areaquad

Surface area of latitude-longitude quadrangle

Syntax

a = areaquad(lat1,lon1,lat2,lon2)

a = areaquad(lat1,lon1,lat2,lon2,ellipsoid)

a = areaquad(___,units)

Description

a = areaquad(lat1,lon1,lat2,lon2) calculates the surface area of the latitude-longitude quadrangle bound by the parallels lat1 and lat2 and the meridians lon1 and lon2. This syntax references the coordinates to a unit sphere and returns a as the fraction of the sphere that the quadrangle covers.

a = areaquad(lat1,lon1,lat2,lon2,ellipsoid) specifies the reference ellipsoid for the parallels and meridians. This syntax returns the area in square units using the units of the semimajor axis of the reference ellipsoid.

a = areaquad(___,units) specifies the angle units for the parallels and meridians.

Examples

Calculate Area of Quadrangle

Find the surface area of the quadrangle bound by the parallels 30ºN and 45ºN and the meridians 25ºW and 60ºE. When you do not specify a reference ellipsoid as input, the areaquad function references the quadrangle to the unit sphere and returns the area as the fraction of the sphere that the quadrangle covers, where 1 is the entire sphere.

a = areaquad(30,-25,45,60)

a = 
0.0245

This quadrangle covers approximately 2.45% of the unit sphere.

Calculate Area of Quadrangle on Ellipsoid

Create a World Geodetic System of 1984 (WGS84) reference ellipsoid with a length unit of kilometers.

wgs84 = wgs84Ellipsoid("km");

Find the area of the quadrangle that is bound by the parallels 30ºN and 45ºN and the meridians 25ºW and 60ºE. When you specify a reference ellipsoid as input, the areaquad function returns area in square units using the length unit of the ellipsoid.

a = areaquad(30,-25,45,60,wgs84)

a = 
1.2477e+07

Input Arguments

lat1 — Latitude of first parallel

scalar | vector | matrix | N-D array

Latitude of the first parallel, specified as a scalar, vector, matrix, or N-D array.

When you specify a vector, matrix, or N-D array, each element specifies the latitude of the first parallel of a separate quadrangle.

The sizes of lat1, lon1, lat2, and lon2 must match.

Data Types: double

lon1 — Longitude of first meridian

scalar | vector | matrix | N-D array

Longitude of the first meridian, specified as a scalar, vector, matrix, or N-D array.

When you specify a vector, matrix, or N-D array, each element specifies the longitude of the first meridian of a separate quadrangle.

The sizes of lat1, lon1, lat2, and lon2 must match.

Data Types: double

lat2 — Latitude of second parallel

scalar | vector | matrix | N-D array

Latitude of the second parallel, specified as a scalar, vector, matrix, or N-D array.

When you specify a vector, matrix, or N-D array, each element specifies the latitude of the second parallel of a separate quadrangle.

The sizes of lat1, lon1, lat2, and lon2 must match.

Data Types: double

lon2 — Longitude of second meridian

scalar | vector | matrix | N-D array

Longitude of the second meridian, specified as a scalar, vector, matrix, or N-D array.

When you specify a vector, matrix, or N-D array, each element specifies the longitude of the second meridian of a separate quadrangle.

The sizes of lat1, lon1, lat2, and lon2 must match.

Data Types: 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 units of parallels and meridians

"degrees" (default) | "radians"

Angle units of the parallels and meridians, specified as one of these options:

• "degrees" — Degrees

• "radians" — Radians

Data Types: char | string

Output Arguments

a — Surface area of quadrangle

scalar | vector | matrix | N-D array

Surface area of the quadrangle, returned as a scalar, vector, matrix, or N-D array of the same size as lat1, lon1, lat2, and lon2. Each element of a is the area for the quadrangle defined by the corresponding elements of lat1, lon1, lat2, and lon2.

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 quadrangle covers.

More About

Latitude-Longitude Quadrangle

A latitude-longitude quadrangle is a region bounded by two meridians and two parallels. In spherical geometry, a quadrangle is the intersection of a lune (a section bounded by two meridians) and a zone (a section bounded by two parallels).

Algorithms

• The areaquad function uses spherical geometry and returns exact calculations.

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

Version History

Introduced before R2006a