lwalgorithm.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 2008 Paul Ramsey
 *
 **********************************************************************/


#include "liblwgeom_internal.h"
#include "lwgeom_log.h"
#include <ctype.h> /* for tolower */

int
p4d_same(const POINT4D *p1, const POINT4D *p2)
{
        if( FP_EQUALS(p1->x,p2->x) && FP_EQUALS(p1->y,p2->y) && FP_EQUALS(p1->z,p2->z) && FP_EQUALS(p1->m,p2->m) )
                return LW_TRUE;
        else
                return LW_FALSE;
}

int
p3d_same(const POINT3D *p1, const POINT3D *p2)
{
        if( FP_EQUALS(p1->x,p2->x) && FP_EQUALS(p1->y,p2->y) && FP_EQUALS(p1->z,p2->z) )
                return LW_TRUE;
        else
                return LW_FALSE;
}

int
p2d_same(const POINT2D *p1, const POINT2D *p2)
{
        if( FP_EQUALS(p1->x,p2->x) && FP_EQUALS(p1->y,p2->y) )
                return LW_TRUE;
        else
                return LW_FALSE;
}

int lw_segment_side(const POINT2D *p1, const POINT2D *p2, const POINT2D *q)
{
        double side = ( (q->x - p1->x) * (p2->y - p1->y) - (p2->x - p1->x) * (q->y - p1->y) );
        return SIGNUM(side);
}

double
lw_seg_length(const POINT2D *A1, const POINT2D *A2)
{
        return sqrt((A1->x-A2->x)*(A1->x-A2->x)+(A1->y-A2->y)*(A1->y-A2->y));
}

int
lw_pt_in_arc(const POINT2D *P, const POINT2D *A1, const POINT2D *A2, const POINT2D *A3)
{
        return lw_segment_side(A1, A3, A2) == lw_segment_side(A1, A3, P);
}

int
lw_pt_in_seg(const POINT2D *P, const POINT2D *A1, const POINT2D *A2)
{
        return ((A1->x <= P->x && P->x < A2->x) || (A1->x >= P->x && P->x > A2->x)) ||
               ((A1->y <= P->y && P->y < A2->y) || (A1->y >= P->y && P->y > A2->y));
}

int
lw_arc_is_pt(const POINT2D *A1, const POINT2D *A2, const POINT2D *A3)
{
        if ( A1->x == A2->x && A2->x == A3->x &&
             A1->y == A2->y && A2->y == A3->y )
                return LW_TRUE;
        else
                return LW_FALSE;
}

double
lw_arc_length(const POINT2D *A1, const POINT2D *A2, const POINT2D *A3)
{
        POINT2D C;
        double radius_A, circumference_A;
        int a2_side, clockwise;
        double a1, a3;
        double angle;

        if ( lw_arc_is_pt(A1, A2, A3) )
                return 0.0;

        radius_A = lw_arc_center(A1, A2, A3, &C);

        /* Co-linear! Return linear distance! */
        if ( radius_A < 0 )
        {
        double dx = A1->x - A3->x;
        double dy = A1->y - A3->y;
                return sqrt(dx*dx + dy*dy);
        }

        /* Closed circle! Return the circumference! */
        circumference_A = M_PI * 2 * radius_A;
        if ( p2d_same(A1, A3) )
                return circumference_A;

        /* Determine the orientation of the arc */
        a2_side = lw_segment_side(A1, A3, A2);

        /* The side of the A1/A3 line that A2 falls on dictates the sweep
           direction from A1 to A3. */
        if ( a2_side == -1 )
                clockwise = LW_TRUE;
        else
                clockwise = LW_FALSE;

        /* Angles of each point that defines the arc section */
        a1 = atan2(A1->y - C.y, A1->x - C.x);
        a3 = atan2(A3->y - C.y, A3->x - C.x);

        /* What's the sweep from A1 to A3? */
        if ( clockwise )
        {
                if ( a1 > a3 )
                        angle = a1 - a3;
                else
                        angle = 2*M_PI + a1 - a3;
        }
        else
        {
                if ( a3 > a1 )
                        angle = a3 - a1;
                else
                        angle = 2*M_PI + a3 - a1;
        }

