lwgeom_spheroid.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) 2001-2003 Refractions Research Inc.
 *
 **********************************************************************/
 
 
#include "postgres.h"
 
 
#include <math.h>
#include <float.h>
#include <string.h>
#include <stdio.h>
 
#include "access/gist.h"
#include "access/itup.h"
 
#include "fmgr.h"
#include "utils/elog.h"
 
#include "../postgis_config.h"
#include "liblwgeom.h"
#include "lwgeom_pg.h"
 
#define SHOW_DIGS_DOUBLE 15
#define MAX_DIGS_DOUBLE (SHOW_DIGS_DOUBLE + 6 + 1 + 3 +1)
 
/*
 * distance from -126 49  to -126 49.011096139863
 * in  'SPHEROID["GRS_1980",6378137,298.257222101]'
 * is 1234.000
 */
 
 
/* PG-exposed  */
Datum ellipsoid_in(PG_FUNCTION_ARGS);
Datum ellipsoid_out(PG_FUNCTION_ARGS);
Datum LWGEOM_length2d_ellipsoid(PG_FUNCTION_ARGS);
Datum LWGEOM_length_ellipsoid_linestring(PG_FUNCTION_ARGS);
Datum LWGEOM_distance_ellipsoid(PG_FUNCTION_ARGS);
Datum LWGEOM_distance_sphere(PG_FUNCTION_ARGS);
Datum geometry_distance_spheroid(PG_FUNCTION_ARGS);
 
/* internal */
double distance_sphere_method(double lat1, double long1,double lat2,double long2, SPHEROID *sphere);
double distance_ellipse_calculation(double lat1, double long1, double lat2, double long2, SPHEROID *sphere);
double  distance_ellipse(double lat1, double long1, double lat2, double long2, SPHEROID *sphere);
double deltaLongitude(double azimuth, double sigma, double tsm,SPHEROID *sphere);
double mu2(double azimuth,SPHEROID *sphere);
double bigA(double u2);
double bigB(double u2);
 
 
/*
 * Use the WKT definition of an ellipsoid
 * ie. SPHEROID["name",A,rf] or SPHEROID("name",A,rf)
 *        SPHEROID["GRS_1980",6378137,298.257222101]
 * wkt says you can use "(" or "["
 */
PG_FUNCTION_INFO_V1(ellipsoid_in);
Datum ellipsoid_in(PG_FUNCTION_ARGS)
{
        char *str = PG_GETARG_CSTRING(0);
        SPHEROID *sphere = (SPHEROID *) palloc(sizeof(SPHEROID));
        int nitems;
        double rf;
 
        memset(sphere,0, sizeof(SPHEROID));
 
        if (strstr(str,"SPHEROID") !=  str )
        {
                elog(ERROR,"SPHEROID parser - doesn't start with SPHEROID");
                pfree(sphere);
                PG_RETURN_NULL();
        }
 
        nitems = sscanf(str,"SPHEROID[\"%19[^\"]\",%lf,%lf]",
                        sphere->name, &sphere->a, &rf);
 
        if (nitems != 3)
                nitems = sscanf(str,"SPHEROID(\"%19[^\"]\",%lf,%lf)",
                                sphere->name, &sphere->a, &rf);
 
        if (nitems != 3)
        {
                elog(ERROR,"SPHEROID parser - couldn't parse the spheroid");
                pfree(sphere);
                PG_RETURN_NULL();
        }
 
        sphere->f = 1.0/rf;
        sphere->b = sphere->a - (1.0/rf)*sphere->a;
        sphere->e_sq = ((sphere->a*sphere->a) - (sphere->b*sphere->b)) /
                       (sphere->a*sphere->a);
        sphere->e = sqrt(sphere->e_sq);
 
        PG_RETURN_POINTER(sphere);
 
}
 
PG_FUNCTION_INFO_V1(ellipsoid_out);
Datum ellipsoid_out(PG_FUNCTION_ARGS)
{
        SPHEROID *sphere = (SPHEROID *) PG_GETARG_POINTER(0);
        char *result;
        size_t sz = MAX_DIGS_DOUBLE + MAX_DIGS_DOUBLE + 20 + 9 + 2;
        result = palloc(sz);
 
        snprintf(result, sz, "SPHEROID(\"%s\",%.15g,%.15g)",
                sphere->name, sphere->a, 1.0/sphere->f);
 
