lwlinearreferencing.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) 2015 Sandro Santilli <strk@kbt.io>
 * Copyright (C) 2011 Paul Ramsey
 *
 **********************************************************************/
 
#include "liblwgeom_internal.h"
#include "lwgeom_log.h"
#include "measures3d.h"
 
static int
segment_locate_along(const POINT4D *p1, const POINT4D *p2, double m, double offset, POINT4D *pn)
{
        double m1 = p1->m;
        double m2 = p2->m;
        double mprop;
 
        /* M is out of range, no new point generated. */
        if ((m < FP_MIN(m1, m2)) || (m > FP_MAX(m1, m2)))
        {
                return LW_FALSE;
        }
 
        if (m1 == m2)
        {
                /* Degenerate case: same M on both points.
                   If they are the same point we just return one of them. */
                if (p4d_same(p1, p2))
                {
                        *pn = *p1;
                        return LW_TRUE;
                }
                /* If the points are different we split the difference */
                mprop = 0.5;
        }
        else
        {
                mprop = (m - m1) / (m2 - m1);
        }
 
        /* M is in range, new point to be generated. */
        pn->x = p1->x + (p2->x - p1->x) * mprop;
        pn->y = p1->y + (p2->y - p1->y) * mprop;
        pn->z = p1->z + (p2->z - p1->z) * mprop;
        pn->m = m;
 
        /* Offset to the left or right, if necessary. */
        if (offset != 0.0)
        {
                double theta = atan2(p2->y - p1->y, p2->x - p1->x);
                pn->x -= sin(theta) * offset;
                pn->y += cos(theta) * offset;
        }
 
        return LW_TRUE;
}
 
static POINTARRAY *
ptarray_locate_along(const POINTARRAY *pa, double m, double offset)
{
        uint32_t i;
        POINT4D p1, p2, pn;
        POINTARRAY *dpa = NULL;
 
        /* Can't do anything with degenerate point arrays */
        if (!pa || pa->npoints < 2)
                return NULL;
 
        /* Walk through each segment in the point array */
        for (i = 1; i < pa->npoints; i++)
        {
                getPoint4d_p(pa, i - 1, &p1);
                getPoint4d_p(pa, i, &p2);
 
                /* No derived point? Move to next segment. */
                if (segment_locate_along(&p1, &p2, m, offset, &pn) == LW_FALSE)
                        continue;
 
                /* No pointarray, make a fresh one */
                if (dpa == NULL)
                        dpa = ptarray_construct_empty(ptarray_has_z(pa), ptarray_has_m(pa), 8);
 
                /* Add our new point to the array */
                ptarray_append_point(dpa, &pn, 0);
        }
 
        return dpa;
}
 
static LWMPOINT *
lwline_locate_along(const LWLINE *lwline, double m, double offset)
{
        POINTARRAY *opa = NULL;
        LWMPOINT *mp = NULL;
        LWGEOM *lwg = lwline_as_lwgeom(lwline);
        int hasz, hasm, srid;
 
        /* Return degenerates upwards */
        if (!lwline)
                return NULL;
 
        /* Create empty return shell */
        srid = lwgeom_get_srid(lwg);
        hasz = lwgeom_has_z(lwg);
        hasm = lwgeom_has_m(lwg);
 
        if (hasm)
        {
                /* Find points along */
                opa = ptarray_locate_along(lwline->points, m, offset);
        }
        else
        {
                LWLINE *lwline_measured = lwline_measured_from_lwline(lwline, 0.0, 1.0);
                opa = ptarray_locate_along(lwline_measured->points, m, offset);
                lwline_free(lwline_measured);
        }
 
        /* Return NULL as EMPTY */
        if (!opa)
                return lwmpoint_construct_empty(srid, hasz, hasm);
 
        /* Convert pointarray into a multipoint */
        mp = lwmpoint_construct(srid, opa);
        ptarray_free(opa);
        return mp;
}
 
static LWMPOINT *
lwmline_locate_along(const LWMLINE *lwmline, double m, double offset)
{
        LWMPOINT *lwmpoint = NULL;
        LWGEOM *lwg = lwmline_as_lwgeom(lwmline);
        uint32_t i, j;
 
        /* Return degenerates upwards */
        if ((!lwmline) || (lwmline->ngeoms < 1))
                return NULL;
 
        /* Construct return */
        lwmpoint = lwmpoint_construct_empty(lwgeom_get_srid(lwg), lwgeom_has_z(lwg), lwgeom_has_m(lwg));
 
        /* Locate along each sub-line */
        for (i = 0; i < lwmline->ngeoms; i++)
        {
                LWMPOINT *along = lwline_locate_along(lwmline->geoms[i], m, offset);
                if (along)
                {
                        if (!lwgeom_is_empty((LWGEOM *)along))
                        {
                                for (j = 0; j < along->ngeoms; j++)
                                {
                                        lwmpoint_add_lwpoint(lwmpoint, along->geoms[j]);
                                }
                        }
                        /* Free the containing geometry, but leave the sub-geometries around */
                        along->ngeoms = 0;
                        lwmpoint_free(along);
                }
        }
        return lwmpoint;
}
 
static LWMPOINT *
lwpoint_locate_along(const LWPOINT *lwpoint, double m, __attribute__((__unused__)) double offset)
{
        double point_m = lwpoint_get_m(lwpoint);
        LWGEOM *lwg = lwpoint_as_lwgeom(lwpoint);
        LWMPOINT *r = lwmpoint_construct_empty(lwgeom_get_srid(lwg), lwgeom_has_z(lwg), lwgeom_has_m(lwg));
        if (FP_EQUALS(m, point_m))
        {
                lwmpoint_add_lwpoint(r, lwpoint_clone(lwpoint));
        }
        return r;
}
 
static LWMPOINT *
lwmpoint_locate_along(const LWMPOINT *lwin, double m, __attribute__((__unused__)) double offset)
{
        LWGEOM *lwg = lwmpoint_as_lwgeom(lwin);
        LWMPOINT *lwout = NULL;
        uint32_t i;
 
