Implemented IGH Oceanic View (#2226)

- The current implementation of the Interrupted Goode Homolosine
  projection emphasizes land area. This is a compliment projection
  that emphasizes ocean area.
- A value of lon0=-160 produces a reasonable real-world map.

5 files changed, 331 insertions, 33 deletions

diff --git a/src/Makefile.am b/src/Makefile.am
index 9f24a60d..3f5b2968 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -150,6 +150,7 @@ libproj_la_SOURCES = \
 	projections/gn_sinu.cpp \
 	projections/goode.cpp \
 	projections/igh.cpp \
+	projections/igh_o.cpp \
 	projections/hatano.cpp \
 	projections/loxim.cpp \
 	projections/mbt_fps.cpp \
diff --git a/src/lib_proj.cmake b/src/lib_proj.cmake
index c318a266..4eca0256 100644
--- a/src/lib_proj.cmake
+++ b/src/lib_proj.cmake
@@ -134,6 +134,7 @@ set(SRC_LIBPROJ_PROJECTIONS
   projections/gn_sinu.cpp
   projections/goode.cpp
   projections/igh.cpp
+  projections/igh_o.cpp
   projections/hatano.cpp
   projections/loxim.cpp
   projections/mbt_fps.cpp
diff --git a/src/pj_list.h b/src/pj_list.h
index cf81ae0e..c7e6d209 100644
--- a/src/pj_list.h
+++ b/src/pj_list.h
@@ -69,6 +69,7 @@ PROJ_HEAD(helmert,   "3- and 7-parameter Helmert shift")
 PROJ_HEAD(hgridshift, "Horizontal grid shift")
 PROJ_HEAD(horner,    "Horner polynomial evaluation")
 PROJ_HEAD(igh,  "Interrupted Goode Homolosine")
+PROJ_HEAD(igh_o,  "Interrupted Goode Homolosine Oceanic View")
 PROJ_HEAD(imw_p, "International Map of the World Polyconic")
 PROJ_HEAD(isea, "Icosahedral Snyder Equal Area")
 PROJ_HEAD(kav5, "Kavraisky V")
diff --git a/src/projections/igh.cpp b/src/projections/igh.cpp
index 8a41cea3..2be94889 100644
--- a/src/projections/igh.cpp
+++ b/src/projections/igh.cpp
@@ -8,15 +8,31 @@
 
 PROJ_HEAD(igh, "Interrupted Goode Homolosine") "\n\tPCyl, Sph";
 
+/*
+This projection is a compilation of 12 separate sub-projections.
+Sinusoidal projections are found near the equator and Mollweide
+projections are found at higher latitudes. The transition between
+the two occurs at 40 degrees latitude and is represented by the 
+constant `phi_boundary`.
+
+Each sub-projection is assigned an integer label
+numbered 1 through 12. Most of this code contains logic to assign
+the labels based on latitude (phi) and longitude (lam) regions.
+
+Original Reference:
+J. Paul Goode (1925) THE HOMOLOSINE PROJECTION: A NEW DEVICE FOR 
+    PORTRAYING THE EARTH'S SURFACE ENTIRE, Annals of the Association of 
+    American Geographers, 15:3, 119-125, DOI: 10.1080/00045602509356949
+*/
+
 C_NAMESPACE PJ *pj_sinu(PJ *), *pj_moll(PJ *);
 
-/* 40d 44' 11.8" [degrees] */
-/*
-static const double d4044118 = (40 + 44/60. + 11.8/3600.) * DEG_TO_RAD;
-has been replaced by this define, to eliminate portability issue:
-Initializer element not computable at load time
+/* 
+Transition from sinusoidal to Mollweide projection
+Latitude (phi): 40deg 44' 11.8" 
 */
-#define d4044118 ((40 + 44/60. + 11.8/3600.) * DEG_TO_RAD)
+
+static const double phi_boundary = (40 + 44/60. + 11.8/3600.) * DEG_TO_RAD;
 
 static const double d10  =  10 * DEG_TO_RAD;
 static const double d20  =  20 * DEG_TO_RAD;
@@ -46,13 +62,13 @@ static PJ_XY igh_s_forward (PJ_LP lp, PJ *P) {           /* Spheroidal, forward
     struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
     int z;
 