        PG_RETURN_CSTRING(result);
}
 
/*
 * support function for distance calc
 * code is taken from David Skea
 * Geographic Data BC, Province of British Columbia, Canada.
 * Thanks to GDBC and David Skea for allowing this to be
 * put in PostGIS.
 */
double
deltaLongitude(double azimuth, double sigma, double tsm,SPHEROID *sphere)
{
        /* compute the expansion C */
        double das,C;
        double ctsm,DL;
 
        das = cos(azimuth)*cos(azimuth);
        C = sphere->f/16.0 * das * (4.0 + sphere->f * (4.0 - 3.0 * das));
 
        /* compute the difference in longitude */
        ctsm = cos(tsm);
        DL = ctsm + C * cos(sigma) * (-1.0 + 2.0 * ctsm*ctsm);
        DL = sigma + C * sin(sigma) * DL;
        return (1.0 - C) * sphere->f * sin(azimuth) * DL;
}
 
 
/*
 * support function for distance calc
 * code is taken from David Skea
 * Geographic Data BC, Province of British Columbia, Canada.
 *  Thanks to GDBC and David Skea for allowing this to be
 *  put in PostGIS.
 */
double
mu2(double azimuth,SPHEROID *sphere)
{
        double    e2;
 
        e2 = sqrt(sphere->a*sphere->a-sphere->b*sphere->b)/sphere->b;
        return cos(azimuth)*cos(azimuth) * e2*e2;
}
 
 
/*
 * Support function for distance calc
 * code is taken from David Skea
 * Geographic Data BC, Province of British Columbia, Canada.
 *  Thanks to GDBC and David Skea for allowing this to be
 *  put in PostGIS.
 */
double
bigA(double u2)
{
        return 1.0 + u2/256.0 * (64.0 + u2 * (-12.0 + 5.0 * u2));
}
 
 
/*
 * Support function for distance calc
 * code is taken from David Skea
 * Geographic Data BC, Province of British Columbia, Canada.
 *  Thanks to GDBC and David Skea for allowing this to be
 *  put in PostGIS.
 */
double
bigB(double u2)
{
        return u2/512.0 * (128.0 + u2 * (-64.0 + 37.0 * u2));
}
 
 
 
double
distance_ellipse(double lat1, double long1,
                 double lat2, double long2, SPHEROID *sphere)
{
        double result = 0;
#if POSTGIS_DEBUG_LEVEL >= 4
        double result2 = 0;
#endif
 
        if ( (lat1==lat2) && (long1 == long2) )
        {
                return 0.0; /* same point, therefore zero distance */
        }
 
        result = distance_ellipse_calculation(lat1,long1,lat2,long2,sphere);
 
#if POSTGIS_DEBUG_LEVEL >= 4
        result2 =  distance_sphere_method(lat1, long1,lat2,long2, sphere);
 
        POSTGIS_DEBUGF(4, "delta = %lf, skae says: %.15lf,2 circle says: %.15lf",
                 (result2-result),result,result2);
        POSTGIS_DEBUGF(4, "2 circle says: %.15lf",result2);
#endif
 
        if (result != result)  /* NaN check
                                                * (x==x for all x except NaN by IEEE definition)
                                                */
        {
                result =  distance_sphere_method(lat1, long1,
                                                 lat2,long2, sphere);
        }
 
        return result;
}
 
/*
 * Given 2 lat/longs and ellipse, find the distance
 * note original r = 1st, s=2nd location
 */
double
distance_ellipse_calculation(double lat1, double long1,
                             double lat2, double long2, SPHEROID *sphere)
{
        /*
         * Code is taken from David Skea
         * Geographic Data BC, Province of British Columbia, Canada.
         *  Thanks to GDBC and David Skea for allowing this to be
         *  put in PostGIS.
         */
 
        double L1,L2,sinU1,sinU2,cosU1,cosU2;
        double dl,dl1,dl2,dl3,cosdl1,sindl1;
        double cosSigma,sigma,azimuthEQ,tsm;
        double u2,A,B;
        double dsigma;
 
        double TEMP;
 
        int iterations;
 
