ptarray.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) 2012-2021 Sandro Santilli <strk@kbt.io>
 * Copyright (C) 2001-2006 Refractions Research Inc.
 *
 **********************************************************************/
 
 
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
 
#include "../postgis_config.h"
/*#define POSTGIS_DEBUG_LEVEL 4*/
#include "liblwgeom_internal.h"
#include "lwgeom_log.h"
 
int
ptarray_has_z(const POINTARRAY *pa)
{
        if ( ! pa ) return LW_FALSE;
        return FLAGS_GET_Z(pa->flags);
}
 
int
ptarray_has_m(const POINTARRAY *pa)
{
        if ( ! pa ) return LW_FALSE;
        return FLAGS_GET_M(pa->flags);
}
 
POINTARRAY*
ptarray_construct(char hasz, char hasm, uint32_t npoints)
{
        POINTARRAY *pa = ptarray_construct_empty(hasz, hasm, npoints);
        pa->npoints = npoints;
        return pa;
}
 
POINTARRAY*
ptarray_construct_empty(char hasz, char hasm, uint32_t maxpoints)
{
        POINTARRAY *pa = lwalloc(sizeof(POINTARRAY));
        pa->serialized_pointlist = NULL;
 
        /* Set our dimensionality info on the bitmap */
        pa->flags = lwflags(hasz, hasm, 0);
 
        /* We will be allocating a bit of room */
        pa->npoints = 0;
        pa->maxpoints = maxpoints;
 
        /* Allocate the coordinate array */
        if ( maxpoints > 0 )
                pa->serialized_pointlist = lwalloc(maxpoints * ptarray_point_size(pa));
        else
                pa->serialized_pointlist = NULL;
 
        return pa;
}
 
/*
* Add a point into a pointarray. Only adds as many dimensions as the
* pointarray supports.
*/
int
ptarray_insert_point(POINTARRAY *pa, const POINT4D *p, uint32_t where)
{
        if (!pa || !p)
                return LW_FAILURE;
        size_t point_size = ptarray_point_size(pa);
        LWDEBUGF(5,"pa = %p; p = %p; where = %d", pa, p, where);
        LWDEBUGF(5,"pa->npoints = %d; pa->maxpoints = %d", pa->npoints, pa->maxpoints);
 
        if ( FLAGS_GET_READONLY(pa->flags) )
        {
                lwerror("ptarray_insert_point: called on read-only point array");
                return LW_FAILURE;
        }
 
        /* Error on invalid offset value */
        if ( where > pa->npoints )
        {
                lwerror("ptarray_insert_point: offset out of range (%d)", where);
                return LW_FAILURE;
        }
 
        /* If we have no storage, let's allocate some */
        if( pa->maxpoints == 0 || ! pa->serialized_pointlist )
        {
                pa->maxpoints = 32;
                pa->npoints = 0;
                pa->serialized_pointlist = lwalloc(ptarray_point_size(pa) * pa->maxpoints);
        }
 
        /* Error out if we have a bad situation */
        if ( pa->npoints > pa->maxpoints )
        {
                lwerror("npoints (%d) is greater than maxpoints (%d)", pa->npoints, pa->maxpoints);
                return LW_FAILURE;
        }
 
        /* Check if we have enough storage, add more if necessary */
        if( pa->npoints == pa->maxpoints )
        {
                pa->maxpoints *= 2;
                pa->serialized_pointlist = lwrealloc(pa->serialized_pointlist, ptarray_point_size(pa) * pa->maxpoints);
        }
 
        /* Make space to insert the new point */
        if( where < pa->npoints )
        {
                size_t copy_size = point_size * (pa->npoints - where);
                memmove(getPoint_internal(pa, where+1), getPoint_internal(pa, where), copy_size);
                LWDEBUGF(5,"copying %zu bytes to start vertex %d from start vertex %d", copy_size, where+1, where);
        }
 
        /* We have one more point */
        ++pa->npoints;
 
        /* Copy the new point into the gap */
        ptarray_set_point4d(pa, where, p);
        LWDEBUGF(5,"copying new point to start vertex %zu", point_size);
 
        return LW_SUCCESS;
}
 
int
ptarray_append_point(POINTARRAY *pa, const POINT4D *pt, int repeated_points)
{
        /* Check for pathology */
        if( ! pa || ! pt )
        {
                lwerror("ptarray_append_point: null input");
                return LW_FAILURE;
        }
 
        /* Check for duplicate end point */
        if ( repeated_points == LW_FALSE && pa->npoints > 0 )
        {
                POINT4D tmp;
                getPoint4d_p(pa, pa->npoints-1, &tmp);
                LWDEBUGF(4,"checking for duplicate end point (pt = POINT(%g %g) pa->npoints-q = POINT(%g %g))",pt->x,pt->y,tmp.x,tmp.y);
 
                /* Return LW_SUCCESS and do nothing else if previous point in list is equal to this one */
                if ( (pt->x == tmp.x) && (pt->y == tmp.y) &&
                     (FLAGS_GET_Z(pa->flags) ? pt->z == tmp.z : 1) &&
                     (FLAGS_GET_M(pa->flags) ? pt->m == tmp.m : 1) )
                {
                        return LW_SUCCESS;
                }
        }
 
        /* Append is just a special case of insert */
        return ptarray_insert_point(pa, pt, pa->npoints);
}
 
int
ptarray_append_ptarray(POINTARRAY *pa1, POINTARRAY *pa2, double gap_tolerance)
{
        unsigned int poff = 0;
        unsigned int npoints;
        unsigned int ncap;
        unsigned int ptsize;
 
        /* Check for pathology */
        if( ! pa1 || ! pa2 )
        {
                lwerror("%s: null input", __func__);
                return LW_FAILURE;
        }
 
        npoints = pa2->npoints;
 
        if ( ! npoints ) return LW_SUCCESS; /* nothing more to do */
 
        if( FLAGS_GET_READONLY(pa1->flags) )
        {
                lwerror("%s: target pointarray is read-only", __func__);
                return LW_FAILURE;
        }
 
        if( FLAGS_GET_ZM(pa1->flags) != FLAGS_GET_ZM(pa2->flags) )
        {
                lwerror("%s: appending mixed dimensionality is not allowed", __func__);
                return LW_FAILURE;
        }
 
        ptsize = ptarray_point_size(pa1);
 
        /* Check for duplicate end point */
        if ( pa1->npoints )
        {
                const POINT2D *tmp1, *tmp2;
                tmp1 = getPoint2d_cp(pa1, pa1->npoints-1);
                tmp2 = getPoint2d_cp(pa2, 0);
 
                /* If the end point and start point are the same, then don't copy start point */
                if (p2d_same(tmp1, tmp2)) {
                        poff = 1;
                        --npoints;
                }
                else if ((gap_tolerance == 0) ||
                         (gap_tolerance > 0 && distance2d_pt_pt(tmp1, tmp2) > gap_tolerance) )
                {
                        lwerror("Second line start point too far from first line end point");
                        return LW_FAILURE;
                }
        }
 
        /* Check if we need extra space */
        ncap = pa1->npoints + npoints;
        if ( pa1->maxpoints < ncap )
        {
                if ( pa1->maxpoints )
                {
                        pa1->maxpoints = ncap > pa1->maxpoints*2 ?
                                                                                         ncap : pa1->maxpoints*2;
                        pa1->serialized_pointlist = lwrealloc(pa1->serialized_pointlist, (size_t)ptsize * pa1->maxpoints);
                }
                else
                {
                        pa1->maxpoints = ncap;
                        pa1->serialized_pointlist = lwalloc((size_t)ptsize * pa1->maxpoints);
                }
        }
 
        memcpy(getPoint_internal(pa1, pa1->npoints),
               getPoint_internal(pa2, poff), (size_t)ptsize * npoints);
 
        pa1->npoints = ncap;
 
        return LW_SUCCESS;
}
 
/*
* Add a point into a pointarray. Only adds as many dimensions as the
* pointarray supports.
*/
int
ptarray_remove_point(POINTARRAY *pa, uint32_t where)
{
        /* Check for pathology */
        if( ! pa )
        {
                lwerror("ptarray_remove_point: null input");
                return LW_FAILURE;
        }
 
        /* Error on invalid offset value */
        if ( where >= pa->npoints )
        {
                lwerror("ptarray_remove_point: offset out of range (%d)", where);
                return LW_FAILURE;
        }
 
        /* If the point is any but the last, we need to copy the data back one point */
        if (where < pa->npoints - 1)
                memmove(getPoint_internal(pa, where),
                        getPoint_internal(pa, where + 1),
                        ptarray_point_size(pa) * (pa->npoints - where - 1));
 
        /* We have one less point */
        pa->npoints--;
 
        return LW_SUCCESS;
}
 
POINTARRAY* ptarray_construct_reference_data(char hasz, char hasm, uint32_t npoints, uint8_t *ptlist)
{
        POINTARRAY *pa = lwalloc(sizeof(POINTARRAY));
        LWDEBUGF(5, "hasz = %d, hasm = %d, npoints = %d, ptlist = %p", hasz, hasm, npoints, ptlist);
        pa->flags = lwflags(hasz, hasm, 0);
        FLAGS_SET_READONLY(pa->flags, 1); /* We don't own this memory, so we can't alter or free it. */
        pa->npoints = npoints;
        pa->maxpoints = npoints;
        pa->serialized_pointlist = ptlist;
        return pa;
}
 
