lwstroke.c

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/**********************************************************************
 *
 * PostGIS - Spatial Types for PostgreSQL
 * http://postgis.net
 *
 * PostGIS is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 2 of the License, or
 * (at your option) any later version.
 *
 * PostGIS is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with PostGIS.  If not, see <http://www.gnu.org/licenses/>.
 *
 **********************************************************************
 *
 * Copyright (C) 2001-2006 Refractions Research Inc.
 * Copyright (C) 2017      Sandro Santilli <strk@kbt.io>
 * Copyright (C) 2018      Daniel Baston <dbaston@gmail.com>
 *
 **********************************************************************/
 
 
#include <stdio.h>
#include <stdlib.h>
#include <stdarg.h>
#include <string.h>
 
#include "../postgis_config.h"
 
/*#define POSTGIS_DEBUG_LEVEL 3*/
 
#include "lwgeom_log.h"
 
#include "liblwgeom_internal.h"
 
LWGEOM *pta_unstroke(const POINTARRAY *points, int32_t srid);
LWGEOM* lwline_unstroke(const LWLINE *line);
LWGEOM* lwpolygon_unstroke(const LWPOLY *poly);
LWGEOM* lwmline_unstroke(const LWMLINE *mline);
LWGEOM* lwmpolygon_unstroke(const LWMPOLY *mpoly);
LWGEOM* lwcollection_unstroke(const LWCOLLECTION *c);
LWGEOM* lwgeom_unstroke(const LWGEOM *geom);
 
 
/*
 * Determines (recursively in the case of collections) whether the geometry
 * contains at least on arc geometry or segment.
 */
int
lwgeom_has_arc(const LWGEOM *geom)
{
        LWCOLLECTION *col;
        uint32_t i;
 
        LWDEBUG(2, "lwgeom_has_arc called.");
 
        switch (geom->type)
        {
        case POINTTYPE:
        case LINETYPE:
        case POLYGONTYPE:
        case TRIANGLETYPE:
        case MULTIPOINTTYPE:
        case MULTILINETYPE:
        case MULTIPOLYGONTYPE:
        case POLYHEDRALSURFACETYPE:
        case TINTYPE:
                return LW_FALSE;
        case CIRCSTRINGTYPE:
                return LW_TRUE;
        /* It's a collection that MAY contain an arc */
        default:
                col = (LWCOLLECTION *)geom;
                for (i=0; i<col->ngeoms; i++)
                {
                        if (lwgeom_has_arc(col->geoms[i]) == LW_TRUE)
                                return LW_TRUE;
                }
                return LW_FALSE;
        }
}
 
int
lwgeom_type_arc(const LWGEOM *geom)
{
        switch (geom->type)
        {
        case COMPOUNDTYPE:
        case CIRCSTRINGTYPE:
        case CURVEPOLYTYPE:
        case MULTISURFACETYPE:
        case MULTICURVETYPE:
                return LW_TRUE;
        default:
                return LW_FALSE;
        }
}
 
/*******************************************************************************
 * Begin curve segmentize functions
 ******************************************************************************/
 
static double interpolate_arc(double angle, double a1, double a2, double a3, double zm1, double zm2, double zm3)
{
        LWDEBUGF(4,"angle %.05g a1 %.05g a2 %.05g a3 %.05g zm1 %.05g zm2 %.05g zm3 %.05g",angle,a1,a2,a3,zm1,zm2,zm3);
        /* Counter-clockwise sweep */
        if ( a1 < a2 )
        {
                if ( angle <= a2 )
                        return zm1 + (zm2-zm1) * (angle-a1) / (a2-a1);
                else
                        return zm2 + (zm3-zm2) * (angle-a2) / (a3-a2);
        }
        /* Clockwise sweep */
        else
        {
                if ( angle >= a2 )
                        return zm1 + (zm2-zm1) * (a1-angle) / (a1-a2);
                else
                        return zm2 + (zm3-zm2) * (a2-angle) / (a2-a3);
        }
}
 
/* Compute the angle covered by a single segment such that
 * a given number of segments per quadrant is achieved. */
static double angle_increment_using_segments_per_quad(double tol)
{
        double increment;
        int perQuad = rint(tol);
        // error out if tol != perQuad ? (not-round)
        if ( perQuad != tol )
        {
                lwerror("lwarc_linearize: segments per quadrant must be an integer value, got %.15g", tol);
                return -1;
        }
        if ( perQuad < 1 )
        {
                lwerror("lwarc_linearize: segments per quadrant must be at least 1, got %d", perQuad);
                return -1;
        }
        increment = fabs(M_PI_2 / perQuad);
        LWDEBUGF(2, "lwarc_linearize: perQuad:%d, increment:%g (%g degrees)", perQuad, increment, increment*180/M_PI);
 
        return increment;
}
 
/* Compute the angle covered by a single quadrant such that
 * the segment deviates from the arc by no more than a given
 * amount. */
static double angle_increment_using_max_deviation(double max_deviation, double radius)
{
        double increment, halfAngle, maxErr;
        if ( max_deviation <= 0 )
        {
                lwerror("lwarc_linearize: max deviation must be bigger than 0, got %.15g", max_deviation);
                return -1;
        }
 