 
        L1 = atan((1.0 - sphere->f ) * tan( lat1) );
        L2 = atan((1.0 - sphere->f ) * tan( lat2) );
        sinU1 = sin(L1);
        sinU2 = sin(L2);
        cosU1 = cos(L1);
        cosU2 = cos(L2);
 
        dl = long2- long1;
        dl1 = dl;
        cosdl1 = cos(dl);
        sindl1 = sin(dl);
        iterations = 0;
        do
        {
                cosSigma = sinU1 * sinU2 + cosU1 * cosU2 * cosdl1;
                sigma = acos(cosSigma);
                azimuthEQ = asin((cosU1 * cosU2 * sindl1)/sin(sigma));
 
                /*
                 * Patch from Patrica Tozer to handle minor
                 * mathematical stability problem
                 */
                TEMP = cosSigma - (2.0 * sinU1 * sinU2)/
                       (cos(azimuthEQ)*cos(azimuthEQ));
                if (TEMP > 1)
                {
                        TEMP = 1;
                }
                else if (TEMP < -1)
                {
                        TEMP = -1;
                }
                tsm = acos(TEMP);
 
 
                /* (old code?)
                tsm = acos(cosSigma - (2.0 * sinU1 * sinU2)/(cos(azimuthEQ)*cos(azimuthEQ)));
                */
 
                dl2 = deltaLongitude(azimuthEQ, sigma, tsm,sphere);
                dl3 = dl1 - (dl + dl2);
                dl1 = dl + dl2;
                cosdl1 = cos(dl1);
                sindl1 = sin(dl1);
                iterations++;
        }
        while ( (iterations<999) && (fabs(dl3) > 1.0e-032));
 
        /* compute expansions A and B */
        u2 = mu2(azimuthEQ,sphere);
        A = bigA(u2);
        B = bigB(u2);
 
        /* compute length of geodesic */
        dsigma = B * sin(sigma) * (cos(tsm) +
                                   (B*cosSigma*(-1.0 + 2.0 * (cos(tsm)*cos(tsm))))/4.0);
        return sphere->b * (A * (sigma - dsigma));
}
 
 
/*
 * Find the "length of a geometry"
 * length2d_spheroid(point, sphere) = 0
 * length2d_spheroid(line, sphere) = length of line
 * length2d_spheroid(polygon, sphere) = 0
 *      -- could make sense to return sum(ring perimeter)
 * uses ellipsoidal math to find the distance
 * x's are longitude, and y's are latitude - both in decimal degrees
 */
PG_FUNCTION_INFO_V1(LWGEOM_length2d_ellipsoid);
Datum LWGEOM_length2d_ellipsoid(PG_FUNCTION_ARGS)
{
        GSERIALIZED *geom = PG_GETARG_GSERIALIZED_P(0);
        SPHEROID *sphere = (SPHEROID *) PG_GETARG_POINTER(1);
        LWGEOM *lwgeom = lwgeom_from_gserialized(geom);
        double dist = lwgeom_length_spheroid(lwgeom, sphere);
        lwgeom_free(lwgeom);
        PG_FREE_IF_COPY(geom, 0);
        PG_RETURN_FLOAT8(dist);
}
 
 
/*
 * Find the "length of a geometry"
 *
 * length2d_spheroid(point, sphere) = 0
 * length2d_spheroid(line, sphere) = length of line
 * length2d_spheroid(polygon, sphere) = 0
 *      -- could make sense to return sum(ring perimeter)
 * uses ellipsoidal math to find the distance
 * x's are longitude, and y's are latitude - both in decimal degrees
 */
PG_FUNCTION_INFO_V1(LWGEOM_length_ellipsoid_linestring);
Datum LWGEOM_length_ellipsoid_linestring(PG_FUNCTION_ARGS)
{
        GSERIALIZED *geom = PG_GETARG_GSERIALIZED_P(0);
        LWGEOM *lwgeom = lwgeom_from_gserialized(geom);
        SPHEROID *sphere = (SPHEROID *) PG_GETARG_POINTER(1);
        double length = 0.0;
 