 
POINTARRAY*
ptarray_construct_copy_data(char hasz, char hasm, uint32_t npoints, const uint8_t *ptlist)
{
        POINTARRAY *pa = lwalloc(sizeof(POINTARRAY));
 
        pa->flags = lwflags(hasz, hasm, 0);
        pa->npoints = npoints;
        pa->maxpoints = npoints;
 
        if ( npoints > 0 )
        {
                pa->serialized_pointlist = lwalloc(ptarray_point_size(pa) * npoints);
                memcpy(pa->serialized_pointlist, ptlist, ptarray_point_size(pa) * npoints);
        }
        else
        {
                pa->serialized_pointlist = NULL;
        }
 
        return pa;
}
 
void
ptarray_free(POINTARRAY *pa)
{
        if (pa)
        {
                if (pa->serialized_pointlist && (!FLAGS_GET_READONLY(pa->flags)))
                        lwfree(pa->serialized_pointlist);
                lwfree(pa);
        }
}
 
 
void
ptarray_reverse_in_place(POINTARRAY *pa)
{
        if (!pa->npoints)
                return;
        uint32_t i;
        uint32_t last = pa->npoints - 1;
        uint32_t mid = pa->npoints / 2;
 
        double *d = (double*)(pa->serialized_pointlist);
        int j;
        int ndims = FLAGS_NDIMS(pa->flags);
        for (i = 0; i < mid; i++)
        {
                for (j = 0; j < ndims; j++)
                {
                        double buf;
                        buf = d[i*ndims+j];
                        d[i*ndims+j] = d[(last-i)*ndims+j];
                        d[(last-i)*ndims+j] = buf;
                }
        }
        return;
}
 
 
POINTARRAY*
ptarray_flip_coordinates(POINTARRAY *pa)
{
        uint32_t i;
        double d;
        POINT4D p;
 
        for (i=0 ; i < pa->npoints ; i++)
        {
                getPoint4d_p(pa, i, &p);
                d = p.y;
                p.y = p.x;
                p.x = d;
                ptarray_set_point4d(pa, i, &p);
        }
 
        return pa;
}
 
void
ptarray_swap_ordinates(POINTARRAY *pa, LWORD o1, LWORD o2)
{
        uint32_t i;
        double d, *dp1, *dp2;
        POINT4D p;
 
        dp1 = ((double*)&p)+(unsigned)o1;
        dp2 = ((double*)&p)+(unsigned)o2;
        for (i=0 ; i < pa->npoints ; i++)
        {
                getPoint4d_p(pa, i, &p);
                d = *dp2;
                *dp2 = *dp1;
                *dp1 = d;
                ptarray_set_point4d(pa, i, &p);
        }
}
 
POINTARRAY *
ptarray_segmentize2d(const POINTARRAY *ipa, double dist)
{
        double segdist;
        POINT4D p1, p2;
        POINT4D pbuf;
        POINTARRAY *opa;
        uint32_t i, j, nseg;
        int hasz = FLAGS_GET_Z(ipa->flags);
        int hasm = FLAGS_GET_M(ipa->flags);
 
        pbuf.x = pbuf.y = pbuf.z = pbuf.m = 0;
 
        /* Initial storage */
        opa = ptarray_construct_empty(hasz, hasm, ipa->npoints);
 
        /* Add first point */
        getPoint4d_p(ipa, 0, &p1);
        ptarray_append_point(opa, &p1, LW_FALSE);
 
        /* Loop on all other input points */
        for (i = 1; i < ipa->npoints; i++)
        {
                /*
                 * We use these pointers to avoid
                 * "strict-aliasing rules break" warning raised
                 * by gcc (3.3 and up).
                 *
                 * It looks that casting a variable address (also
                 * referred to as "type-punned pointer")
                 * breaks those "strict" rules.
                 */
                POINT4D *p1ptr=&p1, *p2ptr=&p2;
                double segments;
 
                getPoint4d_p(ipa, i, &p2);
 
                segdist = distance2d_pt_pt((POINT2D *)p1ptr, (POINT2D *)p2ptr);
                /* Split input segment into shorter even chunks */
                segments = ceil(segdist / dist);
 
                /* Uses INT32_MAX instead of UINT32_MAX to be safe that it fits */
                if (segments >= INT32_MAX)
                {
                        lwnotice("%s:%d - %s: Too many segments required (%e)",
                                __FILE__, __LINE__,__func__, segments);
                        ptarray_free(opa);
                        return NULL;
                }
                nseg = segments;
 
                for (j = 1; j < nseg; j++)
                {
                        pbuf.x = p1.x + (p2.x - p1.x) * j / nseg;
                        pbuf.y = p1.y + (p2.y - p1.y) * j / nseg;
                        if (hasz)
                                pbuf.z = p1.z + (p2.z - p1.z) * j / nseg;
                        if (hasm)
                                pbuf.m = p1.m + (p2.m - p1.m) * j / nseg;
                        ptarray_append_point(opa, &pbuf, LW_FALSE);
                        LW_ON_INTERRUPT(ptarray_free(opa); return NULL);
                }
 
                ptarray_append_point(opa, &p2, (ipa->npoints == 2) ? LW_TRUE : LW_FALSE);
                p1 = p2;
                LW_ON_INTERRUPT(ptarray_free(opa); return NULL);
        }
 
        return opa;
}
 
char
ptarray_same(const POINTARRAY *pa1, const POINTARRAY *pa2)
{
        uint32_t i;
        size_t ptsize;
 
        if ( FLAGS_GET_ZM(pa1->flags) != FLAGS_GET_ZM(pa2->flags) ) return LW_FALSE;
        LWDEBUG(5,"dimensions are the same");
 
        if ( pa1->npoints != pa2->npoints ) return LW_FALSE;
        LWDEBUG(5,"npoints are the same");
 
        ptsize = ptarray_point_size(pa1);
        LWDEBUGF(5, "ptsize = %zu", ptsize);
 
        for (i=0; i<pa1->npoints; i++)
        {
                if ( memcmp(getPoint_internal(pa1, i), getPoint_internal(pa2, i), ptsize) )
                        return LW_FALSE;
                LWDEBUGF(5,"point #%d is the same",i);
        }
 
        return LW_TRUE;
}
 
char
ptarray_same2d(const POINTARRAY *pa1, const POINTARRAY *pa2)
{
        uint32_t i;
 
        if ( FLAGS_GET_ZM(pa1->flags) != FLAGS_GET_ZM(pa2->flags) ) return LW_FALSE;
        LWDEBUG(5,"dimensions are the same");
 
        if ( pa1->npoints != pa2->npoints ) return LW_FALSE;
        LWDEBUG(5,"npoints are the same");
 
        for (i=0; i<pa1->npoints; i++)
        {
                if ( memcmp(getPoint_internal(pa1, i), getPoint_internal(pa2, i), sizeof(POINT2D)) )
                        return LW_FALSE;
                LWDEBUGF(5,"point #%d is the same",i);
        }
 
        return LW_TRUE;
}
 
POINTARRAY *
ptarray_addPoint(const POINTARRAY *pa, uint8_t *p, size_t pdims, uint32_t where)
{
        POINTARRAY *ret;
        POINT4D pbuf;
        size_t ptsize = ptarray_point_size(pa);
 
        LWDEBUGF(3, "pa %p p %p size %zu where %u",
                 pa, p, pdims, where);
 
        if ( pdims < 2 || pdims > 4 )
        {
                lwerror("ptarray_addPoint: point dimension out of range (%zu)",
                        pdims);
                return NULL;
        }
 
        if ( where > pa->npoints )
        {
                lwerror("ptarray_addPoint: offset out of range (%d)",
                        where);
                return NULL;
        }
 
        LWDEBUG(3, "called with a point");
 
        pbuf.x = pbuf.y = pbuf.z = pbuf.m = 0.0;
        memcpy((uint8_t *)&pbuf, p, pdims*sizeof(double));
 
        LWDEBUG(3, "initialized point buffer");
 
        ret = ptarray_construct(FLAGS_GET_Z(pa->flags),
                                FLAGS_GET_M(pa->flags), pa->npoints+1);
 
 
        if ( where )
        {
                memcpy(getPoint_internal(ret, 0), getPoint_internal(pa, 0), ptsize*where);
        }
 
        memcpy(getPoint_internal(ret, where), (uint8_t *)&pbuf, ptsize);
 
        if ( where+1 != ret->npoints )
        {
                memcpy(getPoint_internal(ret, where+1),
                       getPoint_internal(pa, where),
                       ptsize*(pa->npoints-where));
        }
 
        return ret;
}
 
POINTARRAY *
ptarray_removePoint(POINTARRAY *pa, uint32_t which)
{
        POINTARRAY *ret;
        size_t ptsize = ptarray_point_size(pa);
 