        /*
         * Ref: https://en.wikipedia.org/wiki/Sagitta_(geometry)
         *
         * An arc "sagitta" (distance between middle point of arc and
         * middle point of corresponding chord) is defined as:
         *
         *   sagitta = radius * ( 1 - cos( angle ) );
         *
         * We want our sagitta to be at most "tolerance" long,
         * and we want to find out angle, so we use the inverse
         * formula:
         *
         *   tol = radius * ( 1 - cos( angle ) );
         *   1 - cos( angle ) =  tol/radius
         *   - cos( angle ) =  tol/radius - 1
         *   cos( angle ) =  - tol/radius + 1
         *   angle = acos( 1 - tol/radius )
         *
         * Constraints: 1.0 - tol/radius must be between -1 and 1
         * which means tol must be between 0 and 2 times
         * the radius, which makes sense as you cannot have a
         * sagitta bigger than twice the radius!
         *
         */
        maxErr = max_deviation;
        if ( maxErr > radius * 2 )
        {
                maxErr = radius * 2;
                LWDEBUGF(2,
                         "lwarc_linearize: tolerance %g is too big, "
                         "using arc-max 2 * radius == %g",
                         max_deviation,
                         maxErr);
        }
        do {
                halfAngle = acos( 1.0 - maxErr / radius );
                /* TODO: avoid a loop here, going rather straight to
                 *       a minimum angle value */
                if ( halfAngle != 0 ) break;
                LWDEBUGF(2, "lwarc_linearize: tolerance %g is too small for this arc"
                                                                " to compute approximation angle, doubling it", maxErr);
                maxErr *= 2;
        } while(1);
        increment = 2 * halfAngle;
        LWDEBUGF(2,
                 "lwarc_linearize: maxDiff:%g, radius:%g, halfAngle:%g, increment:%g (%g degrees)",
                 max_deviation,
                 radius,
                 halfAngle,
                 increment,
                 increment * 180 / M_PI);
 
        return increment;
}
 
/* Check that a given angle is positive and, if so, take
 * it to be the angle covered by a single segment. */
static double angle_increment_using_max_angle(double tol)
{
        if ( tol <= 0 )
        {
                lwerror("lwarc_linearize: max angle must be bigger than 0, got %.15g", tol);
                return -1;
        }
 
        return tol;
}
 
 
static int
lwarc_linearize(POINTARRAY *to,
                 const POINT4D *p1, const POINT4D *p2, const POINT4D *p3,
                 double tol, LW_LINEARIZE_TOLERANCE_TYPE tolerance_type,
                 int flags)
{
        POINT2D center;
        POINT2D *t1 = (POINT2D*)p1;
        POINT2D *t2 = (POINT2D*)p2;
        POINT2D *t3 = (POINT2D*)p3;
        POINT4D pt;
        int p2_side = 0;
        int clockwise = LW_TRUE;
        double radius; /* Arc radius */
        double increment; /* Angle per segment */
        double angle_shift = 0;
        double a1, a2, a3;
        POINTARRAY *pa;
        int is_circle = LW_FALSE;
        int points_added = 0;
        int reverse = 0;
        int segments = 0;
 
        LWDEBUG(2, "lwarc_linearize called.");
 
        LWDEBUGF(2, " curve is CIRCULARSTRING(%.15g %.15f, %.15f %.15f, %.15f %15f)",
                t1->x, t1->y, t2->x, t2->y, t3->x, t3->y);
 
        p2_side = lw_segment_side(t1, t3, t2);
 
        LWDEBUGF(2, " p2 side is %d", p2_side);
 
        /* Force counterclockwise scan if SYMMETRIC operation is requested */
        if ( p2_side == -1 && flags & LW_LINEARIZE_FLAG_SYMMETRIC )
        {
                /* swap p1-p3 */
                t1 = (POINT2D*)p3;
                t3 = (POINT2D*)p1;
                p1 = (POINT4D*)t1;
                p3 = (POINT4D*)t3;
                p2_side = 1;
                reverse = 1;
        }
 
        radius = lw_arc_center(t1, t2, t3, &center);
        LWDEBUGF(2, " center is POINT(%.15g %.15g) - radius:%g", center.x, center.y, radius);
 
        /* Matched start/end points imply circle */
        if ( p1->x == p3->x && p1->y == p3->y )
                is_circle = LW_TRUE;
 
        /* Negative radius signals straight line, p1/p2/p3 are collinear */
        if ( (radius < 0.0 || p2_side == 0) && ! is_circle )
            return 0;
 
        /* The side of the p1/p3 line that p2 falls on dictates the sweep
           direction from p1 to p3. */
        if ( p2_side == -1 )
                clockwise = LW_TRUE;
        else
                clockwise = LW_FALSE;
 
        /* Compute the increment (angle per segment) depending on
         * our tolerance type. */
        switch(tolerance_type)
        {
                case LW_LINEARIZE_TOLERANCE_TYPE_SEGS_PER_QUAD:
                        increment = angle_increment_using_segments_per_quad(tol);
                        break;
                case LW_LINEARIZE_TOLERANCE_TYPE_MAX_DEVIATION:
                        increment = angle_increment_using_max_deviation(tol, radius);
                        break;
                case LW_LINEARIZE_TOLERANCE_TYPE_MAX_ANGLE:
                        increment = angle_increment_using_max_angle(tol);
                        break;
                default:
                        lwerror("lwarc_linearize: unsupported tolerance type %d", tolerance_type);
                        return -1;
        }
 
        if (increment < 0)
        {
                /* Error occurred in increment calculation somewhere
                 * (lwerror already called)
                 */
                return -1;
        }
 
        /* Angles of each point that defines the arc section */
        a1 = atan2(p1->y - center.y, p1->x - center.x);
        a2 = atan2(p2->y - center.y, p2->x - center.x);
        a3 = atan2(p3->y - center.y, p3->x - center.x);
 
        LWDEBUGF(2, "lwarc_linearize A1:%g (%g) A2:%g (%g) A3:%g (%g)",
                a1, a1*180/M_PI, a2, a2*180/M_PI, a3, a3*180/M_PI);
 
        /* Calculate total arc angle, in radians */
        double total_angle = clockwise ? a1 - a3 : a3 - a1;
        if ( total_angle <= 0 ) total_angle += M_PI * 2;
 