        /* Construct return */
        lwout = lwmpoint_construct_empty(lwgeom_get_srid(lwg), lwgeom_has_z(lwg), lwgeom_has_m(lwg));
 
        for (i = 0; i < lwin->ngeoms; i++)
        {
                double point_m = lwpoint_get_m(lwin->geoms[i]);
                if (FP_EQUALS(m, point_m))
                {
                        lwmpoint_add_lwpoint(lwout, lwpoint_clone(lwin->geoms[i]));
                }
        }
 
        return lwout;
}
 
LWGEOM *
lwgeom_locate_along(const LWGEOM *lwin, double m, double offset)
{
        if (!lwin)
                return NULL;
 
        if (!lwgeom_has_m(lwin))
                lwerror("Input geometry does not have a measure dimension");
 
        switch (lwin->type)
        {
        case POINTTYPE:
                return (LWGEOM *)lwpoint_locate_along((LWPOINT *)lwin, m, offset);
        case MULTIPOINTTYPE:
                return (LWGEOM *)lwmpoint_locate_along((LWMPOINT *)lwin, m, offset);
        case LINETYPE:
                return (LWGEOM *)lwline_locate_along((LWLINE *)lwin, m, offset);
        case MULTILINETYPE:
                return (LWGEOM *)lwmline_locate_along((LWMLINE *)lwin, m, offset);
        /* Only line types supported right now */
        /* TO DO: CurveString, CompoundCurve, MultiCurve */
        /* TO DO: Point, MultiPoint */
        default:
                lwerror("Only linear geometries are supported, %s provided.", lwtype_name(lwin->type));
                return NULL;
        }
        return NULL;
}
 
inline double
lwpoint_get_ordinate(const POINT4D *p, char ordinate)
{
        if (!p)
        {
                lwerror("Null input geometry.");
                return 0.0;
        }
 
        switch (ordinate)
        {
        case 'X':
                return p->x;
        case 'Y':
                return p->y;
        case 'Z':
                return p->z;
        case 'M':
                return p->m;
        }
        lwerror("Cannot extract %c ordinate.", ordinate);
        return 0.0;
}
 
inline void
lwpoint_set_ordinate(POINT4D *p, char ordinate, double value)
{
        if (!p)
        {
                lwerror("Null input geometry.");
                return;
        }
 
        switch (ordinate)
        {
        case 'X':
                p->x = value;
                return;
        case 'Y':
                p->y = value;
                return;
        case 'Z':
                p->z = value;
                return;
        case 'M':
                p->m = value;
                return;
        }
        lwerror("Cannot set %c ordinate.", ordinate);
        return;
}
 
inline int
point_interpolate(const POINT4D *p1,
                  const POINT4D *p2,
                  POINT4D *p,
                  int hasz,
                  int hasm,
                  char ordinate,
                  double interpolation_value)
{
        static char *dims = "XYZM";
        double p1_value = lwpoint_get_ordinate(p1, ordinate);
        double p2_value = lwpoint_get_ordinate(p2, ordinate);
        double proportion;
        int i = 0;
 
        assert(ordinate == 'X' || ordinate == 'Y' ||
               ordinate == 'Z' || ordinate == 'M');
        assert(FP_MIN(p1_value, p2_value) <= interpolation_value &&
               FP_MAX(p1_value, p2_value) >= interpolation_value);
 
        proportion = (interpolation_value - p1_value) / (p2_value - p1_value);
 
        for (i = 0; i < 4; i++)
        {
                if (dims[i] == 'Z' && !hasz)
                        continue;
                if (dims[i] == 'M' && !hasm)
                        continue;
                if (dims[i] == ordinate)
                        lwpoint_set_ordinate(p, dims[i], interpolation_value);
                else
                {
                        double newordinate = 0.0;
                        p1_value = lwpoint_get_ordinate(p1, dims[i]);
                        p2_value = lwpoint_get_ordinate(p2, dims[i]);
                        newordinate = p1_value + proportion * (p2_value - p1_value);
                        lwpoint_set_ordinate(p, dims[i], newordinate);
                }
        }
 
        return LW_SUCCESS;
}
 
static inline LWCOLLECTION *
lwpoint_clip_to_ordinate_range(const LWPOINT *point, char ordinate, double from, double to)
{
        LWCOLLECTION *lwgeom_out = NULL;
        char hasz, hasm;
        POINT4D p4d;
        double ordinate_value;
 
        /* Read Z/M info */
        hasz = lwgeom_has_z(lwpoint_as_lwgeom(point));
        hasm = lwgeom_has_m(lwpoint_as_lwgeom(point));
 
        /* Prepare return object */
        lwgeom_out = lwcollection_construct_empty(MULTIPOINTTYPE, point->srid, hasz, hasm);
 
        /* Test if ordinate is in range */
        lwpoint_getPoint4d_p(point, &p4d);
        ordinate_value = lwpoint_get_ordinate(&p4d, ordinate);
        if (from <= ordinate_value && to >= ordinate_value)
        {
                LWPOINT *lwp = lwpoint_clone(point);
                lwcollection_add_lwgeom(lwgeom_out, lwpoint_as_lwgeom(lwp));
        }
 
        return lwgeom_out;
}
 
static inline LWCOLLECTION *
lwmpoint_clip_to_ordinate_range(const LWMPOINT *mpoint, char ordinate, double from, double to)
{
        LWCOLLECTION *lwgeom_out = NULL;
        char hasz, hasm;
        uint32_t i;
 
        /* Read Z/M info */
        hasz = lwgeom_has_z(lwmpoint_as_lwgeom(mpoint));
        hasm = lwgeom_has_m(lwmpoint_as_lwgeom(mpoint));
 
        /* Prepare return object */
        lwgeom_out = lwcollection_construct_empty(MULTIPOINTTYPE, mpoint->srid, hasz, hasm);
 
        /* For each point, is its ordinate value between from and to? */
        for (i = 0; i < mpoint->ngeoms; i++)
        {
                POINT4D p4d;
                double ordinate_value;
 
                lwpoint_getPoint4d_p(mpoint->geoms[i], &p4d);
                ordinate_value = lwpoint_get_ordinate(&p4d, ordinate);
 
                if (from <= ordinate_value && to >= ordinate_value)
                {
                        LWPOINT *lwp = lwpoint_clone(mpoint->geoms[i]);
                        lwcollection_add_lwgeom(lwgeom_out, lwpoint_as_lwgeom(lwp));
                }
        }
 