        /* Length as proportion of circumference */
        return circumference_A * (angle / (2*M_PI));
}

int lw_arc_side(const POINT2D *A1, const POINT2D *A2, const POINT2D *A3, const POINT2D *Q)
{
        POINT2D C;
        double radius_A;
        double side_Q, side_A2;
        double d;

        side_Q = lw_segment_side(A1, A3, Q);
        radius_A = lw_arc_center(A1, A2, A3, &C);
        side_A2 = lw_segment_side(A1, A3, A2);

        /* Linear case */
        if ( radius_A < 0 )
                return side_Q;

        d = distance2d_pt_pt(Q, &C);

        /* Q is on the arc boundary */
        if ( d == radius_A && side_Q == side_A2 )
        {
                return 0;
        }

        /* Q on A1-A3 line, so its on opposite side to A2 */
        if ( side_Q == 0 )
        {
                return -1 * side_A2;
        }

        /*
        * Q is inside the arc boundary, so it's not on the side we
        * might think from examining only the end points
        */
        if ( d < radius_A && side_Q == side_A2 )
        {
                side_Q *= -1;
        }

        return side_Q;
}

double
lw_arc_center(const POINT2D *p1, const POINT2D *p2, const POINT2D *p3, POINT2D *result)
{
        POINT2D c;
        double cx, cy, cr;
        double dx21, dy21, dx31, dy31, h21, h31, d;

        c.x = c.y = 0.0;

        LWDEBUGF(2, "lw_arc_center called (%.16f,%.16f), (%.16f,%.16f), (%.16f,%.16f).", p1->x, p1->y, p2->x, p2->y, p3->x, p3->y);

        /* Closed circle */
        if (fabs(p1->x - p3->x) < EPSILON_SQLMM &&
            fabs(p1->y - p3->y) < EPSILON_SQLMM)
        {
                cx = p1->x + (p2->x - p1->x) / 2.0;
                cy = p1->y + (p2->y - p1->y) / 2.0;
                c.x = cx;
                c.y = cy;
                *result = c;
                cr = sqrt(pow(cx - p1->x, 2.0) + pow(cy - p1->y, 2.0));
                return cr;
        }

        /* Using cartesian eguations from page https://en.wikipedia.org/wiki/Circumscribed_circle */
        dx21 = p2->x - p1->x;
        dy21 = p2->y - p1->y;
        dx31 = p3->x - p1->x;
        dy31 = p3->y - p1->y;

        h21 = pow(dx21, 2.0) + pow(dy21, 2.0);
        h31 = pow(dx31, 2.0) + pow(dy31, 2.0);

        /* 2 * |Cross product|, d<0 means clockwise and d>0 counterclockwise sweeping angle */
        d = 2 * (dx21 * dy31 - dx31 * dy21);

        /* Check colinearity, |Cross product| = 0 */
        if (fabs(d) < EPSILON_SQLMM)
                return -1.0;

        /* Calculate centroid coordinates and radius */
        cx = p1->x + (h21 * dy31 - h31 * dy21) / d;
        cy = p1->y - (h21 * dx31 - h31 * dx21) / d;
        c.x = cx;
        c.y = cy;
        *result = c;
        cr = sqrt(pow(cx - p1->x, 2) + pow(cy - p1->y, 2));

        LWDEBUGF(2, "lw_arc_center center is (%.16f,%.16f)", result->x, result->y);

        return cr;
}

int
pt_in_ring_2d(const POINT2D *p, const POINTARRAY *ring)
{
        int cn = 0;    /* the crossing number counter */
        int i;
        const POINT2D *v1, *v2;
        const POINT2D *first, *last;

        first = getPoint2d_cp(ring, 0);
        last = getPoint2d_cp(ring, ring->npoints-1);
        if ( memcmp(first, last, sizeof(POINT2D)) )
        {
                lwerror("pt_in_ring_2d: V[n] != V[0] (%g %g != %g %g)",
                        first->x, first->y, last->x, last->y);
                return LW_FALSE;

        }

        LWDEBUGF(2, "pt_in_ring_2d called with point: %g %g", p->x, p->y);
        /* printPA(ring); */

