/*
**  delaunay.c : compute 2D delaunay triangulation in the plane.
**  Copyright (C) 2005  Wael El Oraiby <wael.eloraiby@gmail.com>
**
**
**  This program 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 3 of the License, or
**  (at your option) any later version.
**
**  This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
*/

#include <QtGlobal>
#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#include "delaunay.h"

QT_WARNING_PUSH
QT_WARNING_DISABLE_GCC("-Wold-style-cast")
// cppcheck-suppress unknownMacro
QT_WARNING_DISABLE_CLANG("-Wold-style-cast")
QT_WARNING_DISABLE_GCC("-Wcast-qual")
QT_WARNING_DISABLE_CLANG("-Wcast-qual")
QT_WARNING_DISABLE_GCC("-Walloc-zero")

#if PREDICATE == EXACT_PREDICATE
extern void exactinit();
extern auto incircle(real *pa, real *pb, real *pc, real *pd) -> real;
#endif

#define ON_RIGHT 1
#define ON_SEG 0
#define ON_LEFT -1

#define OUTSIDE -1
#define ON_CIRCLE 0
#define INSIDE 1

struct delaunay_s;
struct face_s;
struct halfedge_s;
struct point2d_s;

#ifdef USE_DOUBLE
#define REAL_ZERO 0.0
#define REAL_ONE 1.0
#define REAL_TWO 2.0
#define REAL_FOUR 4.0
#define TOLERANCE (1024.0 * 1024.0)
#else
#define REAL_ZERO 0.0f
#define REAL_ONE 1.0f
#define REAL_TWO 2.0f
#define REAL_FOUR 4.0f
#define TOLERANCE (16.0f)
#endif

#define EPSILON (REAL_ONE / TOLERANCE)

typedef point2d_s point2d_t;
typedef face_s face_t;
typedef halfedge_s halfedge_t;
typedef delaunay_s delaunay_t;
typedef real mat3_t[3][3];

struct point2d_s
{
    real x, y;      /* point coordinates */
    halfedge_t *he; /* point halfedge */
    quint32 idx;    /* point index in input buffer */
};

struct face_s
{
    /*	real			radius;
        real			cx, cy;
        point2d_t*		p[3];
    */
    halfedge_t *he;    /* a pointing half edge */
    quint32 num_verts; /* number of vertices on this face */
};

struct halfedge_s
{
    point2d_t *vertex; /* vertex */
    halfedge_t *pair;  /* pair */
    halfedge_t *next;  /* next */
    halfedge_t *prev;  /* next^-1 */
    face_t *face;      /* halfedge face */
};

struct delaunay_s
{
    halfedge_t *rightmost_he; /* right most halfedge */
    halfedge_t *leftmost_he;  /* left most halfedge */
    point2d_t **points;       /* pointer to points */
    face_t *faces;            /* faces of delaunay */
    quint32 num_faces;        /* face count */
    quint32 start_point;      /* start point index */
    quint32 end_point;        /* end point index */
};

/*
 * 3x3 matrix determinant
 */
// static real det3( mat3_t *m )
//{
//	real		res;

//	res		= ((*m)[0][0]) * (((*m)[1][1]) * ((*m)[2][2]) - ((*m)[1][2]) * ((*m)[2][1]))
//			- ((*m)[0][1]) * (((*m)[1][0]) * ((*m)[2][2]) - ((*m)[1][2]) * ((*m)[2][0]))
//			+ ((*m)[0][2]) * (((*m)[1][0]) * ((*m)[2][1]) - ((*m)[1][1]) * ((*m)[2][0]));

//	return res;
//}

/*
 * allocate a point
 */
static auto point_alloc() -> point2d_t *
{
    point2d_t *p;

    p = (point2d_t *)malloc(sizeof(point2d_t));
    assert(p != nullptr);
    // cppcheck-suppress memsetClassFloat
    memset(p, 0, sizeof(point2d_t));

    return p;
}

/*
 * free a point
 */
static void point_free(point2d_t *p)
{
    assert(p != nullptr);
    free(p);
}