        LWDEBUGF(3, "pa %p which %u", pa, which);
 
        assert(which <= pa->npoints-1);
        assert(pa->npoints >= 3);
 
        ret = ptarray_construct(FLAGS_GET_Z(pa->flags),
                                FLAGS_GET_M(pa->flags), pa->npoints-1);
 
        /* copy initial part */
        if ( which )
        {
                memcpy(getPoint_internal(ret, 0), getPoint_internal(pa, 0), ptsize*which);
        }
 
        /* copy final part */
        if ( which < pa->npoints-1 )
        {
                memcpy(getPoint_internal(ret, which), getPoint_internal(pa, which+1),
                       ptsize*(pa->npoints-which-1));
        }
 
        return ret;
}
 
POINTARRAY *
ptarray_merge(POINTARRAY *pa1, POINTARRAY *pa2)
{
        POINTARRAY *pa;
        size_t ptsize = ptarray_point_size(pa1);
 
        if (FLAGS_GET_ZM(pa1->flags) != FLAGS_GET_ZM(pa2->flags))
                lwerror("ptarray_cat: Mixed dimension");
 
        pa = ptarray_construct( FLAGS_GET_Z(pa1->flags),
                                FLAGS_GET_M(pa1->flags),
                                pa1->npoints + pa2->npoints);
 
        memcpy(         getPoint_internal(pa, 0),
                        getPoint_internal(pa1, 0),
                        ptsize*(pa1->npoints));
 
        memcpy(         getPoint_internal(pa, pa1->npoints),
                        getPoint_internal(pa2, 0),
                        ptsize*(pa2->npoints));
 
        ptarray_free(pa1);
        ptarray_free(pa2);
 
        return pa;
}
 
 
POINTARRAY *
ptarray_clone_deep(const POINTARRAY *in)
{
        POINTARRAY *out = lwalloc(sizeof(POINTARRAY));
 
        LWDEBUG(3, "ptarray_clone_deep called.");
 
        out->flags = in->flags;
        out->npoints = in->npoints;
        out->maxpoints = in->npoints;
 
        FLAGS_SET_READONLY(out->flags, 0);
 
        if (!in->npoints)
        {
                // Avoid calling lwalloc of 0 bytes
                out->serialized_pointlist = NULL;
        }
        else
        {
                size_t size = in->npoints * ptarray_point_size(in);
                out->serialized_pointlist = lwalloc(size);
                memcpy(out->serialized_pointlist, in->serialized_pointlist, size);
        }
 
        return out;
}
 
POINTARRAY *
ptarray_clone(const POINTARRAY *in)
{
        POINTARRAY *out = lwalloc(sizeof(POINTARRAY));
 
        LWDEBUG(3, "ptarray_clone called.");
 
        out->flags = in->flags;
        out->npoints = in->npoints;
        out->maxpoints = in->maxpoints;
 
        FLAGS_SET_READONLY(out->flags, 1);
 
        out->serialized_pointlist = in->serialized_pointlist;
 
        return out;
}
 
int
ptarray_is_closed(const POINTARRAY *in)
{
        if (!in)
        {
                lwerror("ptarray_is_closed: called with null point array");
                return 0;
        }
        if (in->npoints <= 1 ) return in->npoints; /* single-point are closed, empty not closed */
 
        return 0 == memcmp(getPoint_internal(in, 0), getPoint_internal(in, in->npoints-1), ptarray_point_size(in));
}
 
 
int
ptarray_is_closed_2d(const POINTARRAY *in)
{
        if (!in)
        {
                lwerror("ptarray_is_closed_2d: called with null point array");
                return 0;
        }
        if (in->npoints <= 1 ) return in->npoints; /* single-point are closed, empty not closed */
 
        return 0 == memcmp(getPoint_internal(in, 0), getPoint_internal(in, in->npoints-1), sizeof(POINT2D) );
}
 
int
ptarray_is_closed_3d(const POINTARRAY *in)
{
        if (!in)
        {
                lwerror("ptarray_is_closed_3d: called with null point array");
                return 0;
        }
        if (in->npoints <= 1 ) return in->npoints; /* single-point are closed, empty not closed */
 
        return 0 == memcmp(getPoint_internal(in, 0), getPoint_internal(in, in->npoints-1), sizeof(POINT3D) );
}
 
int
ptarray_is_closed_z(const POINTARRAY *in)
{
        if ( FLAGS_GET_Z(in->flags) )
                return ptarray_is_closed_3d(in);
        else
                return ptarray_is_closed_2d(in);
}
 
int
ptarray_contains_point(const POINTARRAY *pa, const POINT2D *pt)
{
        const POINT2D *seg1, *seg2;
        int wn = 0;
 
        seg1 = getPoint2d_cp(pa, 0);
        seg2 = getPoint2d_cp(pa, pa->npoints-1);
        if (!p2d_same(seg1, seg2))
                lwerror("ptarray_contains_point called on unclosed ring");
 
        for (uint32_t i = 1; i < pa->npoints; i++)
        {
                double side, ymin, ymax;
 
                seg2 = getPoint2d_cp(pa, i);
 
                /* Zero length segments are ignored. */
                if (p2d_same(seg1, seg2))
                {
                        seg1 = seg2;
                        continue;
                }
 
                ymin = FP_MIN(seg1->y, seg2->y);
                ymax = FP_MAX(seg1->y, seg2->y);
 
                /* Only test segments in our vertical range */
                if (pt->y > ymax || pt->y < ymin)
                {
                        seg1 = seg2;
                        continue;
                }
 
                side = lw_segment_side(seg1, seg2, pt);
 
                /*
                * A point on the boundary of a ring is not contained.
                * WAS: if (fabs(side) < 1e-12), see #852
                */
                if ((side == 0) && lw_pt_in_seg(pt, seg1, seg2))
                {
                        return LW_BOUNDARY;
                }
 
                /*
                * If the point is to the left of the line, and it's rising,
                * then the line is to the right of the point and
                * circling counter-clockwise, so increment.
                */
                if ((side < 0) && (seg1->y <= pt->y) && (pt->y < seg2->y))
                {
                        wn++;
                }
 
                /*
                * If the point is to the right of the line, and it's falling,
                * then the line is to the right of the point and circling
                * clockwise, so decrement.
                */
                else if ( (side > 0) && (seg2->y <= pt->y) && (pt->y < seg1->y) )
                {
                        wn--;
                }
 
                seg1 = seg2;
        }
 
        /* wn == 0 => Outside, wn != 0 => Inside */
        return wn == 0 ? LW_OUTSIDE : LW_INSIDE;
}
 
int
ptarray_raycast_intersections(const POINTARRAY *pa, const POINT2D *p, int *on_boundary)
{
        // A valid linestring must have at least 2 point
        if (pa->npoints < 2)
                lwerror("%s called on invalid linestring", __func__);
 
        int intersections = 0;
        double px = p->x;
        double py = p->y;
 
        // Iterate through each edge of the polygon
        for (uint32_t i = 0; i < pa->npoints-1; ++i)
        {
                const POINT2D* p1 = getPoint2d_cp(pa, i);
                const POINT2D* p2 = getPoint2d_cp(pa, i+1);
 
                /* Skip zero-length edges */
                if (p2d_same(p1, p2))
                        continue;
 
                /* --- Step 1: Check if the point is ON the boundary edge --- */
                if (lw_pt_on_segment(p1, p2, p))
                {
                        *on_boundary = LW_TRUE;
                        return 0;
                }
 
                /* --- Step 2: Perform the Ray Casting intersection test --- */
 
                /*
                 * Check if the horizontal ray from p intersects the edge (p1, p2).
                 * This is the core condition for handling vertices correctly:
                 *   - One vertex must be strictly above the ray (py < vertex.y)
                 *   - The other must be on or below the ray (py >= vertex.y)
                 */
                if (((p1->y <= py) && (py < p2->y)) || ((p2->y <= py) && (py < p1->y)))
                {
                        /*
                         * Calculate the x-coordinate where the edge intersects the ray's horizontal line.
                         * Formula: x = x1 + (y - y1) * (x2 - x1) / (y2 - y1)
                         */
                        double x_intersection = p1->x + (py - p1->y) * (p2->x - p1->x) / (p2->y - p1->y);
 
                        /*
                         * If the intersection point is to the right of our test point,
                         * it's a valid "crossing".
                         */
                        if (x_intersection > px)
                        {
                                intersections++;
                        }
                }
        }
 
        return intersections;
}
 
 
static int
circle_raycast_intersections(const POINT2D *center, double radius, double ray, POINT2D *i0, POINT2D *i1)
{
        // Calculate the vertical distance from the circle's center to the horizontal line.
        double dy = ray - center->y;
 
        // If the absolute vertical distance is greater than the radius, there are no intersections.
        if (fabs(dy) > radius)
                return 0;
 
        // Use the Pythagorean theorem to find the horizontal distance (dx) from the
        // center's x-coordinate to the intersection points.
        // dx^2 + dy^2 = radius^2  =>  dx^2 = radius^2 - dy^2
        double dx_squared = radius * radius - dy * dy;
 