        /* loop through all edges of the polygon */
        v1 = getPoint2d_cp(ring, 0);
        for (i=0; i<ring->npoints-1; i++)
        {
                double vt;
                v2 = getPoint2d_cp(ring, i+1);

                /* edge from vertex i to vertex i+1 */
                if
                (
                    /* an upward crossing */
                    ((v1->y <= p->y) && (v2->y > p->y))
                    /* a downward crossing */
                    || ((v1->y > p->y) && (v2->y <= p->y))
                )
                {

                        vt = (double)(p->y - v1->y) / (v2->y - v1->y);

                        /* P->x <intersect */
                        if (p->x < v1->x + vt * (v2->x - v1->x))
                        {
                                /* a valid crossing of y=p->y right of p->x */
                                ++cn;
                        }
                }
                v1 = v2;
        }

        LWDEBUGF(3, "pt_in_ring_2d returning %d", cn&1);

        return (cn&1);    /* 0 if even (out), and 1 if odd (in) */
}


static int
lw_seg_interact(const POINT2D *p1, const POINT2D *p2, const POINT2D *q1, const POINT2D *q2)
{
        double minq=FP_MIN(q1->x,q2->x);
        double maxq=FP_MAX(q1->x,q2->x);
        double minp=FP_MIN(p1->x,p2->x);
        double maxp=FP_MAX(p1->x,p2->x);

        if (FP_GT(minp,maxq) || FP_LT(maxp,minq))
                return LW_FALSE;

        minq=FP_MIN(q1->y,q2->y);
        maxq=FP_MAX(q1->y,q2->y);
        minp=FP_MIN(p1->y,p2->y);
        maxp=FP_MAX(p1->y,p2->y);

        if (FP_GT(minp,maxq) || FP_LT(maxp,minq))
                return LW_FALSE;

        return LW_TRUE;
}

int lw_segment_intersects(const POINT2D *p1, const POINT2D *p2, const POINT2D *q1, const POINT2D *q2)
{

        int pq1, pq2, qp1, qp2;

        /* No envelope interaction => we are done. */
        if (!lw_seg_interact(p1, p2, q1, p2))
        {
                return SEG_NO_INTERSECTION;
        }

        /* Are the start and end points of q on the same side of p? */
        pq1=lw_segment_side(p1,p2,q1);
        pq2=lw_segment_side(p1,p2,q2);
        if ((pq1>0 && pq2>0) || (pq1<0 && pq2<0))
        {
                return SEG_NO_INTERSECTION;
        }

        /* Are the start and end points of p on the same side of q? */
        qp1=lw_segment_side(q1,q2,p1);
        qp2=lw_segment_side(q1,q2,p2);
        if ( (qp1 > 0.0 && qp2 > 0.0) || (qp1 < 0.0 && qp2 < 0.0) )
        {
                return SEG_NO_INTERSECTION;
        }

        /* Nobody is on one side or another? Must be colinear. */
        if ( pq1 == 0.0 && pq2 == 0.0 && qp1 == 0.0 && qp2 == 0.0 )
        {
                return SEG_COLINEAR;
        }

        /*
        ** When one end-point touches, the sidedness is determined by the
        ** location of the other end-point. Only touches by the first point
        ** will be considered "real" to avoid double counting.
        */
        LWDEBUGF(4, "pq1=%.15g pq2=%.15g", pq1, pq2);
        LWDEBUGF(4, "qp1=%.15g qp2=%.15g", qp1, qp2);

        /* Second point of p or q touches, it's not a crossing. */
        if ( pq2 == 0 || qp2 == 0 )
        {
                return SEG_NO_INTERSECTION;
        }

        /* First point of p touches, it's a "crossing". */
        if ( pq1 == 0 )
        {
                if ( pq2 > 0 )
                        return SEG_CROSS_RIGHT;
                else
                        return SEG_CROSS_LEFT;
        }

        /* First point of q touches, it's a crossing. */
        if ( qp1 == 0 )
        {
                if ( pq1 < pq2 )
                        return SEG_CROSS_RIGHT;
                else
                        return SEG_CROSS_LEFT;
        }

        /* The segments cross, what direction is the crossing? */
        if ( pq1 < pq2 )
                return SEG_CROSS_RIGHT;
        else
                return SEG_CROSS_LEFT;