/*
 * allocate a halfedge
 */
static auto halfedge_alloc() -> halfedge_t *
{
    halfedge_t *d;

    d = (halfedge_t *)malloc(sizeof(halfedge_t));
    assert(d != nullptr);
    memset(d, 0, sizeof(halfedge_t));

    return d;
}

/*
 * free a halfedge
 */
static void halfedge_free(halfedge_t *d)
{
    assert(d != nullptr);
    memset(d, 0, sizeof(halfedge_t));
    free(d);
}

/*
 * free all delaunay halfedges
 */
void del_free_halfedges(delaunay_t *del);
void del_free_halfedges(delaunay_t *del)
{
    quint32 i;
    halfedge_t *d, *sig;

    /* if there is nothing to do */
    if (del->points == nullptr)
        return;

    for (i = 0; i <= (del->end_point - del->start_point); i++)
    {
        /* free all the halfedges around the point */
        d = del->points[i]->he;
        if (d != nullptr)
        {
            do
            {
                sig = d->next;
                halfedge_free(d);
                d = sig;
            } while (d != del->points[i]->he);
            del->points[i]->he = nullptr;
        }
    }
}

/*
 * allocate memory for a face
 */
// static face_t* face_alloc()
//{
//	face_t	*f = (face_t*)malloc(sizeof(face_t));
//	assert( f != nullptr );
//	memset(f, 0, sizeof(face_t));
//	return f;
// }

/*
 * free a face
 */
// static void face_free(face_t *f)
//{
//	assert( f != nullptr );
//	free(f);
// }

/*
 * compare 2 points when sorting
 */
static auto cmp_points(const void *_pt0, const void *_pt1) -> int
{
    point2d_t *pt0, *pt1;

    pt0 = (point2d_t *)(*((point2d_t **)_pt0));
    pt1 = (point2d_t *)(*((point2d_t **)_pt1));

    if (pt0->x < pt1->x)
        return -1;
    else if (pt0->x > pt1->x)
        return 1;
    else if (pt0->y < pt1->y)
        return -1;
    else if (pt0->y > pt1->y)
        return 1;
    assert(0 && "2 or more points share the same exact coordinate");
    return 0; /* Should not be given! */
}

/*
 * classify a point relative to a segment
 */
static auto classify_point_seg(point2d_t *s, point2d_t *e, point2d_t *pt) -> int
{
    point2d_t se, spt;
    real res;

    se.x = e->x - s->x;
    se.y = e->y - s->y;

    spt.x = pt->x - s->x;
    spt.y = pt->y - s->y;

    res = ((se.x * spt.y) - (se.y * spt.x));
    if (res < REAL_ZERO)
        return ON_RIGHT;
    else if (res > REAL_ZERO)
        return ON_LEFT;

    return ON_SEG;
}

/*
 * classify a point relative to a halfedge, -1 is left, 0 is on, 1 is right
 */
static auto del_classify_point(halfedge_t *d, point2d_t *pt) -> int
{
    point2d_t *s, *e;

    s = d->vertex;
    e = d->pair->vertex;

    return classify_point_seg(s, e, pt);
}

/*
 * return the absolute value
 */
// static real dabs( real a )
//{
//	if( a < REAL_ZERO )
//		return (-a);
//	return a;
// }

/*
 * compute the circle given 3 points
 */
#if PREDICATE == LOOSE_PREDICATE
static void compute_circle(point2d_t *pt0, point2d_t *pt1, point2d_t *pt2, real *cx, real *cy, real *radius)
{
    mat3_t ma, mbx, mby, mc;
    real x0y0, x1y1, x2y2;
    real a, bx, by, c;

    /* calculate x0y0, .... */
    x0y0 = pt0->x * pt0->x + pt0->y * pt0->y;
    x1y1 = pt1->x * pt1->x + pt1->y * pt1->y;
    x2y2 = pt2->x * pt2->x + pt2->y * pt2->y;

    /* setup A matrix */
    ma[0][0] = pt0->x;
    ma[0][1] = pt0->y;
    ma[1][0] = pt1->x;
    ma[1][1] = pt1->y;
    ma[2][0] = pt2->x;
    ma[2][1] = pt2->y;
    ma[0][2] = ma[1][2] = ma[2][2] = REAL_ONE;