        // Case 1: One intersection (tangent)
        // This occurs when the line just touches the top or bottom of the circle.
        // dx_squared will be zero. We check against a small epsilon for floating-point safety.
        if (FP_EQUALS(dx_squared, 0.0))
        {
                i0->x = center->x;
                i0->y = ray;
                return 1;
        }
 
        // Case 2: Two intersections
        // The line cuts through the circle.
        double dx = sqrt(dx_squared);
 
        // The first intersection point has the smaller x-value.
        i0->x = center->x - dx;
        i0->y = ray;
 
        // The second intersection point has the larger x-value.
        i1->x = center->x + dx;
        i1->y = ray;
 
        return 2;
}
 
 
int
ptarrayarc_raycast_intersections(const POINTARRAY *pa, const POINT2D *p, int *on_boundary)
{
        int intersections = 0;
        double px = p->x;
        double py = p->y;
 
        assert(on_boundary);
 
        // A valid circular arc must have at least 3 vertices (circle).
        if (pa->npoints < 3)
                lwerror("%s called on invalid circularstring", __func__);
 
        if (pa->npoints % 2 == 0)
                lwerror("%s called with even number of points", __func__);
 
        // Iterate through each arc of the circularstring
        for (uint32_t i = 1; i < pa->npoints-1; i +=2)
        {
                const POINT2D* p0 = getPoint2d_cp(pa, i-1);
                const POINT2D* p1 = getPoint2d_cp(pa, i);
                const POINT2D* p2 = getPoint2d_cp(pa, i+1);
                POINT2D center = {0,0};
                double radius, d;
                GBOX gbox;
 
                // Skip zero-length arc
                if (lw_arc_is_pt(p0, p1, p2))
                        continue;
 
                // --- Step 1: Check if the point is ON the boundary edge ---
                if (p2d_same(p0, p) || p2d_same(p1, p) || p2d_same(p2, p))
                {
                        *on_boundary = LW_TRUE;
                        return 0;
                }
 
                // Calculate some important pieces
                radius = lw_arc_center(p0, p1, p2, &center);
 
                d = distance2d_pt_pt(p, &center);
                if (FP_EQUALS(d, radius) && lw_pt_in_arc(p, p0, p1, p2))
                {
                        *on_boundary = LW_TRUE;
                        return 0;
                }
 
                // --- Step 2: Perform the Ray Casting intersection test ---
 
                // Only process arcs that our ray crosses
                lw_arc_calculate_gbox_cartesian_2d(p0, p1, p2, &gbox);
                if ((gbox.ymin <= py) && (py < gbox.ymax))
                {
                        // Point of intersection on the circle that defines the arc
                        POINT2D i0, i1;
 
                        // How many points of intersection are there
                        int iCount = circle_raycast_intersections(&center, radius, py, &i0, &i1);
 
                        // Nothing to see here
                        if (iCount == 0)
                                continue;
 
                        // Cannot think of a case where a grazing is not a
                        // no-op
                        if (iCount == 1)
                                continue;
 
                        // So we must have 2 intersections
                        // Only increment the counter for intersections to the right
                        // of the test point
                        if (i0.x > px && lw_pt_in_arc(&i0, p0, p1, p2))
                                intersections++;
 
                        if (i1.x > px && lw_pt_in_arc(&i1, p0, p1, p2))
                                intersections++;
                }
        }
 
        return intersections;
}
 
/*
 * The following is based on the "Fast Winding Number Inclusion of a Point
 * in a Polygon" algorithm by Dan Sunday.
 * http://softsurfer.com/Archive/algorithm_0103/algorithm_0103.htm#Winding%20Number
 */
int
ptarray_contains_point_partial(const POINTARRAY *pa, const POINT2D *pt, int check_closed, int *winding_number)
{
        int wn = 0;
        uint32_t i;
        double side;
        const POINT2D *seg1, *seg2;
        double ymin, ymax;
 
        seg1 = getPoint2d_cp(pa, 0);
        seg2 = getPoint2d_cp(pa, pa->npoints-1);
        if ( check_closed && ! p2d_same(seg1, seg2) )
                lwerror("ptarray_contains_point called on unclosed ring");
 
        for ( i=1; i < pa->npoints; i++ )
        {
                seg2 = getPoint2d_cp(pa, i);
 
                /* Zero length segments are ignored. */
                if ( seg1->x == seg2->x && seg1->y == seg2->y )
                {
                        seg1 = seg2;
                        continue;
                }
 
                ymin = FP_MIN(seg1->y, seg2->y);
                ymax = FP_MAX(seg1->y, seg2->y);
 
                /* Only test segments in our vertical range */
                if ( pt->y > ymax || pt->y < ymin )
                {
                        seg1 = seg2;
                        continue;
                }
 
                side = lw_segment_side(seg1, seg2, pt);
 
                /*
                * A point on the boundary of a ring is not contained.
                * WAS: if (fabs(side) < 1e-12), see #852
                */
                if ( (side == 0) && lw_pt_in_seg(pt, seg1, seg2) )
                {
                        return LW_BOUNDARY;
                }
 
                /*
                * If the point is to the left of the line, and it's rising,
                * then the line is to the right of the point and
                * circling counter-clockwise, so increment.
                */
                if ( (side < 0) && (seg1->y <= pt->y) && (pt->y < seg2->y) )
                {
                        wn++;
                }
 
                /*
                * If the point is to the right of the line, and it's falling,
                * then the line is to the right of the point and circling
                * clockwise, so decrement.
                */
                else if ( (side > 0) && (seg2->y <= pt->y) && (pt->y < seg1->y) )
                {
                        wn--;
                }
 
                seg1 = seg2;
        }
 
        /* Sent out the winding number for calls that are building on this as a primitive */
        if ( winding_number )
                *winding_number = wn;
 
        /* Outside */
        if (wn == 0)
        {
                return LW_OUTSIDE;
        }
 
        /* Inside */
        return LW_INSIDE;
}
 
int
ptarrayarc_contains_point(const POINTARRAY *pa, const POINT2D *pt)
{
        int on_boundary = LW_FALSE;
        int intersections;
        if (!ptarray_is_closed_2d(pa))
                lwerror("%s called on unclosed ring", __func__);
 
        intersections = ptarrayarc_raycast_intersections(pa, pt, &on_boundary);
        if (on_boundary)
                return LW_BOUNDARY;
        else
                return (intersections % 2) ? LW_INSIDE : LW_OUTSIDE;
}
 
double
ptarray_signed_area(const POINTARRAY *pa)
{
        const POINT2D *P1;
        const POINT2D *P2;
        const POINT2D *P3;
        double sum = 0.0;
        double x0, x, y1, y2;
        uint32_t i;
 
        if (! pa || pa->npoints < 3 )
                return 0.0;
 
        P1 = getPoint2d_cp(pa, 0);
        P2 = getPoint2d_cp(pa, 1);
        x0 = P1->x;
        for ( i = 2; i < pa->npoints; i++ )
        {
                P3 = getPoint2d_cp(pa, i);
                x = P2->x - x0;
                y1 = P3->y;
                y2 = P1->y;
                sum += x * (y2-y1);
 
                /* Move forwards! */
                P1 = P2;
                P2 = P3;
        }
        return sum / 2.0;
}
 
int
ptarray_has_orientation(const POINTARRAY *pa, int orientation)
{
        if (ptarray_signed_area(pa) > 0)
                return orientation == LW_CLOCKWISE;
        else
                return orientation == LW_COUNTERCLOCKWISE;
}
 
int ptarray_isccw(const POINTARRAY *pa)
{
        return ptarray_has_orientation(pa, LW_COUNTERCLOCKWISE);
}
 
POINTARRAY*
ptarray_force_dims(const POINTARRAY *pa, int hasz, int hasm, double zval, double mval)
{
        /* TODO handle zero-length point arrays */
        uint32_t i;
        int in_hasz = FLAGS_GET_Z(pa->flags);
        int in_hasm = FLAGS_GET_M(pa->flags);
        POINT4D pt;
        POINTARRAY *pa_out = ptarray_construct_empty(hasz, hasm, pa->npoints);
 
        for( i = 0; i < pa->npoints; i++ )
        {
                getPoint4d_p(pa, i, &pt);
                if( hasz && ! in_hasz )
                        pt.z = zval;
                if( hasm && ! in_hasm )
                        pt.m = mval;
                ptarray_append_point(pa_out, &pt, LW_TRUE);
        }
 
        return pa_out;
}
 
POINTARRAY *
ptarray_substring(POINTARRAY *ipa, double from, double to, double tolerance)
{
        POINTARRAY *dpa;
        POINT4D pt;
        POINT4D p1, p2;
        POINT4D *p1ptr=&p1; /* don't break strict-aliasing rule */
        POINT4D *p2ptr=&p2;
        int nsegs, i;
        double length, slength, tlength;
        int state = 0; /* 0=before, 1=inside */
 
