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Display contours of constant map distortion on axesm-based map


mdistort off
mdistort parameter
h = mdistort(...)


mdistort, with no input arguments, toggles the display of contours of projection-induced distortion on the current axesm-based map. The magnitude of the distortion is reported in percent.

mdistort off removes the contours.

mdistort parameter displays contours of distortion for the specified parameter. Units are in percent deviation (except for angles for which degrees are used).

Parameter Value
'angles'maximum angular distortion of right angles
'scale' or 'maxscale'maximum scale (the default)
'minscale'minimum scale
'parscale'scale along the parallels
'merscale'scale along the meridians
'scaleratio'ratio of maximum and minimum scale

mdistort(parameter,levels) specifies the levels for which the contours are drawn. levels is a vector of values as used by contour. If empty, the default levels are used.

mdistort(parameter,levels,gsize) controls the size of the underlying graticule matrix used to compute the contours. gsize is a two-element vector containing the number of rows and columns. If omitted, the default Mapping Toolbox™ graticule size of [50 100] is assumed.

h = mdistort(...) returns a handle to the contour group object containing the contours and text.


Map projections inevitably introduce distortions in the shape and size of objects as they are transformed from three-dimensional spherical coordinates to two-dimensional Cartesian coordinates. The amount and type of distortion vary between projections, over the projection, and with the selection of projection parameters such as standard parallels. This function provides a quantitative graphical display of distortion parameters.

mdistort is not intended for use with UTM. Distortion is minimal within a given UTM zone. mdistort issues a warning if a UTM projection is encountered.


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The extreme area distortion of the Mercator projection. This makes it ill-suited for global displays.

axesm mercator
load coastlines
plotm(coastlat,coastlon,'color',.5*[1 1 1])
mdistort('area', [1 30 100 200 500 1000])

View lines of distortion for the Bonne projection.

axesm bonne
load coastlines
plotm(coastlat,coastlon,'color',0.5*[1 1 1])

An equidistant conic projection with properly chosen parallels can map the conterminous United States with less than 1.5% distortion.

usamap conus
load conus
patchm(uslat, uslon, [1 0.7 0])
plotm(statelat, statelon)
patchm(gtlakelat, gtlakelon, 'cyan')
framem off; gridm off; mlabel off; plabel off
mdistort('parscale', -2:.5:2)

Create a map in normal aspect using a Hammer projection and plot a graticule and frame. Load the coast data set and plot it as gray patches.

load coastlines
patchm(coastlat,coastlon,'FaceColor',[0.95 0.95 0.95])

Plot contours of minimum-to-maximum scale ratios by using the mdistort function. Notice that the region of minimum distortion is centered around (0,0).


Repeat this diagram with a Bonne projection in a new figure window. Notice that the region of minimum distortion is centered around (30,0) which is where the single standard parallel is.

patchm(coastlat,coastlon,'FaceColor',[0.95 0.95 0.95])


mdistort can help in the placement of standard parallels for projections. Standard parallels are generally placed to minimize distortion over the region of interest. The default parallel locations might not be appropriate for maps of smaller regions.