From df574ae332d57f556fd56314883b3354cab1d0ff Mon Sep 17 00:00:00 2001 From: Even Rouault Date: Wed, 19 Dec 2018 13:00:37 +0100 Subject: cpp conversion: remove useless pj_, PJ_ and proj_ filename prefixes --- src/phi2.cpp | 46 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 46 insertions(+) create mode 100644 src/phi2.cpp (limited to 'src/phi2.cpp') diff --git a/src/phi2.cpp b/src/phi2.cpp new file mode 100644 index 00000000..a83302e6 --- /dev/null +++ b/src/phi2.cpp @@ -0,0 +1,46 @@ +/* Determine latitude angle phi-2. */ + +#include + +#include "projects.h" + +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; + + 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; +} -- cgit v1.2.3