/**********************************************************************
*
* PostGIS - Spatial Types for PostgreSQL
* http://postgis.net
*
* PostGIS 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 2 of the License, or
* (at your option) any later version.
*
* PostGIS 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 PostGIS. If not, see .
*
**********************************************************************
*
* Copyright (C) 2009 Paul Ramsey
* Copyright (C) 2009 David Skea
*
**********************************************************************/
#include "liblwgeom_internal.h"
#include "lwgeodetic.h"
#include "lwgeom_log.h"
/* In proj4.9, GeographicLib is in special header */
#ifdef PROJ_GEODESIC
#include
#endif
/**
* Initialize spheroid object based on major and minor axis
*/
void spheroid_init(SPHEROID *s, double a, double b)
{
s->a = a;
s->b = b;
s->f = (a - b) / a;
s->e_sq = (a*a - b*b)/(a*a);
s->radius = (2.0 * a + b ) / 3.0;
}
#ifndef PROJ_GEODESIC
static double spheroid_mu2(double alpha, const SPHEROID *s)
{
double b2 = POW2(s->b);
return POW2(cos(alpha)) * (POW2(s->a) - b2) / b2;
}
static double spheroid_big_a(double u2)
{
return 1.0 + (u2 / 16384.0) * (4096.0 + u2 * (-768.0 + u2 * (320.0 - 175.0 * u2)));
}
static double spheroid_big_b(double u2)
{
return (u2 / 1024.0) * (256.0 + u2 * (-128.0 + u2 * (74.0 - 47.0 * u2)));
}
#endif /* ! PROJ_GEODESIC */
#ifdef PROJ_GEODESIC
/**
* Computes the shortest distance along the surface of the spheroid
* between two points, using the inverse geodesic problem from
* GeographicLib (Karney 2013).
*
* @param a - location of first point
* @param b - location of second point
* @param s - spheroid to calculate on
* @return spheroidal distance between a and b in spheroid units
*/
double spheroid_distance(const GEOGRAPHIC_POINT *a, const GEOGRAPHIC_POINT *b, const SPHEROID *spheroid)
{
struct geod_geodesic gd;
/* Same point => zero distance */
if ( geographic_point_equals(a, b) )
return 0.0;
geod_init(&gd, spheroid->a, spheroid->f);
double lat1 = a->lat * 180.0 / M_PI;
double lon1 = a->lon * 180.0 / M_PI;
double lat2 = b->lat * 180.0 / M_PI;
double lon2 = b->lon * 180.0 / M_PI;
double s12 = 0.0; /* return distance */
geod_inverse(&gd, lat1, lon1, lat2, lon2, &s12, 0, 0);
return s12;
}
/**
* Computes the forward azimuth of the geodesic joining two points on
* the spheroid, using the inverse geodesic problem (Karney 2013).
*
* @param r - location of first point
* @param s - location of second point
* @return azimuth of line joining r to s (but not reverse)
*/
double spheroid_direction(const GEOGRAPHIC_POINT *a, const GEOGRAPHIC_POINT *b, const SPHEROID *spheroid)
{
struct geod_geodesic gd;
geod_init(&gd, spheroid->a, spheroid->f);
double lat1 = a->lat * 180.0 / M_PI;
double lon1 = a->lon * 180.0 / M_PI;
double lat2 = b->lat * 180.0 / M_PI;
double lon2 = b->lon * 180.0 / M_PI;
double azi1; /* return azimuth */
geod_inverse(&gd, lat1, lon1, lat2, lon2, 0, &azi1, 0);
return azi1 * M_PI / 180.0;
}
/**
* Given a location, an azimuth and a distance, computes the location of
* the projected point. Using the direct geodesic problem from
* GeographicLib (Karney 2013).