        /* At extreme tolerance values (very low or very high, depending on
         * the semantic) we may cause our arc to collapse. In this case,
         * we want shrink the increment enough so that we get two segments
         * for a standard arc, or three segments for a complete circle. */
        int min_segs = is_circle ? 3 : 2;
        segments = ceil(total_angle / increment);
        if (segments < min_segs)
        {
                segments = min_segs;
                increment = total_angle / min_segs;
        }
 
        if ( flags & LW_LINEARIZE_FLAG_SYMMETRIC )
        {
                LWDEBUGF(2, "lwarc_linearize SYMMETRIC requested - total angle %g deg", total_angle * 180 / M_PI);
 
                if ( flags & LW_LINEARIZE_FLAG_RETAIN_ANGLE )
                {
                        /* Number of complete steps */
                        segments = trunc(total_angle / increment);
 
                        /* Figure out the angle remainder, i.e. the amount of the angle
                         * that is left after we can take no more complete angle
                         * increments. */
                        double angle_remainder = total_angle - (increment * segments);
 
                        /* Shift the starting angle by half of the remainder. This
                         * will have the effect of evenly distributing the remainder
                         * among the first and last segments in the arc. */
                        angle_shift = angle_remainder / 2.0;
 
                        LWDEBUGF(2,
                                 "lwarc_linearize RETAIN_ANGLE operation requested - "
                                 "total angle %g, steps %d, increment %g, remainder %g",
                                 total_angle * 180 / M_PI,
                                 segments,
                                 increment * 180 / M_PI,
                                 angle_remainder * 180 / M_PI);
                }
                else
                {
                        /* Number of segments in output */
                        segments = ceil(total_angle / increment);
                        /* Tweak increment to be regular for all the arc */
                        increment = total_angle / segments;
 
                        LWDEBUGF(2,
                                 "lwarc_linearize SYMMETRIC operation requested - "
                                 "total angle %g degrees - LINESTRING(%g %g,%g %g,%g %g) - S:%d -   I:%g",
                                 total_angle * 180 / M_PI,
                                 p1->x,
                                 p1->y,
                                 center.x,
                                 center.y,
                                 p3->x,
                                 p3->y,
                                 segments,
                                 increment * 180 / M_PI);
                }
        }
 
        /* p2 on left side => clockwise sweep */
        if ( clockwise )
        {
                LWDEBUG(2, " Clockwise sweep");
                increment *= -1;
                angle_shift *= -1;
                /* Adjust a3 down so we can decrement from a1 to a3 cleanly */
                if ( a3 > a1 )
                        a3 -= 2.0 * M_PI;
                if ( a2 > a1 )
                        a2 -= 2.0 * M_PI;
        }
        /* p2 on right side => counter-clockwise sweep */
        else
        {
                LWDEBUG(2, " Counterclockwise sweep");
                /* Adjust a3 up so we can increment from a1 to a3 cleanly */
                if ( a3 < a1 )
                        a3 += 2.0 * M_PI;
                if ( a2 < a1 )
                        a2 += 2.0 * M_PI;
        }
 
        /* Override angles for circle case */
        if( is_circle )
        {
                increment = fabs(increment);
                segments = ceil(total_angle / increment);
                if (segments < 3)
                {
                        segments = 3;
                        increment = total_angle / 3;
                }
                a3 = a1 + 2.0 * M_PI;
                a2 = a1 + M_PI;
                clockwise = LW_FALSE;
                angle_shift = 0.0;
        }
 
        LWDEBUGF(2, "lwarc_linearize angle_shift:%g, increment:%g",
                angle_shift * 180/M_PI, increment * 180/M_PI);
 
        if ( reverse )
        {
                /* Append points in order to a temporary POINTARRAY and
                 * reverse them before writing to the output POINTARRAY. */
                const int capacity = 8; /* TODO: compute exactly ? */
                pa = ptarray_construct_empty(ptarray_has_z(to), ptarray_has_m(to), capacity);
        }
        else
        {
                /* Append points directly to the output POINTARRAY,
                 * starting with p1. */
                pa = to;
 
                ptarray_append_point(pa, p1, LW_FALSE);
                ++points_added;
        }
 
        /* Sweep from a1 to a3 */
        int seg_start = 1; /* First point is added manually */
        int seg_end = segments;
        if (angle_shift != 0.0)
        {
                /* When we have extra angles we need to add the extra segments at the
                 * start and end that cover those parts of the arc */
                seg_start = 0;
                seg_end = segments + 1;
        }
        LWDEBUGF(2, "a1:%g (%g deg), a3:%g (%g deg), inc:%g, shi:%g, cw:%d",
                a1, a1 * 180 / M_PI, a3, a3 * 180 / M_PI, increment, angle_shift, clockwise);
        for (int s = seg_start; s < seg_end; s++)
        {
                double angle = a1 + increment * s + angle_shift;
                LWDEBUGF(2, " SA: %g ( %g deg )", angle, angle*180/M_PI);
                pt.x = center.x + radius * cos(angle);
                pt.y = center.y + radius * sin(angle);
                pt.z = interpolate_arc(angle, a1, a2, a3, p1->z, p2->z, p3->z);
                pt.m = interpolate_arc(angle, a1, a2, a3, p1->m, p2->m, p3->m);
                ptarray_append_point(pa, &pt, LW_FALSE);
                ++points_added;
        }
 
