EVOLUTION-MANAGER

Edit File: PJ_aitoff.c

/****************************************************************************** * 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" enum Mode { AITOFF = 0, WINKEL_TRIPEL = 1 }; struct pj_opaque { double cosphi1; enum Mode mode; }; 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 = 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 = 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 = pj_calloc (1, sizeof (struct pj_opaque)); if (0==Q) return pj_default_destructor(P, ENOMEM); P->opaque = Q; Q->mode = AITOFF; return setup(P); } PJ *PROJECTION(wintri) { struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque)); if (0==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); }