*
* @param r - location of first point
* @param distance - distance in meters
* @param azimuth - azimuth in radians
* @return g - location of projected point
*/
int spheroid_project(const GEOGRAPHIC_POINT *r, const SPHEROID *spheroid, double distance, double azimuth, GEOGRAPHIC_POINT *g)
{
struct geod_geodesic gd;
geod_init(&gd, spheroid->a, spheroid->f);
double lat1 = r->lat * 180.0 / M_PI;
double lon1 = r->lon * 180.0 / M_PI;
double lat2, lon2; /* return projected position */
geod_direct(&gd, lat1, lon1, azimuth * 180.0 / M_PI, distance, &lat2, &lon2, 0);
g->lat = lat2 * M_PI / 180.0;
g->lon = lon2 * M_PI / 180.0;
return LW_SUCCESS;
}
static double ptarray_area_spheroid(const POINTARRAY *pa, const SPHEROID *spheroid)
{
/* Return zero on non-sensical inputs */
if ( ! pa || pa->npoints < 4 )
return 0.0;
struct geod_geodesic gd;
geod_init(&gd, spheroid->a, spheroid->f);
struct geod_polygon poly;
geod_polygon_init(&poly, 0);
uint32_t i;
double area; /* returned polygon area */
POINT2D p; /* long/lat units are degrees */
/* Pass points from point array; don't close the linearring */
for ( i = 0; i < pa->npoints - 1; i++ )
{
getPoint2d_p(pa, i, &p);
geod_polygon_addpoint(&gd, &poly, p.y, p.x);
LWDEBUGF(4, "geod_polygon_addpoint %d: %.12g %.12g", i, p.y, p.x);
}
i = geod_polygon_compute(&gd, &poly, 0, 1, &area, 0);
if ( i != pa->npoints - 1 )
{
lwerror("ptarray_area_spheroid: different number of points %d vs %d",
i, pa->npoints - 1);
}
LWDEBUGF(4, "geod_polygon_compute area: %.12g", area);
return fabs(area);
}
/* Above use Proj GeographicLib */
#else /* ! PROJ_GEODESIC */
/* Below use pre-version 2.2 geodesic functions */
/**
* Computes the shortest distance along the surface of the spheroid
* between two points. Based on Vincenty's formula for the geodetic
* inverse problem as described in "Geocentric Datum of Australia
* Technical Manual", Chapter 4. Tested against:
* http://mascot.gdbc.gov.bc.ca/mascot/util1a.html
* and
* http://www.ga.gov.au/nmd/geodesy/datums/vincenty_inverse.jsp
*
* @param a - location of first point.
* @param b - location of second point.
* @param s - spheroid to calculate on
* @return spheroidal distance between a and b in spheroid units.
*/
double spheroid_distance(const GEOGRAPHIC_POINT *a, const GEOGRAPHIC_POINT *b, const SPHEROID *spheroid)
{
double lambda = (b->lon - a->lon);
double f = spheroid->f;
double omf = 1 - spheroid->f;
double u1, u2;
double cos_u1, cos_u2;
double sin_u1, sin_u2;
double big_a, big_b, delta_sigma;
double alpha, sin_alpha, cos_alphasq, c;
double sigma, sin_sigma, cos_sigma, cos2_sigma_m, sqrsin_sigma, last_lambda, omega;
double cos_lambda, sin_lambda;
double distance;
int i = 0;
/* Same point => zero distance */
if ( geographic_point_equals(a, b) )
