rsphere

Radii of auxiliary spheres

Syntax

r = rsphere('biaxial',ellipsoid)
r = rsphere('biaxial',ellipsoid,method)
r = rsphere('triaxial',ellipsoid)
r = rsphere('triaxial',ellipsoid,method)
r = rsphere('eqavol',ellipsoid)
r = rsphere('authalic',ellipsoid)
r = rsphere('rectifying',ellipsoid)
r = rsphere('curve',ellipsoid,lat)
r = rsphere('curve',ellipsoid,lat,method)
r = rsphere('euler',lat1,lon1,lat2,lon2,ellipsoid)
r = rsphere('curve', ..., angleUnits)
r = rsphere(‘euler', ..., angleUnits)

Description

r = rsphere('biaxial',ellipsoid) computes the arithmetic mean i.e., (a+b)/2 where a and b are the semimajor and semiminor axes of the specified ellipsoid. ellipsoid is a referenceSphere, referenceEllipsoid, or oblateSpheroid object, or a vector of the form [semimajor_axis eccentricity].

r = rsphere('biaxial',ellipsoid,method) computes the arithmetic mean if the string method is 'mean' and the geometric mean, sqrt(a*b), if method is 'norm'.

r = rsphere('triaxial',ellipsoid) computes the triaxial arithmetic mean of the semimajor axes, a, and semininor axes, b of the ellipsoid, (2*a+b)/3.

r = rsphere('triaxial',ellipsoid,method) computes the arithmetic mean if the string method is 'mean' and the triaxial geometric mean, (a^2*b)^(1/3), if method is ‘norm'.

r = rsphere('eqavol',ellipsoid) returns the radius of a sphere with a volume equal to that of the ellipsoid.

r = rsphere('authalic',ellipsoid) returns the radius of a sphere with a surface area equal to that of the ellipsoid.

r = rsphere('rectifying',ellipsoid) returns the radius of a sphere with meridional distances equal to those of the ellipsoid.

r = rsphere('curve',ellipsoid,lat) computes the arithmetic mean of the transverse and meridional radii of curvature at the latitude, lat. lat is in degrees.

r = rsphere('curve',ellipsoid,lat,method) computes an arithmetic mean if the string ‘method' is ‘mean' and a geometric mean if ‘method' is ‘norm'.

r = rsphere('euler',lat1,lon1,lat2,lon2,ellipsoid) computes the Euler radius of curvature at the midpoint of the geodesic arc defined by the endpoints (lat1,lon1) and (lat2,lon2). lat1, lon1,lat2, and lon2 are in degrees.

r = rsphere('curve', ..., angleUnits) and r = rsphere(‘euler', ..., angleUnits) use the angleUnits string to specify the units of the latitude and longitude inputs. angleUnits can be ‘degrees' or ‘radians'.

Examples

Different criteria result in different spheres:

r = rsphere('biaxial',referenceEllipsoid('earth','km'))

r =
   6.3674e+03

r = rsphere('triaxial',referenceEllipsoid('earth','km'))

r =
   6.3710e+03

r = rsphere('curve',referenceEllipsoid('earth','km'))

r =
   6.3781e+03

See Also

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