        /* Ensure the final point is EXACTLY the same as the first for the circular case */
        if ( is_circle )
        {
                ptarray_remove_point(pa, pa->npoints - 1);
                ptarray_append_point(pa, p1, LW_FALSE);
        }
 
        if ( reverse )
        {
                int i;
                ptarray_append_point(to, p3, LW_FALSE);
                for ( i=pa->npoints; i>0; i-- ) {
                        getPoint4d_p(pa, i-1, &pt);
                        ptarray_append_point(to, &pt, LW_FALSE);
                }
                ptarray_free(pa);
        }
 
        return points_added;
}
 
/*
 * @param icurve input curve
 * @param tol tolerance, semantic driven by tolerance_type
 * @param tolerance_type see LW_LINEARIZE_TOLERANCE_TYPE
 * @param flags see flags in lwarc_linearize
 *
 * @return a newly allocated LWLINE
 */
static LWLINE *
lwcircstring_linearize(const LWCIRCSTRING *icurve, double tol,
                        LW_LINEARIZE_TOLERANCE_TYPE tolerance_type,
                        int flags)
{
        LWLINE *oline;
        POINTARRAY *ptarray;
        uint32_t i, j;
        POINT4D p1, p2, p3, p4;
        int ret;
 
        LWDEBUGF(2, "lwcircstring_linearize called., dim = %d", icurve->points->flags);
 
        ptarray = ptarray_construct_empty(FLAGS_GET_Z(icurve->points->flags), FLAGS_GET_M(icurve->points->flags), 64);
 
        for (i = 2; i < icurve->points->npoints; i+=2)
        {
                LWDEBUGF(3, "lwcircstring_linearize: arc ending at point %d", i);
 
                getPoint4d_p(icurve->points, i - 2, &p1);
                getPoint4d_p(icurve->points, i - 1, &p2);
                getPoint4d_p(icurve->points, i, &p3);
 
                ret = lwarc_linearize(ptarray, &p1, &p2, &p3, tol, tolerance_type, flags);
                if ( ret > 0 )
                {
                        LWDEBUGF(3, "lwcircstring_linearize: generated %d points", ptarray->npoints);
                }
                else if ( ret == 0 )
                {
                        LWDEBUG(3, "lwcircstring_linearize: points are colinear, returning curve points as line");
 
                        for (j = i - 2 ; j < i ; j++)
                        {
                                getPoint4d_p(icurve->points, j, &p4);
                                ptarray_append_point(ptarray, &p4, LW_TRUE);
                        }
                }
                else
                {
                        /* An error occurred, lwerror should have been called by now */
                        ptarray_free(ptarray);
                        return NULL;
                }
        }
        getPoint4d_p(icurve->points, icurve->points->npoints-1, &p1);
        ptarray_append_point(ptarray, &p1, LW_FALSE);
 
        oline = lwline_construct(icurve->srid, NULL, ptarray);
        return oline;
}
 
/*
 * @param icompound input compound curve
 * @param tol tolerance, semantic driven by tolerance_type
 * @param tolerance_type see LW_LINEARIZE_TOLERANCE_TYPE
 * @param flags see flags in lwarc_linearize
 *
 * @return a newly allocated LWLINE
 */
static LWLINE *
lwcompound_linearize(const LWCOMPOUND *icompound, double tol,
                      LW_LINEARIZE_TOLERANCE_TYPE tolerance_type,
                      int flags)
{
        LWGEOM *geom;
        POINTARRAY *ptarray = NULL;
        LWLINE *tmp = NULL;
        uint32_t i, j;
        POINT4D p;
 
        LWDEBUG(2, "lwcompound_stroke called.");
 
        ptarray = ptarray_construct_empty(FLAGS_GET_Z(icompound->flags), FLAGS_GET_M(icompound->flags), 64);
 
        for (i = 0; i < icompound->ngeoms; i++)
        {
                geom = icompound->geoms[i];
                if (geom->type == CIRCSTRINGTYPE)
                {
                        tmp = lwcircstring_linearize((LWCIRCSTRING *)geom, tol, tolerance_type, flags);
                        for (j = 0; j < tmp->points->npoints; j++)
                        {
                                getPoint4d_p(tmp->points, j, &p);
                                ptarray_append_point(ptarray, &p, LW_TRUE);
                        }
                        lwline_free(tmp);
                }
                else if (geom->type == LINETYPE)
                {
                        tmp = (LWLINE *)geom;
                        for (j = 0; j < tmp->points->npoints; j++)
                        {
                                getPoint4d_p(tmp->points, j, &p);
                                ptarray_append_point(ptarray, &p, LW_TRUE);
                        }
                }
                else
                {
                        lwerror("%s: Unsupported geometry type: %s", __func__, lwtype_name(geom->type));
                        return NULL;
                }
        }
 
        ptarray_remove_repeated_points_in_place(ptarray, 0.0, 2);
        return lwline_construct(icompound->srid, NULL, ptarray);
}
 
 
/*
 * @param icompound input curve polygon
 * @param tol tolerance, semantic driven by tolerance_type
 * @param tolerance_type see LW_LINEARIZE_TOLERANCE_TYPE
 * @param flags see flags in lwarc_linearize
 *
 * @return a newly allocated LWPOLY
 */
static LWPOLY *
lwcurvepoly_linearize(const LWCURVEPOLY *curvepoly, double tol,
                       LW_LINEARIZE_TOLERANCE_TYPE tolerance_type,
                       int flags)
{
        LWPOLY *ogeom;
        LWGEOM *tmp;
        LWLINE *line;
        POINTARRAY **ptarray;
        uint32_t i;
 