        /* Set the bbox, if necessary */
        if (mpoint->bbox)
                lwgeom_refresh_bbox((LWGEOM *)lwgeom_out);
 
        return lwgeom_out;
}
 
static inline POINTARRAY *
ptarray_clamp_to_ordinate_range(const POINTARRAY *ipa, char ordinate, double from, double to, uint8_t is_closed)
{
        POINT4D p1, p2;
        POINTARRAY *opa;
        double ovp1, ovp2;
        POINT4D *t;
        int8_t p1out, p2out; /* -1 - smaller than from, 0 - in range, 1 - larger than to */
        uint32_t i;
        uint8_t hasz = FLAGS_GET_Z(ipa->flags);
        uint8_t hasm = FLAGS_GET_M(ipa->flags);
 
        assert(from <= to);
 
        t = lwalloc(sizeof(POINT4D));
 
        /* Initial storage */
        opa = ptarray_construct_empty(hasz, hasm, ipa->npoints);
 
        /* Add first point */
        getPoint4d_p(ipa, 0, &p1);
        ovp1 = lwpoint_get_ordinate(&p1, ordinate);
 
        p1out = (ovp1 < from) ? -1 : ((ovp1 > to) ? 1 : 0);
 
        if (from <= ovp1 && ovp1 <= to)
                ptarray_append_point(opa, &p1, LW_FALSE);
 
        /* Loop on all other input points */
        for (i = 1; i < ipa->npoints; i++)
        {
                getPoint4d_p(ipa, i, &p2);
                ovp2 = lwpoint_get_ordinate(&p2, ordinate);
                p2out = (ovp2 < from) ? -1 : ((ovp2 > to) ? 1 : 0);
 
                if (p1out == 0 && p2out == 0) /* both visible */
                {
                        ptarray_append_point(opa, &p2, LW_FALSE);
                }
                else if (p1out == p2out && p1out != 0) /* both invisible on the same side */
                {
                        /* skip */
                }
                else if (p1out == -1 && p2out == 0)
                {
                        point_interpolate(&p1, &p2, t, hasz, hasm, ordinate, from);
                        ptarray_append_point(opa, t, LW_FALSE);
                        ptarray_append_point(opa, &p2, LW_FALSE);
                }
                else if (p1out == -1 && p2out == 1)
                {
                        point_interpolate(&p1, &p2, t, hasz, hasm, ordinate, from);
                        ptarray_append_point(opa, t, LW_FALSE);
                        point_interpolate(&p1, &p2, t, hasz, hasm, ordinate, to);
                        ptarray_append_point(opa, t, LW_FALSE);
                }
                else if (p1out == 0 && p2out == -1)
                {
                        point_interpolate(&p1, &p2, t, hasz, hasm, ordinate, from);
                        ptarray_append_point(opa, t, LW_FALSE);
                }
                else if (p1out == 0 && p2out == 1)
                {
                        point_interpolate(&p1, &p2, t, hasz, hasm, ordinate, to);
                        ptarray_append_point(opa, t, LW_FALSE);
                }
                else if (p1out == 1 && p2out == -1)
                {
                        point_interpolate(&p1, &p2, t, hasz, hasm, ordinate, to);
                        ptarray_append_point(opa, t, LW_FALSE);
                        point_interpolate(&p1, &p2, t, hasz, hasm, ordinate, from);
                        ptarray_append_point(opa, t, LW_FALSE);
                }
                else if (p1out == 1 && p2out == 0)
                {
                        point_interpolate(&p1, &p2, t, hasz, hasm, ordinate, to);
                        ptarray_append_point(opa, t, LW_FALSE);
                        ptarray_append_point(opa, &p2, LW_FALSE);
                }
 
                p1 = p2;
                p1out = p2out;
                LW_ON_INTERRUPT(ptarray_free(opa); return NULL);
        }
 
        if (is_closed && opa->npoints > 2)
        {
                getPoint4d_p(opa, 0, &p1);
                ptarray_append_point(opa, &p1, LW_FALSE);
        }
        lwfree(t);
 
        return opa;
}
 
static inline LWCOLLECTION *
lwline_clip_to_ordinate_range(const LWLINE *line, char ordinate, double from, double to)
{
        POINTARRAY *pa_in = NULL;
        LWCOLLECTION *lwgeom_out = NULL;
        POINTARRAY *dp = NULL;
        uint32_t i;
        int added_last_point = 0;
        POINT4D *p = NULL, *q = NULL, *r = NULL;
        double ordinate_value_p = 0.0, ordinate_value_q = 0.0;
        char hasz, hasm;
        char dims;
 
        /* Null input, nothing we can do. */
        assert(line);
        hasz = lwgeom_has_z(lwline_as_lwgeom(line));
        hasm = lwgeom_has_m(lwline_as_lwgeom(line));
        dims = FLAGS_NDIMS(line->flags);
 
        /* Asking for an ordinate we don't have. Error. */
        if ((ordinate == 'Z' && !hasz) || (ordinate == 'M' && !hasm))
        {
                lwerror("Cannot clip on ordinate %d in a %d-d geometry.", ordinate, dims);
                return NULL;
        }
 
        /* Prepare our working point objects. */
        p = lwalloc(sizeof(POINT4D));
        q = lwalloc(sizeof(POINT4D));
        r = lwalloc(sizeof(POINT4D));
 
        /* Construct a collection to hold our outputs. */
        lwgeom_out = lwcollection_construct_empty(MULTILINETYPE, line->srid, hasz, hasm);
 
        /* Get our input point array */
        pa_in = line->points;
 
        for (i = 0; i < pa_in->npoints; i++)
        {
                if (i > 0)
                {
                        *q = *p;
                        ordinate_value_q = ordinate_value_p;
                }
                getPoint4d_p(pa_in, i, p);
                ordinate_value_p = lwpoint_get_ordinate(p, ordinate);
 
                /* Is this point inside the ordinate range? Yes. */
                if (ordinate_value_p >= from && ordinate_value_p <= to)
                {
 
                        if (!added_last_point)
                        {
                                /* We didn't add the previous point, so this is a new segment.
                                 *  Make a new point array. */
                                dp = ptarray_construct_empty(hasz, hasm, 32);
 