-    if (lp.phi >=  d4044118) {          /* 1|2 */
+    if (lp.phi >=  phi_boundary) {          /* 1|2 */
       z = (lp.lam <= -d40 ? 1: 2);
     }
     else if (lp.phi >=  0) {            /* 3|4 */
       z = (lp.lam <= -d40 ? 3: 4);
     }
-    else if (lp.phi >= -d4044118) {     /* 5|6|7|8 */
+    else if (lp.phi >= -phi_boundary) {     /* 5|6|7|8 */
            if (lp.lam <= -d100) z =  5; /* 5 */
       else if (lp.lam <=  -d20) z =  6; /* 6 */
       else if (lp.lam <=   d80) z =  7; /* 7 */
@@ -82,11 +98,11 @@ static PJ_LP igh_s_inverse (PJ_XY xy, PJ *P) {           /* Spheroidal, inverse
     int z = 0;
     if (xy.y > y90+EPSLN || xy.y < -y90+EPSLN) /* 0 */
       z = 0;
-    else if (xy.y >=  d4044118)       /* 1|2 */
+    else if (xy.y >=  phi_boundary)       /* 1|2 */
       z = (xy.x <= -d40? 1: 2);
     else if (xy.y >=  0)              /* 3|4 */
       z = (xy.x <= -d40? 3: 4);
-    else if (xy.y >= -d4044118) {     /* 5|6|7|8 */
+    else if (xy.y >= -phi_boundary) {     /* 5|6|7|8 */
            if (xy.x <= -d100) z =  5; /* 5 */
       else if (xy.x <=  -d20) z =  6; /* 6 */
       else if (xy.x <=   d80) z =  7; /* 7 */
@@ -100,7 +116,7 @@ static PJ_LP igh_s_inverse (PJ_XY xy, PJ *P) {           /* Spheroidal, inverse
     }
 
     if (z) {
-        int ok = 0;
+        bool ok = false;
 
         xy.x -= Q->pj[z-1]->x0;
         xy.y -= Q->pj[z-1]->y0;
@@ -145,9 +161,11 @@ static PJ *destructor (PJ *P, int errlev) {
     if (nullptr==P->opaque)
         return pj_default_destructor (P, errlev);
 
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+
     for (i = 0; i < 12; ++i) {
-        if (static_cast<struct pj_opaque*>(P->opaque)->pj[i])
-            static_cast<struct pj_opaque*>(P->opaque)->pj[i]->destructor(static_cast<struct pj_opaque*>(P->opaque)->pj[i], errlev);
+        if (Q->pj[i])
+            Q->pj[i]->destructor(Q->pj[i], errlev);
     }
 
     return pj_default_destructor(P, errlev);
@@ -175,18 +193,21 @@ static PJ *destructor (PJ *P, int errlev) {
     -180    -100      -20         80          180
 */
 
-#define SETUP(n, proj, x_0, y_0, lon_0) \
-    if (!(Q->pj[n-1] = pj_##proj(nullptr))) return destructor(P, ENOMEM); \
-    if (!(Q->pj[n-1] = pj_##proj(Q->pj[n-1]))) return destructor(P, ENOMEM); \
-    Q->pj[n-1]->ctx = P->ctx; \
-    Q->pj[n-1]->x0 = x_0; \
-    Q->pj[n-1]->y0 = y_0; \
+static bool setup_zone(PJ *P, struct pj_opaque *Q, int n,
+                       PJ*(*proj_ptr)(PJ*), double x_0,
+                       double y_0, double lon_0) {
+    if (!(Q->pj[n-1] = proj_ptr(nullptr))) return false;
+    if (!(Q->pj[n-1] = proj_ptr(Q->pj[n-1]))) return false;
+    Q->pj[n-1]->ctx = P->ctx;
+    Q->pj[n-1]->x0 = x_0;
+    Q->pj[n-1]->y0 = y_0;
     Q->pj[n-1]->lam0 = lon_0;
-
+    return true;
+}
 
