Main Content

Coordinate Reference Systems

Representing coordinate reference systems, projecting and unprojecting coordinates, analyzing distortion

A coordinate reference system (CRS) provides a framework for defining real-world locations. Represent latitude-longitude data using a geographic CRS or x-y map data using a projected CRS.

Transform coordinates between systems using various projection methods. Though all projection methods cause distortion, you can preserve attributes such as area, shape, or direction by choosing an appropriate projection method.


expand all

CRS Objects

geocrsGeographic coordinate reference system object
projcrsProjected coordinate reference system object
wktstringWell-known text string

Map Projection Structures

defaultmInitialize or reset map projection structure
geotiff2mstructConvert GeoTIFF information to map projection structure
maplistMap projection support for map axes and map projection structures
mapsList map projections for map axes and map projection structures
projlistGeoTIFF info structure support for projfwd and projinv
utmgeoidSelect ellipsoids for given UTM zone
utmzoneSelect UTM zone given latitude and longitude
utmzoneuiChoose or identify UTM zone by clicking map
projfwdProject latitude-longitude coordinates to x-y map coordinates
projinvUnproject x-y map coordinates to latitude-longitude coordinates
vfwdtranTransform azimuth on ellipsoid to direction on map
vinvtranTransform direction on map to azimuth on ellipsoid
clipdataClip data at +/-pi in longitude, +/-pi in latitude
mdistortDisplay contours of constant map distortion
distortcalcDistortion parameters for map projections
tissotProject Tissot indicatrices on map axes
rotatemTransform vector map data to new origin and orientation
newpoleOrigin vector to place specific point at pole
putpoleOrigin vector to place north pole at specified point
org2polLocation of north pole in rotated map


Map Projections

Summary and Guide to Projections

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

Quantitative Properties of Map Projections

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

Projection Parameters

Variable projection parameters control the appearance of map projections. Projection parameters include aspect, origin, and scale.

Project Data

Transform Coordinates to a Different Projected CRS

Transform coordinates from a projected CRS to a different projected CRS that uses the same geographic CRS.

Project and Display Raster Data

Project or unproject raster data by referencing the coordinates to a grid, then display the data.

Universal Transverse Mercator (UTM) System

Create a UTM Map

Create a map for a zone in the Universal Transverse Mercator (UTM) system.

Set UTM Parameters Interactively

You can interact with a map of the world to select a UTM zone and adjust map settings, such as the limits, origin, parallels, and aspect.

Work in UTM Without a Displayed Map

This example shows how to select a UTM zone by specifying the coordinate of a location. You can then create a UTM coordinate system using the suggested ellipsoid vector of the zone.

Use the Transverse Aspect to Map Across UTM Zones

This example shows how to display areas that extend across more than one UTM zone by using the Mercator projection in a transverse aspect.

Analyze Distortion

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.

Visualize Spatial Error Using Tissot Indicatrices

A standard method of visualizing map projection distortion is to project small circles spaced at regular intervals across the globe.

Quantify Map Distortions at Point Locations

You can calculate quantitative position-specific map error statistics, such as area scale, angular deformation of right angles, and directional scale distortions along meridians and parallels.

Rotate Orientation of Map Display

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.

Rotational Transformations on the Globe

You can redefine a coordinate system and transform all points to the new coordinate system. The transformation can be useful independent of map displays.