                                /* We're transiting into the range so add an interpolated
                                 *  point at the range boundary.
                                 *  If we're on a boundary and crossing from the far side,
                                 *  we also need an interpolated point. */
                                if (i > 0 &&
                                    (/* Don't try to interpolate if this is the first point */
                                     (ordinate_value_p > from && ordinate_value_p < to) ||  /* Inside */
                                     (ordinate_value_p == from && ordinate_value_q > to) || /* Hopping from above */
                                     (ordinate_value_p == to && ordinate_value_q < from)))  /* Hopping from below */
                                {
                                        double interpolation_value;
                                        (ordinate_value_q > to) ? (interpolation_value = to)
                                                                : (interpolation_value = from);
                                        point_interpolate(q, p, r, hasz, hasm, ordinate, interpolation_value);
                                        ptarray_append_point(dp, r, LW_FALSE);
                                }
                        }
                        /* Add the current vertex to the point array. */
                        ptarray_append_point(dp, p, LW_FALSE);
                        if (ordinate_value_p == from || ordinate_value_p == to)
                                added_last_point = 2; /* Added on boundary. */
                        else
                                added_last_point = 1; /* Added inside range. */
                }
                /* Is this point inside the ordinate range? No. */
                else
                {
                        if (added_last_point == 1)
                        {
                                /* We're transiting out of the range, so add an interpolated point
                                 *  to the point array at the range boundary. */
                                double interpolation_value;
                                (ordinate_value_p > to) ? (interpolation_value = to) : (interpolation_value = from);
                                point_interpolate(q, p, r, hasz, hasm, ordinate, interpolation_value);
                                ptarray_append_point(dp, r, LW_FALSE);
                        }
                        else if (added_last_point == 2)
                        {
                                /* We're out and the last point was on the boundary.
                                 *  If the last point was the near boundary, nothing to do.
                                 *  If it was the far boundary, we need an interpolated point. */
                                if (from != to && ((ordinate_value_q == from && ordinate_value_p > from) ||
                                                   (ordinate_value_q == to && ordinate_value_p < to)))
                                {
                                        double interpolation_value;
                                        (ordinate_value_p > to) ? (interpolation_value = to)
                                                                : (interpolation_value = from);
                                        point_interpolate(q, p, r, hasz, hasm, ordinate, interpolation_value);
                                        ptarray_append_point(dp, r, LW_FALSE);
                                }
                        }
                        else if (i && ordinate_value_q < from && ordinate_value_p > to)
                        {
                                /* We just hopped over the whole range, from bottom to top,
                                 *  so we need to add *two* interpolated points! */
                                dp = ptarray_construct(hasz, hasm, 2);
                                /* Interpolate lower point. */
                                point_interpolate(p, q, r, hasz, hasm, ordinate, from);
                                ptarray_set_point4d(dp, 0, r);
                                /* Interpolate upper point. */
                                point_interpolate(p, q, r, hasz, hasm, ordinate, to);
                                ptarray_set_point4d(dp, 1, r);
                        }
                        else if (i && ordinate_value_q > to && ordinate_value_p < from)
                        {
                                /* We just hopped over the whole range, from top to bottom,
                                 *  so we need to add *two* interpolated points! */
                                dp = ptarray_construct(hasz, hasm, 2);
                                /* Interpolate upper point. */
                                point_interpolate(p, q, r, hasz, hasm, ordinate, to);
                                ptarray_set_point4d(dp, 0, r);
                                /* Interpolate lower point. */
                                point_interpolate(p, q, r, hasz, hasm, ordinate, from);
                                ptarray_set_point4d(dp, 1, r);
                        }
                        /* We have an extant point-array, save it out to a multi-line. */
                        if (dp)
                        {
                                /* Only one point, so we have to make an lwpoint to hold this
                                 *  and set the overall output type to a generic collection. */
                                if (dp->npoints == 1)
                                {
                                        LWPOINT *opoint = lwpoint_construct(line->srid, NULL, dp);
                                        lwgeom_out->type = COLLECTIONTYPE;
                                        lwgeom_out = lwcollection_add_lwgeom(lwgeom_out, lwpoint_as_lwgeom(opoint));
                                }
                                else
                                {
                                        LWLINE *oline = lwline_construct(line->srid, NULL, dp);
                                        lwgeom_out = lwcollection_add_lwgeom(lwgeom_out, lwline_as_lwgeom(oline));
                                }
 
                                /* Pointarray is now owned by lwgeom_out, so drop reference to it */
                                dp = NULL;
                        }
                        added_last_point = 0;
                }
        }
 
        /* Still some points left to be saved out. */
        if (dp)
        {
                if (dp->npoints == 1)
                {
                        LWPOINT *opoint = lwpoint_construct(line->srid, NULL, dp);
                        lwgeom_out->type = COLLECTIONTYPE;
                        lwgeom_out = lwcollection_add_lwgeom(lwgeom_out, lwpoint_as_lwgeom(opoint));
                }
                else if (dp->npoints > 1)
                {
                        LWLINE *oline = lwline_construct(line->srid, NULL, dp);
                        lwgeom_out = lwcollection_add_lwgeom(lwgeom_out, lwline_as_lwgeom(oline));
                }
                else
                        ptarray_free(dp);
        }
 
        lwfree(p);
        lwfree(q);
        lwfree(r);
 
        if (line->bbox && lwgeom_out->ngeoms > 0)
                lwgeom_refresh_bbox((LWGEOM *)lwgeom_out);
 
        return lwgeom_out;
}
 
static inline LWCOLLECTION *
lwpoly_clip_to_ordinate_range(const LWPOLY *poly, char ordinate, double from, double to)
{
        assert(poly);
        char hasz = FLAGS_GET_Z(poly->flags), hasm = FLAGS_GET_M(poly->flags);
        LWPOLY *poly_res = lwpoly_construct_empty(poly->srid, hasz, hasm);
        LWCOLLECTION *lwgeom_out = lwcollection_construct_empty(MULTIPOLYGONTYPE, poly->srid, hasz, hasm);
 
        for (uint32_t i = 0; i < poly->nrings; i++)
        {
                /* Ret number of points */
                POINTARRAY *pa = ptarray_clamp_to_ordinate_range(poly->rings[i], ordinate, from, to, LW_TRUE);
 
                if (!pa)
                        return NULL;
 