        /*
         * Create a dynamic pointarray with an initial capacity
         * equal to full copy of input points
         */
        dpa = ptarray_construct_empty(FLAGS_GET_Z(ipa->flags), FLAGS_GET_M(ipa->flags), ipa->npoints);
 
        /* Compute total line length */
        length = ptarray_length_2d(ipa);
 
 
        LWDEBUGF(3, "Total length: %g", length);
 
 
        /* Get 'from' and 'to' lengths */
        from = length*from;
        to = length*to;
 
 
        LWDEBUGF(3, "From/To: %g/%g", from, to);
 
 
        tlength = 0;
        getPoint4d_p(ipa, 0, &p1);
        nsegs = ipa->npoints - 1;
        for ( i = 0; i < nsegs; i++ )
        {
                double dseg;
 
                getPoint4d_p(ipa, i+1, &p2);
 
 
                LWDEBUGF(3 ,"Segment %d: (%g,%g,%g,%g)-(%g,%g,%g,%g)",
                         i, p1.x, p1.y, p1.z, p1.m, p2.x, p2.y, p2.z, p2.m);
 
 
                /* Find the length of this segment */
                slength = distance2d_pt_pt((POINT2D *)p1ptr, (POINT2D *)p2ptr);
 
                /*
                 * We are before requested start.
                 */
                if ( state == 0 ) /* before */
                {
 
                        LWDEBUG(3, " Before start");
 
                        if ( fabs ( from - ( tlength + slength ) ) <= tolerance )
                        {
 
                                LWDEBUG(3, "  Second point is our start");
 
                                /*
                                 * Second point is our start
                                 */
                                ptarray_append_point(dpa, &p2, LW_FALSE);
                                state=1; /* we're inside now */
                                goto END;
                        }
 
                        else if ( fabs(from - tlength) <= tolerance )
                        {
 
                                LWDEBUG(3, "  First point is our start");
 
                                /*
                                 * First point is our start
                                 */
                                ptarray_append_point(dpa, &p1, LW_FALSE);
 
                                /*
                                 * We're inside now, but will check
                                 * 'to' point as well
                                 */
                                state=1;
                        }
 
                        /*
                         * Didn't reach the 'from' point,
                         * nothing to do
                         */
                        else if ( from > tlength + slength ) goto END;
 
                        else  /* tlength < from < tlength+slength */
                        {
 
                                LWDEBUG(3, "  Seg contains first point");
 
                                /*
                                 * Our start is between first and
                                 * second point
                                 */
                                dseg = (from - tlength) / slength;
 
                                interpolate_point4d(&p1, &p2, &pt, dseg);
 
                                ptarray_append_point(dpa, &pt, LW_FALSE);
 
                                /*
                                 * We're inside now, but will check
                                 * 'to' point as well
                                 */
                                state=1;
                        }
                }
 
                if ( state == 1 ) /* inside */
                {
 
                        LWDEBUG(3, " Inside");
 
                        /*
                         * 'to' point is our second point.
                         */
                        if ( fabs(to - ( tlength + slength ) ) <= tolerance )
                        {
 
                                LWDEBUG(3, " Second point is our end");
 
                                ptarray_append_point(dpa, &p2, LW_FALSE);
                                break; /* substring complete */
                        }
 
                        /*
                         * 'to' point is our first point.
                         * (should only happen if 'to' is 0)
                         */
                        else if ( fabs(to - tlength) <= tolerance )
                        {
 
                                LWDEBUG(3, " First point is our end");
 
                                ptarray_append_point(dpa, &p1, LW_FALSE);
 
                                break; /* substring complete */
                        }
 
                        /*
                         * Didn't reach the 'end' point,
                         * just copy second point
                         */
                        else if ( to > tlength + slength )
                        {
                                ptarray_append_point(dpa, &p2, LW_FALSE);
                                goto END;
                        }
 
                        /*
                         * 'to' point falls on this segment
                         * Interpolate and break.
                         */
                        else if ( to < tlength + slength )
                        {
 
                                LWDEBUG(3, " Seg contains our end");
 
                                dseg = (to - tlength) / slength;
                                interpolate_point4d(&p1, &p2, &pt, dseg);
 
                                ptarray_append_point(dpa, &pt, LW_FALSE);
 
                                break;
                        }
 
                        else
                        {
                                LWDEBUG(3, "Unhandled case");
                        }
                }
 
 
END:
 
                tlength += slength;
                memcpy(&p1, &p2, sizeof(POINT4D));
        }
 
        LWDEBUGF(3, "Out of loop, ptarray has %d points", dpa->npoints);
 
        return dpa;
}
 
/*
 * Write into the *ret argument coordinates of the closes point on
 * the given segment to the reference input point.
 */
void
closest_point_on_segment(const POINT4D *p, const POINT4D *A, const POINT4D *B, POINT4D *ret)
{
        double r;
 
        if (  FP_EQUALS(A->x, B->x) && FP_EQUALS(A->y, B->y) )
        {
                *ret = *A;
                return;
        }
 
        /*
         * We use comp.graphics.algorithms Frequently Asked Questions method
         *
         * (1)           AC dot AB
         *           r = ----------
         *                ||AB||^2
         *      r has the following meaning:
         *      r=0 P = A
         *      r=1 P = B
         *      r<0 P is on the backward extension of AB
         *      r>1 P is on the forward extension of AB
         *      0<r<1 P is interior to AB
         *
         */
        r = ( (p->x-A->x) * (B->x-A->x) + (p->y-A->y) * (B->y-A->y) )/( (B->x-A->x)*(B->x-A->x) +(B->y-A->y)*(B->y-A->y) );
 
        if (r<=0)
        {
                *ret = *A;
                return;
        }
        if (r>=1)
        {
                *ret = *B;
                return;
        }
 
        ret->x = A->x + ( (B->x - A->x) * r );
        ret->y = A->y + ( (B->y - A->y) * r );
        ret->z = A->z + ( (B->z - A->z) * r );
        ret->m = A->m + ( (B->m - A->m) * r );
}
 
int
ptarray_closest_segment_2d(const POINTARRAY *pa, const POINT2D *qp, double *dist)
{
        const POINT2D *start = getPoint2d_cp(pa, 0), *end = NULL;
        uint32_t t, seg=0;
        double mindist=DBL_MAX;
 
        /* Loop through pointarray looking for nearest segment */
        for (t=1; t<pa->npoints; t++)
        {
                double dist_sqr;
                end = getPoint2d_cp(pa, t);
                dist_sqr = distance2d_sqr_pt_seg(qp, start, end);
 
                if (dist_sqr < mindist)
                {
                        mindist = dist_sqr;
                        seg=t-1;
                        if ( mindist == 0 )
                        {
                                LWDEBUG(3, "Breaking on mindist=0");
                                break;
                        }
                }
 
                start = end;
        }
 
        if ( dist ) *dist = sqrt(mindist);
        return seg;
}
 
 
int
ptarray_closest_vertex_2d(const POINTARRAY *pa, const POINT2D *qp, double *dist)
{
        uint32_t t, pn=0;
        const POINT2D *p;
        double mindist = DBL_MAX;
 
        /* Loop through pointarray looking for nearest segment */
        for (t=0; t<pa->npoints; t++)
        {
                double dist_sqr;
                p = getPoint2d_cp(pa, t);
                dist_sqr = distance2d_sqr_pt_pt(p, qp);
 
                if (dist_sqr < mindist)
                {
                        mindist = dist_sqr;
                        pn = t;
                        if ( mindist == 0 )
                        {
                                LWDEBUG(3, "Breaking on mindist=0");
                                break;
                        }
                }
        }
        if ( dist ) *dist = sqrt(mindist);
        return pn;
}
 
/*
 * Given a point, returns the location of closest point on pointarray
 * and, optionally, it's actual distance from the point array.
 */
double
ptarray_locate_point(const POINTARRAY *pa, const POINT4D *p4d, double *mindistout, POINT4D *proj4d)
{
        double mindist=DBL_MAX;
        double tlen, plen;
        uint32_t t, seg=0;
        POINT4D start4d, end4d, projtmp;
        POINT2D proj, p;
        const POINT2D *start = NULL, *end = NULL;
 
        /* Initialize our 2D copy of the input parameter */
        p.x = p4d->x;
        p.y = p4d->y;
 
        if ( ! proj4d ) proj4d = &projtmp;
 
        /* Check for special cases (length 0 and 1) */
        if ( pa->npoints <= 1 )
        {
                if ( pa->npoints == 1 )
                {
                        getPoint4d_p(pa, 0, proj4d);
                        if ( mindistout )
                                *mindistout = distance2d_pt_pt(&p, getPoint2d_cp(pa, 0));
                }
                return 0.0;
        }
 
        start = getPoint2d_cp(pa, 0);
        /* Loop through pointarray looking for nearest segment */
        for (t=1; t<pa->npoints; t++)
        {
                double dist_sqr;
                end = getPoint2d_cp(pa, t);
                dist_sqr = distance2d_sqr_pt_seg(&p, start, end);
 
                if (dist_sqr < mindist)
                {
                        mindist = dist_sqr;
                        seg=t-1;
                        if ( mindist == 0 )
                        {
                                LWDEBUG(3, "Breaking on mindist=0");
                                break;
                        }
                }
 
                start = end;
        }
        mindist = sqrt(mindist);
 
        if ( mindistout ) *mindistout = mindist;
 
