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Diffstat (limited to 'src/projections/aitoff.cpp')
| -rw-r--r-- | src/projections/aitoff.cpp | 201 |
1 files changed, 201 insertions, 0 deletions
diff --git a/src/projections/aitoff.cpp b/src/projections/aitoff.cpp new file mode 100644 index 00000000..effd2c29 --- /dev/null +++ b/src/projections/aitoff.cpp @@ -0,0 +1,201 @@ +/****************************************************************************** + * 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 XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */ + 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 LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */ + 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); +} |
