vcs.maemo.org Git - navit-package/blob - navit/transform.c

   1 /**
   2  * Navit, a modular navigation system.
   3  * Copyright (C) 2005-2008 Navit Team
   4  *
   5  * This program is free software; you can redistribute it and/or
   6  * modify it under the terms of the GNU General Public License
   7  * version 2 as published by the Free Software Foundation.
   8  *
   9  * This program is distributed in the hope that it will be useful,
  10  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  11  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  12  * GNU General Public License for more details.
  13  *
  14  * You should have received a copy of the GNU General Public License
  15  * along with this program; if not, write to the
  16  * Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
  17  * Boston, MA  02110-1301, USA.
  18  */
  19
  20 #include <assert.h>
  21 #include <stdio.h>
  22 #include <math.h>
  23 #include <limits.h>
  24 #include <glib.h>
  25 #include <string.h>
  26 #include "config.h"
  27 #include "coord.h"
  28 #include "debug.h"
  29 #include "map.h"
  30 #include "transform.h"
  31 #include "projection.h"
  32 #include "point.h"
  33
  34 struct transformation {
  35         long scale;             /* Scale factor */
  36         int angle;              /* Rotation angle */
  37         double cos_val,sin_val; /* cos and sin of rotation angle */
  38         enum projection pro;
  39         struct map_selection *map_sel;
  40         struct map_selection *screen_sel;
  41         struct point screen_center;
  42         struct coord map_center;        /* Center of source rectangle */
  43 };
  44
  45 struct transformation *
  46 transform_new(void)
  47 {
  48         struct transformation *this_;
  49
  50         this_=g_new0(struct transformation, 1);
  51
  52         return this_;
  53 }
  54
  55 static const double gar2geo_units = 360.0/(1<<24);
  56 static const double geo2gar_units = 1/(360.0/(1<<24));
  57
  58 void
  59 transform_to_geo(enum projection pro, struct coord *c, struct coord_geo *g)
  60 {
  61         switch (pro) {
  62         case projection_mg:
  63                 g->lng=c->x/6371000.0/M_PI*180;
  64                 g->lat=atan(exp(c->y/6371000.0))/M_PI*360-90;
  65                 break;
  66         case projection_garmin:
  67                 g->lng=c->x*gar2geo_units;
  68                 g->lat=c->y*gar2geo_units;
  69                 break;
  70         default:
  71                 break;
  72         }
  73 }
  74
  75 void
  76 transform_from_geo(enum projection pro, struct coord_geo *g, struct coord *c)
  77 {
  78         switch (pro) {
  79         case projection_mg:
  80                 c->x=g->lng*6371000.0*M_PI/180;
  81                 c->y=log(tan(M_PI_4+g->lat*M_PI/360))*6371000.0;
  82                 break;
  83         case projection_garmin:
  84                 c->x=g->lng*geo2gar_units;
  85                 c->y=g->lat*geo2gar_units;
  86                 break;
  87         default:
  88                 break;
  89         }
  90 }
  91
  92 void
  93 transform_from_to(struct coord *cfrom, enum projection from, struct coord *cto, enum projection to)
  94 {
  95         struct coord_geo g;
  96         transform_to_geo(from, cfrom, &g);
  97         transform_from_geo(to, &g, cto);
  98 }
  99
 100 void
 101 transform_geo_to_cart(struct coord_geo *geo, double a, double b, struct coord_geo_cart *cart)
 102 {
 103         double n,ee=1-b*b/(a*a);
 104         n = a/sqrt(1-ee*sin(geo->lat)*sin(geo->lat));
 105         cart->x=n*cos(geo->lat)*cos(geo->lng);
 106         cart->y=n*cos(geo->lat)*sin(geo->lng);
 107         cart->z=n*(1-ee)*sin(geo->lat);
 108 }
 109
 110 void
 111 transform_cart_to_geo(struct coord_geo_cart *cart, double a, double b, struct coord_geo *geo)
 112 {
 113         double lat,lati,n,ee=1-b*b/(a*a), lng = atan(cart->y/cart->x);
 114
 115         lat = atan(cart->z / sqrt((cart->x * cart->x) + (cart->y * cart->y)));
 116         do
 117         {