    /* setup Bx matrix */
    mbx[0][0] = x0y0;
    mbx[1][0] = x1y1;
    mbx[2][0] = x2y2;
    mbx[0][1] = pt0->y;
    mbx[1][1] = pt1->y;
    mbx[2][1] = pt2->y;
    mbx[0][2] = mbx[1][2] = mbx[2][2] = REAL_ONE;

    /* setup By matrix */
    mby[0][0] = x0y0;
    mby[1][0] = x1y1;
    mby[2][0] = x2y2;
    mby[0][1] = pt0->x;
    mby[1][1] = pt1->x;
    mby[2][1] = pt2->x;
    mby[0][2] = mby[1][2] = mby[2][2] = REAL_ONE;

    /* setup C matrix */
    mc[0][0] = x0y0;
    mc[1][0] = x1y1;
    mc[2][0] = x2y2;
    mc[0][1] = pt0->x;
    mc[1][1] = pt1->x;
    mc[2][1] = pt2->x;
    mc[0][2] = pt0->y;
    mc[1][2] = pt1->y;
    mc[2][2] = pt2->y;

    /* compute a, bx, by and c */
    a = det3(&ma);
    bx = det3(&mbx);
    by = -det3(&mby);
    c = -det3(&mc);

    *cx = bx / (REAL_TWO * a);
    *cy = by / (REAL_TWO * a);
    *radius = sqrt(bx * bx + by * by - REAL_FOUR * a * c) / (REAL_TWO * dabs(a));
}
#endif

/*
 * test if a point is inside a circle given by 3 points, 1 if inside, 0 if outside
 */
static auto in_circle(point2d_t *pt0, point2d_t *pt1, point2d_t *pt2, point2d_t *p) -> int
{
#if PREDICATE == EXACT_PREDICATE
    real res = incircle(&(pt0->x), &(pt1->x), &(pt2->x), &(p->x));
    if (res > REAL_ZERO)
        return INSIDE;
    else if (res < REAL_ZERO)
        return OUTSIDE;

    return ON_CIRCLE;
#endif
#if PREDICATE == LOOSE_PREDICATE
    real cx, cy, radius;
    compute_circle(pt0, pt1, pt2, &cx, &cy, &radius);

    real distance = sqrt((p->x - cx) * (p->x - cx) + (p->y - cy) * (p->y - cy));
    if (distance < radius - EPSILON)
        return INSIDE;
    else if (distance > radius + EPSILON)
        return OUTSIDE;
    return ON_CIRCLE;
#endif
#if PREDICATE == FAST_PREDICATE
    mat3_t ma, mbx, mby, mc;
    real x0y0, x1y1, x2y2;
    real a, bx, by, c, res;

    /* calculate x0y0, .... */
    x0y0 = pt0->x * pt0->x + pt0->y * pt0->y;
    x1y1 = pt1->x * pt1->x + pt1->y * pt1->y;
    x2y2 = pt2->x * pt2->x + pt2->y * pt2->y;

    /* setup A matrix */
    ma[0][0] = pt0->x;
    ma[0][1] = pt0->y;
    ma[1][0] = pt1->x;
    ma[1][1] = pt1->y;
    ma[2][0] = pt2->x;
    ma[2][1] = pt2->y;
    ma[0][2] = ma[1][2] = ma[2][2] = REAL_ONE;

    /* setup Bx matrix */
    mbx[0][0] = x0y0;
    mbx[1][0] = x1y1;
    mbx[2][0] = x2y2;
    mbx[0][1] = pt0->y;
    mbx[1][1] = pt1->y;
    mbx[2][1] = pt2->y;
    mbx[0][2] = mbx[1][2] = mbx[2][2] = REAL_ONE;

    /* setup By matrix */
    mby[0][0] = x0y0;
    mby[1][0] = x1y1;
    mby[2][0] = x2y2;
    mby[0][1] = pt0->x;
    mby[1][1] = pt1->x;
    mby[2][1] = pt2->x;
    mby[0][2] = mby[1][2] = mby[2][2] = REAL_ONE;

