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:

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

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 )

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

◆ G_meridional_radius_of_curvature()

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

lon	longitude
a	ellipsoid semi-major axis
e2	ellipsoid eccentricity squared

Returns: radius value

Definition at line 80 of file radii.c.

References G_meridional_radius_of_curvature(), Radians, and x.

Referenced by G_meridional_radius_of_curvature().

◆ G_radius_of_conformal_tangent_sphere()

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

lon	longitude
a	ellipsoid semi-major axis
e2	ellipsoid eccentricity squared

Returns: radius value

Definition at line 133 of file radii.c.

References G_radius_of_conformal_tangent_sphere(), Radians, and x.

Referenced by G_radius_of_conformal_tangent_sphere().

◆ G_transverse_radius_of_curvature()

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

lon	longitude
a	ellipsoid semi-major axis
e2	ellipsoid eccentricity squared

Returns: radius value

Definition at line 106 of file radii.c.

References G_transverse_radius_of_curvature(), Radians, and x.

Referenced by G_transverse_radius_of_curvature().

Functions

Detailed Description

Function Documentation

◆ G_meridional_radius_of_curvature()

◆ G_radius_of_conformal_tangent_sphere()

◆ G_transverse_radius_of_curvature()