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Cross_country.cc
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Cross_country.cc
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/***************************************************************
Cross_country.cc
Copyright (c) R. Burghall 2017 all rights reserved
Issued under GPL v3.0. If you copy and/or distribute
this program, copy and/or distribute this licence with it.
Version 0.1 RB 2017-12-21
Written to investigate the merits of Haversine and
Vincenty methods of determining the distance between
two points on the surface of the Earth.
The Haversine formula is said to be a crude and inaccurate
method while the Vincenty algorithm is complex, difficult
and highly accurate - except that the Earth isn't really
an ellipsoid, WGS84 or otherwise. There are hills!
***************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <iostream>
#include <math.h>
#include <cmath>
#include <assert.h>
#include "Vincenty.h"
using namespace std;
#define VINCENTY true
#define HALVERSINE false
#define VERSION 0.1
double toRad(double degrees)
{
return(degrees * M_PI / 180.0);
}
double square(double x)
{
return(x * x);
}
double arcsin(double x)
{
return(2.0 * atan(x / (1.0 + sqrt(1.0 - x*x))));
}
double hav(double theta)
{
return(sin(theta/2.0) * sin(theta/2.0));
}
double haversine(Position p1, Position p2)
{
double R = 6371.0;
double d = 2.0 * R * arcsin(sqrt(hav(p1.GetLat( )-p2.GetLat( ))+cos(p1.GetLat( ))*cos(p2.GetLat( ))*hav(p2.GetLong( )-p1.GetLong( ))));
return(d);
}
double Vincenty(Position x1, Position x2, double &bearing)
{
double a, b; /// Major and minor semiaxes of the ellipsoid.
a = 6378137.0;
b = 6356752.314245;
double f = (a - b) / a; /// Flattening.
assert((f > 1.0 / 298.257224) && (f < 1.0 / 298.257223));
double long1, long2;
double Phi1 = x1.GetLat( ),
Phi2 = x2.GetLat( ); /// Geodetic latitude.
double L = x2.GetLong( )-x1.GetLong( ); /// Difference in longitude.
double U1 = atan((1.0 - f) * tan(Phi1)); /// "Reduced latitude" = atan((1 - f) * tan(Phi1)).
double U2 = atan((1.0 - f) * tan(Phi2)); /// "Reduced latitude" = atan((1 - f) * tan(Phi2)).
double Lambda = L; /// = L as first approximation.
double Lambda1, diff;
double sigma, sinsigma, cossigma, deltasigma;
double sinalpha, cossqalpha, cos2sigmam, C;
double alpha1, alpha2;
double usq, A, B, s;
double sinlambda, coslambda;
double sinU1 = sin(U1), sinU2 = sin(U2), cosU1 = cos(U1), cosU2 = cos(U2);
double i = 0, n = 100;
do {
sinlambda = sin(Lambda), coslambda = cos(Lambda);
sinsigma = sqrt(square(cosU2 * sinlambda) + square(cosU1 * sinU2 - sinU1 * cosU2 * coslambda));
if(sinsigma == 0.0) return(0.0);
cossigma = sinU1 * sinU2 + cosU1 * cosU2 * coslambda;
sigma = atan2(sinsigma, cossigma);
sinalpha = cosU1 * cosU2 * sinlambda / sinsigma;
cossqalpha = 1.0 - sinalpha * sinalpha;
cos2sigmam = cossigma - 2.0 * sinU1 * sinU2 / cossqalpha;
C = f / 16.0 * cossqalpha * (4.0 + f *(4.0 - 3.0 * cossqalpha));
Lambda1 = L + (1.0 - C) * f * sinalpha * (sigma + C * sinsigma * (cos2sigmam + C * cossigma * (-1.0 + 2.0 * cos2sigmam * cos2sigmam)));
diff = Lambda - Lambda1;
Lambda = Lambda1;
// cout << "Lambda = " << Lambda << "\n";
if(++i > n) break;
} while(fabs(diff) > 1e-13);
usq = cossqalpha * (a * a - b * b) / (b * b);
A = 1.0 + usq / 16384.0 * (4096.0 + usq * (-768.0 + usq * (320.0 -175.0 * usq)));
B = usq / 1024.0 * (256.0 + usq * (-128.0 + usq * (74.0 - 47.0 * usq)));
deltasigma = B * sinsigma * (cos2sigmam + B / 4.0 * (cossigma * (-1.0 + 2.0 * cos2sigmam * cos2sigmam) - B / 6.0 * cos2sigmam * (-3.0 + 4.0 * sinsigma * sinsigma) * (-3.0 + 4.0 * cos2sigmam * cos2sigmam)));
s = b * A * (sigma - deltasigma);
alpha1 = atan2(cosU2 * sin(Lambda), cosU1 * sinU2 - sinU1 * cosU2 * cos(Lambda));
alpha2 = atan2(cosU1 * sin(Lambda), -sinU1 * cosU2 + cosU1 * sinU2 * cos(Lambda));
bearing = (alpha1+alpha2)/2.0;
return(s);
}
/*!