    /* setup C matrix */
    mc[0][0] = x0y0;
    mc[1][0] = x1y1;
    mc[2][0] = x2y2;
    mc[0][1] = pt0->x;
    mc[1][1] = pt1->x;
    mc[2][1] = pt2->x;
    mc[0][2] = pt0->y;
    mc[1][2] = pt1->y;
    mc[2][2] = pt2->y;

    /* compute a, bx, by and c */
    a = det3(&ma);
    bx = det3(&mbx);
    by = -det3(&mby);
    c = -det3(&mc);

    res = a * (p->x * p->x + p->y * p->y) - bx * p->x - by * p->y + c;

    if (res < REAL_ZERO)
        return INSIDE;
    else if (res > REAL_ZERO)
        return OUTSIDE;

    return ON_CIRCLE;
#endif
}

/*
 * initialize delaunay segment
 */
static auto del_init_seg(delaunay_t *del, int start) -> int
{
    halfedge_t *d0, *d1;
    point2d_t *pt0, *pt1;

    /* init delaunay */
    del->start_point = static_cast<quint32>(start);
    del->end_point = static_cast<quint32>(start + 1);

    /* setup pt0 and pt1 */
    pt0 = del->points[start];
    pt1 = del->points[start + 1];

    /* allocate the halfedges and setup them */
    d0 = halfedge_alloc();
    d1 = halfedge_alloc();

    d0->vertex = pt0;
    d1->vertex = pt1;

    d0->next = d0->prev = d0;
    d1->next = d1->prev = d1;

    d0->pair = d1;
    d1->pair = d0;

    pt0->he = d0;
    pt1->he = d1;

    del->rightmost_he = d1;
    del->leftmost_he = d0;

    return 0;
}

/*
 * initialize delaunay triangle
 */
static auto del_init_tri(delaunay_t *del, int start) -> int
{
    halfedge_t *d0, *d1, *d2, *d3, *d4, *d5;
    point2d_t *pt0, *pt1, *pt2;

    /* initiate delaunay */
    del->start_point = static_cast<quint32>(start);
    del->end_point = static_cast<quint32>(start + 2);

    /* setup the points */
    pt0 = del->points[start];
    pt1 = del->points[start + 1];
    pt2 = del->points[start + 2];

    /* allocate the 6 halfedges */
    d0 = halfedge_alloc();
    d1 = halfedge_alloc();
    d2 = halfedge_alloc();
    d3 = halfedge_alloc();
    d4 = halfedge_alloc();
    d5 = halfedge_alloc();

    if (classify_point_seg(pt0, pt2, pt1) == ON_LEFT) /* first case */
    {
        /* set halfedges points */
        d0->vertex = pt0;
        d1->vertex = pt2;
        d2->vertex = pt1;

        d3->vertex = pt2;
        d4->vertex = pt1;
        d5->vertex = pt0;

        /* set points halfedges */
        pt0->he = d0;
        pt1->he = d2;
        pt2->he = d1;

        /* next and next -1 setup */
        d0->next = d5;
        d0->prev = d5;

        d1->next = d3;
        d1->prev = d3;

        d2->next = d4;
        d2->prev = d4;

        d3->next = d1;
        d3->prev = d1;

        d4->next = d2;
        d4->prev = d2;

        d5->next = d0;
        d5->prev = d0;

        /* set halfedges pair */
        d0->pair = d3;
        d3->pair = d0;

        d1->pair = d4;
        d4->pair = d1;

        d2->pair = d5;
        d5->pair = d2;

        del->rightmost_he = d1;
        del->leftmost_he = d0;
    }
    else /* 2nd case */
    {
        /* set halfedges points */
        d0->vertex = pt0;
        d1->vertex = pt1;
        d2->vertex = pt2;

        d3->vertex = pt1;
        d4->vertex = pt2;
        d5->vertex = pt0;

        /* set points halfedges */
        pt0->he = d0;
        pt1->he = d1;
        pt2->he = d2;

        /* next and next -1 setup */
        d0->next = d5;
        d0->prev = d5;

        d1->next = d3;
        d1->prev = d3;

        d2->next = d4;
        d2->prev = d4;

        d3->next = d1;
        d3->prev = d1;

        d4->next = d2;
        d4->prev = d2;

        d5->next = d0;
        d5->prev = d0;

