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 lat and lon. The calculation uses a line integral approach. The output, area, 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 referenceSphere, referenceEllipsoid, or oblateSpheroid object, or a vector of the form [semimajor_axis eccentricity]. The output, area, is in squares units corresponding to the units of ellipsoid.

area = areaint(lat,lon,units) uses the units defined by units, the string scalar or character vector 'degrees' or 'radians'. If omitted, default units of degrees are assumed.

area = areaint(lat,lon,ellipsoid,units) uses both the inputs ellipsoid and 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 areaquad to get an exact solution:

area = areaquad(90,0,-90,30)
area =

This is 1/12 the spherical area. The more points used to define this polygon, the more integration steps areaint takes, improving the estimate. This first attempt takes a point every 30º of latitude:

lats = [-90:30:90,60:-30:-60]';
lons = [zeros(1,7), 30*ones(1,5)]';
area = areaint(lats,lons)
area =

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 =


Regardless of the polygon vertex order, the values returned by areaint are positive.


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 areaint function 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.

Introduced before R2006a