 118                 lati = lat;
 119
 120                 n = a / sqrt(1-ee*sin(lat)*sin(lat));
 121                 lat = atan((cart->z + ee * n * sin(lat)) / sqrt(cart->x * cart->x + cart->y * cart->y));
 122         }
 123         while (fabs(lat - lati) >= 0.000000000000001);
 124
 125         geo->lng=lng/M_PI*180;
 126         geo->lat=lat/M_PI*180;
 127 }
 128
 129
 130 void
 131 transform_datum(struct coord_geo *from, enum map_datum from_datum, struct coord_geo *to, enum map_datum to_datum)
 132 {
 133 }
 134
 135 int
 136 transform(struct transformation *t, enum projection pro, struct coord *c, struct point *p, int count, int unique)
 137 {
 138         struct coord c1;
 139         int xcn, ycn;
 140         struct coord_geo g;
 141 #ifdef AVOID_FLOAT
 142         int xc,yc;
 143 #else
 144         double xc,yc;
 145 #endif
 146         int i,j = 0;
 147         for (i=0; i < count; i++) {
 148                 if (pro == t->pro) {
 149                         xc=c[i].x;
 150                         yc=c[i].y;
 151                 } else {
 152                         transform_to_geo(pro, &c[i], &g);
 153                         transform_from_geo(t->pro, &g, &c1);
 154                         xc=c1.x;
 155                         yc=c1.y;
 156                 }
 157 //              dbg(2,"0x%x, 0x%x - 0x%x,0x%x contains 0x%x,0x%x\n", t->r.lu.x, t->r.lu.y, t->r.rl.x, t->r.rl.y, c->x, c->y);
 158 //              ret=coord_rect_contains(&t->r, c);
 159                 xc-=t->map_center.x;
 160                 yc-=t->map_center.y;
 161                 yc=-yc;
 162                 if (t->angle) {
 163                         xcn=xc*t->cos_val+yc*t->sin_val;
 164                         ycn=-xc*t->sin_val+yc*t->cos_val;
 165                         xc=xcn;
 166                         yc=ycn;
 167                 }
 168                 xc=xc*16;
 169                 yc=yc*16;
 170 #ifndef AVOID_FLOAT
 171                 if (t->scale!=1) {
 172                         xc=xc/(double)(t->scale);
 173                         yc=yc/(double)(t->scale);
 174                 }
 175 #else
 176                 if (t->scale!=1) {
 177                         xc=xc/t->scale;
 178                         yc=yc/t->scale;
 179                 }
 180 #endif
 181                 xc+=t->screen_center.x;
 182                 yc+=t->screen_center.y;
 183                 if (xc < -0x8000)
 184                         xc=-0x8000;
 185                 if (xc > 0x7fff) {
 186                         xc=0x7fff;
 187                 }
 188                 if (yc < -0x8000)
 189                         yc=-0x8000;
 190                 if (yc > 0x7fff)
 191                         yc=0x7fff;
 192                 if (j == 0 || !unique || p[j-1].x != xc || p[j-1].y != yc) {
 193                         p[j].x=xc;
 194                         p[j].y=yc;
 195                         j++;
 196                 }
 197         }
 198         return j;
 199 }
 200
 201 void
 202 transform_reverse(struct transformation *t, struct point *p, struct coord *c)
 203 {
 204         int xc,yc;
 205         xc=p->x;
 206         yc=p->y;
 207         xc-=t->screen_center.x;
 208         yc-=t->screen_center.y;
 209         xc=xc*t->scale/16;
 210         yc=-yc*t->scale/16;
 211         if (t->angle) {
 212                 int xcn, ycn;
 213                 xcn=xc*t->cos_val+yc*t->sin_val;
 214                 ycn=-xc*t->sin_val+yc*t->cos_val;
 215                 xc=xcn;
 216                 yc=ycn;
 217         }
 218         c->x=t->map_center.x+xc;
 219         c->y=t->map_center.y+yc;
 220 }
 221
 222 enum projection
 223 transform_get_projection(struct transformation *this_)
 224 {
 225         return this_->pro;
 226 }
 227
 228 void
 229 transform_set_projection(struct transformation *this_, enum projection pro)
 230 {
 231         this_->pro=pro;
 232 }
 233
 234 static int
 235 min4(int v1,int v2, int v3, int v4)
 236 {
 237         int res=v1;
 238         if (v2 < res)
 239                 res=v2;
