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# vec2mtx

Convert latitude-longitude vectors to regular data grid

## Syntax

[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')

## Description

[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]`

or a 3-by-2 referencing matrix that transforms raster row and column indices to/from geographic coordinates according to:

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

If 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.

## Notes

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.

## Examples

### Example 1

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))```

### Example 2

Combine two separate calls to vec2mtx to create a 4-color raster map showing interior land areas, coastlines, oceans, and world rivers.

```   coast = load('coast.mat');
[Z, R] = vec2mtx(coast.lat, coast.long, ...
1, [-90 90], [-90 270], 'filled');
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])```

## Example 3

This example illustrates the following syntax in the case where R1 is a spatial referencing object:

```[Z, R] = vec2mtx(lat, lon, Z1, R1)
```
```% Import US state outlines.
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 spatialref.GeoRasterReference 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))
```