航行时，计算地球上2个位置的距离，方位角度程序

/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*-
/*
* location.cpp
* Copyright (C) Andrew Tridgell 2011
*
* This file is free software: you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the
* Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This file is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
* See the GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program.  If not, see <http://www.gnu.org/licenses/>.
*/

/*
*  this module deals with calculations involving struct Location
*/
#include <AP_HAL/AP_HAL.h>
#include <stdlib.h>
#include "AP_Math.h"
#include "location.h"

// scaling factor from 1e-7 degrees to meters at equater
// == 1.0e-7 * DEG_TO_RAD * RADIUS_OF_EARTH
#define LOCATION_SCALING_FACTOR 0.011131884502145034f
// inverse of LOCATION_SCALING_FACTOR
#define LOCATION_SCALING_FACTOR_INV 89.83204953368922f

float longitude_scale(const struct Location &loc)
{
#if HAL_CPU_CLASS < HAL_CPU_CLASS_150
static int32_t last_lat;
static float scale = 1.0;
// don't optimise on faster CPUs. It causes some minor errors on Replay
if (labs(last_lat - loc.lat) < 100000) {
// we are within 0.01 degrees (about 1km) of the
// same latitude. We can avoid the cos() and return
// the same scale factor.
return scale;
}
scale = cosf(loc.lat * 1.0e-7f * DEG_TO_RAD);
scale = constrain_float(scale, 0.01f, 1.0f);
last_lat = loc.lat;
return scale;
#else
float scale = cosf(loc.lat * 1.0e-7f * DEG_TO_RAD);
return constrain_float(scale, 0.01f, 1.0f);
#endif
}

// return distance in meters between two locations
float get_distance(const struct Location &loc1, const struct Location &loc2)
{
float dlat              = (float)(loc2.lat - loc1.lat);
float dlong             = ((float)(loc2.lng - loc1.lng)) * longitude_scale(loc2);
return pythagorous2(dlat, dlong) * LOCATION_SCALING_FACTOR;
}

// return distance in centimeters to between two locations
uint32_t get_distance_cm(const struct Location &loc1, const struct Location &loc2)
{
return get_distance(loc1, loc2) * 100;
}

// return bearing in centi-degrees between two locations
int32_t get_bearing_cd(const struct Location &loc1, const struct Location &loc2)
{
int32_t off_x = loc2.lng - loc1.lng;
int32_t off_y = (loc2.lat - loc1.lat) / longitude_scale(loc2);
int32_t bearing = 9000 + atan2f(-off_y, off_x) * 5729.57795f;
if (bearing < 0) bearing += 36000;
return bearing;
}

// see if location is past a line perpendicular to
// the line between point1 and point2. If point1 is
// our previous waypoint and point2 is our target waypoint
// then this function returns true if we have flown past
// the target waypoint
bool location_passed_point(const struct Location &location,
const struct Location &point1,
const struct Location &point2)
{
return location_path_proportion(location, point1, point2) >= 1.0f;
}

/*
return the proportion we are along the path from point1 to
point2, along a line parallel to point1<->point2.

This will be less than >1 if we have passed point2
*/
float location_path_proportion(const struct Location &location,
const struct Location &point1,
const struct Location &point2)
{
Vector2f vec1 = location_diff(point1, point2);
Vector2f vec2 = location_diff(point1, location);
float dsquared = sq(vec1.x) + sq(vec1.y);
if (dsquared < 0.001f) {
// the two points are very close together
return 1.0f;
}
return (vec1 * vec2) / dsquared;
}

/*
*  extrapolate latitude/longitude given bearing and distance
* Note that this function is accurate to about 1mm at a distance of
* 100m. This function has the advantage that it works in relative
* positions, so it keeps the accuracy even when dealing with small
* distances and floating point numbers
*/
void location_update(struct Location &loc, float bearing, float distance)
{
float ofs_north = cosf(radians(bearing))*distance;
float ofs_east  = sinf(radians(bearing))*distance;
location_offset(loc, ofs_north, ofs_east);
}