        LWDEBUGF(3, "Closest segment: %d", seg);
        LWDEBUGF(3, "mindist: %g", mindist);
 
        /*
         * We need to project the
         * point on the closest segment.
         */
        getPoint4d_p(pa, seg, &start4d);
        getPoint4d_p(pa, seg+1, &end4d);
        closest_point_on_segment(p4d, &start4d, &end4d, proj4d);
 
        /* Copy 4D values into 2D holder */
        proj.x = proj4d->x;
        proj.y = proj4d->y;
 
        LWDEBUGF(3, "Closest segment:%d, npoints:%d", seg, pa->npoints);
 
        /* For robustness, force 1 when closest point == endpoint */
        if ( (seg >= (pa->npoints-2)) && p2d_same(&proj, end) )
        {
                return 1.0;
        }
 
        LWDEBUGF(3, "Closest point on segment: %g,%g", proj.x, proj.y);
 
        tlen = ptarray_length_2d(pa);
 
        LWDEBUGF(3, "tlen %g", tlen);
 
        /* Location of any point on a zero-length line is 0 */
        /* See http://trac.osgeo.org/postgis/ticket/1772#comment:2 */
        if ( tlen == 0 ) return 0;
 
        plen=0;
        start = getPoint2d_cp(pa, 0);
        for (t=0; t<seg; t++, start=end)
        {
                end = getPoint2d_cp(pa, t+1);
                plen += distance2d_pt_pt(start, end);
 
                LWDEBUGF(4, "Segment %d made plen %g", t, plen);
        }
 
        plen+=distance2d_pt_pt(&proj, start);
 
        LWDEBUGF(3, "plen %g, tlen %g", plen, tlen);
 
        /* Floating point arithmetic is not reliable, make sure we return values [0,1] */
        double result = plen / tlen;
        if ( result < 0.0 ) {
                result = 0.0;
        } else if ( result > 1.0 ) {
                result = 1.0;
        }
        return result;
}
 
void
ptarray_longitude_shift(POINTARRAY *pa)
{
        uint32_t i;
        double x;
 
        for (i=0; i<pa->npoints; i++)
        {
                memcpy(&x, getPoint_internal(pa, i), sizeof(double));
                if ( x < 0 ) x+= 360;
                else if ( x > 180 ) x -= 360;
                memcpy(getPoint_internal(pa, i), &x, sizeof(double));
        }
}
 
 
/*
 * Returns a POINTARRAY with consecutive equal points
 * removed. Equality test on all dimensions of input.
 *
 * Always returns a newly allocated object.
 */
static POINTARRAY *
ptarray_remove_repeated_points_minpoints(const POINTARRAY *in, double tolerance, int minpoints)
{
        POINTARRAY *out = ptarray_clone_deep(in);
        ptarray_remove_repeated_points_in_place(out, tolerance, minpoints);
        return out;
}
 
POINTARRAY *
ptarray_remove_repeated_points(const POINTARRAY *in, double tolerance)
{
        return ptarray_remove_repeated_points_minpoints(in, tolerance, 2);
}
 
 
void
ptarray_remove_repeated_points_in_place(POINTARRAY *pa, double tolerance, uint32_t min_points)
{
        uint32_t i;
        double tolsq = tolerance * tolerance;
        const POINT2D *last = NULL;
        const POINT2D *pt;
        uint32_t n_points = pa->npoints;
        uint32_t n_points_out = 1;
        size_t pt_size = ptarray_point_size(pa);
 
        double dsq = FLT_MAX;
 
        /* No-op on short inputs */
        if ( n_points <= min_points ) return;
 
        last = getPoint2d_cp(pa, 0);
        void *p_to = ((char *)last) + pt_size;
        for (i = 1; i < n_points; i++)
        {
                int last_point = (i == n_points - 1);
 
                /* Look straight into the abyss */
                pt = getPoint2d_cp(pa, i);
 
                /* Don't drop points if we are running short of points */
                if (n_points + n_points_out > min_points + i)
                {
                        if (tolerance > 0.0)
                        {
                                /* Only drop points that are within our tolerance */
                                dsq = distance2d_sqr_pt_pt(last, pt);
                                /* Allow any point but the last one to be dropped */
                                if (!last_point && dsq <= tolsq)
                                {
                                        continue;
                                }
                        }
                        else
                        {
                                /* At tolerance zero, only skip exact dupes */
                                if (memcmp((char*)pt, (char*)last, pt_size) == 0)
                                        continue;
                        }
 
                        /* Got to last point, and it's not very different from */
                        /* the point that preceded it. We want to keep the last */
                        /* point, not the second-to-last one, so we pull our write */
                        /* index back one value */
                        if (last_point && n_points_out > 1 && tolerance > 0.0 && dsq <= tolsq)
                        {
                                n_points_out--;
                                p_to = (char*)p_to - pt_size;
                        }
                }
 
                /* Compact all remaining values to front of array */
                memcpy(p_to, pt, pt_size);
                n_points_out++;
                p_to = (char*)p_to + pt_size;
                last = pt;
        }
        /* Adjust array length */
        pa->npoints = n_points_out;
        return;
}
 
/* Out of the points in pa [itfist .. itlast], finds the one that's farthest away from
 * the segment determined by pts[itfist] and pts[itlast].
 * Returns itfirst if no point was found further away than max_distance_sqr
 */
static uint32_t
ptarray_dp_findsplit_in_place(const POINTARRAY *pts, uint32_t it_first, uint32_t it_last, double max_distance_sqr)
{
        uint32_t split = it_first;
        if ((it_first - it_last) < 2)
                return it_first;
 
        const POINT2D *A = getPoint2d_cp(pts, it_first);
        const POINT2D *B = getPoint2d_cp(pts, it_last);
 
        if (distance2d_sqr_pt_pt(A, B) < DBL_EPSILON)
        {
                /* If p1 == p2, we can just calculate the distance from each point to A */
                for (uint32_t itk = it_first + 1; itk < it_last; itk++)
                {
                        const POINT2D *pk = getPoint2d_cp(pts, itk);
                        double distance_sqr = distance2d_sqr_pt_pt(pk, A);
                        if (distance_sqr > max_distance_sqr)
                        {
                                split = itk;
                                max_distance_sqr = distance_sqr;
                        }
                }
                return split;
        }
 
        /* This is based on distance2d_sqr_pt_seg, but heavily inlined here to avoid recalculations */
        double ba_x = (B->x - A->x);
        double ba_y = (B->y - A->y);
        double ab_length_sqr = (ba_x * ba_x + ba_y * ba_y);
        /* To avoid the division by ab_length_sqr in the 3rd path, we normalize here
         * and multiply in the first two paths [(dot_ac_ab < 0) and (> ab_length_sqr)] */
        max_distance_sqr *= ab_length_sqr;
        for (uint32_t itk = it_first + 1; itk < it_last; itk++)
        {
                const POINT2D *C = getPoint2d_cp(pts, itk);
                double distance_sqr;
                double ca_x = (C->x - A->x);
                double ca_y = (C->y - A->y);
                double dot_ac_ab = (ca_x * ba_x + ca_y * ba_y);
 
                if (dot_ac_ab <= 0.0)
                {
                        distance_sqr = distance2d_sqr_pt_pt(C, A) * ab_length_sqr;
                }
                else if (dot_ac_ab >= ab_length_sqr)
                {
                        distance_sqr = distance2d_sqr_pt_pt(C, B) * ab_length_sqr;
                }
                else
                {
                        double s_numerator = ca_x * ba_y - ca_y * ba_x;
                        distance_sqr = s_numerator * s_numerator; /* Missing division by ab_length_sqr on purpose */
                }
 
                if (distance_sqr > max_distance_sqr)
                {
                        split = itk;
                        max_distance_sqr = distance_sqr;
                }
        }
        return split;
}
 
/* O(N) simplification for tolerance = 0 */
static void
ptarray_simplify_in_place_tolerance0(POINTARRAY *pa)
{
        uint32_t kept_it = 0;
        uint32_t last_it = pa->npoints - 1;
        const POINT2D *kept_pt = getPoint2d_cp(pa, 0);
        const size_t pt_size = ptarray_point_size(pa);
 
        for (uint32_t i = 1; i < last_it; i++)
        {
                const POINT2D *curr_pt = getPoint2d_cp(pa, i);
                const POINT2D *next_pt = getPoint2d_cp(pa, i + 1);
 
                double ba_x = next_pt->x - kept_pt->x;
                double ba_y = next_pt->y - kept_pt->y;
                double ab_length_sqr = ba_x * ba_x + ba_y * ba_y;
 
                double ca_x = curr_pt->x - kept_pt->x;
                double ca_y = curr_pt->y - kept_pt->y;
                double dot_ac_ab = ca_x * ba_x + ca_y * ba_y;
                double s_numerator = ca_x * ba_y - ca_y * ba_x;
 
                if (p2d_same(kept_pt, next_pt) ||
                        dot_ac_ab < 0.0 ||
                        dot_ac_ab > ab_length_sqr ||
                        s_numerator != 0)
 
