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
|
/******************************************************************************
* Project: PROJ.4
* Purpose: Implementation of the aitoff (Aitoff) and wintri (Winkel Tripel)
* projections.
* Author: Gerald Evenden (1995)
* Drazen Tutic, Lovro Gradiser (2015) - add inverse
* Thomas Knudsen (2016) - revise/add regression tests
*
******************************************************************************
* Copyright (c) 1995, Gerald Evenden
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
* DEALINGS IN THE SOFTWARE.
*****************************************************************************/
#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "proj.h"
#include "projects.h"
namespace { // anonymous namespace
enum Mode {
AITOFF = 0,
WINKEL_TRIPEL = 1
};
} // anonymous namespace
namespace { // anonymous namespace
struct pj_opaque {
double cosphi1;
enum Mode mode;
};
} // anonymous namespace
PROJ_HEAD(aitoff, "Aitoff") "\n\tMisc Sph";
PROJ_HEAD(wintri, "Winkel Tripel") "\n\tMisc Sph\n\tlat_1";
#if 0
FORWARD(s_forward); /* spheroid */
#endif
static PJ_XY s_forward (PJ_LP lp, PJ *P) { /* Spheroidal, forward */
PJ_XY xy = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double c, d;
if((d = acos(cos(lp.phi) * cos(c = 0.5 * lp.lam))) != 0.0) {/* basic Aitoff */
xy.x = 2. * d * cos(lp.phi) * sin(c) * (xy.y = 1. / sin(d));
xy.y *= d * sin(lp.phi);
} else
xy.x = xy.y = 0.;
if (Q->mode == WINKEL_TRIPEL) {
xy.x = (xy.x + lp.lam * Q->cosphi1) * 0.5;
xy.y = (xy.y + lp.phi) * 0.5;
}
return (xy);
}
/***********************************************************************************
*
* Inverse functions added by Drazen Tutic and Lovro Gradiser based on paper:
*
* I.Özbug Biklirici and Cengizhan Ipbüker. A General Algorithm for the Inverse
* Transformation of Map Projections Using Jacobian Matrices. In Proceedings of the
* Third International Symposium Mathematical & Computational Applications,
* pages 175{182, Turkey, September 2002.
*
* Expected accuracy is defined by EPSILON = 1e-12. Should be appropriate for
* most applications of Aitoff and Winkel Tripel projections.
*
* Longitudes of 180W and 180E can be mixed in solution obtained.
*
* Inverse for Aitoff projection in poles is undefined, longitude value of 0 is assumed.
*
* Contact : dtutic@geof.hr
* Date: 2015-02-16
*
************************************************************************************/
static PJ_LP 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);
int iter, MAXITER = 10, round = 0, MAXROUND = 20;
double EPSILON = 1e-12, D, C, f1, f2, f1p, f1l, f2p, f2l, dp, dl, sl, sp, cp, cl, x, y;
if ((fabs(xy.x) < EPSILON) && (fabs(xy.y) < EPSILON )) { lp.phi = 0.; lp.lam = 0.; return lp; }
/* initial values for Newton-Raphson method */
lp.phi = xy.y; lp.lam = xy.x;
do {
iter = 0;
do {
sl = sin(lp.lam * 0.5); cl = cos(lp.lam * 0.5);
sp = sin(lp.phi); cp = cos(lp.phi);
D = cp * cl;
C = 1. - D * D;
D = acos(D) / pow(C, 1.5);
f1 = 2. * D * C * cp * sl;
f2 = D * C * sp;
f1p = 2.* (sl * cl * sp * cp / C - D * sp * sl);
f1l = cp * cp * sl * sl / C + D * cp * cl * sp * sp;
f2p = sp * sp * cl / C + D * sl * sl * cp;
f2l = 0.5 * (sp * cp * sl / C - D * sp * cp * cp * sl * cl);
if (Q->mode == WINKEL_TRIPEL) {
f1 = 0.5 * (f1 + lp.lam * Q->cosphi1);
f2 = 0.5 * (f2 + lp.phi);
f1p *= 0.5;
f1l = 0.5 * (f1l + Q->cosphi1);
f2p = 0.5 * (f2p + 1.);
f2l *= 0.5;
}
f1 -= xy.x; f2 -= xy.y;
dl = (f2 * f1p - f1 * f2p) / (dp = f1p * f2l - f2p * f1l);
dp = (f1 * f2l - f2 * f1l) / dp;
dl = fmod(dl, M_PI); /* set to interval [-M_PI, M_PI] */
lp.phi -= dp; lp.lam -= dl;
} while ((fabs(dp) > EPSILON || fabs(dl) > EPSILON) && (iter++ < MAXITER));
if (lp.phi > M_PI_2) lp.phi -= 2.*(lp.phi-M_PI_2); /* correct if symmetrical solution for Aitoff */
if (lp.phi < -M_PI_2) lp.phi -= 2.*(lp.phi+M_PI_2); /* correct if symmetrical solution for Aitoff */
if ((fabs(fabs(lp.phi) - M_PI_2) < EPSILON) && (Q->mode == AITOFF)) lp.lam = 0.; /* if pole in Aitoff, return longitude of 0 */
/* calculate x,y coordinates with solution obtained */
if((D = acos(cos(lp.phi) * cos(C = 0.5 * lp.lam))) != 0.0) {/* Aitoff */
x = 2. * D * cos(lp.phi) * sin(C) * (y = 1. / sin(D));
y *= D * sin(lp.phi);
} else
x = y = 0.;
if (Q->mode == WINKEL_TRIPEL) {
x = (x + lp.lam * Q->cosphi1) * 0.5;
y = (y + lp.phi) * 0.5;
}
/* if too far from given values of x,y, repeat with better approximation of phi,lam */
} while (((fabs(xy.x-x) > EPSILON) || (fabs(xy.y-y) > EPSILON)) && (round++ < MAXROUND));
if (iter == MAXITER && round == MAXROUND)
{
pj_ctx_set_errno( P->ctx, PJD_ERR_NON_CONVERGENT );
/* fprintf(stderr, "Warning: Accuracy of 1e-12 not reached. Last increments: dlat=%e and dlon=%e\n", dp, dl); */
}
return lp;
}
static PJ *setup(PJ *P) {
P->inv = s_inverse;
P->fwd = s_forward;
P->es = 0.;
return P;
}
PJ *PROJECTION(aitoff) {
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;
Q->mode = AITOFF;
return setup(P);
}
PJ *PROJECTION(wintri) {
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;
Q->mode = WINKEL_TRIPEL;
if (pj_param(P->ctx, P->params, "tlat_1").i) {
if ((Q->cosphi1 = cos(pj_param(P->ctx, P->params, "rlat_1").f)) == 0.)
return pj_default_destructor (P, PJD_ERR_LAT_LARGER_THAN_90);
}
else /* 50d28' or acos(2/pi) */
Q->cosphi1 = 0.636619772367581343;
return setup(P);
}
|