                if (pa->npoints >= 4)
                        lwpoly_add_ring(poly_res, pa);
                else
                {
                        ptarray_free(pa);
                        if (i == 0)
                                break;
                }
        }
        if (poly_res->nrings > 0)
                lwgeom_out = lwcollection_add_lwgeom(lwgeom_out, (LWGEOM *)poly_res);
        else
                lwpoly_free(poly_res);
 
        return lwgeom_out;
}
 
static inline LWCOLLECTION *
lwtriangle_clip_to_ordinate_range(const LWTRIANGLE *tri, char ordinate, double from, double to)
{
        assert(tri);
        char hasz = FLAGS_GET_Z(tri->flags), hasm = FLAGS_GET_M(tri->flags);
        LWCOLLECTION *lwgeom_out = lwcollection_construct_empty(TINTYPE, tri->srid, hasz, hasm);
        POINTARRAY *pa = ptarray_clamp_to_ordinate_range(tri->points, ordinate, from, to, LW_TRUE);
 
        if (!pa)
                return NULL;
 
        if (pa->npoints >= 4)
        {
                POINT4D first = getPoint4d(pa, 0);
                for (uint32_t i = 1; i < pa->npoints - 2; i++)
                {
                        POINT4D p;
                        POINTARRAY *tpa = ptarray_construct_empty(hasz, hasm, 4);
                        ptarray_append_point(tpa, &first, LW_TRUE);
                        getPoint4d_p(pa, i, &p);
                        ptarray_append_point(tpa, &p, LW_TRUE);
                        getPoint4d_p(pa, i + 1, &p);
                        ptarray_append_point(tpa, &p, LW_TRUE);
                        ptarray_append_point(tpa, &first, LW_TRUE);
                        LWTRIANGLE *otri = lwtriangle_construct(tri->srid, NULL, tpa);
                        lwgeom_out = lwcollection_add_lwgeom(lwgeom_out, (LWGEOM *)otri);
                }
        }
        ptarray_free(pa);
        return lwgeom_out;
}
 
static inline LWCOLLECTION *
lwcollection_clip_to_ordinate_range(const LWCOLLECTION *icol, char ordinate, double from, double to)
{
        LWCOLLECTION *lwgeom_out;
 
        assert(icol);
        if (icol->ngeoms == 1)
                lwgeom_out = lwgeom_clip_to_ordinate_range(icol->geoms[0], ordinate, from, to, 0);
        else
        {
                LWCOLLECTION *col;
                char hasz = lwgeom_has_z(lwcollection_as_lwgeom(icol));
                char hasm = lwgeom_has_m(lwcollection_as_lwgeom(icol));
                uint32_t i;
                lwgeom_out = lwcollection_construct_empty(icol->type, icol->srid, hasz, hasm);
                FLAGS_SET_Z(lwgeom_out->flags, hasz);
                FLAGS_SET_M(lwgeom_out->flags, hasm);
                for (i = 0; i < icol->ngeoms; i++)
                {
                        col = lwgeom_clip_to_ordinate_range(icol->geoms[i], ordinate, from, to, 0);
                        if (col)
                        {
                                if (col->type != icol->type)
                                        lwgeom_out->type = COLLECTIONTYPE;
                                lwgeom_out = lwcollection_concat_in_place(lwgeom_out, col);
                                lwfree(col->geoms);
                                lwcollection_release(col);
                        }
                }
        }
 
        if (icol->bbox)
                lwgeom_refresh_bbox((LWGEOM *)lwgeom_out);
 
        return lwgeom_out;
}
 
LWCOLLECTION *
lwgeom_clip_to_ordinate_range(const LWGEOM *lwin, char ordinate, double from, double to, double offset)
{
        LWCOLLECTION *out_col;
        LWCOLLECTION *out_offset;
        uint32_t i;
 
        /* Ensure 'from' is less than 'to'. */
        if (to < from)
        {
                double t = from;
                from = to;
                to = t;
        }
 
        if (!lwin)
                lwerror("lwgeom_clip_to_ordinate_range: null input geometry!");
 
        switch (lwin->type)
        {
        case LINETYPE:
                out_col = lwline_clip_to_ordinate_range((LWLINE *)lwin, ordinate, from, to);
                break;
        case MULTIPOINTTYPE:
                out_col = lwmpoint_clip_to_ordinate_range((LWMPOINT *)lwin, ordinate, from, to);
                break;
        case POINTTYPE:
                out_col = lwpoint_clip_to_ordinate_range((LWPOINT *)lwin, ordinate, from, to);
                break;
        case POLYGONTYPE:
                out_col = lwpoly_clip_to_ordinate_range((LWPOLY *)lwin, ordinate, from, to);
                break;
        case TRIANGLETYPE:
                out_col = lwtriangle_clip_to_ordinate_range((LWTRIANGLE *)lwin, ordinate, from, to);
                break;
        case TINTYPE:
        case MULTILINETYPE:
        case MULTIPOLYGONTYPE:
        case COLLECTIONTYPE:
        case POLYHEDRALSURFACETYPE:
                out_col = lwcollection_clip_to_ordinate_range((LWCOLLECTION *)lwin, ordinate, from, to);
                break;
        default:
                lwerror("This function does not accept %s geometries.", lwtype_name(lwin->type));
                return NULL;
        }
 
        /* Stop if result is NULL */
        if (!out_col)
                lwerror("lwgeom_clip_to_ordinate_range clipping routine returned NULL");
 
        /* Return if we aren't going to offset the result */
        if (FP_IS_ZERO(offset) || lwgeom_is_empty(lwcollection_as_lwgeom(out_col)))
                return out_col;
 
        /* Construct a collection to hold our outputs. */
        /* Things get ugly: GEOS offset drops Z's and M's so we have to drop ours */
        out_offset = lwcollection_construct_empty(MULTILINETYPE, lwin->srid, 0, 0);
 
