1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
|
#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "proj.h"
#include "proj_internal.h"
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 *);
/*
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 d30 = 30 * DEG_TO_RAD;
static const double d40 = 40 * DEG_TO_RAD;
static const double d50 = 50 * DEG_TO_RAD;
static const double d60 = 60 * DEG_TO_RAD;
static const double d80 = 80 * DEG_TO_RAD;
static const double d90 = 90 * DEG_TO_RAD;
static const double d100 = 100 * DEG_TO_RAD;
static const double d140 = 140 * DEG_TO_RAD;
static const double d160 = 160 * 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
static PJ_XY igh_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) { /* 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 >= -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 */
else z = 8; /* 8 */
}
else { /* 9|10|11|12 */
if (lp.lam <= -d100) z = 9; /* 9 */
else if (lp.lam <= -d20) z = 10; /* 10 */
else if (lp.lam <= d80) z = 11; /* 11 */
else z = 12; /* 12 */
}
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_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) /* 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 >= -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 */
else z = 8; /* 8 */
}
else { /* 9|10|11|12 */
if (xy.x <= -d100) z = 9; /* 9 */
else if (xy.x <= -d20) z = 10; /* 10 */
else if (xy.x <= d80) z = 11; /* 11 */
else z = 12; /* 12 */
}
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) {
case 1: ok = (lp.lam >= -d180-EPSLN && lp.lam <= -d40+EPSLN) ||
((lp.lam >= -d40-EPSLN && lp.lam <= -d10+EPSLN) &&
(lp.phi >= d60-EPSLN && lp.phi <= d90+EPSLN)); break;
case 2: ok = (lp.lam >= -d40-EPSLN && lp.lam <= d180+EPSLN) ||
((lp.lam >= -d180-EPSLN && lp.lam <= -d160+EPSLN) &&
(lp.phi >= d50-EPSLN && lp.phi <= d90+EPSLN)) ||
((lp.lam >= -d50-EPSLN && lp.lam <= -d40+EPSLN) &&
(lp.phi >= d60-EPSLN && lp.phi <= d90+EPSLN)); break;
case 3: ok = (lp.lam >= -d180-EPSLN && lp.lam <= -d40+EPSLN); break;
case 4: ok = (lp.lam >= -d40-EPSLN && lp.lam <= d180+EPSLN); break;
case 5: ok = (lp.lam >= -d180-EPSLN && lp.lam <= -d100+EPSLN); break;
case 6: ok = (lp.lam >= -d100-EPSLN && lp.lam <= -d20+EPSLN); break;
case 7: ok = (lp.lam >= -d20-EPSLN && lp.lam <= d80+EPSLN); break;
case 8: ok = (lp.lam >= d80-EPSLN && lp.lam <= d180+EPSLN); break;
case 9: ok = (lp.lam >= -d180-EPSLN && lp.lam <= -d100+EPSLN); break;
case 10: ok = (lp.lam >= -d100-EPSLN && lp.lam <= -d20+EPSLN); break;
case 11: ok = (lp.lam >= -d20-EPSLN && lp.lam <= d80+EPSLN); break;
case 12: ok = (lp.lam >= d80-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 -40 180
+--------------+-------------------------+ Zones 1,2,9,10,11 & 12:
|1 |2 | Mollweide projection
| | |
+--------------+-------------------------+ Zones 3,4,5,6,7 & 8:
|3 |4 | Sinusoidal projection
| | |
0 +-------+------+-+-----------+-----------+
|5 |6 |7 |8 |
| | | | |
+-------+--------+-----------+-----------+
|9 |10 |11 |12 |
| | | | |
+-------+--------+-----------+-----------+
-180 -100 -20 80 180
*/
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) {
PJ_XY xy1, xy3;
PJ_LP lp = { 0, phi_boundary };
struct pj_opaque *Q = static_cast<struct pj_opaque*>(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, 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_zone(P, Q, 1, pj_moll, -d100, 0, -d100);
/* y0 ? */
xy1 = Q->pj[0]->fwd(lp, Q->pj[0]); /* zone 1 */
xy3 = Q->pj[2]->fwd(lp, Q->pj[2]); /* zone 3 */
/* y0 + xy1.y = xy3.y for lt = 40d44'11.8" */
Q->dy0 = xy3.y - xy1.y;
Q->pj[0]->y0 = Q->dy0;
/* mollweide zones (cont'd) */
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;
P->destructor = destructor;
P->es = 0.;
return P;
}
|