                {
                        kept_it++;
                        kept_pt = curr_pt;
                        if (kept_it != i)
                                memcpy(pa->serialized_pointlist + pt_size * kept_it,
                                       pa->serialized_pointlist + pt_size * i,
                                       pt_size);
                }
        }
 
        /* Append last point */
        kept_it++;
        if (kept_it != last_it)
                memcpy(pa->serialized_pointlist + pt_size * kept_it,
                       pa->serialized_pointlist + pt_size * last_it,
                       pt_size);
        pa->npoints = kept_it + 1;
}
 
void
ptarray_simplify_in_place(POINTARRAY *pa, double tolerance, uint32_t minpts)
{
        /* Do not try to simplify really short things */
        if (pa->npoints < 3 || pa->npoints <= minpts)
                return;
 
        if (tolerance == 0 && minpts <= 2)
        {
                ptarray_simplify_in_place_tolerance0(pa);
                return;
        }
 
        /* We use this array to keep track of the points we are keeping, so
         * we store just TRUE / FALSE in their position */
        uint8_t *kept_points = lwalloc(sizeof(uint8_t) * pa->npoints);
        memset(kept_points, LW_FALSE, sizeof(uint8_t) * pa->npoints);
        kept_points[0] = LW_TRUE;
        kept_points[pa->npoints - 1] = LW_TRUE;
        uint32_t keptn = 2;
 
        /* We use this array as a stack to store the iterators that we are going to need
         * in the following steps.
         * This is ~10% faster than iterating over @kept_points looking for them
         */
        uint32_t *iterator_stack = lwalloc(sizeof(uint32_t) * pa->npoints);
        iterator_stack[0] = 0;
        uint32_t iterator_stack_size = 1;
 
        uint32_t it_first = 0;
        uint32_t it_last = pa->npoints - 1;
 
        const double tolerance_sqr = tolerance * tolerance;
        /* For the first @minpts points we ignore the tolerance */
        double it_tol = keptn >= minpts ? tolerance_sqr : -1.0;
 
        while (iterator_stack_size)
        {
                uint32_t split = ptarray_dp_findsplit_in_place(pa, it_first, it_last, it_tol);
                if (split == it_first)
                {
                        it_first = it_last;
                        it_last = iterator_stack[--iterator_stack_size];
                }
                else
                {
                        kept_points[split] = LW_TRUE;
                        keptn++;
 
                        iterator_stack[iterator_stack_size++] = it_last;
                        it_last = split;
                        it_tol = keptn >= minpts ? tolerance_sqr : -1.0;
                }
        }
 
        const size_t pt_size = ptarray_point_size(pa);
        /* The first point is already in place, so we don't need to copy it */
        size_t kept_it = 1;
        if (keptn == 2)
        {
                /* If there are 2 points remaining, it has to be first and last as
                 * we added those at the start */
                memcpy(pa->serialized_pointlist + pt_size * kept_it,
                       pa->serialized_pointlist + pt_size * (pa->npoints - 1),
                       pt_size);
        }
        else if (pa->npoints != keptn) /* We don't need to move any points if we are keeping them all */
        {
                for (uint32_t i = 1; i < pa->npoints; i++)
                {
                        if (kept_points[i])
                        {
                                memcpy(pa->serialized_pointlist + pt_size * kept_it,
                                       pa->serialized_pointlist + pt_size * i,
                                       pt_size);
                                kept_it++;
                        }
                }
        }
        pa->npoints = keptn;
 
        lwfree(kept_points);
        lwfree(iterator_stack);
}
 
/************************************************************************/
 
double
ptarray_arc_length_2d(const POINTARRAY *pts)
{
        double dist = 0.0;
        uint32_t i;
        const POINT2D *a1;
        const POINT2D *a2;
        const POINT2D *a3;
 
        if ( pts->npoints % 2 != 1 )
                lwerror("arc point array with even number of points");
 
        a1 = getPoint2d_cp(pts, 0);
 
        for ( i=2; i < pts->npoints; i += 2 )
        {
                a2 = getPoint2d_cp(pts, i-1);
                a3 = getPoint2d_cp(pts, i);
                dist += lw_arc_length(a1, a2, a3);
                a1 = a3;
        }
        return dist;
}
 
double
ptarray_length_2d(const POINTARRAY *pts)
{
        double dist = 0.0;
        uint32_t i;
        const POINT2D *frm;
        const POINT2D *to;
 
        if ( pts->npoints < 2 ) return 0.0;
 
        frm = getPoint2d_cp(pts, 0);
 
        for ( i=1; i < pts->npoints; i++ )
        {
                to = getPoint2d_cp(pts, i);
 
                dist += sqrt( ((frm->x - to->x)*(frm->x - to->x))  +
                              ((frm->y - to->y)*(frm->y - to->y)) );
 
                frm = to;
        }
        return dist;
}
 
double
ptarray_length(const POINTARRAY *pts)
{
        double dist = 0.0;
        uint32_t i;
        POINT3DZ frm;
        POINT3DZ to;
 
        if ( pts->npoints < 2 ) return 0.0;
 
        /* compute 2d length if 3d is not available */
        if ( ! FLAGS_GET_Z(pts->flags) ) return ptarray_length_2d(pts);
 
        getPoint3dz_p(pts, 0, &frm);
        for ( i=1; i < pts->npoints; i++ )
        {
                getPoint3dz_p(pts, i, &to);
                dist += sqrt( ((frm.x - to.x)*(frm.x - to.x)) +
                              ((frm.y - to.y)*(frm.y - to.y)) +
                              ((frm.z - to.z)*(frm.z - to.z)) );
                frm = to;
        }
        return dist;
}
 
 
 
void
ptarray_affine(POINTARRAY *pa, const AFFINE *a)
{
        if (FLAGS_GET_Z(pa->flags))
        {
                for (uint32_t i = 0; i < pa->npoints; i++)
                {
                        POINT4D *p4d = (POINT4D *)(getPoint_internal(pa, i));
                        double x = p4d->x;
                        double y = p4d->y;
                        double z = p4d->z;
                        p4d->x = a->afac * x + a->bfac * y + a->cfac * z + a->xoff;
                        p4d->y = a->dfac * x + a->efac * y + a->ffac * z + a->yoff;
                        p4d->z = a->gfac * x + a->hfac * y + a->ifac * z + a->zoff;
                }
        }
        else
        {
                for (uint32_t i = 0; i < pa->npoints; i++)
                {
                        POINT2D *pt = (POINT2D *)(getPoint_internal(pa, i));
                        double x = pt->x;
                        double y = pt->y;
                        pt->x = a->afac * x + a->bfac * y + a->xoff;
                        pt->y = a->dfac * x + a->efac * y + a->yoff;
                }
        }
}
 
#if 0
static int gluInvertMatrix(const double *m, double *invOut)
{
    double inv[16], det;
    int i;
 
    inv[0] = m[5]  * m[10] * m[15] -
             m[5]  * m[11] * m[14] -
             m[9]  * m[6]  * m[15] +
             m[9]  * m[7]  * m[14] +
             m[13] * m[6]  * m[11] -
             m[13] * m[7]  * m[10];
 
    inv[4] = -m[4]  * m[10] * m[15] +
              m[4]  * m[11] * m[14] +
              m[8]  * m[6]  * m[15] -
              m[8]  * m[7]  * m[14] -
              m[12] * m[6]  * m[11] +
              m[12] * m[7]  * m[10];
 
    inv[8] = m[4]  * m[9] * m[15] -
             m[4]  * m[11] * m[13] -
             m[8]  * m[5] * m[15] +
             m[8]  * m[7] * m[13] +
             m[12] * m[5] * m[11] -
             m[12] * m[7] * m[9];
 
    inv[12] = -m[4]  * m[9] * m[14] +
               m[4]  * m[10] * m[13] +
               m[8]  * m[5] * m[14] -
               m[8]  * m[6] * m[13] -
               m[12] * m[5] * m[10] +
               m[12] * m[6] * m[9];
 
    inv[1] = -m[1]  * m[10] * m[15] +
              m[1]  * m[11] * m[14] +
              m[9]  * m[2] * m[15] -
              m[9]  * m[3] * m[14] -
              m[13] * m[2] * m[11] +
              m[13] * m[3] * m[10];
 
    inv[5] = m[0]  * m[10] * m[15] -
             m[0]  * m[11] * m[14] -
             m[8]  * m[2] * m[15] +
             m[8]  * m[3] * m[14] +
             m[12] * m[2] * m[11] -
             m[12] * m[3] * m[10];
 
    inv[9] = -m[0]  * m[9] * m[15] +
              m[0]  * m[11] * m[13] +
              m[8]  * m[1] * m[15] -
              m[8]  * m[3] * m[13] -
              m[12] * m[1] * m[11] +
              m[12] * m[3] * m[9];
 
