Surface area of polygon on sphere or ellipsoid
area = areaint(lat,lon)
area = areaint(lat,lon,ellipsoid)
area = areaint(lat,lon,units)
area = areaint(lat,lon,ellipsoid,units)
area = areaint(lat,lon) calculates
the spherical surface area of the polygon specified by the input vectors
The calculation uses a line integral approach. The output,
is the fraction of surface area covered by the polygon on a unit sphere.
To supply multiple polygons, separate the polygons by NaNs in the
input vectors. Accuracy of the integration method is inversely proportional
to the distance between lat/lon points.
area = areaint(lat,lon,ellipsoid) calculates the
surface area of the polygon on the ellipsoid or sphere defined by the input
ellipsoid, which can be a
oblateSpheroid object, or a vector of the form
eccentricity]. The output,
area, is in squares units
corresponding to the units of
area = areaint(lat,lon,units) uses the units defined by
units, the string scalar or character vector
'radians'. If omitted, default
units of degrees are assumed.
area = areaint(lat,lon,ellipsoid,units) uses both the inputs
units in the calculation.
Consider the area enclosed by a 30º lune from pole to pole
and bounded by the prime meridian and 30ºE. You can use the function
get an exact solution:
area = areaquad(90,0,-90,30) area = 0.0833
This is 1/12 the spherical area. The more points used to define
this polygon, the more integration steps
improving the estimate. This first attempt takes a point every 30º
lats = [-90:30:90,60:-30:-60]'; lons = [zeros(1,7), 30*ones(1,5)]'; area = areaint(lats,lons) area = 0.0792
Now, calculate a better estimate, with one point every 1º of latitude:
lats = [-90:1:90,89:-1:-89]'; lons = [zeros(1,181), 30*ones(1,179)]'; area = areaint(lats,lons) area = 0.0833
This function enables the measurement of areas enclosed by arbitrary polygons. This is a numerical estimate, using a line integral based on Green's Theorem. As such, it is limited by the accuracy and resolution of the input data.
Given sufficient data, the
is the best method for determining the areas of complex polygons,
such as continents, cloud cover, and other natural or derived features.
The calculations in this function employ a spherical Earth assumption.
For nonspherical ellipsoids, the latitude data is converted to the
auxiliary authalic sphere.