 PJ *PROJECTION(igh) {
     PJ_XY xy1, xy3;
-    PJ_LP lp = { 0, d4044118 };
+    PJ_LP lp = { 0, phi_boundary };
     struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
     if (nullptr==Q)
         return pj_default_destructor (P, ENOMEM);
@@ -194,15 +215,18 @@ PJ *PROJECTION(igh) {
 
 
     /* sinusoidal zones */
-    SETUP(3, sinu, -d100, 0, -d100);
-    SETUP(4, sinu,   d30, 0,   d30);
-    SETUP(5, sinu, -d160, 0, -d160);
-    SETUP(6, sinu,  -d60, 0,  -d60);
-    SETUP(7, sinu,   d20, 0,   d20);
-    SETUP(8, sinu,  d140, 0,  d140);
+    if (!setup_zone(P, Q, 3, pj_sinu, -d100, 0, -d100) ||
+        !setup_zone(P, Q, 4, pj_sinu,   d30, 0,   d30) ||
+        !setup_zone(P, Q, 5, pj_sinu, -d160, 0, -d160) ||
+        !setup_zone(P, Q, 6, pj_sinu,  -d60, 0,  -d60) ||
+        !setup_zone(P, Q, 7, pj_sinu,   d20, 0,   d20) ||
+        !setup_zone(P, Q, 8, pj_sinu,  d140, 0,  d140))
+    {
+       return destructor(P, ENOMEM);
+    }
 
     /* mollweide zones */
-    SETUP(1, moll, -d100, 0, -d100);
+    setup_zone(P, Q, 1, pj_moll, -d100, 0, -d100);
 
     /* y0 ? */
     xy1 = Q->pj[0]->fwd(lp, Q->pj[0]); /* zone 1 */
@@ -213,11 +237,14 @@ PJ *PROJECTION(igh) {
     Q->pj[0]->y0 = Q->dy0;
 
     /* mollweide zones (cont'd) */
-    SETUP( 2, moll,   d30,  Q->dy0,   d30);
-    SETUP( 9, moll, -d160, -Q->dy0, -d160);
-    SETUP(10, moll,  -d60, -Q->dy0,  -d60);
-    SETUP(11, moll,   d20, -Q->dy0,   d20);
-    SETUP(12, moll,  d140, -Q->dy0,  d140);
+    if (!setup_zone(P, Q, 2, pj_moll,   d30,  Q->dy0,   d30) ||
+        !setup_zone(P, Q, 9, pj_moll, -d160, -Q->dy0, -d160) ||
+        !setup_zone(P, Q,10, pj_moll,  -d60, -Q->dy0,  -d60) ||
+        !setup_zone(P, Q,11, pj_moll,   d20, -Q->dy0,   d20) ||
+        !setup_zone(P, Q,12, pj_moll,  d140, -Q->dy0,  d140))
+    {
+       return destructor(P, ENOMEM);
+    }
 