/*
*  extrapolate latitude/longitude given distances north and east
*/
void location_offset(struct Location &loc, float ofs_north, float ofs_east)
{
if (!is_zero(ofs_north) || !is_zero(ofs_east)) {
int32_t dlat = ofs_north * LOCATION_SCALING_FACTOR_INV;
int32_t dlng = (ofs_east * LOCATION_SCALING_FACTOR_INV) / longitude_scale(loc);
loc.lat += dlat;
loc.lng += dlng;
}
}

/*
return the distance in meters in North/East plane as a N/E vector
from loc1 to loc2
*/
Vector2f location_diff(const struct Location &loc1, const struct Location &loc2)
{
return Vector2f((loc2.lat - loc1.lat) * LOCATION_SCALING_FACTOR,
(loc2.lng - loc1.lng) * LOCATION_SCALING_FACTOR * longitude_scale(loc1));
}

/*
wrap an angle in centi-degrees to 0..35999
*/
int32_t wrap_360_cd(int32_t error)
{
if (error > 360000 || error < -360000) {
// for very large numbers use modulus
error = error % 36000;
}
while (error >= 36000) error -= 36000;
while (error < 0) error += 36000;
return error;
}

/*
wrap an angle in centi-degrees to -18000..18000
*/
int32_t wrap_180_cd(int32_t error)
{
if (error > 360000 || error < -360000) {
// for very large numbers use modulus
error = error % 36000;
}
while (error > 18000) { error -= 36000; }
while (error < -18000) { error += 36000; }
return error;
}

/*
wrap an angle in centi-degrees to 0..35999
*/
float wrap_360_cd_float(float angle)
{
if (angle >= 72000.0f || angle < -36000.0f) {
// for larger number use fmodulus
angle = fmod(angle, 36000.0f);
}
if (angle >= 36000.0f) angle -= 36000.0f;
if (angle < 0.0f) angle += 36000.0f;
return angle;
}

/*
wrap an angle in centi-degrees to -18000..18000
*/
float wrap_180_cd_float(float angle)
{
if (angle > 54000.0f || angle < -54000.0f) {
// for large numbers use modulus
angle = fmod(angle,36000.0f);
}
if (angle > 18000.0f) { angle -= 36000.0f; }
if (angle < -18000.0f) { angle += 36000.0f; }
return angle;
}

/*
wrap an angle defined in radians to -PI ~ PI (equivalent to +- 180 degrees)
*/
float wrap_PI(float angle_in_radians)
{
if (angle_in_radians > 10*M_PI || angle_in_radians < -10*M_PI) {
// for very large numbers use modulus
angle_in_radians = fmodf(angle_in_radians, 2*M_PI);
}
while (angle_in_radians > M_PI) angle_in_radians -= 2*M_PI;
while (angle_in_radians < -M_PI) angle_in_radians += 2*M_PI;
return angle_in_radians;
}

/*
* wrap an angle in radians to 0..2PI
*/
float wrap_2PI(float angle)
{
if (angle > 10*M_PI || angle < -10*M_PI) {
// for very large numbers use modulus
angle = fmodf(angle, 2*M_PI);
}
while (angle > 2*M_PI) angle -= 2*M_PI;
while (angle < 0) angle += 2*M_PI;
return angle;
}

/*
return true if lat and lng match. Ignores altitude and options
*/
bool locations_are_same(const struct Location &loc1, const struct Location &loc2) {
return (loc1.lat == loc2.lat) && (loc1.lng == loc2.lng);
}

/*
print a int32_t lat/long in decimal degrees
*/
void print_latlon(AP_HAL::BetterStream *s, int32_t lat_or_lon)
{
int32_t dec_portion, frac_portion;
int32_t abs_lat_or_lon = labs(lat_or_lon);

// extract decimal portion (special handling of negative numbers to ensure we round towards zero)
dec_portion = abs_lat_or_lon / 10000000UL;

// extract fractional portion
frac_portion = abs_lat_or_lon - dec_portion*10000000UL;

