the Bertin 1953 projection

docs/plot/plotdefs.json

@@ -87,6 +87,18 @@
         "res": "low",
         "type": "poly"
     },
+    {
+        "filename": "bertin1953.png",
+        "latmax": 90,
+        "latmin": -90,
+        "latmin": -60,
+        "lonmax": 180,
+        "lonmin": -180,
+        "name": "bertin1953",
+        "projstring": "+proj=bertin1953",
+        "res": "low",
+        "type": "poly"
+    },
     {
         "filename": "bipc.png",
         "latmax": 90,

docs/source/operations/projections/bertin1953.rst

@@ -0,0 +1,64 @@
+.. _bertin1953:
+
+********************************************************************************
+Bertin 1953
+********************************************************************************
+
+.. versionadded:: 6.0.0
+
++---------------------+-------------------------------+
+| **Classification**  | Miscellaneous                 |
++---------------------+-------------------------------+
+| **Available forms** | Forward, spherical projection |
++---------------------+-------------------------------+
+| **Defined area**    | Global                        |
++---------------------+-------------------------------+
+| **Alias**           | bertin1953                    |
++---------------------+-------------------------------+
+| **Domain**          | 2D                            |
++---------------------+-------------------------------+
+| **Input type**      | Geodetic coordinates          |
++---------------------+-------------------------------+
+| **Output type**     | Projected coordinates         |
++---------------------+-------------------------------+
+
+
+
+.. figure:: ./images/bertin1953.png
+   :width: 500 px
+   :align: center
+   :alt:   Bertin 1953
+
+   proj-string: ``+proj=bertin1953``
+
+
+The Bertin 1953 projection is intended for making world maps. Created by Jacques Bertin
+in 1953, this projection was the go-to choice of the French cartographic school when they
+wished to represent phenomena on a global scale. The projection was formulated in 2017
+by Philippe Rivière for visionscarto.net.
+
+
+Usage
+###############################################################################
+
+The Bertin 1953 projection has no special options. Its rotation parameters
+are fixed. Here is an example of a forward projection with scale 1:
+
+    $ echo 122 47 | src/proj +proj=bertin1953 +R=1
+    0.72	0.73
+
+Parameters
+################################################################################
+
+.. note:: All parameters for the projection are optional.
+
+.. include:: ../options/R.rst
+
+.. include:: ../options/x_0.rst
+
+.. include:: ../options/y_0.rst
+
+Further reading
+################################################################################
+
+#. Philippe Rivière (2017). `Bertin Projection (1953) <https://visionscarto.net/bertin-projection-1953>`, Visionscarto.net.

docs/source/operations/projections/index.rst

@@ -20,6 +20,7 @@ Projections map the spherical 3D space to a flat 2D space.
    apian
    august
    bacon
+   bertin1953
    bipc
    boggs
    bonne

src/Makefile.am

@@ -55,7 +55,7 @@ libproj_la_SOURCES = \
 	PJ_mill.c PJ_ocea.c PJ_omerc.c PJ_somerc.c \
 	PJ_tcc.c PJ_tcea.c PJ_times.c PJ_tmerc.c \
 	PJ_airy.c PJ_aitoff.c PJ_august.c PJ_bacon.c \
-	PJ_chamb.c PJ_hammer.c PJ_lagrng.c PJ_larr.c \
+	PJ_bertin1953.c PJ_chamb.c PJ_hammer.c PJ_lagrng.c PJ_larr.c \
 	PJ_lask.c PJ_latlong.c PJ_nocol.c PJ_ob_tran.c PJ_oea.c \
 	PJ_tpeqd.c PJ_vandg.c PJ_vandg2.c PJ_vandg4.c \
 	PJ_wag7.c PJ_lcca.c PJ_geos.c proj_etmerc.c \

