diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/pj_phi2.c | 64 |
1 files changed, 41 insertions, 23 deletions
diff --git a/src/pj_phi2.c b/src/pj_phi2.c index 13419df8..a83302e6 100644 --- a/src/pj_phi2.c +++ b/src/pj_phi2.c @@ -1,28 +1,46 @@ -/* determine latitude angle phi-2 */ +/* Determine latitude angle phi-2. */ + +#include <math.h> + #include "projects.h" -#define TOL 1.0e-10 -#define N_ITER 15 +static const double TOL = 1.0e-10; +static const int N_ITER = 15; + +/*****************************************************************************/ +double pj_phi2(projCtx ctx, double ts, double e) { +/****************************************************************************** +Determine latitude angle phi-2. +Inputs: + ts = exp(-psi) where psi is the isometric latitude (dimensionless) + e = eccentricity of the ellipsoid (dimensionless) +Output: + phi = geographic latitude (radians) +Here isometric latitude is defined by + psi = log( tan(pi/4 + phi/2) * + ( (1 - e*sin(phi)) / (1 + e*sin(phi)) )^(e/2) ) + = asinh(tan(phi)) - e * atanh(e * sin(phi)) +This routine inverts this relation using the iterative scheme given +by Snyder (1987), Eqs. (7-9) - (7-11) +*******************************************************************************/ + double eccnth = .5 * e; + double Phi = M_HALFPI - 2. * atan(ts); + double con; + int i = N_ITER; + + for(;;) { + double dphi; + con = e * sin(Phi); + dphi = M_HALFPI - 2. * atan(ts * pow((1. - con) / + (1. + con), eccnth)) - Phi; - double -pj_phi2(projCtx ctx, double ts, double e) { - double eccnth, Phi, con; - int i; + Phi += dphi; - eccnth = .5 * e; - Phi = M_HALFPI - 2. * atan (ts); - i = N_ITER; - for(;;) { - double dphi; - con = e * sin (Phi); - dphi = M_HALFPI - 2. * atan (ts * pow((1. - con) / - (1. + con), eccnth)) - Phi; - Phi += dphi; - if( fabs(dphi) > TOL && --i ) - continue; - break; - } - if (i <= 0) - pj_ctx_set_errno( ctx, PJD_ERR_NON_CON_INV_PHI2 ); - return Phi; + if (fabs(dphi) > TOL && --i) + continue; + break; + } + if (i <= 0) + pj_ctx_set_errno(ctx, PJD_ERR_NON_CON_INV_PHI2); + return Phi; } |