/src/gdal/proj/src/projections/tpeqd.cpp
Line | Count | Source (jump to first uncovered line) |
1 | | |
2 | | #include "proj.h" |
3 | | #include "proj_internal.h" |
4 | | #include <errno.h> |
5 | | #include <math.h> |
6 | | |
7 | | PROJ_HEAD(tpeqd, "Two Point Equidistant") |
8 | | "\n\tMisc Sph\n\tlat_1= lon_1= lat_2= lon_2="; |
9 | | |
10 | | namespace { // anonymous namespace |
11 | | struct pj_tpeqd { |
12 | | double cp1, sp1, cp2, sp2, ccs, cs, sc, r2z0, z02, dlam2; |
13 | | double hz0, thz0, rhshz0, ca, sa, lp, lamc; |
14 | | }; |
15 | | } // anonymous namespace |
16 | | |
17 | 0 | static PJ_XY tpeqd_s_forward(PJ_LP lp, PJ *P) { /* Spheroidal, forward */ |
18 | 0 | PJ_XY xy = {0.0, 0.0}; |
19 | 0 | struct pj_tpeqd *Q = static_cast<struct pj_tpeqd *>(P->opaque); |
20 | 0 | double t, z1, z2, dl1, dl2, sp, cp; |
21 | |
|
22 | 0 | sp = sin(lp.phi); |
23 | 0 | cp = cos(lp.phi); |
24 | 0 | z1 = |
25 | 0 | aacos(P->ctx, Q->sp1 * sp + Q->cp1 * cp * cos(dl1 = lp.lam + Q->dlam2)); |
26 | 0 | z2 = |
27 | 0 | aacos(P->ctx, Q->sp2 * sp + Q->cp2 * cp * cos(dl2 = lp.lam - Q->dlam2)); |
28 | 0 | z1 *= z1; |
29 | 0 | z2 *= z2; |
30 | |
|
31 | 0 | t = z1 - z2; |
32 | 0 | xy.x = Q->r2z0 * t; |
33 | 0 | t = Q->z02 - t; |
34 | 0 | xy.y = Q->r2z0 * asqrt(4. * Q->z02 * z2 - t * t); |
35 | 0 | if ((Q->ccs * sp - cp * (Q->cs * sin(dl1) - Q->sc * sin(dl2))) < 0.) |
36 | 0 | xy.y = -xy.y; |
37 | 0 | return xy; |
38 | 0 | } |
39 | | |
40 | 0 | static PJ_LP tpeqd_s_inverse(PJ_XY xy, PJ *P) { /* Spheroidal, inverse */ |
41 | 0 | PJ_LP lp = {0.0, 0.0}; |
42 | 0 | struct pj_tpeqd *Q = static_cast<struct pj_tpeqd *>(P->opaque); |
43 | 0 | double cz1, cz2, s, d, cp, sp; |
44 | |
|
45 | 0 | cz1 = cos(hypot(xy.y, xy.x + Q->hz0)); |
46 | 0 | cz2 = cos(hypot(xy.y, xy.x - Q->hz0)); |
47 | 0 | s = cz1 + cz2; |
48 | 0 | d = cz1 - cz2; |
49 | 0 | lp.lam = -atan2(d, (s * Q->thz0)); |
50 | 0 | lp.phi = aacos(P->ctx, hypot(Q->thz0 * s, d) * Q->rhshz0); |
51 | 0 | if (xy.y < 0.) |
52 | 0 | lp.phi = -lp.phi; |
53 | | /* lam--phi now in system relative to P1--P2 base equator */ |
54 | 0 | sp = sin(lp.phi); |
55 | 0 | cp = cos(lp.phi); |
56 | 0 | lp.lam -= Q->lp; |
57 | 0 | s = cos(lp.lam); |
58 | 0 | lp.phi = aasin(P->ctx, Q->sa * sp + Q->ca * cp * s); |
59 | 0 | lp.lam = atan2(cp * sin(lp.lam), Q->sa * cp * s - Q->ca * sp) + Q->lamc; |
60 | 0 | return lp; |
61 | 0 | } |
62 | | |
63 | 6.57k | PJ *PJ_PROJECTION(tpeqd) { |
64 | 6.57k | double lam_1, lam_2, phi_1, phi_2, A12; |
65 | 6.57k | struct pj_tpeqd *Q = |
66 | 6.57k | static_cast<struct pj_tpeqd *>(calloc(1, sizeof(struct pj_tpeqd))); |
67 | 6.57k | if (nullptr == Q) |
68 | 0 | return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/); |