        /* This should never happen! */
        return SEG_ERROR;
}

int lwline_crossing_direction(const LWLINE *l1, const LWLINE *l2)
{
        int i = 0, j = 0;
        const POINT2D *p1, *p2, *q1, *q2;
        POINTARRAY *pa1 = NULL, *pa2 = NULL;
        int cross_left = 0;
        int cross_right = 0;
        int first_cross = 0;
        int this_cross = 0;

        pa1 = (POINTARRAY*)l1->points;
        pa2 = (POINTARRAY*)l2->points;

        /* One-point lines can't intersect (and shouldn't exist). */
        if ( pa1->npoints < 2 || pa2->npoints < 2 )
                return LINE_NO_CROSS;

        LWDEBUGF(4, "l1 = %s", lwgeom_to_ewkt((LWGEOM*)l1));
        LWDEBUGF(4, "l2 = %s", lwgeom_to_ewkt((LWGEOM*)l2));

        /* Initialize first point of q */
        q1 = getPoint2d_cp(pa2, 0);

        for ( i = 1; i < pa2->npoints; i++ )
        {

                /* Update second point of q to next value */
                q2 = getPoint2d_cp(pa2, i);

                /* Initialize first point of p */
                p1 = getPoint2d_cp(pa1, 0);

                for ( j = 1; j < pa1->npoints; j++ )
                {

                        /* Update second point of p to next value */
                        p2 = getPoint2d_cp(pa1, j);

                        this_cross = lw_segment_intersects(p1, p2, q1, q2);

                        LWDEBUGF(4, "i=%d, j=%d (%.8g %.8g, %.8g %.8g)", this_cross, i, j, p1->x, p1->y, p2->x, p2->y);

                        if ( this_cross == SEG_CROSS_LEFT )
                        {
                                LWDEBUG(4,"this_cross == SEG_CROSS_LEFT");
                                cross_left++;
                                if ( ! first_cross )
                                        first_cross = SEG_CROSS_LEFT;
                        }

                        if ( this_cross == SEG_CROSS_RIGHT )
                        {
                                LWDEBUG(4,"this_cross == SEG_CROSS_RIGHT");
                                cross_right++;
                                if ( ! first_cross )
                                        first_cross = SEG_CROSS_LEFT;
                        }

                        /*
                        ** Crossing at a co-linearity can be turned handled by extending
                        ** segment to next vertext and seeing if the end points straddle
                        ** the co-linear segment.
                        */
                        if ( this_cross == SEG_COLINEAR )
                        {
                                LWDEBUG(4,"this_cross == SEG_COLINEAR");
                                /* TODO: Add logic here and in segment_intersects()
                                continue;
                                */
                        }

                        LWDEBUG(4,"this_cross == SEG_NO_INTERSECTION");

                        /* Turn second point of p into first point */
                        p1 = p2;

                }

                /* Turn second point of q into first point */
                q1 = q2;

        }

        LWDEBUGF(4, "first_cross=%d, cross_left=%d, cross_right=%d", first_cross, cross_left, cross_right);

        if ( !cross_left && !cross_right )
                return LINE_NO_CROSS;

        if ( !cross_left && cross_right == 1 )
                return LINE_CROSS_RIGHT;

        if ( !cross_right && cross_left == 1 )
                return LINE_CROSS_LEFT;

        if ( cross_left - cross_right == 1 )
                return LINE_MULTICROSS_END_LEFT;

        if ( cross_left - cross_right == -1 )
                return LINE_MULTICROSS_END_RIGHT;

        if ( cross_left - cross_right == 0 && first_cross == SEG_CROSS_LEFT )
                return LINE_MULTICROSS_END_SAME_FIRST_LEFT;

        if ( cross_left - cross_right == 0 && first_cross == SEG_CROSS_RIGHT )
                return LINE_MULTICROSS_END_SAME_FIRST_RIGHT;

        return LINE_NO_CROSS;

}





static char *base32 = "0123456789bcdefghjkmnpqrstuvwxyz";