// print output including the minus sign
if( lat_or_lon < 0 ) {
s->printf("-");
}
s->printf("%ld.%07ld",(long)dec_portion,(long)frac_portion);
}

void wgsllh2ecef(const Vector3d &llh, Vector3d &ecef) {
double d = WGS84_E * sin(llh[0]);
double N = WGS84_A / sqrt(1. - d*d);

ecef[0] = (N + llh[2]) * cos(llh[0]) * cos(llh[1]);
ecef[1] = (N + llh[2]) * cos(llh[0]) * sin(llh[1]);
ecef[2] = ((1 - WGS84_E*WGS84_E)*N + llh[2]) * sin(llh[0]);
}

void wgsecef2llh(const Vector3d &ecef, Vector3d &llh) {
/* Distance from polar axis. */
const double p = sqrt(ecef[0]*ecef[0] + ecef[1]*ecef[1]);

/* Compute longitude first, this can be done exactly. */
if (!is_zero(p))
llh[1] = atan2(ecef[1], ecef[0]);
else
llh[1] = 0;

/* If we are close to the pole then convergence is very slow, treat this is a
* special case. */
if (p < WGS84_A*1e-16) {
llh[0] = copysign(M_PI_2, ecef[2]);
llh[2] = fabs(ecef[2]) - WGS84_B;
return;
}

/* Caluclate some other constants as defined in the Fukushima paper. */
const double P = p / WGS84_A;
const double e_c = sqrt(1. - WGS84_E*WGS84_E);
const double Z = fabs(ecef[2]) * e_c / WGS84_A;

/* Initial values for S and C correspond to a zero height solution. */
double S = Z;
double C = e_c * P;

/* Neither S nor C can be negative on the first iteration so
* starting prev = -1 will not cause and early exit. */
double prev_C = -1;
double prev_S = -1;

double A_n, B_n, D_n, F_n;

/* Iterate a maximum of 10 times. This should be way more than enough for all
* sane inputs */
for (int i=0; i<10; i++)
{
/* Calculate some intermmediate variables used in the update step based on
* the current state. */
A_n = sqrt(S*S + C*C);
D_n = Z*A_n*A_n*A_n + WGS84_E*WGS84_E*S*S*S;
F_n = P*A_n*A_n*A_n - WGS84_E*WGS84_E*C*C*C;
B_n = 1.5*WGS84_E*S*C*C*(A_n*(P*S - Z*C) - WGS84_E*S*C);

/* Update step. */
S = D_n*F_n - B_n*S;
C = F_n*F_n - B_n*C;

/* The original algorithm as presented in the paper by Fukushima has a
* problem with numerical stability. S and C can grow very large or small
* and over or underflow a double. In the paper this is acknowledged and
* the proposed resolution is to non-dimensionalise the equations for S and
* C. However, this does not completely solve the problem. The author caps
* the solution to only a couple of iterations and in this period over or
* underflow is unlikely but as we require a bit more precision and hence
* more iterations so this is still a concern for us.
*
* As the only thing that is important is the ratio T = S/C, my solution is
* to divide both S and C by either S or C. The scaling is chosen such that
* one of S or C is scaled to unity whilst the other is scaled to a value
* less than one. By dividing by the larger of S or C we ensure that we do
* not divide by zero as only one of S or C should ever be zero.
*
* This incurs an extra division each iteration which the author was
* explicityl trying to avoid and it may be that this solution is just
* reverting back to the method of iterating on T directly, perhaps this
* bears more thought?
*/

if (S > C) {
C = C / S;
S = 1;
} else {
S = S / C;
C = 1;
}

/* Check for convergence and exit early if we have converged. */
if (fabs(S - prev_S) < 1e-16 && fabs(C - prev_C) < 1e-16) {
break;
} else {
prev_S = S;
prev_C = C;
}
}

A_n = sqrt(S*S + C*C);
llh[0] = copysign(1.0, ecef[2]) * atan(S / (e_c*C));
llh[2] = (p*e_c*C + fabs(ecef[2])*S - WGS84_A*e_c*A_n) / sqrt(e_c*e_c*C*C + S*S);
}