Convert latitude or longitude string to a double.
*/
double str_to_val(char *ptr)
{
int n;
int dd = 0.0;
double mm = 0.0;
while(*ptr == ' ') ptr++;
strcat(ptr, "\n");
n = sscanf(ptr, "%d%lf", &dd, &mm);
return(dd + mm / 60.0);
}
void clean(char* line)
{
static char *ptr;
for(ptr = line; (*ptr != '\r') && (*ptr != '\n'); ptr++) {
if(*ptr == '\r') *ptr = '\0';
if(*ptr == '\n') *ptr = '\0';
}
*ptr = '\0';
}
bool cfound(char *ptr, char c)
{
int i;
int n = strlen(ptr);
for(i=0; i < n; i++) if(*ptr++ == c) return(true);
return(false);
}
double leg(char *a1, char *a2, double &h, double &v)
{
char c1, c2;
int d1, d2;
double m1, m2;
char name[258], bfr[258];
char tp1[258], tp2[258];
bool found = false;
int l;
FILE *tpfile;
Position x1, x2;
// Open TP file.
tpfile = fopen("./TurnPoints.dat", "r");
if (tpfile == NULL) { perror ("Error opening file"); return(-1); }
else {
while(!found) {
// Read a line; it should be the name of the turning point.
if(fgets(name, 256, tpfile) == NULL) ;
clean(name);
// Get the next line, which should be the trigraph.
if(fgets(bfr, 256, tpfile) == NULL) ;
clean(bfr);
l = 1;
// Have we found it?
if(strncmp(bfr, a1, 256) == 0) {
// puts(name);
found = true;
}
// Look for location.
if(found) for(;;) {
bfr[0] = '\0';
if(fgets(bfr, 256, tpfile) == NULL) ;
clean(bfr);
l++;
if(found && (l == 9)) {
strncpy(tp1, bfr, 256) ;
break;
}
}
// Look for a blank line between TPs
do {
if(fgets(bfr, 256, tpfile) == NULL) ;
clean(bfr);
if(strlen(bfr) == 0) break;
} while((bfr[0] != '\r') && (bfr[0] != '\n'));
if(found) break; // We found it - don't keep looking
if(feof(tpfile)) exit(-3); // End of file? What should we do?
}
if(found) { printf("%s: %s\n", name, tp1); }
}
fclose(tpfile);
tpfile = NULL;
tpfile = fopen("./TurnPoints.dat", "r");
found = false;
if (tpfile == NULL) { perror ("Error opening file"); return(-1); }
else {
while(!found) {
// Read a line; it should be the name of the turning point.
if(fgets(name, 256, tpfile) == NULL) ;
clean(name);
// Get the next line, which should be the trigraph.
if(fgets(bfr, 256, tpfile) == NULL) ;
clean(bfr);
l = 1;
// Have we found it?