        LWDEBUG(2, "lwcurvepoly_linearize called.");
 
        ptarray = lwalloc(sizeof(POINTARRAY *)*curvepoly->nrings);
 
        for (i = 0; i < curvepoly->nrings; i++)
        {
                tmp = curvepoly->rings[i];
                if (tmp->type == CIRCSTRINGTYPE)
                {
                        line = lwcircstring_linearize((LWCIRCSTRING *)tmp, tol, tolerance_type, flags);
                        ptarray[i] = ptarray_clone_deep(line->points);
                        lwline_free(line);
                }
                else if (tmp->type == LINETYPE)
                {
                        line = (LWLINE *)tmp;
                        ptarray[i] = ptarray_clone_deep(line->points);
                }
                else if (tmp->type == COMPOUNDTYPE)
                {
                        line = lwcompound_linearize((LWCOMPOUND *)tmp, tol, tolerance_type, flags);
                        ptarray[i] = ptarray_clone_deep(line->points);
                        lwline_free(line);
                }
                else
                {
                        lwerror("Invalid ring type found in CurvePoly.");
                        return NULL;
                }
        }
 
        ogeom = lwpoly_construct(curvepoly->srid, NULL, curvepoly->nrings, ptarray);
        return ogeom;
}
 
/* Kept for backward compatibility - TODO: drop */
LWPOLY *
lwcurvepoly_stroke(const LWCURVEPOLY *curvepoly, uint32_t perQuad)
{
                return lwcurvepoly_linearize(curvepoly, perQuad, LW_LINEARIZE_TOLERANCE_TYPE_SEGS_PER_QUAD, 0);
}
 
 
static LWMLINE *
lwmcurve_linearize(const LWMCURVE *mcurve, double tol,
                    LW_LINEARIZE_TOLERANCE_TYPE type,
                    int flags)
{
        LWMLINE *ogeom;
        LWGEOM **lines;
        uint32_t i;
 
        LWDEBUGF(2, "lwmcurve_linearize called, geoms=%d, dim=%d.", mcurve->ngeoms, FLAGS_NDIMS(mcurve->flags));
 
        lines = lwalloc(sizeof(LWGEOM *)*mcurve->ngeoms);
 
        for (i = 0; i < mcurve->ngeoms; i++)
        {
                const LWGEOM *tmp = mcurve->geoms[i];
                if (tmp->type == CIRCSTRINGTYPE)
                {
                        lines[i] = (LWGEOM *)lwcircstring_linearize((LWCIRCSTRING *)tmp, tol, type, flags);
                }
                else if (tmp->type == LINETYPE)
                {
                        lines[i] = (LWGEOM *)lwline_construct(mcurve->srid, NULL, ptarray_clone_deep(((LWLINE *)tmp)->points));
                }
                else if (tmp->type == COMPOUNDTYPE)
                {
                        lines[i] = (LWGEOM *)lwcompound_linearize((LWCOMPOUND *)tmp, tol, type, flags);
                }
                else
                {
                        lwerror("Unsupported geometry found in MultiCurve.");
                        return NULL;
                }
        }
 
        ogeom = (LWMLINE *)lwcollection_construct(MULTILINETYPE, mcurve->srid, NULL, mcurve->ngeoms, lines);
        return ogeom;
}
 
static LWMPOLY *
lwmsurface_linearize(const LWMSURFACE *msurface, double tol,
                      LW_LINEARIZE_TOLERANCE_TYPE type,
                      int flags)
{
        LWMPOLY *ogeom;
        LWGEOM *tmp;
        LWPOLY *poly;
        LWGEOM **polys;
        POINTARRAY **ptarray;
        uint32_t i, j;
 
        LWDEBUG(2, "lwmsurface_linearize called.");
 
        polys = lwalloc(sizeof(LWGEOM *)*msurface->ngeoms);
 
        for (i = 0; i < msurface->ngeoms; i++)
        {
                tmp = msurface->geoms[i];
                if (tmp->type == CURVEPOLYTYPE)
                {
                        polys[i] = (LWGEOM *)lwcurvepoly_linearize((LWCURVEPOLY *)tmp, tol, type, flags);
                }
                else if (tmp->type == POLYGONTYPE)
                {
                        poly = (LWPOLY *)tmp;
                        ptarray = lwalloc(sizeof(POINTARRAY *)*poly->nrings);
                        for (j = 0; j < poly->nrings; j++)
                        {
                                ptarray[j] = ptarray_clone_deep(poly->rings[j]);
                        }
                        polys[i] = (LWGEOM *)lwpoly_construct(msurface->srid, NULL, poly->nrings, ptarray);
                }
        }
        ogeom = (LWMPOLY *)lwcollection_construct(MULTIPOLYGONTYPE, msurface->srid, NULL, msurface->ngeoms, polys);
        return ogeom;
}
 
static LWCOLLECTION *
lwcollection_linearize(const LWCOLLECTION *collection, double tol,
                    LW_LINEARIZE_TOLERANCE_TYPE type,
                    int flags)
{
        LWCOLLECTION *ocol;
        LWGEOM *tmp;
        LWGEOM **geoms;
        uint32_t i;
 
        LWDEBUG(2, "lwcollection_linearize called.");
 
        geoms = lwalloc(sizeof(LWGEOM *)*collection->ngeoms);
 
        for (i=0; i<collection->ngeoms; i++)
        {
                tmp = collection->geoms[i];
                switch (tmp->type)
                {
                case CIRCSTRINGTYPE:
                        geoms[i] = (LWGEOM *)lwcircstring_linearize((LWCIRCSTRING *)tmp, tol, type, flags);
                        break;
                case COMPOUNDTYPE:
                        geoms[i] = (LWGEOM *)lwcompound_linearize((LWCOMPOUND *)tmp, tol, type, flags);
                        break;
                case CURVEPOLYTYPE:
                        geoms[i] = (LWGEOM *)lwcurvepoly_linearize((LWCURVEPOLY *)tmp, tol, type, flags);
                        break;
                case MULTICURVETYPE:
                case MULTISURFACETYPE:
                case COLLECTIONTYPE:
                        geoms[i] = (LWGEOM *)lwcollection_linearize((LWCOLLECTION *)tmp, tol, type, flags);
                        break;
                default:
                        geoms[i] = lwgeom_clone_deep(tmp);
                        break;
                }
        }
        ocol = lwcollection_construct(COLLECTIONTYPE, collection->srid, NULL, collection->ngeoms, geoms);
        return ocol;
}
 