     P->inv = igh_s_inverse;
     P->fwd = igh_s_forward;
diff --git a/src/projections/igh_o.cpp b/src/projections/igh_o.cpp
new file mode 100644
index 00000000..785a8784
--- /dev/null
+++ b/src/projections/igh_o.cpp
@@ -0,0 +1,268 @@
+#define PJ_LIB__
+
+#include <errno.h>
+#include <math.h>
+
+#include "proj.h"
+#include "proj_internal.h"
+
+PROJ_HEAD(igh_o, "Interrupted Goode Homolosine Oceanic View") "\n\tPCyl, Sph";
+
+/*
+This projection is a variant of the Interrupted Goode Homolosine
+projection that emphasizes ocean areas. The projection is a
+compilation of 12 separate sub-projections. Sinusoidal projections
+are found near the equator and Mollweide projections are found at
+higher latitudes. The transition between the two occurs at 40 degrees
+latitude and is represented by `phi_boundary`.
+
+Each sub-projection is assigned an integer label
+numbered 1 through 12. Most of this code contains logic to assign
+the labels based on latitude (phi) and longitude (lam) regions.
+
+Original Reference:
+J. Paul Goode (1925) THE HOMOLOSINE PROJECTION: A NEW DEVICE FOR 
+    PORTRAYING THE EARTH'S SURFACE ENTIRE, Annals of the Association of 
+    American Geographers, 15:3, 119-125, DOI: 10.1080/00045602509356949
+*/
+
+C_NAMESPACE PJ *pj_sinu(PJ *), *pj_moll(PJ *);
+
+/* 
+Transition from sinusoidal to Mollweide projection
+Latitude (phi): 40deg 44' 11.8" 
+*/
+
+static const double phi_boundary = (40 + 44/60. + 11.8/3600.) * DEG_TO_RAD;
+
+static const double d10  =  10 * DEG_TO_RAD;
+static const double d20  =  20 * DEG_TO_RAD;
+static const double d50  =  50 * DEG_TO_RAD;
+static const double d60  =  60 * DEG_TO_RAD;
+static const double d90  =  90 * DEG_TO_RAD;
+static const double d110 = 110 * DEG_TO_RAD;
+static const double d140 = 140 * DEG_TO_RAD;
+static const double d150 = 150 * DEG_TO_RAD;
+static const double d160 = 160 * DEG_TO_RAD;
+static const double d130 = 130 * DEG_TO_RAD;
+static const double d180 = 180 * DEG_TO_RAD;
+
+static const double EPSLN = 1.e-10; /* allow a little 'slack' on zone edge positions */
+
+namespace { // anonymous namespace
+struct pj_opaque {
+    struct PJconsts* pj[12]; \
+    double dy0;
+};
+} // anonymous namespace
+
+
+/*
+Assign an integer index representing each of the 12 
+sub-projection zones based on latitude (phi) and
+longitude (lam) ranges.
+*/
+
+static PJ_XY igh_o_s_forward (PJ_LP lp, PJ *P) {           /* Spheroidal, forward */
+    PJ_XY xy;
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+    int z;
+
+    if (lp.phi >=  phi_boundary) {
+           if (lp.lam <=   -d90) z =  1;
+      else if (lp.lam >=    d60) z =  3;
+      else z = 2;
+    }
+    else if (lp.phi >=  0) {
+           if (lp.lam <=   -d90) z =  4;
+      else if (lp.lam >=    d60) z =  6;
+      else z = 5;
+    }
+    else if (lp.phi >= -phi_boundary) {
+           if (lp.lam <=  -d60) z =  7;
+      else if (lp.lam >=   d90) z =  9;
+      else z = 8;
+    }
+    else {
+           if (lp.lam <=  -d60) z =  10;
+      else if (lp.lam >=   d90) z =  12;
+      else z = 11;