/*
** Calculate the geohash, iterating downwards and gaining precision.
** From geohash-native.c, (c) 2008 David Troy <dave@roundhousetech.com>
** Released under the MIT License.
*/
char *geohash_point(double longitude, double latitude, int precision)
{
        int is_even=1, i=0;
        double lat[2], lon[2], mid;
        char bits[] = {16,8,4,2,1};
        int bit=0, ch=0;
        char *geohash = NULL;

        geohash = lwalloc(precision + 1);

        lat[0] = -90.0;
        lat[1] = 90.0;
        lon[0] = -180.0;
        lon[1] = 180.0;

        while (i < precision)
        {
                if (is_even)
                {
                        mid = (lon[0] + lon[1]) / 2;
                        if (longitude >= mid)
                        {
                                ch |= bits[bit];
                                lon[0] = mid;
                        }
                        else
                        {
                                lon[1] = mid;
                        }
                }
                else
                {
                        mid = (lat[0] + lat[1]) / 2;
                        if (latitude >= mid)
                        {
                                ch |= bits[bit];
                                lat[0] = mid;
                        }
                        else
                        {
                                lat[1] = mid;
                        }
                }

                is_even = !is_even;
                if (bit < 4)
                {
                        bit++;
                }
                else
                {
                        geohash[i++] = base32[ch];
                        bit = 0;
                        ch = 0;
                }
        }
        geohash[i] = 0;
        return geohash;
}


/*
** Calculate the geohash, iterating downwards and gaining precision.
** From geohash-native.c, (c) 2008 David Troy <dave@roundhousetech.com>
** Released under the MIT License.
*/
unsigned int geohash_point_as_int(POINT2D *pt)
{
        int is_even=1;
        double lat[2], lon[2], mid;
        int bit=32;
        unsigned int ch = 0;

        double longitude = pt->x;
        double latitude = pt->y;

        lat[0] = -90.0;
        lat[1] = 90.0;
        lon[0] = -180.0;
        lon[1] = 180.0;

        while (--bit >= 0)
        {
                if (is_even)
                {
                        mid = (lon[0] + lon[1]) / 2;
                        if (longitude > mid)
                        {
                                ch |= 0x0001u << bit;
                                lon[0] = mid;
                        }
                        else
                        {
                                lon[1] = mid;
                        }
                }
                else
                {
                        mid = (lat[0] + lat[1]) / 2;
                        if (latitude > mid)
                        {
                                ch |= 0x0001 << bit;
                                lat[0] = mid;
                        }
                        else
                        {
                                lat[1] = mid;
                        }
                }

                is_even = !is_even;
        }
        return ch;
}

/*
** Decode a GeoHash into a bounding box. The lat and lon arguments should
** both be passed as double arrays of length 2 at a minimum where the values
** set in them will be the southwest and northeast coordinates of the bounding
** box accordingly. A precision less than 0 indicates that the entire length
** of the GeoHash should be used.
** It will call `lwerror` if an invalid character is found
*/
void decode_geohash_bbox(char *geohash, double *lat, double *lon, int precision)
{
        int i, j, hashlen;
        char c, cd, mask, is_even = 1;
        static char bits[] = {16, 8, 4, 2, 1};

        lat[0] = -90.0;
        lat[1] = 90.0;
        lon[0] = -180.0;
        lon[1] = 180.0;

        hashlen = strlen(geohash);

        if (precision < 0 || precision > hashlen)
        {
                precision = hashlen;
        }

        for (i = 0; i < precision; i++)
        {
                c = tolower(geohash[i]);
                /* Valid characters are all digits and letters except a, i, l and o */
                if (!(((c >= '0') && (c <= '9')) ||
                      ((c >= 'b') && (c <= 'z') && (c != 'i') && (c != 'l') && (c != 'o'))))
                {
                        lwerror("%s: Invalid character '%c'", __func__, geohash[i]);
                        return;
                }
                cd = strchr(base32, c) - base32;

                for (j = 0; j < 5; j++)
                {
                        mask = bits[j];
                        if (is_even)
                        {
                                lon[!(cd & mask)] = (lon[0] + lon[1]) / 2;
                        }
                        else
                        {
                                lat[!(cd & mask)] = (lat[0] + lat[1]) / 2;
                        }
                        is_even = !is_even;
                }
        }
}

int lwgeom_geohash_precision(GBOX bbox, GBOX *bounds)
{
        double minx, miny, maxx, maxy;
        double latmax, latmin, lonmax, lonmin;
        double lonwidth, latwidth;
        double latmaxadjust, lonmaxadjust, latminadjust, lonminadjust;
        int precision = 0;