LWGEOM *
lwcurve_linearize(const LWGEOM *geom, double tol,
                  LW_LINEARIZE_TOLERANCE_TYPE type,
                  int flags)
{
        LWGEOM * ogeom = NULL;
        switch (geom->type)
        {
        case CIRCSTRINGTYPE:
                ogeom = (LWGEOM *)lwcircstring_linearize((LWCIRCSTRING *)geom, tol, type, flags);
                break;
        case COMPOUNDTYPE:
                ogeom = (LWGEOM *)lwcompound_linearize((LWCOMPOUND *)geom, tol, type, flags);
                break;
        case CURVEPOLYTYPE:
                ogeom = (LWGEOM *)lwcurvepoly_linearize((LWCURVEPOLY *)geom, tol, type, flags);
                break;
        case MULTICURVETYPE:
                ogeom = (LWGEOM *)lwmcurve_linearize((LWMCURVE *)geom, tol, type, flags);
                break;
        case MULTISURFACETYPE:
                ogeom = (LWGEOM *)lwmsurface_linearize((LWMSURFACE *)geom, tol, type, flags);
                break;
        case COLLECTIONTYPE:
                ogeom = (LWGEOM *)lwcollection_linearize((LWCOLLECTION *)geom, tol, type, flags);
                break;
        default:
                ogeom = lwgeom_clone_deep(geom);
        }
        return ogeom;
}
 
/* Kept for backward compatibility - TODO: drop */
LWGEOM *
lwgeom_stroke(const LWGEOM *geom, uint32_t perQuad)
{
        return lwcurve_linearize(geom, perQuad, LW_LINEARIZE_TOLERANCE_TYPE_SEGS_PER_QUAD, 0);
}
 
static double
lw_arc_angle(const POINT2D *a, const POINT2D *b, const POINT2D *c)
{
  POINT2D ab, cb;
 
  ab.x = b->x - a->x;
  ab.y = b->y - a->y;
 
  cb.x = b->x - c->x;
  cb.y = b->y - c->y;
 
  double dot = (ab.x * cb.x + ab.y * cb.y); /* dot product */
  double cross = (ab.x * cb.y - ab.y * cb.x); /* cross product */
 
  double alpha = atan2(cross, dot);
 
  return alpha;
}
 
static int pt_continues_arc(const POINT4D *a1, const POINT4D *a2, const POINT4D *a3, const POINT4D *b)
{
        POINT2D center;
        POINT2D *t1 = (POINT2D*)a1;
        POINT2D *t2 = (POINT2D*)a2;
        POINT2D *t3 = (POINT2D*)a3;
        POINT2D *tb = (POINT2D*)b;
        double radius = lw_arc_center(t1, t2, t3, &center);
        double b_distance, diff;
 
        /* Co-linear a1/a2/a3 */
        if ( radius < 0.0 )
                return LW_FALSE;
 
        b_distance = distance2d_pt_pt(tb, &center);
        diff = fabs(radius - b_distance);
        LWDEBUGF(4, "circle_radius=%g, b_distance=%g, diff=%g, percentage=%g", radius, b_distance, diff, diff/radius);
 
        /* Is the point b on the circle? */
        if ( diff < EPSILON_SQLMM )
        {
                int a2_side = lw_segment_side(t1, t3, t2);
                int b_side  = lw_segment_side(t1, t3, tb);
                double angle1 = lw_arc_angle(t1, t2, t3);
                double angle2 = lw_arc_angle(t2, t3, tb);
 
                /* Is the angle similar to the previous one ? */
                diff = fabs(angle1 - angle2);
                LWDEBUGF(4, " angle1: %g, angle2: %g, diff:%g", angle1, angle2, diff);
                if ( diff > EPSILON_SQLMM )
                {
                        return LW_FALSE;
                }
 
                /* Is the point b on the same side of a1/a3 as the mid-point a2 is? */
                /* If not, it's in the unbounded part of the circle, so it continues the arc, return true. */
                if ( b_side != a2_side )
                        return LW_TRUE;
        }
        return LW_FALSE;
}
 
static LWGEOM *
linestring_from_pa(const POINTARRAY *pa, int32_t srid, int start, int end)
{
        int i = 0, j = 0;
        POINT4D p;
        POINTARRAY *pao = ptarray_construct(ptarray_has_z(pa), ptarray_has_m(pa), end-start+2);
        LWDEBUGF(4, "srid=%d, start=%d, end=%d", srid, start, end);
        for( i = start; i < end + 2; i++ )
        {
                getPoint4d_p(pa, i, &p);
                ptarray_set_point4d(pao, j++, &p);
        }
        return lwline_as_lwgeom(lwline_construct(srid, NULL, pao));
}
 
static LWGEOM *
circstring_from_pa(const POINTARRAY *pa, int32_t srid, int start, int end)
{
 
        POINT4D p0, p1, p2;
        POINTARRAY *pao = ptarray_construct(ptarray_has_z(pa), ptarray_has_m(pa), 3);
        LWDEBUGF(4, "srid=%d, start=%d, end=%d", srid, start, end);
        getPoint4d_p(pa, start, &p0);
        ptarray_set_point4d(pao, 0, &p0);
        getPoint4d_p(pa, (start+end+1)/2, &p1);
        ptarray_set_point4d(pao, 1, &p1);
        getPoint4d_p(pa, end+1, &p2);
        ptarray_set_point4d(pao, 2, &p2);
        return lwcircstring_as_lwgeom(lwcircstring_construct(srid, NULL, pao));
}
 
static LWGEOM *
geom_from_pa(const POINTARRAY *pa, int32_t srid, int is_arc, int start, int end)
{
        LWDEBUGF(4, "srid=%d, is_arc=%d, start=%d, end=%d", srid, is_arc, start, end);
        if ( is_arc )
                return circstring_from_pa(pa, srid, start, end);
        else
                return linestring_from_pa(pa, srid, start, end);
}
 
