# meshgrat

Construct map graticule for surface object display

## Syntax

```[lat, lon] = meshgrat(Z, R) [lat, lon] = meshgrat(Z, R, gratsize) [lat, lon] = meshgrat(lat, lon) [lat, lon] = meshgrat(latlim, lonlim, gratsize) [lat, lon] = meshgrat(lat, lon, angleunits) [lat, lon] = meshgrat(latlim, lonlim, angleunits) [lat, lon] = meshgrat(latlim, lonlim, gratsize, angleunits) ```

## Description

`[lat, lon] = meshgrat(Z, R)` constructs a graticule for use in displaying a regular data grid, `Z`. In typical usage, a latitude-longitude graticule is projected, and the grid is warped to the graticule using MATLAB® graphics functions. In this two-argument calling form, the graticule size is equal to the size of `Z`. `R` can be a geographic raster reference object, a referencing vector, or a referencing matrix.

If `R` is a geographic raster reference object, its `RasterSize` property must be consistent with `size(Z)`.

If `R` is a referencing vector, it must be 1-by-3 with elements:

`[cells/degree northern_latitude_limit western_longitude_limit]`
If `R` is a referencing matrix, it must be 3-by-2 and transform raster row and column indices to/from geographic coordinates according to:
`[lon lat] = [row col 1] * R`
If `R` 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.

`[lat, lon] = meshgrat(Z, R, gratsize)` produces a graticule of size `gratsize`. `gratsize` is a two-element vector of the form `[number_of_parallels number_of_meridians]`. If `gratsize = []`, then the graticule returned has the default size 50-by-100. (But if `gratsize` is omitted, a graticule of the same size as `Z` is returned.) A finer graticule uses larger arrays and takes more memory and time but produces a higher fidelity map.

`[lat, lon] = meshgrat(lat, lon)` takes the vectors `lat` and `lon` and returns graticule arrays of size `numel(lat)-by-numel(lon)`. In this form, `meshgrat` is similar to the MATLAB function `meshgrid`.

```[lat, lon] = meshgrat(latlim, lonlim, gratsize)``` returns a graticule mesh of size `gratsize` that covers the geographic limits defined by the two-element vectors `latlim` and `lonlim`.

`[lat, lon] = meshgrat(lat, lon, angleunits)`, ```[lat, lon] = meshgrat(latlim, lonlim, angleunits)```, and `[lat, lon] = meshgrat(latlim, lonlim, gratsize, angleunits)` where `angleunits` can be either `'degrees'` (the default) or `'radians'`.

The graticule mesh is a grid of points that are projected on a map axes and to which surface map objects are warped. The fineness, or resolution, of this grid determines the quality of the projection and the speed of plotting. There is no hard and fast rule for sufficient graticule resolution, but in general, cylindrical projections need very few graticules in the longitudinal direction, while complex curve-generating projections require more.

## Examples

Make a (coarse) graticule for the entire world:

```latlim = [-90 90]; lonlim = [-180 180]; [lat,lon] = meshgrat(latlim,lonlim,[3 6]) lat = -90.0000 -90.0000 -90.0000 -90.0000 -90.0000 -90.0000 0 0 0 0 0 0 90.0000 90.0000 90.0000 90.0000 90.0000 90.0000 lon = -180.0000 -108.0000 -36.0000 36.0000 108.0000 180.0000 -180.0000 -108.0000 -36.0000 36.0000 108.0000 180.0000 -180.0000 -108.0000 -36.0000 36.0000 108.0000 180.0000```

These paired coordinates are the graticule vertices, which are projected according to the requirements of the desired map projection. Then a surface object like the `topo` map can be warped to the grid.