{
return 0.0;
}
u1 = atan(omf * tan(a->lat));
cos_u1 = cos(u1);
sin_u1 = sin(u1);
u2 = atan(omf * tan(b->lat));
cos_u2 = cos(u2);
sin_u2 = sin(u2);
omega = lambda;
do
{
cos_lambda = cos(lambda);
sin_lambda = sin(lambda);
sqrsin_sigma = POW2(cos_u2 * sin_lambda) +
POW2((cos_u1 * sin_u2 - sin_u1 * cos_u2 * cos_lambda));
sin_sigma = sqrt(sqrsin_sigma);
cos_sigma = sin_u1 * sin_u2 + cos_u1 * cos_u2 * cos_lambda;
sigma = atan2(sin_sigma, cos_sigma);
sin_alpha = cos_u1 * cos_u2 * sin_lambda / sin(sigma);
/* Numerical stability issue, ensure asin is not NaN */
if ( sin_alpha > 1.0 )
alpha = M_PI_2;
else if ( sin_alpha < -1.0 )
alpha = -1.0 * M_PI_2;
else
alpha = asin(sin_alpha);
cos_alphasq = POW2(cos(alpha));
cos2_sigma_m = cos(sigma) - (2.0 * sin_u1 * sin_u2 / cos_alphasq);
/* Numerical stability issue, cos2 is in range */
if ( cos2_sigma_m > 1.0 )
cos2_sigma_m = 1.0;
if ( cos2_sigma_m < -1.0 )
cos2_sigma_m = -1.0;
c = (f / 16.0) * cos_alphasq * (4.0 + f * (4.0 - 3.0 * cos_alphasq));
last_lambda = lambda;
lambda = omega + (1.0 - c) * f * sin(alpha) * (sigma + c * sin(sigma) *
(cos2_sigma_m + c * cos(sigma) * (-1.0 + 2.0 * POW2(cos2_sigma_m))));
i++;
}
while ( (i < 999) && (lambda != 0.0) && (fabs((last_lambda - lambda)/lambda) > 1.0e-9) );
u2 = spheroid_mu2(alpha, spheroid);
big_a = spheroid_big_a(u2);
big_b = spheroid_big_b(u2);
delta_sigma = big_b * sin_sigma * (cos2_sigma_m + (big_b / 4.0) * (cos_sigma * (-1.0 + 2.0 * POW2(cos2_sigma_m)) -
(big_b / 6.0) * cos2_sigma_m * (-3.0 + 4.0 * sqrsin_sigma) * (-3.0 + 4.0 * POW2(cos2_sigma_m))));
distance = spheroid->b * big_a * (sigma - delta_sigma);
/* Algorithm failure, distance == NaN, fallback to sphere */
if ( distance != distance )
{
lwerror("spheroid_distance returned NaN: (%.20g %.20g) (%.20g %.20g) a = %.20g b = %.20g",a->lat, a->lon, b->lat, b->lon, spheroid->a, spheroid->b);
return spheroid->radius * sphere_distance(a, b);
}
return distance;
}
/**
* Computes the direction of the geodesic joining two points on
* the spheroid. Based on Vincenty's formula for the geodetic
* inverse problem as described in "Geocentric Datum of Australia
* Technical Manual", Chapter 4. Tested against:
* http://mascot.gdbc.gov.bc.ca/mascot/util1a.html
* and
* http://www.ga.gov.au/nmd/geodesy/datums/vincenty_inverse.jsp
*
* @param r - location of first point
* @param s - location of second point
* @return azimuth of line joining r and s
*/
double spheroid_direction(const GEOGRAPHIC_POINT *r, const GEOGRAPHIC_POINT *s, const SPHEROID *spheroid)
{
int i = 0;
double lambda = s->lon - r->lon;
double omf = 1 - spheroid->f;
double u1 = atan(omf * tan(r->lat));
double cos_u1 = cos(u1);
double sin_u1 = sin(u1);
double u2 = atan(omf * tan(s->lat));