        /* Get the bounding box, return error if things don't work out. */
        minx = bbox.xmin;
        miny = bbox.ymin;
        maxx = bbox.xmax;
        maxy = bbox.ymax;

        if ( minx == maxx && miny == maxy )
        {
                /* It's a point. Doubles have 51 bits of precision.
                ** 2 * 51 / 5 == 20 */
                return 20;
        }

        lonmin = -180.0;
        latmin = -90.0;
        lonmax = 180.0;
        latmax = 90.0;

        /* Shrink a world bounding box until one of the edges interferes with the
        ** bounds of our rectangle. */
        while ( 1 )
        {
                lonwidth = lonmax - lonmin;
                latwidth = latmax - latmin;
                latmaxadjust = lonmaxadjust = latminadjust = lonminadjust = 0.0;

                if ( minx > lonmin + lonwidth / 2.0 )
                {
                        lonminadjust = lonwidth / 2.0;
                }
                else if ( maxx < lonmax - lonwidth / 2.0 )
                {
                        lonmaxadjust = -1 * lonwidth / 2.0;
                }
                if ( lonminadjust || lonmaxadjust )
                {
                        lonmin += lonminadjust;
                        lonmax += lonmaxadjust;
                        /* Each adjustment cycle corresponds to 2 bits of storage in the
                        ** geohash.     */
                        precision++;
                }
                else
                {
                        break;
                }

                if ( miny > latmin + latwidth / 2.0 )
                {
                        latminadjust = latwidth / 2.0;
                }
                else if (maxy < latmax - latwidth / 2.0 )
                {
                        latmaxadjust = -1 * latwidth / 2.0;
                }
                /* Only adjust if adjustments are legal (we haven't crossed any edges). */
                if ( latminadjust || latmaxadjust )
                {
                        latmin += latminadjust;
                        latmax += latmaxadjust;
                        /* Each adjustment cycle corresponds to 2 bits of storage in the
                        ** geohash.     */
                        precision++;
                }
                else
                {
                        break;
                }
        }

        /* Save the edges of our bounds, in case someone cares later. */
        bounds->xmin = lonmin;
        bounds->xmax = lonmax;
        bounds->ymin = latmin;
        bounds->ymax = latmax;

        /* Each geohash character (base32) can contain 5 bits of information.
        ** We are returning the precision in characters, so here we divide. */
        return precision / 5;
}


/*
** Return a geohash string for the geometry. <http://geohash.org>
** Where the precision is non-positive, calculate a precision based on the
** bounds of the feature. Big features have loose precision.
** Small features have tight precision.
*/
char *lwgeom_geohash(const LWGEOM *lwgeom, int precision)
{
        GBOX gbox;
        GBOX gbox_bounds;
        double lat, lon;
        int result;

        gbox_init(&gbox);
        gbox_init(&gbox_bounds);

        result = lwgeom_calculate_gbox_cartesian(lwgeom, &gbox);
        if ( result == LW_FAILURE ) return NULL;

        /* Return error if we are being fed something outside our working bounds */
        if ( gbox.xmin < -180 || gbox.ymin < -90 || gbox.xmax > 180 || gbox.ymax > 90 )
        {
                lwerror("Geohash requires inputs in decimal degrees, got (%g %g, %g %g).",
                         gbox.xmin, gbox.ymin,
                         gbox.xmax, gbox.ymax);
                return NULL;
        }

        /* What is the center of our geometry bounds? We'll use that to
        ** approximate location. */
        lon = gbox.xmin + (gbox.xmax - gbox.xmin) / 2;
        lat = gbox.ymin + (gbox.ymax - gbox.ymin) / 2;

        if ( precision <= 0 )
        {
                precision = lwgeom_geohash_precision(gbox, &gbox_bounds);
        }

        /*
        ** Return the geohash of the center, with a precision determined by the
        ** extent of the bounds.
        ** Possible change: return the point at the center of the precision bounds?
        */
        return geohash_point(lon, lat, precision);
}