southern edge. In images, row indexing
starts at northern edge. The default value is `'south'` . |

`RowsStartFrom` | Character vector | Indicates the row direction of the raster (west-to-east vs.
east-to-west) in terms of the edge from which column indexing starts.
Values are: `'west'` or `'east'` and
they can be shortened, and are case-insensitive. Rows almost always
run from west to east. The default value is `'west'` . |

Create a referencing matrix for an image with square, four-meter
pixels and with its upper left corner (in a map coordinate system)
at *x* = 207000 meters, *y* =
913000 meters. The image follows the typical orientation: *x* increasing
from column to column and *y* decreasing from row
to row.

x11 = 207002; % Two meters east of the upper left corner y11 = 912998; % Two meters south of the upper left corner dx = 4; dy = -4; R = makerefmat(x11, y11, dx, dy)

Create a referencing matrix for a global geoid grid.

% Add array 'geoid' to the workspace: load geoid %'geoid' contains a model of the Earth's geoid sampled in % one-degree-by-one-degree cells. Each column of 'geoid' % contains geoid heights in meters for 180 cells starting % at latitude -90 degrees and extending to +90 degrees, for % a given longitude. Each row contains geoid heights for 360 % cells starting at longitude 0 and extending 360 degrees. geoidR = makerefmat('RasterSize', size(geoid), ... 'Latlim', [-90 90], 'Lonlim', [0 360]) % At its most extreme, the geoid reaches a minimum of slightly % less than -100 meters. This minimum occurs in the Indian Ocean % at approximately 4.5 degrees latitude, 78.5 degrees longitude. % Check the geoid height at its most extreme by using latlon2pix % with the referencing matrix. [row, col] = latlon2pix(geoidR, 4.5, 78.5) geoid(round(row),round(col))

`latlon2pix`

| `map2pix`

| `pix2latlon`

| `pix2map`

| `refvec2mat`

| `worldfileread`

| `worldfilewrite`

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