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radii.c File Reference

GIS Library - Calculating the Meridional Radius of Curvature. More...

#include <math.h>
#include <grass/gis.h>
#include "pi.h"
Include dependency graph for radii.c:

Go to the source code of this file.

Functions

double G_meridional_radius_of_curvature (double lon, double a, double e2)
 Meridional radius of curvature. More...
 
double G_transverse_radius_of_curvature (double lon, double a, double e2)
 Transverse radius of curvature. More...
 
double G_radius_of_conformal_tangent_sphere (double lon, double a, double e2)
 Radius of conformal tangent sphere. More...
 

Detailed Description

GIS Library - Calculating the Meridional Radius of Curvature.

Todo:
Suggestion: all "lon"s in the file "radii.c" should read as "lat"

Comments: on page http://www.mentorsoftwareinc.com/cc/gistips/TIPS0899.HTM down where it says "Meridional Radius of Curvature" is the exact formula out of "radii.c". Quote: "essentially, the radius of curvature, at a specific latitude ...".

See also http://williams.best.vwh.net/ellipsoid/node1.html which has a nice picture showning the parametric latitude and phi, the geodetic latitude. On the next page, http://williams.best.vwh.net/ellipsoid/node2.html, in equation 3, the Meridional Radius of Curvature shows up.

So, it looks like you are calculating the Meridional Radius of Curvature as a function of GEODETIC LATITUDE.

Various formulas for the ellipsoid. Reference: Map Projections by Peter Richardus and Ron K. Alder University of Illinois Library Call Number: 526.8 R39m Parameters are:

  • lon = longitude of the meridian
  • a = ellipsoid semi-major axis
  • e2 = ellipsoid eccentricity squared

meridional radius of curvature (p. 16)

                       2
              a ( 1 - e )
      M = ------------------
                2   2    3/2
          (1 - e sin lon)

transverse radius of curvature (p. 16)

                   a
      N = ------------------
                2   2    1/2
          (1 - e sin lon)

radius of the tangent sphere onto which angles are mapped conformally (p. 24)

      R = sqrt ( N * M )

(C) 2001-2009 by the GRASS Development Team

This program is free software under the GNU General Public License (>=v2). Read the file COPYING that comes with GRASS for details.

Author
CERL

Definition in file radii.c.

Function Documentation

double G_meridional_radius_of_curvature ( double  lon,
double  a,
double  e2 
)

Meridional radius of curvature.

Returns the meridional radius of curvature at a given longitude:

$ \rho = \frac{a (1-e^2)}{(1-e^2\sin^2 lon)^{3/2}} $

Parameters
lonlongitude
aellipsoid semi-major axis
e2ellipsoid eccentricity squared
Returns
radius value

Definition at line 80 of file radii.c.

References Radians, and x.

double G_radius_of_conformal_tangent_sphere ( double  lon,
double  a,
double  e2 
)

Radius of conformal tangent sphere.

Returns the radius of the conformal sphere tangent to ellipsoid at a given longitude:

$ r = \frac{a (1-e^2)^{1/2}}{(1-e^2\sin^2 lon)} $

Parameters
lonlongitude
aellipsoid semi-major axis
e2ellipsoid eccentricity squared
Returns
radius value

Definition at line 133 of file radii.c.

References Radians, and x.

double G_transverse_radius_of_curvature ( double  lon,
double  a,
double  e2 
)

Transverse radius of curvature.

Returns the transverse radius of curvature at a given longitude:

$ \nu = \frac{a}{(1-e^2\sin^2 lon)^{1/2}} $

Parameters
lonlongitude
aellipsoid semi-major axis
e2ellipsoid eccentricity squared
Returns
radius value

Definition at line 106 of file radii.c.

References Radians, and x.