mdistort
Display contours of constant map distortion
Syntax
mdistort
mdistort off
mdistort parameter
mdistort(parameter,levels)
mdistort(parameter,levels,gsize)
h = mdistort(...)
Description
mdistort, with no input
arguments, toggles the display of contours of projection-induced distortion
on the current map axes. The magnitude of the distortion is reported
in percent.
mdistort off removes the
contours.
mdistort parameter displays
contours of distortion for the specified parameter. Recognized parameters
are:
| Parameter | Value |
|---|---|
'area' | |
'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.
Background
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.
Examples
View Extreme Area Distortion of Mercator Projection
The extreme area distortion of the Mercator projection. This makes it ill-suited for global displays.
figure axesm mercator load coastlines framem; plotm(coastlat,coastlon,'color',.5*[1 1 1]) mdistort('area', [1 30 100 200 500 1000])
View Lines of Zero Distortion for Bonne Projection
The lines of zero distortion for the Bonne projection follow the central meridian and the standard parallel.
figure axesm bonne load coastlines framem; plotm(coastlat,coastlon,'color',.5*[1 1 1]) mdistort('angles', 0:15:90) parallelui
View Distortion of Conic Projection with Properly Chosen Parallels
An equidistant conic projection with properly chosen parallels can map the conterminous United States with less than 1.5% distortion.
figure 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) parallelui
Tips
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. By
using mdistort and parallelui,
you can immediately see how the movement of parallels reduces distortion.