        /* EMPTY things have no length */
        if ( lwgeom_is_empty(lwgeom) )
        {
                lwgeom_free(lwgeom);
                PG_RETURN_FLOAT8(0.0);
        }
 
        length = lwgeom_length_spheroid(lwgeom, sphere);
        lwgeom_free(lwgeom);
        PG_FREE_IF_COPY(geom, 0);
 
        /* Something went wrong... */
        if ( length < 0.0 )
        {
                elog(ERROR, "lwgeom_length_spheroid returned length < 0.0");
                PG_RETURN_NULL();
        }
 
        /* Clean up */
        PG_RETURN_FLOAT8(length);
}
 
/*
 *  For some lat/long points, the above method doesn't calculate the distance very well.
 *  Typically this is for two lat/long points that are very very close together (<10cm).
 *  This gets worse closer to the equator.
 *
 *   This method works very well for very close together points, not so well if they're
 *   far away (>1km).
 *
 *  METHOD:
 *    We create two circles (with Radius R and Radius S) and use these to calculate the distance.
 *
 *    The first (R) is basically a (north-south) line of longitude.
 *    Its radius is approximated by looking at the ellipse. Near the equator R = 'a' (earth's major axis)
 *    near the pole R = 'b' (earth's minor axis).
 *
 *    The second (S) is basically a (east-west) line of latitude.
 *    Its radius runs from 'a' (major axis) at the equator, and near 0 at the poles.
 *
 *
 *                North pole
 *                *
 *               *
 *              *\--S--
 *             *  R   +
 *            *    \  +
 *           *     A\ +
 *          * ------ \         Equator/centre of earth
 *           *
 *            *
 *             *
 *              *
 *               *
 *                *
 *                South pole
 *  (side view of earth)
 *
 *   Angle A is lat1
 *   R is the distance from the centre of the earth to the lat1/long1 point on the surface
 *   of the Earth.
 *   S is the circle-of-latitude.  Its calculated from the right triangle defined by
 *      the angle (90-A), and the hypotenuse R.
 *
 *
 *
 *   Once R and S have been calculated, the actual distance between the two points can be
 *   calculated.
 *
 *   We dissolve the vector from lat1,long1 to lat2,long2 into its X and Y components (called DeltaX,DeltaY).
 *   The actual distance that these angle-based measurements represent is taken from the two
 *   circles we just calculated; R (for deltaY) and S (for deltaX).
 *
 *    (if deltaX is 1 degrees, then that distance represents 1/360 of a circle of radius S.)
 *
 *
 *  Parts taken from PROJ - geodetic_to_geocentric() (for calculating Rn)
 *
 *  remember that lat1/long1/lat2/long2 are coming in a *RADIANS* not degrees.
 *
 * By Patricia Tozer and Dave Blasby
 *
 *  This is also called the "curvature method".
 */
 
double distance_sphere_method(double lat1, double long1,double lat2,double long2, SPHEROID *sphere)
{
        double R,S,X,Y,deltaX,deltaY;
 
        double  distance        = 0.0;
        double  sin_lat         = sin(lat1);
        double  sin2_lat        = sin_lat * sin_lat;
 
        double  Geocent_a       = sphere->a;
        double  Geocent_e2      = sphere->e_sq;
 
        R       = Geocent_a / (sqrt(1.0e0 - Geocent_e2 * sin2_lat));
        /* 90 - lat1, but in radians */
        S       = R * sin(M_PI_2 - lat1) ;
 
        deltaX = long2 - long1;  /* in rads */
        deltaY = lat2 - lat1;    /* in rads */
 