LWGEOM *
pta_unstroke(const POINTARRAY *points, int32_t srid)
{
        int i = 0, j, k;
        POINT4D a1, a2, a3, b;
        POINT4D first, center;
        char *edges_in_arcs;
        int found_arc = LW_FALSE;
        int current_arc = 1;
        int num_edges;
        int edge_type; /* non-zero if edge is part of an arc */
        int start, end;
        LWCOLLECTION *outcol;
        /* Minimum number of edges, per quadrant, required to define an arc */
        const unsigned int min_quad_edges = 2;
 
        /* Die on null input */
        if ( ! points )
                lwerror("pta_unstroke called with null pointarray");
 
        /* Null on empty input? */
        if ( points->npoints == 0 )
                return NULL;
 
        /* We can't desegmentize anything shorter than four points */
        if ( points->npoints < 4 )
        {
                /* Return a linestring here*/
                lwerror("pta_unstroke needs implementation for npoints < 4");
        }
 
        /* Allocate our result array of vertices that are part of arcs */
        num_edges = points->npoints - 1;
        edges_in_arcs = lwalloc(num_edges + 1);
        memset(edges_in_arcs, 0, num_edges + 1);
 
        /* We make a candidate arc of the first two edges, */
        /* And then see if the next edge follows it */
        while( i < num_edges-2 )
        {
                unsigned int arc_edges;
                double num_quadrants;
                double angle;
 
                found_arc = LW_FALSE;
                /* Make candidate arc */
                getPoint4d_p(points, i  , &a1);
                getPoint4d_p(points, i+1, &a2);
                getPoint4d_p(points, i+2, &a3);
                memcpy(&first, &a1, sizeof(POINT4D));
 
                for( j = i+3; j < num_edges+1; j++ )
                {
                        LWDEBUGF(4, "i=%d, j=%d", i, j);
                        getPoint4d_p(points, j, &b);
                        /* Does this point fall on our candidate arc? */
                        if ( pt_continues_arc(&a1, &a2, &a3, &b) )
                        {
                                /* Yes. Mark this edge and the two preceding it as arc components */
                                LWDEBUGF(4, "pt_continues_arc #%d", current_arc);
                                found_arc = LW_TRUE;
                                for ( k = j-1; k > j-4; k-- )
                                        edges_in_arcs[k] = current_arc;
                        }
                        else
                        {
                                /* No. So we're done with this candidate arc */
                                LWDEBUG(4, "pt_continues_arc = false");
                                current_arc++;
                                break;
                        }
 
                        memcpy(&a1, &a2, sizeof(POINT4D));
                        memcpy(&a2, &a3, sizeof(POINT4D));
                        memcpy(&a3,  &b, sizeof(POINT4D));
                }
                /* Jump past all the edges that were added to the arc */
                if ( found_arc )
                {
                        /* Check if an arc was composed by enough edges to be
                         * really considered an arc
                         * See http://trac.osgeo.org/postgis/ticket/2420
                         */
                        arc_edges = j - 1 - i;
                        LWDEBUGF(4, "arc defined by %d edges found", arc_edges);
                        if ( first.x == b.x && first.y == b.y ) {
                                LWDEBUG(4, "arc is a circle");
                                num_quadrants = 4;
                        }
                        else {
                                lw_arc_center((POINT2D*)&first, (POINT2D*)&b, (POINT2D*)&a1, (POINT2D*)&center);
                                angle = lw_arc_angle((POINT2D*)&first, (POINT2D*)&center, (POINT2D*)&b);
                                int p2_side = lw_segment_side((POINT2D*)&first, (POINT2D*)&a1, (POINT2D*)&b);
                                if ( p2_side >= 0 ) angle = -angle;
 
                                if ( angle < 0 ) angle = 2 * M_PI + angle;
                                num_quadrants = ( 4 * angle ) / ( 2 * M_PI );
                                LWDEBUGF(4, "arc angle (%g %g, %g %g, %g %g) is %g (side is %d), quadrants:%g", first.x, first.y, center.x, center.y, b.x, b.y, angle, p2_side, num_quadrants);
                        }
                        /* a1 is first point, b is last point */
                        if ( arc_edges < min_quad_edges * num_quadrants ) {
                                LWDEBUGF(4, "Not enough edges for a %g quadrants arc, %g needed", num_quadrants, min_quad_edges * num_quadrants);
                                for ( k = j-1; k >= i; k-- )
                                        edges_in_arcs[k] = 0;
                        }
 
                        i = j-1;
                }
                else
                {
                        /* Mark this edge as a linear edge */
                        edges_in_arcs[i] = 0;
                        i = i+1;
                }
        }
 
#if POSTGIS_DEBUG_LEVEL > 3
        {
                char *edgestr = lwalloc(num_edges+1);
                for ( i = 0; i < num_edges; i++ )
                {
                        if ( edges_in_arcs[i] )
                                edgestr[i] = 48 + edges_in_arcs[i];
                        else
                                edgestr[i] = '.';
                }
                edgestr[num_edges] = 0;
                LWDEBUGF(3, "edge pattern %s", edgestr);
                lwfree(edgestr);
        }
#endif
 
        start = 0;
        edge_type = edges_in_arcs[0];
        outcol = lwcollection_construct_empty(COMPOUNDTYPE, srid, ptarray_has_z(points), ptarray_has_m(points));
        for( i = 1; i < num_edges; i++ )
        {
                if( edge_type != edges_in_arcs[i] )
                {
                        end = i - 1;
                        lwcollection_add_lwgeom(outcol, geom_from_pa(points, srid, edge_type, start, end));
                        start = i;
                        edge_type = edges_in_arcs[i];
                }
        }
        lwfree(edges_in_arcs); /* not needed anymore */
 
