From 5229741fe5cdf2e5fa4772b9141298417331fa98 Mon Sep 17 00:00:00 2001
From: Frank Warmerdam <warmerdam@pobox.com>
Date: Sun, 4 Mar 2012 00:15:57 +0000
Subject: added the Natural Earth projection

git-svn-id: http://svn.osgeo.org/metacrs/proj/trunk@2182 4e78687f-474d-0410-85f9-8d5e500ac6b2
---
 src/PJ_natearth.c | 77 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 77 insertions(+)
 create mode 100644 src/PJ_natearth.c

(limited to 'src/PJ_natearth.c')

diff --git a/src/PJ_natearth.c b/src/PJ_natearth.c
new file mode 100644
index 00000000..f83a3ffd
--- /dev/null
+++ b/src/PJ_natearth.c
@@ -0,0 +1,77 @@
+/*
+The Natural Earth projection was designed by Tom Patterson, US National Park
+Service, in 2007, using Flex Projector. The shape of the original projection
+was defined at every 5 degrees and piece-wise cubic spline interpolation was
+used to compute the complete graticule.
+The code here uses polynomial functions instead of cubic splines and
+is therefore much simpler to program. The polynomial approximation was
+developed by Bojan Savric, in collaboration with Tom Patterson and Bernhard
+Jenny, Institute of Cartography, ETH Zurich. It slightly deviates from
+Patterson's original projection by adding additional curvature to meridians
+where they meet the horizontal pole line. This improvement is by intention
+and designed in collaboration with Tom Patterson.
+Port to PROJ.4 by Bernhard Jenny, 6 June 2011
+*/
+
+#define PJ_LIB__
+#include	<projects.h>
+PROJ_HEAD(natearth, "Natural Earth") "\n\tPCyl., Sph.";
+#define A0 0.8707
+#define A1 -0.131979
+#define A2 -0.013791
+#define A3 0.003971
+#define A4 -0.001529
+#define B0 1.007226
+#define B1 0.015085
+#define B2 -0.044475
+#define B3 0.028874
+#define B4 -0.005916
+#define C0 B0
+#define C1 (3 * B1)
+#define C2 (7 * B2)
+#define C3 (9 * B3)
+#define C4 (11 * B4)
+#define EPS 1e-11
+#define MAX_Y (0.8707 * 0.52 * PI)
+
+FORWARD(s_forward); /* spheroid */
+	double phi2, phi4;
+
+	phi2 = lp.phi * lp.phi;
+	phi4 = phi2 * phi2;
+	xy.x = lp.lam * (A0 + phi2 * (A1 + phi2 * (A2 + phi4 * phi2 * (A3 + phi2 * A4))));
+	xy.y = lp.phi * (B0 + phi2 * (B1 + phi4 * (B2 + B3 * phi2 + B4 * phi4)));
+	return (xy);
+}
+INVERSE(s_inverse); /* spheroid */
+	double yc, tol, y2, y4, f, fder;
+
+        /* make sure y is inside valid range */
+	if (xy.y > MAX_Y) {
+		xy.y = MAX_Y;
+	} else if (xy.y < -MAX_Y) {
+		xy.y = -MAX_Y;
+	}
+
+        /* latitude */
+	yc = xy.y;
+        for (;;) { /* Newton-Raphson */
+		y2 = yc * yc;
+		y4 = y2 * y2;
+		f = (yc * (B0 + y2 * (B1 + y4 * (B2 + B3 * y2 + B4 * y4)))) - xy.y;
+		fder = C0 + y2 * (C1 + y4 * (C2 + C3 * y2 + C4 * y4));
+		yc -= tol = f / fder;
+		if (fabs(tol) < EPS) {
+			break;
+		}
+	}
+	lp.phi = yc;
+
+        /* longitude */
+	y2 = yc * yc;
+	lp.lam = xy.x / (A0 + y2 * (A1 + y2 * (A2 + y2 * y2 * y2 * (A3 + y2 * A4))));
+
+	return (lp);
+}
+FREEUP; if (P) pj_dalloc(P); }
+ENTRY0(natearth) P->es = 0; P->inv = s_inverse; P->fwd = s_forward; ENDENTRY(P)
-- 
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