# Documentation

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# Projected Coordinate Reference Systems

Control transformation from geographic to map coordinates; find area distortion

To represent a curved surface such as the Earth in two dimensions, you must geometrically transform (literally, and in the mathematical sense, “map”) that surface to a plane. Such a transformation is called a map projection. All map projections intruduce distortion compared to maps on gobes.

The following topics describe the basic properties of map projections, the surfaces onto which projections are developed, the types of parameters associated with different classes of projections, and how projected data can be mapped back to the sphere or spheroid it represents.

### Note

Most map projections in the toolbox are implemented as MATLAB® functions; however, these are only used by certain calling functions (such as `geoshow` and `axesm`), and thus have no documented public API.

## Functions

 `defaultm` Initialize or reset map projection structure `geotiff2mstruct` Convert GeoTIFF information to map projection structure `maplist` Available Mapping Toolbox map projections `maps` List available map projections and verify names `mfwdtran` Project geographic features to map coordinates `minvtran` Unproject features from map to geographic coordinates `projlist` Map projections supported by projfwd and projinv `vfwdtran` Direction angle in map plane from azimuth on ellipsoid `vinvtran` Azimuth on ellipsoid from direction angle in map plane
 `clipdata` Clip data at +/-pi in longitude, +/-pi in latitude `distortcalc` Distortion parameters for map projections `maptrims` Trim regular data grid to latitude-longitude quadrangle `mdistort` Display contours of constant map distortion `tissot` Project Tissot indicatrices on map axes

## Topics

### Map Projections

What Is a Map Projection?

A map projection transforms a curved surface such as the Earth onto a two-dimensional plane.

Summary and Guide to Projections

View a list of the supported Mapping Toolbox™ map projections and their properties.

Quantitative Properties of Map Projections

Map projections are influenced and constrained by five characteristic properties.

The Three Main Families of Map Projections

Most map projections can be categorized into three families based on the cylinder, cone, and plane geometric shapes.

Projection Aspect

A projection aspect is the orientation of a map on the page or display screen. An orientation vector controls the map projection aspect.

Projection Parameters

Variable projection parameters control the appearance of map projections.

Using Inverse Projection to Recover Geographic Coordinates

An inverse projection transforms plane coordinates to the spherical geographic coordinates.

Project Coordinates Without Map Axes

This example shows how to perform the same projection computations that are done within Mapping Toolbox display commands by calling the `defaultm` and `mfwdtran` functions.

### Spatial Error of Map Projections

Projection Distortions

All map projections introduce distortions compared to maps on globes. A standard method of visualizing map distortion is to project small circles spaced at regular intervals across the globe.

Quantifying Map Distortions at Point Locations

Compute location-specific map error statistics using the `distortcalc` function.