        /* Try and offset the linear portions of the return value */
        for (i = 0; i < out_col->ngeoms; i++)
        {
                int type = out_col->geoms[i]->type;
                if (type == POINTTYPE)
                {
                        lwnotice("lwgeom_clip_to_ordinate_range cannot offset a clipped point");
                        continue;
                }
                else if (type == LINETYPE)
                {
                        /* lwgeom_offsetcurve(line, offset, quadsegs, joinstyle (round), mitrelimit) */
                        LWGEOM *lwoff = lwgeom_offsetcurve(out_col->geoms[i], offset, 8, 1, 5.0);
                        if (!lwoff)
                        {
                                lwerror("lwgeom_offsetcurve returned null");
                        }
                        lwcollection_add_lwgeom(out_offset, lwoff);
                }
                else
                {
                        lwerror("lwgeom_clip_to_ordinate_range found an unexpected type (%s) in the offset routine",
                                lwtype_name(type));
                }
        }
 
        return out_offset;
}
 
LWCOLLECTION *
lwgeom_locate_between(const LWGEOM *lwin, double from, double to, double offset)
{
        if (!lwgeom_has_m(lwin))
                lwerror("Input geometry does not have a measure dimension");
 
        return lwgeom_clip_to_ordinate_range(lwin, 'M', from, to, offset);
}
 
double
lwgeom_interpolate_point(const LWGEOM *lwin, const LWPOINT *lwpt)
{
        POINT4D p, p_proj;
        double ret = 0.0;
 
        if (!lwin)
                lwerror("lwgeom_interpolate_point: null input geometry!");
 
        if (!lwgeom_has_m(lwin))
                lwerror("Input geometry does not have a measure dimension");
 
        if (lwgeom_is_empty(lwin) || lwpoint_is_empty(lwpt))
                lwerror("Input geometry is empty");
 
        switch (lwin->type)
        {
        case LINETYPE:
        {
                LWLINE *lwline = lwgeom_as_lwline(lwin);
                lwpoint_getPoint4d_p(lwpt, &p);
                ret = ptarray_locate_point(lwline->points, &p, NULL, &p_proj);
                ret = p_proj.m;
                break;
        }
        default:
                lwerror("This function does not accept %s geometries.", lwtype_name(lwin->type));
        }
        return ret;
}
 
/*
 * Time of closest point of approach
 *
 * Given two vectors (p1-p2 and q1-q2) and
 * a time range (t1-t2) return the time in which
 * a point p is closest to a point q on their
 * respective vectors, and the actual points
 *
 * Here we use algorithm from softsurfer.com
 * that can be found here
 * http://softsurfer.com/Archive/algorithm_0106/algorithm_0106.htm
 *
 * @param p0 start of first segment, will be set to actual
 *           closest point of approach on segment.
 * @param p1 end of first segment
 * @param q0 start of second segment, will be set to actual
 *           closest point of approach on segment.
 * @param q1 end of second segment
 * @param t0 start of travel time
 * @param t1 end of travel time
 *
 * @return time of closest point of approach
 *
 */
static double
segments_tcpa(POINT4D *p0, const POINT4D *p1, POINT4D *q0, const POINT4D *q1, double t0, double t1)
{
        POINT3DZ pv; /* velocity of p, aka u */
        POINT3DZ qv; /* velocity of q, aka v */
        POINT3DZ dv; /* velocity difference */
        POINT3DZ w0; /* vector between first points */
 
        /*
          lwnotice("FROM %g,%g,%g,%g -- %g,%g,%g,%g",
            p0->x, p0->y, p0->z, p0->m,
            p1->x, p1->y, p1->z, p1->m);
          lwnotice("  TO %g,%g,%g,%g -- %g,%g,%g,%g",
            q0->x, q0->y, q0->z, q0->m,
            q1->x, q1->y, q1->z, q1->m);
        */
 
        /* PV aka U */
        pv.x = (p1->x - p0->x);
        pv.y = (p1->y - p0->y);
        pv.z = (p1->z - p0->z);
        /*lwnotice("PV:  %g, %g, %g", pv.x, pv.y, pv.z);*/
 
        /* QV aka V */
        qv.x = (q1->x - q0->x);
        qv.y = (q1->y - q0->y);
        qv.z = (q1->z - q0->z);
        /*lwnotice("QV:  %g, %g, %g", qv.x, qv.y, qv.z);*/
 
        dv.x = pv.x - qv.x;
        dv.y = pv.y - qv.y;
        dv.z = pv.z - qv.z;
        /*lwnotice("DV:  %g, %g, %g", dv.x, dv.y, dv.z);*/
 
        double dv2 = DOT(dv, dv);
        /*lwnotice("DOT: %g", dv2);*/
 
        if (dv2 == 0.0)
        {
                /* Distance is the same at any time, we pick the earliest */
                return t0;
        }
 
        /* Distance at any given time, with t0 */
        w0.x = (p0->x - q0->x);
        w0.y = (p0->y - q0->y);
        w0.z = (p0->z - q0->z);
 
        /*lwnotice("W0:  %g, %g, %g", w0.x, w0.y, w0.z);*/
 
        /* Check that at distance dt w0 is distance */
 
        /* This is the fraction of measure difference */
        double t = -DOT(w0, dv) / dv2;
        /*lwnotice("CLOSEST TIME (fraction): %g", t);*/
 
        if (t > 1.0)
        {
                /* Getting closer as we move to the end */
                /*lwnotice("Converging");*/
                t = 1;
        }
        else if (t < 0.0)
        {
                /*lwnotice("Diverging");*/
                t = 0;
        }
 
        /* Interpolate the actual points now */
 
        p0->x += pv.x * t;
        p0->y += pv.y * t;
        p0->z += pv.z * t;
 
        q0->x += qv.x * t;
        q0->y += qv.y * t;
        q0->z += qv.z * t;
 
        t = t0 + (t1 - t0) * t;
        /*lwnotice("CLOSEST TIME (real): %g", t);*/
 
        return t;
}
 
static int
ptarray_collect_mvals(const POINTARRAY *pa, double tmin, double tmax, double *mvals)
{
        POINT4D pbuf;
        uint32_t i, n = 0;
        for (i = 0; i < pa->npoints; ++i)
        {
                getPoint4d_p(pa, i, &pbuf); /* could be optimized */
                if (pbuf.m >= tmin && pbuf.m <= tmax)
                        mvals[n++] = pbuf.m;
        }
        return n;
}
 
static int
compare_double(const void *pa, const void *pb)
{
        double a = *((double *)pa);
        double b = *((double *)pb);
        if (a < b)
                return -1;
        else if (a > b)
                return 1;
        else
                return 0;
}
 
/* Return number of elements in unique array */
static int
uniq(double *vals, int nvals)
{
        int i, last = 0;
        for (i = 1; i < nvals; ++i)
        {
                // lwnotice("(I%d):%g", i, vals[i]);
                if (vals[i] != vals[last])
                {
                        vals[++last] = vals[i];
                        // lwnotice("(O%d):%g", last, vals[last]);
                }
        }
        return last + 1;
}
 