 240         if (v3 < res)
 241                 res=v3;
 242         if (v4 < res)
 243                 res=v4;
 244         return res;
 245 }
 246
 247 static int
 248 max4(int v1,int v2, int v3, int v4)
 249 {
 250         int res=v1;
 251         if (v2 > res)
 252                 res=v2;
 253         if (v3 > res)
 254                 res=v3;
 255         if (v4 > res)
 256                 res=v4;
 257         return res;
 258 }
 259
 260 struct map_selection *
 261 transform_get_selection(struct transformation *this_, enum projection pro, int order)
 262 {
 263
 264         struct map_selection *ret,*curri,*curro;
 265         struct coord_geo g;
 266         int i;
 267
 268         ret=map_selection_dup(this_->map_sel);
 269         curri=this_->map_sel;
 270         curro=ret;
 271         while (curri) {
 272                 if (this_->pro != pro) {
 273                         transform_to_geo(this_->pro, &curri->u.c_rect.lu, &g);
 274                         transform_from_geo(pro, &g, &curro->u.c_rect.lu);
 275                         dbg(1,"%f,%f", g.lat, g.lng);
 276                         transform_to_geo(this_->pro, &curri->u.c_rect.rl, &g);
 277                         transform_from_geo(pro, &g, &curro->u.c_rect.rl);
 278                         dbg(1,": - %f,%f\n", g.lat, g.lng);
 279                 }
 280                 dbg(1,"transform rect for %d is %d,%d - %d,%d\n", pro, curro->u.c_rect.lu.x, curro->u.c_rect.lu.y, curro->u.c_rect.rl.x, curro->u.c_rect.rl.y);
 281                 for (i = 0 ; i < layer_end ; i++)
 282                         curro->order[i]+=order;
 283                 curri=curri->next;
 284                 curro=curro->next;
 285         }
 286         return ret;
 287 }
 288
 289 struct coord *
 290 transform_center(struct transformation *this_)
 291 {
 292         return &this_->map_center;
 293 }
 294
 295 void
 296 transform_set_angle(struct transformation *t,int angle)
 297 {
 298         t->angle=angle;
 299         t->cos_val=cos(M_PI*t->angle/180);
 300         t->sin_val=sin(M_PI*t->angle/180);
 301 }
 302
 303 int
 304 transform_get_angle(struct transformation *this_,int angle)
 305 {
 306         return this_->angle;
 307 }
 308
 309 void
 310 transform_set_screen_selection(struct transformation *t, struct map_selection *sel)
 311 {
 312         map_selection_destroy(t->screen_sel);
 313         t->screen_sel=map_selection_dup(sel);
 314         if (sel) {
 315                 t->screen_center.x=(sel->u.p_rect.rl.x-sel->u.p_rect.lu.x)/2;
 316                 t->screen_center.y=(sel->u.p_rect.rl.y-sel->u.p_rect.lu.y)/2;
 317         }
 318 }
 319
 320 #if 0
 321 void
 322 transform_set_size(struct transformation *t, int width, int height)
 323 {
 324         t->width=width;
 325         t->height=height;
 326 }
 327 #endif
 328
 329 void
 330 transform_get_size(struct transformation *t, int *width, int *height)
 331 {
 332         struct point_rect *r;
 333         if (t->screen_sel) {
 334                 r=&t->screen_sel->u.p_rect;
 335                 *width=r->rl.x-r->lu.x;
 336                 *height=r->rl.y-r->lu.y;
 337         }
 338 }
 339
 340 void
 341 transform_setup(struct transformation *t, struct pcoord *c, int scale, int angle)
 342 {
 343         t->pro=c->pro;
 344         t->map_center.x=c->x;
 345         t->map_center.y=c->y;
 346         t->scale=scale;
 347         transform_set_angle(t, angle);
 348 }
 349
 350 #if 0
 351
 352 void
 353 transform_setup_source_rect_limit(struct transformation *t, struct coord *center, int limit)
 354 {
 355         t->center=*center;
 356         t->scale=1;
 357         t->angle=0;
 358         t->r.lu.x=center->x-limit;
 359         t->r.rl.x=center->x+limit;
 360         t->r.rl.y=center->y-limit;
 361         t->r.lu.y=center->y+limit;
 362 }
 363 #endif
 364
 365 void
 366 transform_setup_source_rect(struct transformation *t)
 367 {
 368         int i;
 369         struct coord screen[4];
 370         struct point screen_pnt[4];
 371         struct point_rect *pr;
