From f1ea5041d5049498e3cd88f9a215ebb0f4b86a34 Mon Sep 17 00:00:00 2001 From: Javier Goizueta Date: Wed, 11 Apr 2018 17:56:08 +0200 Subject: Enhance the precision of Spherical Mercator projection near the equator This uses a linear approximation of tan(x+pi/4) for better precision at small latitudes. As a result points of latitude 0 maintain a 0 Y coordinate and 0,0 is transformed to 0,0 --- src/PJ_merc.c | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) (limited to 'src') diff --git a/src/PJ_merc.c b/src/PJ_merc.c index a3e5e846..3801b828 100644 --- a/src/PJ_merc.c +++ b/src/PJ_merc.c @@ -8,6 +8,13 @@ PROJ_HEAD(webmerc, "Web Mercator / Pseudo Mercator") "\n\tCyl, Sph\n\t"; #define EPS10 1.e-10 +static double _tan_near_fort_pi(double x) { + if (fabs(x) <= __DBL_EPSILON__) { + return 2*x + 1.0; + } + return tan(M_FORTPI + x); +} + static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */ XY xy = {0.0,0.0}; if (fabs(fabs(lp.phi) - M_HALFPI) <= EPS10) { @@ -27,7 +34,7 @@ static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */ return xy; } xy.x = P->k0 * lp.lam; - xy.y = P->k0 * log(tan(M_FORTPI + .5 * lp.phi)); + xy.y = P->k0 * log(_tan_near_fort_pi(.5 * lp.phi)); return xy; } -- cgit v1.2.3