if(strncmp(bfr, a2, 256) == 0) {
// puts(name);
found = true;
}
// Look for the location
if(found) for(;;) {
bfr[0] = '\0';
if(fgets(bfr, 256, tpfile) == NULL) ;
clean(bfr);
l++;
if(found && (l == 9)) {
// This should be the lat & long
strncpy(tp2, bfr, 256) ;
break;
}
}
// Look for a blank line between TPs
do {
if(fgets(bfr, 256, tpfile) == NULL) ;
clean(bfr);
if(strlen(bfr) == 0) break;
} while((bfr[0] != '\r') && (bfr[0] != '\n'));
if(found) break; // We found it - don't keep looking
if(feof(tpfile)) exit(-2); // End of file? What should we do?
}
if(found) { printf("%s: %s\n", name, tp2); }
}
fclose(tpfile);
strncat(tp1, "\n", 256);
sscanf(tp1, "%d %lf%c %d %lf%c", &d1, &m1, &c1, &d2, &m2, &c2);
if(cfound(tp1, 'S')) d1 = -d1, m1 = -m1;
if(cfound(tp1, 'E')) d2 = -d2, m2 = -m2;
x1.SetLat(d1*M_PI/180.0 + m1*M_PI/(180.0*60.0));
x1.SetLong(d2*M_PI/180.0 + m2*M_PI/(180.0*60.0));
// printf("<%d %lf>, ", d1, m1);
// printf("<%d %lf>\n", d2, m2);
strncat(tp2, "\n", 256);
sscanf(tp2, "%d %lf%c %d %lf%c", &d1, &m1, &c1, &d2, &m2, &c2);
if(cfound(tp2, 'S')) d1 = -d1, m1 = -m1;
if(cfound(tp2, 'E')) d2 = -d2, m2 = -m2;
x2.SetLat(d1*M_PI/180.0 + m1*M_PI/(180.0*60.0));
x2.SetLong(d2*M_PI/180.0 + m2*M_PI/(180.0*60.0));
// printf("<%d %lf>, ", d1, m1);
// printf("<%d %lf>\n", d2, m2);
double hdg;
double s = Vincenty(x1, x2, hdg);
printf("Vincenty --> %0.3f km\n", s/1000.0);
hdg = -hdg*180.0/M_PI;
if(hdg < 0.0) hdg = 360.0 + hdg;
printf("Track: %0.1lf\n", hdg);
v = s / 1000.0;
s = haversine(x1, x2);
#if HALVERSINE
printf("Haversine --> %0.3f km\n\n", s);
#endif
h = s;
}
void upper_case(char *ptr)
{
int i;
while(*ptr) {
*ptr = toupper(*ptr);
++ptr;
}
}
/*!
Try 50 3.979, 5 42.885
58 38.64133, 3 4.205667
*/
int main(int argc, char **argv)
{
char c1, c2;
char a1[256], a2[256];
double h, v, htotal = 0.0, vtotal = 0.0;
puts("Enter 'END' as t.p. to end cross-country.\n\n");
if(argc == 1) {
// No parameters after the program name, so enter TPs manually.
puts("Start TP: ");
scanf("%s", a1);
upper_case(a1);
while(1) {
puts("Next TP: ");
a2[0] = '\0';
scanf("%s", a2);
upper_case(a2);
if(strcmp(a2, "END") == 0) break;
leg(a1, a2, h, v);
htotal += h;
vtotal += v;
// leg(a1, a2);
strcpy(a1, a2);
}
#if HALVERSINE
printf("Total distance (Haversine) = %0.3f; ", htotal);
#endif
printf("Total distance (Vincenty) = %0.3f", vtotal);
} else if(argc == 3) {
strncpy(a1, argv[1], 5);
strncpy(a2, argv[2], 5);
leg(a1, a2, htotal, vtotal);
} else {
printf("*** Too many arguments!");
exit(-1);
}
printf("\nBye!\n");
/* getchar( ); // I seem to need to remove a character already waiting
// Now wait to be dismissed
do {
c1 = getchar( );
} while((c1 != ' ') && (c1 != '\r') && (c1 != '\n'));
*/
}