+    }
+
+    lp.lam -= Q->pj[z-1]->lam0;
+    xy = Q->pj[z-1]->fwd(lp, Q->pj[z-1]);
+    xy.x += Q->pj[z-1]->x0;
+    xy.y += Q->pj[z-1]->y0;
+
+    return xy;
+}
+
+
+static PJ_LP igh_o_s_inverse (PJ_XY xy, PJ *P) {           /* Spheroidal, inverse */
+    PJ_LP lp = {0.0,0.0};
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+    const double y90 = Q->dy0 + sqrt(2.0); /* lt=90 corresponds to y=y0+sqrt(2) */
+
+    int z = 0;
+    if (xy.y > y90+EPSLN || xy.y < -y90+EPSLN) /* 0 */
+      z = 0;
+    else if (xy.y >=  phi_boundary)
+           if (xy.x <=   -d90) z =  1;
+      else if (xy.x >=    d60) z =  3;
+      else z = 2;
+    else if (xy.y >=  0)
+           if (xy.x <=   -d90) z =  4;
+      else if (xy.x >=    d60) z =  6;
+      else z = 5;
+    else if (xy.y >= -phi_boundary) {
+           if (xy.x <=   -d60) z =  7;
+      else if (xy.x >=    d90) z =  9;
+      else z = 8;
+    }
+    else {
+           if (xy.x <=   -d60) z =  10;
+      else if (xy.x >=    d90) z =  12;
+      else z = 11;
+    }
+
+    if (z) {
+        bool ok = false;
+
+        xy.x -= Q->pj[z-1]->x0;
+        xy.y -= Q->pj[z-1]->y0;
+        lp = Q->pj[z-1]->inv(xy, Q->pj[z-1]);
+        lp.lam += Q->pj[z-1]->lam0;
+
+        switch (z) {
+        /* Plot projectable ranges with exetension lobes in zones 1 & 3 */
+        case  1:  ok = (lp.lam  >= -d180-EPSLN && lp.lam <=  -d90+EPSLN) ||
+                       ((lp.lam >=  d160-EPSLN && lp.lam <=  d180+EPSLN) &&
+                       (lp.phi  >=   d50-EPSLN && lp.phi <=   d90+EPSLN)); break;
+        case  2:  ok = (lp.lam  >=  -d90-EPSLN && lp.lam <=   d60+EPSLN);  break;
+        case  3:  ok = (lp.lam  >=   d60-EPSLN && lp.lam <=  d180+EPSLN) ||
+                       ((lp.lam >= -d180-EPSLN && lp.lam <= -d160+EPSLN) &&
+                       (lp.phi  >=   d50-EPSLN && lp.phi <=   d90+EPSLN)); break;
+        case  4:  ok = (lp.lam  >= -d180-EPSLN && lp.lam <=  -d90+EPSLN);  break;
+        case  5:  ok = (lp.lam  >=  -d90-EPSLN && lp.lam <=   d60+EPSLN);  break;
+        case  6:  ok = (lp.lam  >=   d60-EPSLN && lp.lam <=  d180+EPSLN);  break;
+        case  7:  ok = (lp.lam  >= -d180-EPSLN && lp.lam <=  -d60+EPSLN);  break;
+        case  8:  ok = (lp.lam  >=  -d60-EPSLN && lp.lam <=   d90+EPSLN);  break;
+        case  9:  ok = (lp.lam  >=   d90-EPSLN && lp.lam <=  d180+EPSLN);  break;
+        case  10: ok = (lp.lam  >= -d180-EPSLN && lp.lam <=  -d60+EPSLN);  break;
+        case  11: ok = (lp.lam  >=  -d60-EPSLN && lp.lam <=   d90+EPSLN);  break;
+        case  12: ok = (lp.lam  >=   d90-EPSLN && lp.lam <=  d180+EPSLN);  break;
+
+        }
+      z = (!ok? 0: z); /* projectable? */
+    }
+
+    if (!z) lp.lam = HUGE_VAL;
+    if (!z) lp.phi = HUGE_VAL;
+
+    return lp;
+}
+
+
+static PJ *destructor (PJ *P, int errlev) {
+    int i;
+    if (nullptr==P)
+        return nullptr;
+
+    if (nullptr==P->opaque)
+        return pj_default_destructor (P, errlev);
+
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
+
+    for (i = 0; i < 12; ++i) {