/*
 * Find point at a given measure
 *
 * The function assumes measures are linear so that always a single point
 * is returned for a single measure.
 *
 * @param pa the point array to perform search on
 * @param m the measure to search for
 * @param p the point to write result into
 * @param from the segment number to start from
 *
 * @return the segment number the point was found into
 *         or -1 if given measure was out of the known range.
 */
static int
ptarray_locate_along_linear(const POINTARRAY *pa, double m, POINT4D *p, uint32_t from)
{
        uint32_t i = from;
        POINT4D p1, p2;
 
        /* Walk through each segment in the point array */
        getPoint4d_p(pa, i, &p1);
        for (i = from + 1; i < pa->npoints; i++)
        {
                getPoint4d_p(pa, i, &p2);
 
                if (segment_locate_along(&p1, &p2, m, 0, p) == LW_TRUE)
                        return i - 1; /* found */
 
                p1 = p2;
        }
 
        return -1; /* not found */
}
 
double
lwgeom_tcpa(const LWGEOM *g1, const LWGEOM *g2, double *mindist)
{
        LWLINE *l1, *l2;
        int i;
        GBOX gbox1, gbox2;
        double tmin, tmax;
        double *mvals;
        int nmvals = 0;
        double mintime;
        double mindist2 = FLT_MAX; /* minimum distance, squared */
 
        if (!lwgeom_has_m(g1) || !lwgeom_has_m(g2))
        {
                lwerror("Both input geometries must have a measure dimension");
                return -1;
        }
 
        l1 = lwgeom_as_lwline(g1);
        l2 = lwgeom_as_lwline(g2);
 
        if (!l1 || !l2)
        {
                lwerror("Both input geometries must be linestrings");
                return -1;
        }
 
        if (l1->points->npoints < 2 || l2->points->npoints < 2)
        {
                lwerror("Both input lines must have at least 2 points");
                return -1;
        }
 
        /* We use lwgeom_calculate_gbox() instead of lwgeom_get_gbox() */
        /* because we cannot afford the float rounding inaccuracy when */
        /* we compare the ranges for overlap below */
        lwgeom_calculate_gbox(g1, &gbox1);
        lwgeom_calculate_gbox(g2, &gbox2);
 
        /*
         * Find overlapping M range
         * WARNING: may be larger than the real one
         */
 
        tmin = FP_MAX(gbox1.mmin, gbox2.mmin);
        tmax = FP_MIN(gbox1.mmax, gbox2.mmax);
 
        if (tmax < tmin)
        {
                LWDEBUG(1, "Inputs never exist at the same time");
                return -2;
        }
 
        // lwnotice("Min:%g, Max:%g", tmin, tmax);
 
        /*
         * Collect M values in common time range from inputs
         */
 
        mvals = lwalloc(sizeof(double) * (l1->points->npoints + l2->points->npoints));
 
        /* TODO: also clip the lines ? */
        nmvals = ptarray_collect_mvals(l1->points, tmin, tmax, mvals);
        nmvals += ptarray_collect_mvals(l2->points, tmin, tmax, mvals + nmvals);
 
        /* Sort values in ascending order */
        qsort(mvals, nmvals, sizeof(double), compare_double);
 
        /* Remove duplicated values */
        nmvals = uniq(mvals, nmvals);
 
        if (nmvals < 2)
        {
                {
                        /* there's a single time, must be that one... */
                        double t0 = mvals[0];
                        POINT4D p0, p1;
                        LWDEBUGF(1, "Inputs only exist both at a single time (%g)", t0);
                        if (mindist)
                        {
                                if (-1 == ptarray_locate_along_linear(l1->points, t0, &p0, 0))
                                {
                                        lwfree(mvals);
                                        lwerror("Could not find point with M=%g on first geom", t0);
                                        return -1;
                                }
                                if (-1 == ptarray_locate_along_linear(l2->points, t0, &p1, 0))
                                {
                                        lwfree(mvals);
                                        lwerror("Could not find point with M=%g on second geom", t0);
                                        return -1;
                                }
                                *mindist = distance3d_pt_pt((POINT3D *)&p0, (POINT3D *)&p1);
                        }
                        lwfree(mvals);
                        return t0;
                }
        }
 
        /*
         * For each consecutive pair of measures, compute time of closest point
         * approach and actual distance between points at that time
         */
        mintime = tmin;
        for (i = 1; i < nmvals; ++i)
        {
                double t0 = mvals[i - 1];
                double t1 = mvals[i];
                double t;
                POINT4D p0, p1, q0, q1;
                int seg;
                double dist2;
 
                // lwnotice("T %g-%g", t0, t1);
 
                seg = ptarray_locate_along_linear(l1->points, t0, &p0, 0);
                if (-1 == seg)
                        continue; /* possible, if GBOX is approximated */
                // lwnotice("Measure %g on segment %d of line 1: %g, %g, %g", t0, seg, p0.x, p0.y, p0.z);
 
                seg = ptarray_locate_along_linear(l1->points, t1, &p1, seg);
                if (-1 == seg)
                        continue; /* possible, if GBOX is approximated */
                // lwnotice("Measure %g on segment %d of line 1: %g, %g, %g", t1, seg, p1.x, p1.y, p1.z);
 
                seg = ptarray_locate_along_linear(l2->points, t0, &q0, 0);
                if (-1 == seg)
                        continue; /* possible, if GBOX is approximated */
                // lwnotice("Measure %g on segment %d of line 2: %g, %g, %g", t0, seg, q0.x, q0.y, q0.z);
 
                seg = ptarray_locate_along_linear(l2->points, t1, &q1, seg);
                if (-1 == seg)
                        continue; /* possible, if GBOX is approximated */
                // lwnotice("Measure %g on segment %d of line 2: %g, %g, %g", t1, seg, q1.x, q1.y, q1.z);
 
                t = segments_tcpa(&p0, &p1, &q0, &q1, t0, t1);
 
