1 #define PJ_LIB__
2 #include <projects.h>
3
4 PROJ_HEAD(tmerc, "Transverse Mercator") "\n\tCyl, Sph&Ell";
5
6
7 struct pj_opaque {
8 double esp; \
9 double ml0; \
10 double *en;
11 };
12
13 #define EPS10 1.e-10
14 #define FC1 1.
15 #define FC2 .5
16 #define FC3 .16666666666666666666
17 #define FC4 .08333333333333333333
18 #define FC5 .05
19 #define FC6 .03333333333333333333
20 #define FC7 .02380952380952380952
21 #define FC8 .01785714285714285714
22
23
e_forward(LP lp,PJ * P)24 static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
25 XY xy = {0.0, 0.0};
26 struct pj_opaque *Q = P->opaque;
27 double al, als, n, cosphi, sinphi, t;
28
29 /*
30 * Fail if our longitude is more than 90 degrees from the
31 * central meridian since the results are essentially garbage.
32 * Is error -20 really an appropriate return value?
33 *
34 * http://trac.osgeo.org/proj/ticket/5
35 */
36 if( lp.lam < -M_HALFPI || lp.lam > M_HALFPI ) {
37 xy.x = HUGE_VAL;
38 xy.y = HUGE_VAL;
39 pj_ctx_set_errno( P->ctx, -14 );
40 return xy;
41 }
42
43 sinphi = sin (lp.phi);
44 cosphi = cos (lp.phi);
45 t = fabs (cosphi) > 1e-10 ? sinphi/cosphi : 0.;
46 t *= t;
47 al = cosphi * lp.lam;
48 als = al * al;
49 al /= sqrt (1. - P->es * sinphi * sinphi);
50 n = Q->esp * cosphi * cosphi;
51 xy.x = P->k0 * al * (FC1 +
52 FC3 * als * (1. - t + n +
53 FC5 * als * (5. + t * (t - 18.) + n * (14. - 58. * t)
54 + FC7 * als * (61. + t * ( t * (179. - t) - 479. ) )
55 )));
56 xy.y = P->k0 * (pj_mlfn(lp.phi, sinphi, cosphi, Q->en) - Q->ml0 +
57 sinphi * al * lp.lam * FC2 * ( 1. +
58 FC4 * als * (5. - t + n * (9. + 4. * n) +
59 FC6 * als * (61. + t * (t - 58.) + n * (270. - 330 * t)
60 + FC8 * als * (1385. + t * ( t * (543. - t) - 3111.) )
61 ))));
62 return (xy);
63 }
64
65
s_forward(LP lp,PJ * P)66 static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
67 XY xy = {0.0,0.0};
68 double b, cosphi;
69
70 /*
71 * Fail if our longitude is more than 90 degrees from the
72 * central meridian since the results are essentially garbage.
73 * Is error -20 really an appropriate return value?
74 *
75 * http://trac.osgeo.org/proj/ticket/5
76 */
77 if( lp.lam < -M_HALFPI || lp.lam > M_HALFPI ) {
78 xy.x = HUGE_VAL;
79 xy.y = HUGE_VAL;
80 pj_ctx_set_errno( P->ctx, -14 );
81 return xy;
82 }
83
84 cosphi = cos(lp.phi);
85 b = cosphi * sin (lp.lam);
86 if (fabs (fabs (b) - 1.) <= EPS10)
87 F_ERROR;
88
89 xy.x = P->opaque->ml0 * log ((1. + b) / (1. - b));
90 xy.y = cosphi * cos (lp.lam) / sqrt (1. - b * b);
91
92 b = fabs ( xy.y );
93 if (b >= 1.) {
94 if ((b - 1.) > EPS10)
95 F_ERROR
96 else xy.y = 0.;
97 } else
98 xy.y = acos (xy.y);
99
100 if (lp.phi < 0.)