    inv[13] = m[0]  * m[9] * m[14] -
              m[0]  * m[10] * m[13] -
              m[8]  * m[1] * m[14] +
              m[8]  * m[2] * m[13] +
              m[12] * m[1] * m[10] -
              m[12] * m[2] * m[9];
 
    inv[2] = m[1]  * m[6] * m[15] -
             m[1]  * m[7] * m[14] -
             m[5]  * m[2] * m[15] +
             m[5]  * m[3] * m[14] +
             m[13] * m[2] * m[7] -
             m[13] * m[3] * m[6];
 
    inv[6] = -m[0]  * m[6] * m[15] +
              m[0]  * m[7] * m[14] +
              m[4]  * m[2] * m[15] -
              m[4]  * m[3] * m[14] -
              m[12] * m[2] * m[7] +
              m[12] * m[3] * m[6];
 
    inv[10] = m[0]  * m[5] * m[15] -
              m[0]  * m[7] * m[13] -
              m[4]  * m[1] * m[15] +
              m[4]  * m[3] * m[13] +
              m[12] * m[1] * m[7] -
              m[12] * m[3] * m[5];
 
    inv[14] = -m[0]  * m[5] * m[14] +
               m[0]  * m[6] * m[13] +
               m[4]  * m[1] * m[14] -
               m[4]  * m[2] * m[13] -
               m[12] * m[1] * m[6] +
               m[12] * m[2] * m[5];
 
    inv[3] = -m[1] * m[6] * m[11] +
              m[1] * m[7] * m[10] +
              m[5] * m[2] * m[11] -
              m[5] * m[3] * m[10] -
              m[9] * m[2] * m[7] +
              m[9] * m[3] * m[6];
 
    inv[7] = m[0] * m[6] * m[11] -
             m[0] * m[7] * m[10] -
             m[4] * m[2] * m[11] +
             m[4] * m[3] * m[10] +
             m[8] * m[2] * m[7] -
             m[8] * m[3] * m[6];
 
    inv[11] = -m[0] * m[5] * m[11] +
               m[0] * m[7] * m[9] +
               m[4] * m[1] * m[11] -
               m[4] * m[3] * m[9] -
               m[8] * m[1] * m[7] +
               m[8] * m[3] * m[5];
 
    inv[15] = m[0] * m[5] * m[10] -
              m[0] * m[6] * m[9] -
              m[4] * m[1] * m[10] +
              m[4] * m[2] * m[9] +
              m[8] * m[1] * m[6] -
              m[8] * m[2] * m[5];
 
    det = m[0] * inv[0] + m[1] * inv[4] + m[2] * inv[8] + m[3] * inv[12];
 
    if (det == 0)
        return LW_FALSE;
 
    det = 1.0 / det;
 
    for (i = 0; i < 16; i++)
        invOut[i] = inv[i] * det;
 
    return LW_TRUE;
}
#endif
 
void
ptarray_scale(POINTARRAY *pa, const POINT4D *fact)
{
        uint32_t i;
        POINT4D p4d;
        LWDEBUG(3, "ptarray_scale start");
        for (i=0; i<pa->npoints; i++)
        {
                getPoint4d_p(pa, i, &p4d);
                p4d.x *= fact->x;
                p4d.y *= fact->y;
                p4d.z *= fact->z;
                p4d.m *= fact->m;
                ptarray_set_point4d(pa, i, &p4d);
        }
        LWDEBUG(3, "ptarray_scale end");
}
 
int
ptarray_startpoint(const POINTARRAY *pa, POINT4D *pt)
{
        return getPoint4d_p(pa, 0, pt);
}
 
 
/*
 * Stick an array of points to the given gridspec.
 * Return "gridded" points in *outpts and their number in *outptsn.
 *
 * Two consecutive points falling on the same grid cell are collapsed
 * into one single point.
 *
 */
void
ptarray_grid_in_place(POINTARRAY *pa, gridspec *grid)
{
        uint32_t j = 0;
        POINT4D *p, *p_out = NULL;
        double x, y, z = 0, m = 0;
        uint32_t ndims = FLAGS_NDIMS(pa->flags);
        uint32_t has_z = FLAGS_GET_Z(pa->flags);
        uint32_t has_m = FLAGS_GET_M(pa->flags);
 
        for (uint32_t i = 0; i < pa->npoints; i++)
        {
                /* Look straight into the abyss */
                p = (POINT4D *)(getPoint_internal(pa, i));
                x = p->x;
                y = p->y;
                if (ndims > 2)
                        z = p->z;
                if (ndims > 3)
                        m = p->m;
 
                /*
                 * See https://github.com/libgeos/geos/pull/956
                 * We use scale for rounding when gridsize is < 1 and
                 * gridsize for rounding when scale < 1.
                 */
                if (grid->xsize > 0) {
                        if (grid->xsize < 1)
                                x = rint((x - grid->ipx) * grid->xscale) / grid->xscale + grid->ipx;
                        else
                                x = rint((x - grid->ipx) / grid->xsize) * grid->xsize + grid->ipx;
                }
 
                if (grid->ysize > 0) {
                        if (grid->ysize < 1)
                                y = rint((y - grid->ipy) * grid->yscale) / grid->yscale + grid->ipy;
                        else
                                y = rint((y - grid->ipy) / grid->ysize) * grid->ysize + grid->ipy;
                }
 
                /* Read and round this point */
                /* Z is always in third position */
                if (has_z && grid->zsize > 0)
                        z = rint((z - grid->ipz) / grid->zsize) * grid->zsize + grid->ipz;
 
                /* M might be in 3rd or 4th position */
                if (has_m && grid->msize > 0)
                {
                        /* In POINT ZM, M is in 4th position, in POINT M, M is in 3rd position which is Z in POINT4D */
                        if (has_z)
                                m = rint((m - grid->ipm) / grid->msize) * grid->msize + grid->ipm;
                        else
                                z = rint((z - grid->ipm) / grid->msize) * grid->msize + grid->ipm;
                }
 
                /* Skip duplicates */
                if (p_out &&
                    p_out->x == x &&
                    p_out->y == y &&
                    (ndims > 2 ? p_out->z == z : 1) &&
                    (ndims > 3 ? p_out->m == m : 1))
                {
                        continue;
                }
 
                /* Write rounded values into the next available point */
                p_out = (POINT4D *)(getPoint_internal(pa, j++));
                p_out->x = x;
                p_out->y = y;
                if (ndims > 2)
                        p_out->z = z;
                if (ndims > 3)
                        p_out->m = m;
        }
 
        /* Update output ptarray length */
        pa->npoints = j;
        return;
}
 
int
ptarray_npoints_in_rect(const POINTARRAY *pa, const GBOX *gbox)
{
        const POINT2D *pt;
        int n = 0;
        uint32_t i;
        for ( i = 0; i < pa->npoints; i++ )
        {
                pt = getPoint2d_cp(pa, i);
                if ( gbox_contains_point2d(gbox, pt) )
                        n++;
        }
        return n;
}
 
 
/*
 * Reorder the vertices of a closed pointarray so that the
 * given point is the first/last one.
 *
 * Error out if pointarray is not closed or it does not
 * contain the given point.
 */
int
ptarray_scroll_in_place(POINTARRAY *pa, const POINT4D *pt)
{
        POINTARRAY *tmp;
        int found;
        uint32_t it;
        int ptsize;
 
        if ( ! ptarray_is_closed_2d(pa) )
        {
                lwerror("ptarray_scroll_in_place: input POINTARRAY is not closed");
                return LW_FAILURE;
        }
 
        ptsize = ptarray_point_size(pa);
 
        /* Find the point in the array */
        found = 0;
        for ( it = 0; it < pa->npoints; ++it )
        {
                if ( ! memcmp(getPoint_internal(pa, it), pt, ptsize) )
                {
                        found = 1;
                        break;
                }
        }
 
        if ( ! found )
        {
                lwerror("ptarray_scroll_in_place: input POINTARRAY does not contain the given point");
                return LW_FAILURE;
        }
 
        if ( 0 == it )
        {
                /* Point is already the start/end point, just clone the input */
                return LW_SUCCESS;
        }
 
        /* TODO: reduce allocations */
        tmp = ptarray_construct(FLAGS_GET_Z(pa->flags), FLAGS_GET_M(pa->flags), pa->npoints);
 
        memset(getPoint_internal(tmp, 0), 0, (size_t)ptsize * pa->npoints);
        /* Copy the block from found point to last point into the output array */
        memcpy(
                getPoint_internal(tmp, 0),
                getPoint_internal(pa, it),
                (size_t)ptsize * ( pa->npoints - it )
        );
 
        /* Copy the block from second point to the found point into the last portion of the
   * return */
        memcpy(
                getPoint_internal(tmp, pa->npoints - it),
                getPoint_internal(pa, 1),
                (size_t)ptsize * ( it )
        );
 
        /* Copy the resulting pointarray back to source one */
        memcpy(
                getPoint_internal(pa, 0),
                getPoint_internal(tmp, 0),
                (size_t)ptsize * ( pa->npoints )
        );
 
        ptarray_free(tmp);
 
        return LW_SUCCESS;
}