| Mapping Toolbox | |
Compute auxiliary sphere radii
Syntax
r = rsphere('biaxial',geoid) r = rsphere('biaxial',geoid,method) r = rsphere('triaxial',geoid) r = rsphere('triaxial',geoid,method) r = rsphere('eqavol',geoid) r = rsphere('authalic',geoid) r = rsphere('rectifying',geoid) r = rsphere('curve',geoid) r = rsphere('curve',geoid,lat) r = rsphere('curve',geoid,method) r = rsphere('curve',geoid,lat,method) r = rsphere('curve',geoid,lat,method,units) r = rsphere('euler',lat1,lon1,lat2,lon2,geoid) r = rsphere('euler',lat1,lon1,lat2,lon2,geoid,units)
Description
This command calculates the radii of auxiliary spheres for the ellipsoid. An auxiliary sphere is a sphere that shares certain desired characteristics with
the ellipsoid.
r = rsphere('biaxial',geoid) calculates the radius of an biaxial auxiliary sphere for the ellipsoid specified by the two-element geoid vector geoid. The output, r, is the radius of this sphere in units consistent with the semimajor axis, that is, the first element of geoid. The biaxial radius is calculated by averaging the semimajor and semiminor axes of the ellipsoid, giving each
equal weight.
r = rsphere('biaxial',geoid,method) specifies the averaging method. If the string method is 'mean' (the default), an arithmetic mean is used. If method is 'norm', a geometric mean is used.
r = rsphere('triaxial',geoid) results in a triaxial radius, which is calculated by averaging the ellipsoidal axes while giving double weight to the semimajor axis to reflect its role in two of the ellipsoid's three dimensions.
r = rsphere('eqavol',geoid) returns the radius of a sphere with a volume equal to that of the ellipsoid.
r = rsphere('authalic',geoid) returns the radius of a sphere with a surface area equal to that of the ellipsoid.
r = rsphere('rectifying',geoid) returns the radius of a sphere with meridional distances equal to those of the ellipsoid.
r = rsphere('curve',geoid,lat,method,units) returns a radius that is the result of averaging the meridianal and transverse radii of curvature at the specified latitude, lat. The units of the input lat can be specified by the valid angle units string units. The default units are 'degrees', the default averaging method is 'mean', and the default latitude is 45°.
r = rsphere('euler',lat1,lon1,lat2,lon2,geoid) calculates a radius using Euler's Theorem. This calculation requires the specification of an arc, which is defined by its endpoints, (lat1,lon1) and (lat2,lon2).
Examples
Different criteria result in different spheres:
r = rsphere('biaxial',almanac('earth','geoid','km')) r = 6.3674e+03 r = rsphere('triaxial',almanac('earth','geoid','km')) r = 6.3710e+03 r = rsphere('curve',almanac('earth','geoid','km')) r = 6.3781e+03
See Also
rcurve |
Radii of curvature for the ellipsoid |
| | roundn | scaleruler | |