lwspheroid.c

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/**********************************************************************
 *
 * 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 <http://www.gnu.org/licenses/>.
 *
 **********************************************************************
 *
 * Copyright (C) 2009 Paul Ramsey <pramsey@cleverelephant.ca>
 * Copyright (C) 2009 David Skea <David.Skea@gov.bc.ca>
 *
 **********************************************************************/


#include "liblwgeom_internal.h"
#include "lwgeodetic.h"
#include "lwgeom_log.h"

/* GeographicLib */
#if PROJ_GEODESIC
#include <geodesic.h>
#endif

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;
}

#if ! 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 */


#if PROJ_GEODESIC

double spheroid_distance(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 s12; /* return distance */
        geod_inverse(&gd, lat1, lon1, lat2, lon2, &s12, 0, 0);
        return s12;
}

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;
}

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);
        int 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 GeographicLib */
#else /* ! PROJ_GEODESIC */
/* Below use pre-version 2.2 geodesic functions */

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;
}

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;
}


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;
}


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);
}

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;
        int i;
        double area = 0.0;
        GBOX gbox2d;
        int in_south = LW_FALSE;
        double delta_lon_tolerance;
        double latitude_min;

        gbox2d.flags = gflags(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 */

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;
                int 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;
                int 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;
}