                /*
                lwnotice("Closest points: %g,%g,%g and %g,%g,%g at time %g",
                p0.x, p0.y, p0.z,
                q0.x, q0.y, q0.z, t);
                */
 
                dist2 = (q0.x - p0.x) * (q0.x - p0.x) + (q0.y - p0.y) * (q0.y - p0.y) + (q0.z - p0.z) * (q0.z - p0.z);
                if (dist2 < mindist2)
                {
                        mindist2 = dist2;
                        mintime = t;
                        // lwnotice("MINTIME: %g", mintime);
                }
        }
 
        /*
         * Release memory
         */
 
        lwfree(mvals);
 
        if (mindist)
        {
                *mindist = sqrt(mindist2);
        }
        /*lwnotice("MINDIST: %g", sqrt(mindist2));*/
 
        return mintime;
}
 
int
lwgeom_cpa_within(const LWGEOM *g1, const LWGEOM *g2, double maxdist)
{
        LWLINE *l1, *l2;
        int i;
        GBOX gbox1, gbox2;
        double tmin, tmax;
        double *mvals;
        int nmvals = 0;
        double maxdist2 = maxdist * maxdist;
        int within = LW_FALSE;
 
        if (!lwgeom_has_m(g1) || !lwgeom_has_m(g2))
        {
                lwerror("Both input geometries must have a measure dimension");
                return LW_FALSE;
        }
 
        l1 = lwgeom_as_lwline(g1);
        l2 = lwgeom_as_lwline(g2);
 
        if (!l1 || !l2)
        {
                lwerror("Both input geometries must be linestrings");
                return LW_FALSE;
        }
 
        if (l1->points->npoints < 2 || l2->points->npoints < 2)
        {
                /* TODO: return distance between these two points */
                lwerror("Both input lines must have at least 2 points");
                return LW_FALSE;
        }
 
        /* We use lwgeom_calculate_gbox() instead of lwgeom_get_gbox() */
        /* because we cannot afford the float rounding inaccuracy when */
        /* we compare the ranges for overlap below */
        lwgeom_calculate_gbox(g1, &gbox1);
        lwgeom_calculate_gbox(g2, &gbox2);
 
        /*
         * Find overlapping M range
         * WARNING: may be larger than the real one
         */
 
        tmin = FP_MAX(gbox1.mmin, gbox2.mmin);
        tmax = FP_MIN(gbox1.mmax, gbox2.mmax);
 
        if (tmax < tmin)
        {
                LWDEBUG(1, "Inputs never exist at the same time");
                return LW_FALSE;
        }
 
        /*
         * Collect M values in common time range from inputs
         */
 
        mvals = lwalloc(sizeof(double) * (l1->points->npoints + l2->points->npoints));
 
        /* TODO: also clip the lines ? */
        nmvals = ptarray_collect_mvals(l1->points, tmin, tmax, mvals);
        nmvals += ptarray_collect_mvals(l2->points, tmin, tmax, mvals + nmvals);
 
        /* Sort values in ascending order */
        qsort(mvals, nmvals, sizeof(double), compare_double);
 
        /* Remove duplicated values */
        nmvals = uniq(mvals, nmvals);
 
        if (nmvals < 2)
        {
                /* there's a single time, must be that one... */
                double t0 = mvals[0];
                POINT4D p0, p1;
                LWDEBUGF(1, "Inputs only exist both at a single time (%g)", t0);
                if (-1 == ptarray_locate_along_linear(l1->points, t0, &p0, 0))
                {
                        lwnotice("Could not find point with M=%g on first geom", t0);
                        return LW_FALSE;
                }
                if (-1 == ptarray_locate_along_linear(l2->points, t0, &p1, 0))
                {
                        lwnotice("Could not find point with M=%g on second geom", t0);
                        return LW_FALSE;
                }
                if (distance3d_pt_pt((POINT3D *)&p0, (POINT3D *)&p1) <= maxdist)
                        within = LW_TRUE;
                lwfree(mvals);
                return within;
        }
 
        /*
         * For each consecutive pair of measures, compute time of closest point
         * approach and actual distance between points at that time
         */
        for (i = 1; i < nmvals; ++i)
        {
                double t0 = mvals[i - 1];
                double t1 = mvals[i];
#if POSTGIS_DEBUG_LEVEL >= 1
                double t;
#endif
                POINT4D p0, p1, q0, q1;
                int seg;
                double dist2;
 
                // lwnotice("T %g-%g", t0, t1);
 
                seg = ptarray_locate_along_linear(l1->points, t0, &p0, 0);
                if (-1 == seg)
                        continue; /* possible, if GBOX is approximated */
                // lwnotice("Measure %g on segment %d of line 1: %g, %g, %g", t0, seg, p0.x, p0.y, p0.z);
 
                seg = ptarray_locate_along_linear(l1->points, t1, &p1, seg);
                if (-1 == seg)
                        continue; /* possible, if GBOX is approximated */
                // lwnotice("Measure %g on segment %d of line 1: %g, %g, %g", t1, seg, p1.x, p1.y, p1.z);
 
                seg = ptarray_locate_along_linear(l2->points, t0, &q0, 0);
                if (-1 == seg)
                        continue; /* possible, if GBOX is approximated */
                // lwnotice("Measure %g on segment %d of line 2: %g, %g, %g", t0, seg, q0.x, q0.y, q0.z);
 
                seg = ptarray_locate_along_linear(l2->points, t1, &q1, seg);
                if (-1 == seg)
                        continue; /* possible, if GBOX is approximated */
                        // lwnotice("Measure %g on segment %d of line 2: %g, %g, %g", t1, seg, q1.x, q1.y, q1.z);
 
#if POSTGIS_DEBUG_LEVEL >= 1
                t =
#endif
                    segments_tcpa(&p0, &p1, &q0, &q1, t0, t1);
 
                /*
                lwnotice("Closest points: %g,%g,%g and %g,%g,%g at time %g",
                p0.x, p0.y, p0.z,
                q0.x, q0.y, q0.z, t);
                */
 
                dist2 = (q0.x - p0.x) * (q0.x - p0.x) + (q0.y - p0.y) * (q0.y - p0.y) + (q0.z - p0.z) * (q0.z - p0.z);
                if (dist2 <= maxdist2)
                {
                        LWDEBUGF(1, "Within distance %g at time %g, breaking", sqrt(dist2), t);
                        within = LW_TRUE;
                        break;
                }
        }
 
        /*
         * Release memory
         */
 
        lwfree(mvals);
 
        return within;
}