        /* Roll out last item */
        end = num_edges - 1;
        lwcollection_add_lwgeom(outcol, geom_from_pa(points, srid, edge_type, start, end));
 
        /* Strip down to singleton if only one entry */
        if ( outcol->ngeoms == 1 )
        {
                LWGEOM *outgeom = outcol->geoms[0];
                outcol->ngeoms = 0; lwcollection_free(outcol);
                return outgeom;
        }
        return lwcollection_as_lwgeom(outcol);
}
 
 
LWGEOM *
lwline_unstroke(const LWLINE *line)
{
        LWDEBUG(2, "lwline_unstroke called.");
 
        if ( line->points->npoints < 4 ) return lwline_as_lwgeom(lwline_clone_deep(line));
        else return pta_unstroke(line->points, line->srid);
}
 
LWGEOM *
lwpolygon_unstroke(const LWPOLY *poly)
{
        LWGEOM **geoms;
        uint32_t i, hascurve = 0;
 
        LWDEBUG(2, "lwpolygon_unstroke called.");
 
        geoms = lwalloc(sizeof(LWGEOM *)*poly->nrings);
        for (i=0; i<poly->nrings; i++)
        {
                geoms[i] = pta_unstroke(poly->rings[i], poly->srid);
                if (geoms[i]->type == CIRCSTRINGTYPE || geoms[i]->type == COMPOUNDTYPE)
                {
                        hascurve = 1;
                }
        }
        if (hascurve == 0)
        {
                for (i=0; i<poly->nrings; i++)
                {
                        lwfree(geoms[i]); /* TODO: should this be lwgeom_free instead ? */
                }
                return lwgeom_clone_deep((LWGEOM *)poly);
        }
 
        return (LWGEOM *)lwcollection_construct(CURVEPOLYTYPE, poly->srid, NULL, poly->nrings, geoms);
}
 
LWGEOM *
lwmline_unstroke(const LWMLINE *mline)
{
        LWGEOM **geoms;
        uint32_t i, hascurve = 0;
 
        LWDEBUG(2, "lwmline_unstroke called.");
 
        geoms = lwalloc(sizeof(LWGEOM *)*mline->ngeoms);
        for (i=0; i<mline->ngeoms; i++)
        {
                geoms[i] = lwline_unstroke((LWLINE *)mline->geoms[i]);
                if (geoms[i]->type == CIRCSTRINGTYPE || geoms[i]->type == COMPOUNDTYPE)
                {
                        hascurve = 1;
                }
        }
        if (hascurve == 0)
        {
                for (i=0; i<mline->ngeoms; i++)
                {
                        lwfree(geoms[i]); /* TODO: should this be lwgeom_free instead ? */
                }
                return lwgeom_clone_deep((LWGEOM *)mline);
        }
        return (LWGEOM *)lwcollection_construct(MULTICURVETYPE, mline->srid, NULL, mline->ngeoms, geoms);
}
 
LWGEOM *
lwmpolygon_unstroke(const LWMPOLY *mpoly)
{
        LWGEOM **geoms;
        uint32_t i, hascurve = 0;
 
        LWDEBUG(2, "lwmpoly_unstroke called.");
 
        geoms = lwalloc(sizeof(LWGEOM *)*mpoly->ngeoms);
        for (i=0; i<mpoly->ngeoms; i++)
        {
                geoms[i] = lwpolygon_unstroke((LWPOLY *)mpoly->geoms[i]);
                if (geoms[i]->type == CURVEPOLYTYPE)
                {
                        hascurve = 1;
                }
        }
        if (hascurve == 0)
        {
                for (i=0; i<mpoly->ngeoms; i++)
                {
                        lwfree(geoms[i]); /* TODO: should this be lwgeom_free instead ? */
                }
                return lwgeom_clone_deep((LWGEOM *)mpoly);
        }
        return (LWGEOM *)lwcollection_construct(MULTISURFACETYPE, mpoly->srid, NULL, mpoly->ngeoms, geoms);
}
 
LWGEOM *
lwcollection_unstroke(const LWCOLLECTION *c)
{
        LWCOLLECTION *ret = lwalloc(sizeof(LWCOLLECTION));
        memcpy(ret, c, sizeof(LWCOLLECTION));
 
        if (c->ngeoms > 0)
        {
                uint32_t i;
                ret->geoms = lwalloc(sizeof(LWGEOM *)*c->ngeoms);
                for (i=0; i < c->ngeoms; i++)
                {
                        ret->geoms[i] = lwgeom_unstroke(c->geoms[i]);
                }
                if (c->bbox)
                {
                        ret->bbox = gbox_copy(c->bbox);
                }
        }
        else
        {
                ret->bbox = NULL;
                ret->geoms = NULL;
        }
        return (LWGEOM *)ret;
}
 
 
LWGEOM *
lwgeom_unstroke(const LWGEOM *geom)
{
        LWDEBUG(2, "lwgeom_unstroke called.");
 
        switch (geom->type)
        {
        case LINETYPE:
                return lwline_unstroke((LWLINE *)geom);
        case POLYGONTYPE:
                return lwpolygon_unstroke((LWPOLY *)geom);
        case MULTILINETYPE:
                return lwmline_unstroke((LWMLINE *)geom);
        case MULTIPOLYGONTYPE:
                return lwmpolygon_unstroke((LWMPOLY *)geom);
        case COLLECTIONTYPE:
                return lwcollection_unstroke((LWCOLLECTION *)geom);
        default:
                return lwgeom_clone_deep(geom);
        }
}