 372         struct map_selection *ms,*msm,*next,**msm_last;
 373         ms=t->map_sel;
 374         while (ms) {
 375                 next=ms->next;
 376                 g_free(ms);
 377                 ms=next;
 378         }
 379         t->map_sel=NULL;
 380         msm_last=&t->map_sel;
 381         ms=t->screen_sel;
 382         while (ms) {
 383                 msm=g_new0(struct map_selection, 1);
 384                 *msm=*ms;
 385                 pr=&ms->u.p_rect;
 386                 screen_pnt[0].x=pr->lu.x;
 387                 screen_pnt[0].y=pr->lu.y;
 388                 screen_pnt[1].x=pr->rl.x;
 389                 screen_pnt[1].y=pr->lu.y;
 390                 screen_pnt[2].x=pr->lu.x;
 391                 screen_pnt[2].y=pr->rl.y;
 392                 screen_pnt[3].x=pr->rl.x;
 393                 screen_pnt[3].y=pr->rl.y;
 394                 for (i = 0 ; i < 4 ; i++) {
 395                         transform_reverse(t, &screen_pnt[i], &screen[i]);
 396                 }
 397                 msm->u.c_rect.lu.x=min4(screen[0].x,screen[1].x,screen[2].x,screen[3].x);
 398                 msm->u.c_rect.rl.x=max4(screen[0].x,screen[1].x,screen[2].x,screen[3].x);
 399                 msm->u.c_rect.rl.y=min4(screen[0].y,screen[1].y,screen[2].y,screen[3].y);
 400                 msm->u.c_rect.lu.y=max4(screen[0].y,screen[1].y,screen[2].y,screen[3].y);
 401                 *msm_last=msm;
 402                 msm_last=&msm->next;
 403                 ms=ms->next;
 404         }
 405 }
 406
 407 long
 408 transform_get_scale(struct transformation *t)
 409 {
 410         return t->scale;
 411 }
 412
 413 void
 414 transform_set_scale(struct transformation *t, long scale)
 415 {
 416         t->scale=scale;
 417 }
 418
 419
 420 int
 421 transform_get_order(struct transformation *t)
 422 {
 423         int scale=t->scale;
 424         int order=0;
 425         while (scale > 1) {
 426                 order++;
 427                 scale>>=1;
 428         }
 429         order=18-order;
 430         if (order < 0)
 431                 order=0;
 432         return order;
 433 }
 434
 435
 436 void
 437 transform_geo_text(struct coord_geo *g, char *buffer)
 438 {
 439         double lng=g->lng;
 440         double lat=g->lat;
 441         char lng_c='E';
 442         char lat_c='N';
 443
 444         if (lng < 0) {
 445                 lng=-lng;
 446                 lng_c='W';
 447         }
 448         if (lat < 0) {
 449                 lat=-lat;
 450                 lat_c='S';
 451         }
 452
 453         sprintf(buffer,"%02.0f%07.4f%c %03.0f%07.4f%c", floor(lat), fmod(lat*60,60), lat_c, floor(lng), fmod(lng*60,60), lng_c);
 454
 455 }
 456
 457 #define TWOPI (M_PI*2)
 458 #define GC2RAD(c) ((c) * TWOPI/(1<<24))
 459 #define minf(a,b) ((a) < (b) ? (a) : (b))
 460
 461 static double
 462 transform_distance_garmin(struct coord *c1, struct coord *c2)
 463 {
 464 #ifdef USE_HALVESINE
 465         static const int earth_radius = 6371*1000; //m change accordingly
 466 // static const int earth_radius  = 3960; //miles
 467
 468 //Point 1 cords
 469         float lat1  = GC2RAD(c1->y);
 470         float long1 = GC2RAD(c1->x);
 471
 472 //Point 2 cords
 473         float lat2  = GC2RAD(c2->y);
 474         float long2 = GC2RAD(c2->x);
 475
 476 //Haversine Formula
 477         float dlong = long2-long1;
 478         float dlat  = lat2-lat1;
 479
 480         float sinlat  = sinf(dlat/2);
 481         float sinlong = sinf(dlong/2);
 482
 483         float a=(sinlat*sinlat)+cosf(lat1)*cosf(lat2)*(sinlong*sinlong);
 484         float c=2*asinf(minf(1,sqrt(a)));
 485 #ifdef AVOID_FLOAT
 486         return round(earth_radius*c);
 487 #else
 488         return earth_radius*c;
 489 #endif
 490 #else
 491 #define GMETER 2.3887499999999999
 492         double dx,dy;
 493         dx=c1->x-c2->x;
 494         dy=c1->y-c2->y;
 495         return sqrt(dx*dx+dy*dy)*GMETER;
 496 #undef GMETER
 497 #endif
 498 }
 499
 500 double
 501 transform_scale(int y)
 502 {