101 xy.y = -xy.y;
102 xy.y = P->opaque->esp * (xy.y - P->phi0);
103 return xy;
104 }
105
106
e_inverse(XY xy,PJ * P)107 static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
108 LP lp = {0.0,0.0};
109 struct pj_opaque *Q = P->opaque;
110 double n, con, cosphi, d, ds, sinphi, t;
111
112 lp.phi = pj_inv_mlfn(P->ctx, Q->ml0 + xy.y / P->k0, P->es, Q->en);
113 if (fabs(lp.phi) >= M_HALFPI) {
114 lp.phi = xy.y < 0. ? -M_HALFPI : M_HALFPI;
115 lp.lam = 0.;
116 } else {
117 sinphi = sin(lp.phi);
118 cosphi = cos(lp.phi);
119 t = fabs (cosphi) > 1e-10 ? sinphi/cosphi : 0.;
120 n = Q->esp * cosphi * cosphi;
121 d = xy.x * sqrt (con = 1. - P->es * sinphi * sinphi) / P->k0;
122 con *= t;
123 t *= t;
124 ds = d * d;
125 lp.phi -= (con * ds / (1.-P->es)) * FC2 * (1. -
126 ds * FC4 * (5. + t * (3. - 9. * n) + n * (1. - 4 * n) -
127 ds * FC6 * (61. + t * (90. - 252. * n +
128 45. * t) + 46. * n
129 - ds * FC8 * (1385. + t * (3633. + t * (4095. + 1574. * t)) )
130 )));
131 lp.lam = d*(FC1 -
132 ds*FC3*( 1. + 2.*t + n -
133 ds*FC5*(5. + t*(28. + 24.*t + 8.*n) + 6.*n
134 - ds * FC7 * (61. + t * (662. + t * (1320. + 720. * t)) )
135 ))) / cosphi;
136 }
137 return lp;
138 }
139
140
s_inverse(XY xy,PJ * P)141 static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
142 LP lp = {0.0, 0.0};
143 double h, g;
144
145 h = exp(xy.x / P->opaque->esp);
146 g = .5 * (h - 1. / h);
147 h = cos (P->phi0 + xy.y / P->opaque->esp);
148 lp.phi = asin(sqrt((1. - h * h) / (1. + g * g)));
149 if (xy.y < 0.) lp.phi = -lp.phi;
150 lp.lam = (g || h) ? atan2 (g, h) : 0.;
151 return lp;
152 }
153
154
freeup_new(PJ * P)155 static void *freeup_new (PJ *P) { /* Destructor */
156 if (0==P)
157 return 0;
158 if (0==P->opaque)
159 return pj_dealloc (P);
160 pj_dealloc (P->opaque->en);
161 pj_dealloc (P->opaque);
162 return pj_dealloc(P);
163 }
164
freeup(PJ * P)165 static void freeup (PJ *P) {
166 freeup_new (P);
167 return;
168 }
169
setup(PJ * P)170 static PJ *setup(PJ *P) { /* general initialization */
171 struct pj_opaque *Q = P->opaque;
172 if (P->es) {
173 if (!(Q->en = pj_enfn(P->es)))
174 E_ERROR_0;
175 Q->ml0 = pj_mlfn(P->phi0, sin(P->phi0), cos(P->phi0), Q->en);
176 Q->esp = P->es / (1. - P->es);
177 P->inv = e_inverse;
178 P->fwd = e_forward;
179 } else {
180 Q->esp = P->k0;
181 Q->ml0 = .5 * Q->esp;
182 P->inv = s_inverse;
183 P->fwd = s_forward;
184 }
185 return P;
186 }
187
188
PROJECTION(tmerc)189 PJ *PROJECTION(tmerc) {
190 struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
191 if (0==Q)
192 return freeup_new (P);
193 P->opaque = Q;
194 return setup(P);
195 }
196
197
198 #ifndef PJ_SELFTEST
pj_tmerc_selftest(void)199 int pj_tmerc_selftest (void) {return 0;}
200 #else
pj_tmerc_selftest(void)201 int pj_tmerc_selftest (void) {
202 double tolerance_lp = 1e-10;
203 double tolerance_xy = 1e-7;
204
205 char e_args[] = {"+proj=tmerc +ellps=GRS80 +lat_1=0.5 +lat_2=2 +n=0.5"};
206 char s_args[] = {"+proj=tmerc +a=6400000 +lat_1=0.5 +lat_2=2 +n=0.5"};
207
208 LP fwd_in[] = {
209 { 2, 1},
210 { 2,-1},
211 {-2, 1},
212 {-2,-1}
213 };
214
215 XY e_fwd_expect[] = {
216 { 222650.79679577847, 110642.22941192707},
217 { 222650.79679577847, -110642.22941192707},
218 {-222650.79679577847, 110642.22941192707},
219 {-222650.79679577847, -110642.22941192707},
220 };
221
222 XY s_fwd_expect[] = {
223 { 223413.46640632232, 111769.14504059685},
224 { 223413.46640632232, -111769.14504059685},
225 {-223413.46640632208, 111769.14504059685},
226 {-223413.46640632208, -111769.14504059685},
227 };
228
229 XY inv_in[] = {
230 { 200, 100},
231 { 200,-100},
232 {-200, 100},
233 {-200,-100}
234 };
235
236 LP e_inv_expect[] = {
237 { 0.0017966305681649396, 0.00090436947663183841},
238 { 0.0017966305681649396, -0.00090436947663183841},
239 {-0.0017966305681649396, 0.00090436947663183841},
240 {-0.0017966305681649396, -0.00090436947663183841},
241 };
242
243 LP s_inv_expect[] = {
244 { 0.0017904931097048034, 0.00089524670602767842},
245 { 0.0017904931097048034, -0.00089524670602767842},
246 {-0.001790493109714345, 0.00089524670602767842},
247 {-0.001790493109714345, -0.00089524670602767842},
248 };
249
250 return pj_generic_selftest (e_args, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, e_fwd_expect, s_fwd_expect, inv_in, e_inv_expect, s_inv_expect);
251 }
252 #endif
253