# Projected Coordinate Reference Systems

Control transformation from geographic to map coordinates

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.

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

## Topics

Map Projections and Distortions

A map projection transforms a curved surface such as the Earth onto a two-dimensional plane. All map projections introduce distortions compared to maps on globes.

Quantitative Properties of Map Projections

Map projections are influenced and constrained by five characteristic properties: shape, distance, direction, scale, and area.

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.

Summary and Guide to Projections

Learn about the map projections supported by the toolbox, and their families and properties.

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. Projection parameters include aspect, origin, and scale.

Project Coordinates Without Map Axes

This example shows how to project latitude and longitude vectors into plane coordinates independently of displaying the projection.

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