areaint

Surface area of polygon on sphere or ellipsoid

Syntax

a = areaint(lat,lon)

a = areaint(lat,lon,ellipsoid)

a = areaint(___,units)

Description

a = areaint(lat,lon) calculates the surface area of the polygon with geographic vertices lat and lon. This syntax references the coordinates to a unit sphere and returns a as the fraction of the sphere that the polygon covers.

a = areaint(lat,lon,ellipsoid) specifies the reference ellipsoid for the vertices. This syntax returns the area in square units using the units of the semimajor axis of the reference ellipsoid.

a = areaint(___,units) specifies the angle units for the vertices.

Examples

Calculate Approximate Area of Polygon

The accuracy of the areaint function depends on the distance between the specified vertices. Calculate more accurate approximations by specifying vertices that are closer together.

Specify vertices for a 30º lune, using a point every 30º of latitude. Approximate the surface area as the fraction of the unit sphere that the lune covers.

lat1 = [-90:30:90 60:-30:-60];
lon1 = [zeros(1,7) 30*ones(1,5)];
a1 = areaint(lat1,lon1)

a1 = 0.0792

Specify vertices for the same lune, this time using a point every 10º of latitude. Approximate the area of the lune using the new vertices.

lat2 = [-90:10:90 80:-10:-80];
lon2 = [zeros(1,19) 30*ones(1,17)];
a2 = areaint(lat2,lon2)

a2 = 0.0829

You can find the exact area of the lune by using the areaquad function. A 30º lune covers 1/12 the surface of the unit sphere.

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

a = 0.0833

Calculate Area of Polygon on Ellipsoid

Load a MAT file containing coordinates for the conterminous United States, Long Island, and Martha's Vineyard into the workspace. Display the coordinates on a map using polygons.

load("conus.mat","uslat","uslon")
figure
usamap([min(uslat) max(uslat)],[min(uslon) max(uslon)])
geoshow(uslat,uslon,"DisplayType","polygon")

Create a World Geodetic System of 1984 (WGS84) reference ellipsoid with a length unit of kilometers. Then, calculate the areas of the polygons in square kilometers by referencing the coordinates to the ellipsoid. In this case, the areaint function returns three areas. The largest area is for the polygon representing the conterminous United States. The other two areas are for the polygons representing Long Island and Martha's Vineyard, respectively.

wgs84 = wgs84Ellipsoid("km");
a = areaint(uslat,uslon,wgs84)

a = 3×1
106 ×

    7.9326
    0.0035
    0.0004

Input Arguments

lat — Latitude coordinates of polygon vertices

numeric vector

Latitude coordinates of the polygon vertices, specified as a numeric vector.

• Define one polygon by specifying a vector, such as [39 45 19 39].

• Define multiple polygons by specifying a vector and indicating breaks between the polygons using NaN values, such as [37 46 31 20 37 NaN 45 49 35 32 45 NaN 35 40 42 35]. The NaN values in lat must correspond to the NaN values in lon.

The size of lat must match the size of lon.

Data Types: single | double

lon — Longitude coordinates of polygon vertices

numeric vector

Longitude coordinates of the polygon vertices, specified as a numeric vector.

• Define one polygon by specifying a vector, such as [39 45 19 39].

• Define multiple polygons by specifying a vector and indicating breaks between the polygons using NaN values, such as [37 46 31 20 37 NaN 45 49 35 32 45 NaN 35 40 42 35]. The NaN values in lon must correspond to the NaN values in lat.

The size of lon must match the size of lat.

Data Types: single | double

ellipsoid — Reference ellipsoid

[1 0] (default) | referenceSphere object | referenceEllipsoid object | oblateSpheroid object | two-element numeric vector

Reference ellipsoid, specified as a referenceSphere object, a referenceEllipsoid object, an oblateSpheroid object, or a two-element vector of the form [semimajor_axis eccentricity], where semimajor_axis is the length of the semimajor axis and eccentricity is the eccentricity. The values semimajor_axis and eccentricity must be of data type double.

The default value of [1 0] represents the unit sphere.

units — Angle unit for vertices

"degrees" (default) | "radians"

Angle unit for the vertices, specified as one of these options:

• "degrees" — Degrees

• "radians" — Radians

Data Types: char | string

Output Arguments

a — Surface area of polygon

scalar | vector

Surface area of the polygon, returned as a scalar or a vector.

• When lat and lon define one polygon, a is a scalar.

• When lat and lon define multiple polygons, a is a vector. Each element of the vector is the area of the corresponding polygon.

When you specify the ellipsoid argument, the area is in square units using the units of the semimajor axis of the reference ellipsoid. Otherwise, the area is the fraction of the unit sphere that the polygon covers.

Regardless of the polygon vertex order, the elements of a are positive.

Data Types: double

Algorithms

• The areaint function measures areas enclosed by arbitrary polygons by using a line integral approach based on Green's Theorem. The accuracy is inversely proportional to the distance between the polygon vertices.

• When you specify ellipsoid as a nonspherical ellipsoid, the function converts the latitude data to the auxiliary authalic sphere.

Version History

Introduced before R2006a