 503         struct coord c;
 504         struct coord_geo g;
 505         c.x=0;
 506         c.y=y;
 507         transform_to_geo(projection_mg, &c, &g);
 508         return 1/cos(g.lat/180*M_PI);
 509 }
 510
 511 #ifdef AVOID_FLOAT
 512 static int
 513 tab_sqrt[]={14142,13379,12806,12364,12018,11741,11517,11333,11180,11051,10943,10850,10770,10701,10640,10587,10540,10499,10462,10429,10400,10373,10349,10327,10307,10289,10273,10257,10243,10231,10219,10208};
 514 #endif
 515
 516 double
 517 transform_distance(enum projection pro, struct coord *c1, struct coord *c2)
 518 {
 519         if (pro == projection_mg) {
 520 #ifndef AVOID_FLOAT
 521         double dx,dy,scale=transform_scale((c1->y+c2->y)/2);
 522         dx=c1->x-c2->x;
 523         dy=c1->y-c2->y;
 524         return sqrt(dx*dx+dy*dy)/scale;
 525 #else
 526         int dx,dy,f,scale=15539;
 527         dx=c1->x-c2->x;
 528         dy=c1->y-c2->y;
 529         if (dx < 0)
 530                 dx=-dx;
 531         if (dy < 0)
 532                 dy=-dy;
 533         while (dx > 20000 || dy > 20000) {
 534                 dx/=10;
 535                 dy/=10;
 536                 scale/=10;
 537         }
 538         if (! dy)
 539                 return dx*10000/scale;
 540         if (! dx)
 541                 return dy*10000/scale;
 542         if (dx > dy) {
 543                 f=dx*8/dy-8;
 544                 if (f >= 32)
 545                         return dx*10000/scale;
 546                 return dx*tab_sqrt[f]/scale;
 547         } else {
 548                 f=dy*8/dx-8;
 549                 if (f >= 32)
 550                         return dy*10000/scale;
 551                 return dy*tab_sqrt[f]/scale;
 552         }
 553 #endif
 554         } else if (pro == projection_garmin) {
 555                 return transform_distance_garmin(c1, c2);
 556         } else {
 557                 printf("Unknown projection: %d\n", pro);
 558                 return 0;
 559         }
 560 }
 561
 562 int
 563 transform_distance_sq(struct coord *c1, struct coord *c2)
 564 {
 565         int dx=c1->x-c2->x;
 566         int dy=c1->y-c2->y;
 567
 568         if (dx > 32767 || dy > 32767 || dx < -32767 || dy < -32767)
 569                 return INT_MAX;
 570         else
 571                 return dx*dx+dy*dy;
 572 }
 573
 574 int
 575 transform_distance_line_sq(struct coord *l0, struct coord *l1, struct coord *ref, struct coord *lpnt)
 576 {
 577         int vx,vy,wx,wy;
 578         int c1,c2;
 579         int climit=1000000;
 580         struct coord l;
 581
 582         vx=l1->x-l0->x;
 583         vy=l1->y-l0->y;
 584         wx=ref->x-l0->x;
 585         wy=ref->y-l0->y;
 586
 587         c1=vx*wx+vy*wy;
 588         if ( c1 <= 0 ) {
 589                 if (lpnt)
 590                         *lpnt=*l0;
 591                 return transform_distance_sq(l0, ref);
 592         }
 593         c2=vx*vx+vy*vy;
 594         if ( c2 <= c1 ) {
 595                 if (lpnt)
 596                         *lpnt=*l1;
 597                 return transform_distance_sq(l1, ref);
 598         }
 599         while (c1 > climit || c2 > climit) {
 600                 c1/=256;
 601                 c2/=256;
 602         }
 603         l.x=l0->x+vx*c1/c2;
 604         l.y=l0->y+vy*c1/c2;
 605         if (lpnt)
 606                 *lpnt=l;
 607         return transform_distance_sq(&l, ref);
 608 }
 609
 610 int
 611 transform_distance_polyline_sq(struct coord *c, int count, struct coord *ref, struct coord *lpnt, int *pos)
 612 {
 613         int i,dist,distn;
 614         struct coord lp;
 615         if (count < 2)
 616                 return INT_MAX;
 617         if (pos)
 618                 *pos=0;
 619         dist=transform_distance_line_sq(&c[0], &c[1], ref, lpnt);
 620         for (i=2 ; i < count ; i++) {
 621                 distn=transform_distance_line_sq(&c[i-1], &c[i], ref, &lp);
 622                 if (distn < dist) {
 623                         dist=distn;
 624                         if (lpnt)
 625                                 *lpnt=lp;