69 | 6.57k | P->opaque = Q; |
70 | | |
71 | | /* get control point locations */ |
72 | 6.57k | phi_1 = pj_param(P->ctx, P->params, "rlat_1").f; |
73 | 6.57k | lam_1 = pj_param(P->ctx, P->params, "rlon_1").f; |
74 | 6.57k | phi_2 = pj_param(P->ctx, P->params, "rlat_2").f; |
75 | 6.57k | lam_2 = pj_param(P->ctx, P->params, "rlon_2").f; |
76 | | |
77 | 6.57k | if (phi_1 == phi_2 && lam_1 == lam_2) { |
78 | 644 | proj_log_error(P, _("Invalid value for lat_1/lon_1/lat_2/lon_2: the 2 " |
79 | 644 | "points should be distinct.")); |
80 | 644 | return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE); |
81 | 644 | } |
82 | | |
83 | 5.92k | P->lam0 = adjlon(0.5 * (lam_1 + lam_2)); |
84 | 5.92k | Q->dlam2 = adjlon(lam_2 - lam_1); |
85 | | |
86 | 5.92k | Q->cp1 = cos(phi_1); |
87 | 5.92k | Q->cp2 = cos(phi_2); |
88 | 5.92k | Q->sp1 = sin(phi_1); |
89 | 5.92k | Q->sp2 = sin(phi_2); |
90 | 5.92k | Q->cs = Q->cp1 * Q->sp2; |
91 | 5.92k | Q->sc = Q->sp1 * Q->cp2; |
92 | 5.92k | Q->ccs = Q->cp1 * Q->cp2 * sin(Q->dlam2); |
93 | | |
94 | 11.8k | const auto SQ = [](double x) { return x * x; }; |
95 | | // Numerically stable formula for computing the central angle from |
96 | | // (phi_1, lam_1) to (phi_2, lam_2). |
97 | | // Special case of Vincenty formula on the sphere. |
98 | | // https://en.wikipedia.org/wiki/Great-circle_distance#Computational_formulae |
99 | 5.92k | const double cs_minus_sc_cos_dlam = Q->cs - Q->sc * cos(Q->dlam2); |
100 | 5.92k | Q->z02 = atan2(sqrt(SQ(Q->cp2 * sin(Q->dlam2)) + SQ(cs_minus_sc_cos_dlam)), |
101 | 5.92k | Q->sp1 * Q->sp2 + Q->cp1 * Q->cp2 * cos(Q->dlam2)); |
102 | 5.92k | if (Q->z02 == 0.0) { |
103 | | // Actually happens when both lat_1 = lat_2 and |lat_1| = 90 |
104 | 0 | proj_log_error(P, _("Invalid value for lat_1 and lat_2: their absolute " |
105 | 0 | "value should be < 90°.")); |
106 | 0 | return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE); |
107 | 0 | } |
108 | 5.92k | Q->hz0 = .5 * Q->z02; |
109 | 5.92k | A12 = atan2(Q->cp2 * sin(Q->dlam2), cs_minus_sc_cos_dlam); |
110 | 5.92k | const double pp = aasin(P->ctx, Q->cp1 * sin(A12)); |
111 | 5.92k | Q->ca = cos(pp); |
112 | 5.92k | Q->sa = sin(pp); |
113 | 5.92k | Q->lp = adjlon(atan2(Q->cp1 * cos(A12), Q->sp1) - Q->hz0); |
114 | 5.92k | Q->dlam2 *= .5; |
115 | 5.92k | Q->lamc = M_HALFPI - atan2(sin(A12) * Q->sp1, cos(A12)) - Q->dlam2; |
116 | 5.92k | Q->thz0 = tan(Q->hz0); |
117 | 5.92k | Q->rhshz0 = .5 / sin(Q->hz0); |
118 | 5.92k | Q->r2z0 = 0.5 / Q->z02; |
119 | 5.92k | Q->z02 *= Q->z02; |
120 | | |
121 | 5.92k | P->inv = tpeqd_s_inverse; |
122 | 5.92k | P->fwd = tpeqd_s_forward; |
123 | 5.92k | P->es = 0.; |
124 | | |
125 | 5.92k | return P; |
126 | 5.92k | } |