        /* think: a % of 2*pi*S */
        X = deltaX/(2.0*M_PI) * 2 * M_PI * S;
        Y = deltaY/(2.0*M_PI) * 2 * M_PI * R;
 
        distance = sqrt((X * X + Y * Y));
 
        return distance;
}
 
/*
 * distance (geometry,geometry, sphere)
 */
PG_FUNCTION_INFO_V1(geometry_distance_spheroid);
Datum geometry_distance_spheroid(PG_FUNCTION_ARGS)
{
        GSERIALIZED *geom1 = PG_GETARG_GSERIALIZED_P(0);
        GSERIALIZED *geom2 = PG_GETARG_GSERIALIZED_P(1);
        SPHEROID *sphere = (SPHEROID *)PG_GETARG_POINTER(2);
        int type1 = gserialized_get_type(geom1);
        int type2 = gserialized_get_type(geom2);
        bool use_spheroid = PG_GETARG_BOOL(3);
        LWGEOM *lwgeom1, *lwgeom2;
        double distance;
        gserialized_error_if_srid_mismatch(geom1, geom2, __func__);
 
        /* Calculate some other parameters on the spheroid */
        spheroid_init(sphere, sphere->a, sphere->b);
 
        /* Catch sphere special case and re-jig spheroid appropriately */
        if ( ! use_spheroid )
        {
                sphere->a = sphere->b = sphere->radius;
        }
 
        if ( ! ( type1 == POINTTYPE || type1 == LINETYPE || type1 == POLYGONTYPE ||
                 type1 == MULTIPOINTTYPE || type1 == MULTILINETYPE || type1 == MULTIPOLYGONTYPE ))
        {
                elog(ERROR, "geometry_distance_spheroid: Only point/line/polygon supported.\n");
                PG_RETURN_NULL();
        }
 
        if ( ! ( type2 == POINTTYPE || type2 == LINETYPE || type2 == POLYGONTYPE ||
                 type2 == MULTIPOINTTYPE || type2 == MULTILINETYPE || type2 == MULTIPOLYGONTYPE ))
        {
                elog(ERROR, "geometry_distance_spheroid: Only point/line/polygon supported.\n");
                PG_RETURN_NULL();
        }
 
        /* Get #LWGEOM structures */
        lwgeom1 = lwgeom_from_gserialized(geom1);
        lwgeom2 = lwgeom_from_gserialized(geom2);
 
        /* We are going to be calculating geodetic distances */
        lwgeom_set_geodetic(lwgeom1, LW_TRUE);
        lwgeom_set_geodetic(lwgeom2, LW_TRUE);
        lwgeom_refresh_bbox(lwgeom1);
        lwgeom_refresh_bbox(lwgeom2);
 
        distance = lwgeom_distance_spheroid(lwgeom1, lwgeom2, sphere, 0.0);
 
        PG_RETURN_FLOAT8(distance);
 
}
 
PG_FUNCTION_INFO_V1(LWGEOM_distance_ellipsoid);
Datum LWGEOM_distance_ellipsoid(PG_FUNCTION_ARGS)
{
        SPHEROID s;
 
        /* No spheroid provided */
        if (PG_NARGS() == 2) {
                /* Init to WGS84 */
                spheroid_init(&s, 6378137.0, 6356752.314245179498);
                PG_RETURN_DATUM(DirectFunctionCall4(geometry_distance_spheroid,
                        PG_GETARG_DATUM(0),
                        PG_GETARG_DATUM(1),
                        PointerGetDatum(&s),
                        BoolGetDatum(true)));
        }
 
        PG_RETURN_DATUM(DirectFunctionCall4(geometry_distance_spheroid,
                PG_GETARG_DATUM(0),
                PG_GETARG_DATUM(1),
                PG_GETARG_DATUM(2),
                BoolGetDatum(true)));
}
 
PG_FUNCTION_INFO_V1(LWGEOM_distance_sphere);
Datum LWGEOM_distance_sphere(PG_FUNCTION_ARGS)
{
        SPHEROID s;
        /* Init to WGS84 */
        spheroid_init(&s, 6378137.0, 6356752.314245179498);
 
        if (PG_NARGS() == 3) {
                s.radius = PG_GETARG_FLOAT8(2);
        }
        s.a = s.b = s.radius;
 
        PG_RETURN_DATUM(DirectFunctionCall4(geometry_distance_spheroid,
                                            PG_GETARG_DATUM(0), PG_GETARG_DATUM(1), PointerGetDatum(&s), BoolGetDatum(false)));
}