+        if (Q->pj[i])
+            Q->pj[i]->destructor(Q->pj[i], errlev);
+    }
+
+    return pj_default_destructor(P, errlev);
+}
+
+
+
+/*
+  Zones:
+
+    -180       -90               60           180
+      +---------+----------------+-------------+    Zones 1,2,3,10,11 & 12:
+      |1        |2               |3            |    Mollweide projection
+      |         |                |             |
+      +---------+----------------+-------------+    Zones 4,5,6,7,8 & 9:
+      |4        |5               |6            |    Sinusoidal projection
+      |         |                |             |
+    0 +---------+--+-------------+--+----------+
+      |7           |8               |9         |
+      |            |                |          |
+      +------------+----------------+----------+
+      |10          |11              |12        |
+      |            |                |          |
+      +------------+----------------+----------+
+    -180          -60               90        180
+*/
+
+static bool setup_zone(PJ *P, struct pj_opaque *Q, int n,
+                       PJ*(*proj_ptr)(PJ*), double x_0,
+                       double y_0, double lon_0) {
+    if (!(Q->pj[n-1] = proj_ptr(nullptr))) return false;
+    if (!(Q->pj[n-1] = proj_ptr(Q->pj[n-1]))) return false;
+    Q->pj[n-1]->ctx = P->ctx;
+    Q->pj[n-1]->x0 = x_0;
+    Q->pj[n-1]->y0 = y_0;
+    Q->pj[n-1]->lam0 = lon_0;
+    return true;
+}
+
+PJ *PROJECTION(igh_o) {
+    PJ_XY xy1, xy4;
+    PJ_LP lp = { 0, phi_boundary };
+    struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
+    if (nullptr==Q)
+        return pj_default_destructor (P, ENOMEM);
+    P->opaque = Q;
+
+
+    /* sinusoidal zones */
+    if (!setup_zone(P, Q, 4, pj_sinu, -d140, 0, -d140) ||
+        !setup_zone(P, Q, 5, pj_sinu,   d10, 0,   d10) ||
+        !setup_zone(P, Q, 6, pj_sinu,  d130, 0,  d130) ||
+        !setup_zone(P, Q, 7, pj_sinu, -d110, 0, -d110) ||
+        !setup_zone(P, Q, 8, pj_sinu,   d20, 0,   d20) ||
+        !setup_zone(P, Q, 9, pj_sinu,  d150, 0,  d150))
+    {
+       return destructor(P, ENOMEM);
+    }
+
+
+    /* mollweide zones */
+    if (!setup_zone(P, Q, 1, pj_moll,  -d140, 0,  -d140)) {
+       return destructor(P, ENOMEM);
+    }
+
+    /* y0 ? */
+    xy1 = Q->pj[0]->fwd(lp, Q->pj[0]); /* zone 1 */
+    xy4 = Q->pj[3]->fwd(lp, Q->pj[3]); /* zone 4 */
+    /* y0 + xy1.y = xy4.y for lt = 40d44'11.8" */
+    Q->dy0 = xy4.y - xy1.y;
+
+    Q->pj[0]->y0 = Q->dy0;
+
+    /* mollweide zones (cont'd) */
+    if (!setup_zone(P, Q,  2, pj_moll,   d10,  Q->dy0,   d10)  ||
+        !setup_zone(P, Q,  3, pj_moll,  d130,  Q->dy0,  d130)  ||
+        !setup_zone(P, Q, 10, pj_moll, -d110, -Q->dy0, -d110)  ||
+        !setup_zone(P, Q, 11, pj_moll,   d20, -Q->dy0,   d20)  ||
+        !setup_zone(P, Q, 12, pj_moll,  d150, -Q->dy0,  d150))
+    {
+       return destructor(P, ENOMEM);
+    }
+
+    P->inv = igh_o_s_inverse;
+    P->fwd = igh_o_s_forward;
+    P->destructor = destructor;
+    P->es = 0.;
+
+    return P;
+}