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.

Functions

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Access CRS Information

CRS Objects

`geocrs`	Geographic coordinate reference system object (Since R2020b)
`projcrs`	Projected coordinate reference system object (Since R2020b)
`wktstring`	Well-known text string (Since R2020b)

Map Projection Structures

`defaultm`	Create or reset map projection structure
`geotiff2mstruct`	Convert GeoTIFF information to map projection structure
`maplist`	Map projection support for `axesm`-based maps and map projection structures
`maps`	List map projections for `axesm`-based maps and map projection structures
`projlist`	GeoTIFF info structure support for `projfwd` and `projinv`
`utmgeoid`	Select ellipsoids for given UTM zone
`utmzone`	UTM zone from latitude and longitude
`utmzoneui`	Identify UTM zone by clicking map

Project Data

`projfwd`	Project latitude-longitude coordinates to x-y map coordinates
`projinv`	Unproject x-y map coordinates to latitude-longitude coordinates
`vfwdtran`	Transform azimuth on ellipsoid to direction on map
`vinvtran`	Transform direction on map to azimuth on ellipsoid

Analyze Distortion

`mdistort`	Display contours of constant map distortion on `axesm`-based map
`distortcalc`	Distortion parameters for map projections
`tissot`	Project Tissot indicatrices on `axesm`-based map

Rotate CRS

`rotatem`	Transform vector map data to new origin and orientation
`newpole`	Origin vector to place specific point at pole
`putpole`	Origin vector to place north pole at specified point
`org2pol`	Location of north pole in rotated map

Topics

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 UTM Maps
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.