double cos_u2 = cos(u2);
double sin_u2 = sin(u2);
double omega = lambda;
double alpha, sigma, sin_sigma, cos_sigma, cos2_sigma_m, sqr_sin_sigma, last_lambda;
double sin_alpha, cos_alphasq, C, alphaFD;
do
{
sqr_sin_sigma = POW2(cos_u2 * sin(lambda)) +
POW2((cos_u1 * sin_u2 - sin_u1 * cos_u2 * cos(lambda)));
sin_sigma = sqrt(sqr_sin_sigma);
cos_sigma = sin_u1 * sin_u2 + cos_u1 * cos_u2 * cos(lambda);
sigma = atan2(sin_sigma, cos_sigma);
sin_alpha = cos_u1 * cos_u2 * sin(lambda) / sin(sigma);
/* Numerical stability issue, ensure asin is not NaN */
if ( sin_alpha > 1.0 )
alpha = M_PI_2;
else if ( sin_alpha < -1.0 )
alpha = -1.0 * M_PI_2;
else
alpha = asin(sin_alpha);
cos_alphasq = POW2(cos(alpha));
cos2_sigma_m = cos(sigma) - (2.0 * sin_u1 * sin_u2 / cos_alphasq);
/* Numerical stability issue, cos2 is in range */
if ( cos2_sigma_m > 1.0 )
cos2_sigma_m = 1.0;
if ( cos2_sigma_m < -1.0 )
cos2_sigma_m = -1.0;
C = (spheroid->f / 16.0) * cos_alphasq * (4.0 + spheroid->f * (4.0 - 3.0 * cos_alphasq));
last_lambda = lambda;
lambda = omega + (1.0 - C) * spheroid->f * sin(alpha) * (sigma + C * sin(sigma) *
(cos2_sigma_m + C * cos(sigma) * (-1.0 + 2.0 * POW2(cos2_sigma_m))));
i++;
}
while ( (i < 999) && (lambda != 0) && (fabs((last_lambda - lambda) / lambda) > 1.0e-9) );
alphaFD = atan2((cos_u2 * sin(lambda)),
(cos_u1 * sin_u2 - sin_u1 * cos_u2 * cos(lambda)));
if (alphaFD < 0.0)
{
alphaFD = alphaFD + 2.0 * M_PI;
}
if (alphaFD > 2.0 * M_PI)
{
alphaFD = alphaFD - 2.0 * M_PI;
}
return alphaFD;
}
/**
* Given a location, an azimuth and a distance, computes the
* location of the projected point. Based on Vincenty's formula
* for the geodetic direct problem as described in "Geocentric
* Datum of Australia Technical Manual", Chapter 4. Tested against:
* http://mascot.gdbc.gov.bc.ca/mascot/util1b.html
* and
* http://www.ga.gov.au/nmd/geodesy/datums/vincenty_direct.jsp
*
* @param r - location of first point.
* @param distance - distance in meters.
* @param azimuth - azimuth in radians.
* @return s - location of projected point.
*/
int spheroid_project(const GEOGRAPHIC_POINT *r, const SPHEROID *spheroid, double distance, double azimuth, GEOGRAPHIC_POINT *g)
{
double omf = 1 - spheroid->f;
double tan_u1 = omf * tan(r->lat);
double u1 = atan(tan_u1);
double sigma, last_sigma, delta_sigma, two_sigma_m;
double sigma1, sin_alpha, alpha, cos_alphasq;
double u2, A, B;
double lat2, lambda, lambda2, C, omega;
int i = 0;
if (azimuth < 0.0)
{
azimuth = azimuth + M_PI * 2.0;
}
if (azimuth > (M_PI * 2.0))
{
azimuth = azimuth - M_PI * 2.0;
}
sigma1 = atan2(tan_u1, cos(azimuth));
sin_alpha = cos(u1) * sin(azimuth);
alpha = asin(sin_alpha);
cos_alphasq = 1.0 - POW2(sin_alpha);
u2 = spheroid_mu2(alpha, spheroid);
A = spheroid_big_a(u2);