src/PJ_bertin1953.c

@@ -0,0 +1,94 @@
+/*
+  Created by Jacques Bertin in 1953, this projection was the go-to choice
+  of the French cartographic school when they wished to represent phenomena
+  on a global scale.
+
+  Formula designed by Philippe Rivière, 2017.
+  https://visionscarto.net/bertin-projection-1953
+
+  Port to PROJ by Philippe Rivière, 21 September 2018
+*/
+
+#define PJ_LIB__
+
+#include <errno.h>
+#include <math.h>
+
+#include "proj_internal.h"
+#include "proj.h"
+#include "projects.h"
+
+PROJ_HEAD(bertin1953, "Bertin 1953")
+    "\n\tMisc Sph no inv.";
+
+struct pj_opaque {
+    double cos_delta_phi, sin_delta_phi, cos_delta_gamma, sin_delta_gamma, deltaLambda;
+};
+
+
+static XY s_forward (LP lp, PJ *P) {
+    XY xy = {0.0,0.0};
+    struct pj_opaque *Q = P->opaque;
+
+    double fu = 1.4, k = 12., w = 1.68, d;
+
+    /* Rotate */
+    double cosphi, x, y, z, z0;
+    lp.lam += PJ_TORAD(-16.5);
+    cosphi = cos(lp.phi);
+    x = cos(lp.lam) * cosphi;
+    y = sin(lp.lam) * cosphi;
+    z = sin(lp.phi);
+    z0 = z * Q->cos_delta_phi + x * Q->sin_delta_phi;
+    lp.lam = atan2(y * Q->cos_delta_gamma - z0 * Q->sin_delta_gamma,
+       x * Q->cos_delta_phi - z * Q->sin_delta_phi);
+    z0 = z0 * Q->cos_delta_gamma + y * Q->sin_delta_gamma;
+    lp.phi = asin(z0);
+
+    lp.lam = adjlon(lp.lam);
+
+    /* Adjust pre-projection */
+    if (lp.lam + lp.phi < -fu) {
+      d = (lp.lam - lp.phi + 1.6) * (lp.lam + lp.phi + fu) / 8.;
+      lp.lam += d;
+      lp.phi -= 0.8 * d * sin(lp.phi + M_PI / 2.);
+    }
+
+    /* Project with Hammer (1.68,2) */
+    cosphi = cos(lp.phi);
+    d = sqrt(2./(1. + cosphi * cos(lp.lam / 2.)));
+    xy.x = w * d * cosphi * sin(lp.lam / 2.);
+    xy.y = d * sin(lp.phi);
+
+    /* Adjust post-projection */
+    d = (1. - cos(lp.lam * lp.phi)) / k;
+    if (xy.y < 0.) {
+      xy.x *= 1. + d;
+    }
+    if (xy.y > 0.) {
+      xy.x *= 1. + d / 1.5 * xy.x * xy.x;
+    }
+
+    return xy;
+}
+
+
+PJ *PROJECTION(bertin1953) {
+    struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
+    if (0==Q)
+        return pj_default_destructor (P, ENOMEM);
+    P->opaque = Q;
+
+    P->lam0 = 0;
+    P->phi0 = PJ_TORAD(-42.);
+
+    Q->cos_delta_phi = cos(P->phi0);
+    Q->sin_delta_phi = sin(P->phi0);
+    Q->cos_delta_gamma = 1.;
+    Q->sin_delta_gamma = 0.;
+
+    P->es = 0.;
+    P->fwd = s_forward;
+
+    return P;
+}

src/lib_proj.cmake

@@ -46,6 +46,7 @@ SET(SRC_LIBPROJ_PJ
         PJ_august.c
         PJ_axisswap.c
         PJ_bacon.c
+        PJ_bertin1953.c
         PJ_bipc.c
         PJ_boggs.c
         PJ_bonne.c

src/pj_list.h

@@ -15,6 +15,7 @@ PROJ_HEAD(apian, "Apian Globular I")
 PROJ_HEAD(august, "August Epicycloidal")
 PROJ_HEAD(axisswap, "Axis ordering")
 PROJ_HEAD(bacon, "Bacon Globular")
+PROJ_HEAD(bertin1953, "Bertin 1953")
 PROJ_HEAD(bipc, "Bipolar conic of western hemisphere")
 PROJ_HEAD(boggs, "Boggs Eumorphic")
 PROJ_HEAD(bonne, "Bonne (Werner lat_1=90)")

test/gie/more_builtins.gie

@@ -59,6 +59,41 @@ roundtrip 100    1 m
 -------------------------------------------------------------------------------
 
 
+-------------------------------------------------------------------------------
+Tests for PJ_bertin1953.c
+-------------------------------------------------------------------------------
+operation proj=bertin1953 +R=1
+-------------------------------------------------------------------------------
+accept    0 0
+expect    -0.260206554508 -0.685226058142
+
+accept    16.5 42
+expect    0.0 0.0
+
+accept    -180 90
+expect    0.0 0.813473286152
+
+accept    0 90
+expect    0.0 0.813473286152
+
+accept    10 -35
+expect    -0.138495501548 -1.221408328101
+
+accept    -70 -35
+expect    -1.504967424950 -0.522846035499
+
+accept    80 7
+expect    0.929377425352 -0.215443296201
+
+accept    128 35
+expect    0.937431733950 0.700084268525
+
+accept    170 -41
+expect    2.162845830414 -0.046534568425
+
+-------------------------------------------------------------------------------
+
+