 626                         if (pos)
 627                                 *pos=i-1;
 628                 }
 629         }
 630         return dist;
 631 }
 632
 633
 634 void
 635 transform_print_deg(double deg)
 636 {
 637         printf("%2.0f:%2.0f:%2.4f", floor(deg), fmod(deg*60,60), fmod(deg*3600,60));
 638 }
 639
 640 #ifdef AVOID_FLOAT
 641 static int tab_atan[]={0,262,524,787,1051,1317,1584,1853,2126,2401,2679,2962,3249,3541,3839,4142,4452,4770,5095,5430,5774,6128,6494,6873,7265,7673,8098,8541,9004,9490,10000,10538};
 642
 643 static int
 644 atan2_int_lookup(int val)
 645 {
 646         int len=sizeof(tab_atan)/sizeof(int);
 647         int i=len/2;
 648         int p=i-1;
 649         for (;;) {
 650                 i>>=1;
 651                 if (val < tab_atan[p])
 652                         p-=i;
 653                 else
 654                         if (val < tab_atan[p+1])
 655                                 return p+(p>>1);
 656                         else
 657                                 p+=i;
 658         }
 659 }
 660
 661 static int
 662 atan2_int(int dx, int dy)
 663 {
 664         int f,mul=1,add=0,ret;
 665         if (! dx) {
 666                 return dy < 0 ? 180 : 0;
 667         }
 668         if (! dy) {
 669                 return dx < 0 ? -90 : 90;
 670         }
 671         if (dx < 0) {
 672                 dx=-dx;
 673                 mul=-1;
 674         }
 675         if (dy < 0) {
 676                 dy=-dy;
 677                 add=180*mul;
 678                 mul*=-1;
 679         }
 680         while (dx > 20000 || dy > 20000) {
 681                 dx/=10;
 682                 dy/=10;
 683         }
 684         if (dx > dy) {
 685                 ret=90-atan2_int_lookup(dy*10000/dx);
 686         } else {
 687                 ret=atan2_int_lookup(dx*10000/dy);
 688         }
 689         return ret*mul+add;
 690 }
 691 #endif
 692
 693 int
 694 transform_get_angle_delta(struct coord *c1, struct coord *c2, int dir)
 695 {
 696         int dx=c2->x-c1->x;
 697         int dy=c2->y-c1->y;
 698 #ifndef AVOID_FLOAT
 699         double angle;
 700         angle=atan2(dx,dy);
 701         angle*=180/M_PI;
 702 #else
 703         int angle;
 704         angle=atan2_int(dx,dy);
 705 #endif
 706         if (dir == -1)
 707                 angle=angle-180;
 708         if (angle < 0)
 709                 angle+=360;
 710         return angle;
 711 }
 712
 713 int
 714 transform_within_border(struct transformation *this_, struct point *p, int border)
 715 {
 716         struct map_selection *ms=this_->screen_sel;
 717         while (ms) {
 718                 struct point_rect *r=&ms->u.p_rect;
 719                 if (p->x >= r->lu.x+border && p->x <= r->rl.x-border &&
 720                     p->y >= r->lu.y+border && p->y <= r->rl.y-border)
 721                         return 1;
 722                 ms=ms->next;
 723         }
 724         return 0;
 725 }
 726
 727 /*
 728 Note: there are many mathematically equivalent ways to express these formulas. As usual, not all of them are computationally equivalent.
 729
 730 L = latitude in radians (positive north)
 731 Lo = longitude in radians (positive east)
 732 E = easting (meters)
 733 N = northing (meters)
 734
 735 For the sphere
 736
 737 E = r Lo
 738 N = r ln [ tan (pi/4 + L/2) ]
 739
 740 where
 741
 742 r = radius of the sphere (meters)
 743 ln() is the natural logarithm
 744
 745 For the ellipsoid
 746
 747 E = a Lo
 748 N = a * ln ( tan (pi/4 + L/2) * ( (1 - e * sin (L)) / (1 + e * sin (L))) ** (e/2)  )
 749
 750
 751                                                e
 752                                                -
 753                    pi     L     1 - e sin(L)   2
 754     =  a ln( tan( ---- + ---) (--------------)   )
 755                    4      2     1 + e sin(L)
 756
 757
 758 where
 759
 760 a = the length of the semi-major axis of the ellipsoid (meters)
 761 e = the first eccentricity of the ellipsoid
 762
 763
 764 */
 765
 766