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Convert latitude-longitude vectors to regular data grid

`[Z, R] = vec2mtx(lat, lon, density)`

[Z, R] = vec2mtx(lat, lon, density,
latlim, lonlim)

[Z, R] = vec2mtx(lat, lon, Z1, R1)

[Z, R] = vec2mtx(..., 'filled')

`[Z, R] = vec2mtx(lat, lon, density)`

creates
a regular data grid `Z`

from vector data, placing
ones in grid cells intersected by a vector and zeroes elsewhere. `R`

is
the referencing vector for the computed grid. `lat`

and `lon`

are
vectors of equal length containing geographic locations in units of
degrees. `density`

indicates the number of grid cells
per unit of latitude and longitude (a value of 10 indicates 10 cells
per degree, for example), and must be scalar-valued. Whenever there
is space, a buffer of two grid cells is included on each of the four
sides of the grid. The buffer is reduced as needed to keep the latitudinal
limits within [-90 90] and to keep the difference in longitude limits
from exceeding 360 degrees.

```
[Z, R] = vec2mtx(lat, lon, density,
latlim, lonlim)
```

uses the two-element vectors `latlim`

and `lonlim`

to
define the latitude and longitude limits of the grid.

`[Z, R] = vec2mtx(lat, lon, Z1, R1)`

uses
a pre-existing data grid `Z1`

, georeferenced by `R1`

,
to define the limits and density of the output grid. `R1`

can
be a referencing vector, a referencing matrix, or a geographic raster
reference object.

If `R1`

is a geographic raster reference object,
its `RasterSize`

property must be consistent with `size(Z1)`

and
its `RasterInterpretation`

must be `'cells'`

.

If `R1`

is a referencing vector, it must be
a 1-by-3 vector containing elements:

[cells/degree northern_latitude_limit western_longitude_limit]

[lon lat] = [row col 1] * R1

`R1`

is
a referencing matrix, it must define a (non-rotational, non-skewed)
relationship in which each column of the data grid falls along a meridian
and each row falls along a parallel. With this syntax, output `R`

is
equal to `R1`

, and may be a referencing object, vector,
or matrix.`[Z, R] = vec2mtx(..., 'filled')`

,
where `lat`

and `lon`

form one or
more closed polygons (with `NaN`

-separators), fills
the area outside the polygons with the value two instead of the value
zero.

Empty `lat,lon`

vertex arrays will result in
an error unless the grid limits are explicitly provided (via `latlim,lonlim`

or `Z1,R1`

).
In the case of explicit limits, `Z`

will be filled
entirely with 0s if the `'filled'`

parameter is omitted,
and 2s if it is included.

It's possible to apply `vec2mtx`

to sets of
polygons that tile without overlap to cover an area, as in Example
1 below, but using `'filled'`

with polygons that
actually overlap may lead to confusion as to which areas are inside
and which are outside.

Convert latitude-longitude polygons to a regular data grid and display as a map.

states = shaperead('usastatelo', 'UseGeoCoords', true); lat = [states.Lat]; lon = [states.Lon]; [Z, R] = vec2mtx(lat, lon, 5, 'filled'); figure; worldmap(Z, R); geoshow(Z, R, 'DisplayType', 'texturemap') colormap(flag(3))

Combine two separate calls to `vec2mtx`

to
create a 4-color raster map showing interior land areas, coastlines,
oceans, and world rivers.

load coastlines [Z, R] = vec2mtx(coastlat, coastlon, ... 1, [-90 90], [-90 270], 'filled'); rivers = shaperead('worldrivers.shp','UseGeoCoords',true); A = vec2mtx([rivers.Lat], [rivers.Lon], Z, R); Z(A == 1) = 3; figure; worldmap(Z, R) geoshow(Z, R, 'DisplayType', 'texturemap') colormap([.45 .60 .30; 0 0 0; 0 0.5 1; 0 0 1])

Import US state outlines.

states = shaperead('usastatelo', 'UseGeoCoords', true); lat = [states.Lat]; lon = [states.Lon];

Choose geographic limits.

latlim = [ 15 75]; lonlim = [-190 -65];

Specify a grid with 5 cells per degree.

density = 5;

Compute raster size. (M and N both work out to be integers.)

M = density * diff(latlim); N = density * diff(lonlim);

Construct a Geographic Raster Reference object.

R = georasterref('RasterSize', [M N], ... 'ColumnsStartFrom', 'north', 'Latlim', latlim, ... 'Lonlim', lonlim);

Create a blank grid that is consistent with `R`

in size. `vec2mtx`

requires a data grid as input.

Z = zeros(R.RasterSize);

Overwrite `Z`

with a new grid including state outlines and interiors.

```
Z = vec2mtx(lat, lon, Z, R, 'filled');
```

Plot the georeferenced grid.

figure; worldmap(Z, R); geoshow(Z, R, 'DisplayType', 'texturemap') colormap(flag(3))

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