B = spheroid_big_b(u2);
sigma = (distance / (spheroid->b * A));
do
{
two_sigma_m = 2.0 * sigma1 + sigma;
delta_sigma = B * sin(sigma) * (cos(two_sigma_m) + (B / 4.0) * (cos(sigma) * (-1.0 + 2.0 * POW2(cos(two_sigma_m)) - (B / 6.0) * cos(two_sigma_m) * (-3.0 + 4.0 * POW2(sin(sigma))) * (-3.0 + 4.0 * POW2(cos(two_sigma_m))))));
last_sigma = sigma;
sigma = (distance / (spheroid->b * A)) + delta_sigma;
i++;
}
while (i < 999 && fabs((last_sigma - sigma) / sigma) > 1.0e-9);
lat2 = atan2((sin(u1) * cos(sigma) + cos(u1) * sin(sigma) *
cos(azimuth)), (omf * sqrt(POW2(sin_alpha) +
POW2(sin(u1) * sin(sigma) - cos(u1) * cos(sigma) *
cos(azimuth)))));
lambda = atan2((sin(sigma) * sin(azimuth)), (cos(u1) * cos(sigma) -
sin(u1) * sin(sigma) * cos(azimuth)));
C = (spheroid->f / 16.0) * cos_alphasq * (4.0 + spheroid->f * (4.0 - 3.0 * cos_alphasq));
omega = lambda - (1.0 - C) * spheroid->f * sin_alpha * (sigma + C * sin(sigma) *
(cos(two_sigma_m) + C * cos(sigma) * (-1.0 + 2.0 * POW2(cos(two_sigma_m)))));
lambda2 = r->lon + omega;
g->lat = lat2;
g->lon = lambda2;
return LW_SUCCESS;
}
static inline double spheroid_prime_vertical_radius_of_curvature(double latitude, const SPHEROID *spheroid)
{
return spheroid->a / (sqrt(1.0 - spheroid->e_sq * POW2(sin(latitude))));
}
static inline double spheroid_parallel_arc_length(double latitude, double deltaLongitude, const SPHEROID *spheroid)
{
return spheroid_prime_vertical_radius_of_curvature(latitude, spheroid)
* cos(latitude)
* deltaLongitude;
}
/**
* Computes the area on the spheroid of a box bounded by meridians and
* parallels. The box is defined by two points, the South West corner
* and the North East corner. Formula based on Bagratuni 1967.
*
* @param southWestCorner - lower left corner of bounding box.
* @param northEastCorner - upper right corner of bounding box.
* @return area in square meters.
*/
static double spheroid_boundingbox_area(const GEOGRAPHIC_POINT *southWestCorner, const GEOGRAPHIC_POINT *northEastCorner, const SPHEROID *spheroid)
{
double z0 = (northEastCorner->lon - southWestCorner->lon) * POW2(spheroid->b) / 2.0;
double e = sqrt(spheroid->e_sq);
double sinPhi1 = sin(southWestCorner->lat);
double sinPhi2 = sin(northEastCorner->lat);
double t1p1 = sinPhi1 / (1.0 - spheroid->e_sq * sinPhi1 * sinPhi1);
double t1p2 = sinPhi2 / (1.0 - spheroid->e_sq * sinPhi2 * sinPhi2);
double oneOver2e = 1.0 / (2.0 * e);
double t2p1 = oneOver2e * log((1.0 + e * sinPhi1) / (1.0 - e * sinPhi1));
double t2p2 = oneOver2e * log((1.0 + e * sinPhi2) / (1.0 - e * sinPhi2));
return z0 * (t1p2 + t2p2) - z0 * (t1p1 + t2p1);
}
/**
* This function doesn't work for edges crossing the dateline or in the southern
* hemisphere. Points are pre-conditioned in ptarray_area_spheroid.
*/
static double spheroid_striparea(const GEOGRAPHIC_POINT *a, const GEOGRAPHIC_POINT *b, double latitude_min, const SPHEROID *spheroid)
{
GEOGRAPHIC_POINT A, B, mL, nR;
double deltaLng, baseArea, topArea;
double bE, tE, ratio, sign;
A = *a;
B = *b;
mL.lat = latitude_min;
mL.lon = FP_MIN(A.lon, B.lon);
nR.lat = FP_MIN(A.lat, B.lat);
nR.lon = FP_MAX(A.lon, B.lon);
LWDEBUGF(4, "mL (%.12g %.12g)", mL.lat, mL.lon);
LWDEBUGF(4, "nR (%.12g %.12g)", nR.lat, nR.lon);
baseArea = spheroid_boundingbox_area(&mL, &nR, spheroid);
LWDEBUGF(4, "baseArea %.12g", baseArea);
mL.lat = FP_MIN(A.lat, B.lat);
mL.lon = FP_MIN(A.lon, B.lon);
nR.lat = FP_MAX(A.lat, B.lat);
nR.lon = FP_MAX(A.lon, B.lon);
LWDEBUGF(4, "mL (%.12g %.12g)", mL.lat, mL.lon);
LWDEBUGF(4, "nR (%.12g %.12g)", nR.lat, nR.lon);
topArea = spheroid_boundingbox_area(&mL, &nR, spheroid);
LWDEBUGF(4, "topArea %.12g", topArea);
deltaLng = B.lon - A.lon;
LWDEBUGF(4, "deltaLng %.12g", deltaLng);
bE = spheroid_parallel_arc_length(A.lat, deltaLng, spheroid);
tE = spheroid_parallel_arc_length(B.lat, deltaLng, spheroid);
LWDEBUGF(4, "bE %.12g", bE);
LWDEBUGF(4, "tE %.12g", tE);
ratio = (bE + tE)/tE;
sign = SIGNUM(B.lon - A.lon);
return (baseArea + topArea / ratio) * sign;
}
static double ptarray_area_spheroid(const POINTARRAY *pa, const SPHEROID *spheroid)
{
GEOGRAPHIC_POINT a, b;
POINT2D p;
uint32_t i;
double area = 0.0;
GBOX gbox2d;
int in_south = LW_FALSE;
double delta_lon_tolerance;
double latitude_min;
gbox2d.flags = lwflags(0, 0, 0);
/* Return zero on non-sensical inputs */
if ( ! pa || pa->npoints < 4 )
return 0.0;
/* Get the raw min/max values for the latitudes */
ptarray_calculate_gbox_cartesian(pa, &gbox2d);
if ( SIGNUM(gbox2d.ymin) != SIGNUM(gbox2d.ymax) )
lwerror("ptarray_area_spheroid: cannot handle ptarray that crosses equator");
/* Geodetic bbox < 0.0 implies geometry is entirely in southern hemisphere */
if ( gbox2d.ymax < 0.0 )
in_south = LW_TRUE;
LWDEBUGF(4, "gbox2d.ymax %.12g", gbox2d.ymax);
/* Tolerance for strip area calculation */
if ( in_south )
{
delta_lon_tolerance = (90.0 / (fabs(gbox2d.ymin) / 8.0) - 2.0) / 10000.0;
latitude_min = deg2rad(fabs(gbox2d.ymax));
}
else
{
delta_lon_tolerance = (90.0 / (fabs(gbox2d.ymax) / 8.0) - 2.0) / 10000.0;
latitude_min = deg2rad(gbox2d.ymin);
}
/* Initialize first point */
getPoint2d_p(pa, 0, &p);
geographic_point_init(p.x, p.y, &a);
for ( i = 1; i < pa->npoints; i++ )
{
GEOGRAPHIC_POINT a1, b1;
double strip_area = 0.0;
double delta_lon = 0.0;
LWDEBUGF(4, "edge #%d", i);
getPoint2d_p(pa, i, &p);
geographic_point_init(p.x, p.y, &b);
a1 = a;
b1 = b;
/* Flip into north if in south */
if ( in_south )
{
a1.lat = -1.0 * a1.lat;
b1.lat = -1.0 * b1.lat;
}
LWDEBUGF(4, "in_south %d", in_south);
LWDEBUGF(4, "crosses_dateline(a, b) %d", crosses_dateline(&a, &b) );
if ( crosses_dateline(&a, &b) )
{
double shift;
if ( a1.lon > 0.0 )
shift = (M_PI - a1.lon) + 0.088; /* About 5deg more */
else
shift = (M_PI - b1.lon) + 0.088; /* About 5deg more */
LWDEBUGF(4, "shift: %.8g", shift);
LWDEBUGF(4, "before shift a1(%.8g %.8g) b1(%.8g %.8g)", a1.lat, a1.lon, b1.lat, b1.lon);
point_shift(&a1, shift);
point_shift(&b1, shift);
LWDEBUGF(4, "after shift a1(%.8g %.8g) b1(%.8g %.8g)", a1.lat, a1.lon, b1.lat, b1.lon);
}
delta_lon = fabs(b1.lon - a1.lon);
LWDEBUGF(4, "a1(%.18g %.18g) b1(%.18g %.18g)", a1.lat, a1.lon, b1.lat, b1.lon);
LWDEBUGF(4, "delta_lon %.18g", delta_lon);
LWDEBUGF(4, "delta_lon_tolerance %.18g", delta_lon_tolerance);
if ( delta_lon > 0.0 )
{
if ( delta_lon < delta_lon_tolerance )
{
strip_area = spheroid_striparea(&a1, &b1, latitude_min, spheroid);
LWDEBUGF(4, "strip_area %.12g", strip_area);
area += strip_area;
}
else
{
GEOGRAPHIC_POINT p, q;
double step = floor(delta_lon / delta_lon_tolerance);
double distance = spheroid_distance(&a1, &b1, spheroid);
double pDistance = 0.0;
int j = 0;
LWDEBUGF(4, "step %.18g", step);
LWDEBUGF(4, "distance %.18g", distance);
step = distance / step;
LWDEBUGF(4, "step %.18g", step);
p = a1;
while (pDistance < (distance - step * 1.01))
{
double azimuth = spheroid_direction(&p, &b1, spheroid);
j++;
LWDEBUGF(4, " iteration %d", j);
LWDEBUGF(4, " azimuth %.12g", azimuth);
pDistance = pDistance + step;
LWDEBUGF(4, " pDistance %.12g", pDistance);
spheroid_project(&p, spheroid, step, azimuth, &q);
strip_area = spheroid_striparea(&p, &q, latitude_min, spheroid);
LWDEBUGF(4, " strip_area %.12g", strip_area);
area += strip_area;
LWDEBUGF(4, " area %.12g", area);
p.lat = q.lat;
p.lon = q.lon;
}
strip_area = spheroid_striparea(&p, &b1, latitude_min, spheroid);
area += strip_area;
}
}
/* B gets incremented in the next loop, so we save the value here */
a = b;
}
return fabs(area);
}
#endif /* else ! PROJ_GEODESIC */
/**
* Calculate the area of an LWGEOM. Anything except POLYGON, MULTIPOLYGON
* and GEOMETRYCOLLECTION return zero immediately. Multi's recurse, polygons
* calculate external ring area and subtract internal ring area. A GBOX is
* required to check relationship to equator an outside point.
* WARNING: Does NOT WORK for polygons over equator or pole.
*/
double lwgeom_area_spheroid(const LWGEOM *lwgeom, const SPHEROID *spheroid)
{
int type;
assert(lwgeom);
/* No area in nothing */
if ( lwgeom_is_empty(lwgeom) )
return 0.0;
/* Read the geometry type number */
type = lwgeom->type;
/* Anything but polygons and collections returns zero */
if ( ! ( type == POLYGONTYPE || type == MULTIPOLYGONTYPE || type == COLLECTIONTYPE ) )
return 0.0;
/* Actually calculate area */
if ( type == POLYGONTYPE )
{
LWPOLY *poly = (LWPOLY*)lwgeom;
uint32_t i;
double area = 0.0;
/* Just in case there's no rings */
if ( poly->nrings < 1 )
return 0.0;
/* First, the area of the outer ring */
area += ptarray_area_spheroid(poly->rings[0], spheroid);
/* Subtract areas of inner rings */
for ( i = 1; i < poly->nrings; i++ )
{
area -= ptarray_area_spheroid(poly->rings[i], spheroid);
}
return area;
}
/* Recurse into sub-geometries to get area */
if ( type == MULTIPOLYGONTYPE || type == COLLECTIONTYPE )
{
LWCOLLECTION *col = (LWCOLLECTION*)lwgeom;
uint32_t i;
double area = 0.0;
for ( i = 0; i < col->ngeoms; i++ )
{
area += lwgeom_area_spheroid(col->geoms[i], spheroid);
}
return area;
}
/* Shouldn't get here. */
return 0.0;
}