        /* set halfedges pair */
        d0->pair = d3;
        d3->pair = d0;

        d1->pair = d4;
        d4->pair = d1;

        d2->pair = d5;
        d5->pair = d2;

        del->rightmost_he = d2;
        del->leftmost_he = d0;
    }

    return 0;
}

/*
 * remove an edge given a halfedge
 */
static void del_remove_edge(halfedge_t *d)
{
    halfedge_t *next, *prev, *pair, *orig_pair;

    orig_pair = d->pair;

    next = d->next;
    prev = d->prev;
    pair = d->pair;

    assert(next != nullptr);
    assert(prev != nullptr);

    next->prev = prev;
    prev->next = next;

    /* check to see if we have already removed pair */
    if (pair)
        pair->pair = nullptr;

    /* check to see if the vertex points to this halfedge */
    if (d->vertex->he == d)
        d->vertex->he = next;

    d->vertex = nullptr;
    d->next = nullptr;
    d->prev = nullptr;
    d->pair = nullptr;

    next = orig_pair->next;
    prev = orig_pair->prev;
    pair = orig_pair->pair;

    assert(next != nullptr);
    assert(prev != nullptr);

    next->prev = prev;
    prev->next = next;

    /* check to see if we have already removed pair */
    if (pair)
        pair->pair = nullptr;

    /* check to see if the vertex points to this halfedge */
    if (orig_pair->vertex->he == orig_pair)
        orig_pair->vertex->he = next;

    orig_pair->vertex = nullptr;
    orig_pair->next = nullptr;
    orig_pair->prev = nullptr;
    orig_pair->pair = nullptr;

    /* finally free the halfedges */
    halfedge_free(d);
    halfedge_free(orig_pair);
}

/*
 * pass through all the halfedges on the left side and validate them
 */
static auto del_valid_left(halfedge_t *b) -> halfedge_t *
{
    point2d_t *g, *d, *u, *v;
    halfedge_t *c, *du, *dg;

    g = b->vertex; /* base halfedge point */
    dg = b;

    d = b->pair->vertex; /* pair(halfedge) point */
    b = b->next;

    u = b->pair->vertex; /* next(pair(halfedge)) point */
    du = b->pair;

    v = b->next->pair->vertex; /* pair(next(next(halfedge)) point */

    if (classify_point_seg(g, d, u) == ON_LEFT)
    {
        /* 3 points aren't colinear */
        /* as long as the 4 points belong to the same circle, do the cleaning */
        assert(v != u && "1: floating point precision error");
        while (v != d && v != g && in_circle(g, d, u, v) == INSIDE)
        {
            c = b->next;
            du = b->next->pair;
            del_remove_edge(b);
            b = c;
            u = du->vertex;
            v = b->next->pair->vertex;
        }

        assert(v != u && "2: floating point precision error");
        if (v != d && v != g && in_circle(g, d, u, v) == ON_CIRCLE)
        {
            du = du->prev;
            del_remove_edge(b);
        }
    }
    else /* treat the case where the 3 points are colinear */
        du = dg;

    assert(du->pair);
    return du;
}

/*
 * pass through all the halfedges on the right side and validate them
 */
static auto del_valid_right(halfedge_t *b) -> halfedge_t *
{
    point2d_t *rv, *lv, *u, *v;
    halfedge_t *c, *dd, *du;

    b = b->pair;
    rv = b->vertex;
    dd = b;
    lv = b->pair->vertex;
    b = b->prev;
    u = b->pair->vertex;
    du = b->pair;

    v = b->prev->pair->vertex;

    if (classify_point_seg(lv, rv, u) == ON_LEFT)
    {
        assert(v != u && "1: floating point precision error");
        while (v != lv && v != rv && in_circle(lv, rv, u, v) == INSIDE)
        {
            c = b->prev;
            du = c->pair;
            del_remove_edge(b);
            b = c;
            u = du->vertex;
            v = b->prev->pair->vertex;
        }

        assert(v != u && "1: floating point precision error");
        if (v != lv && v != rv && in_circle(lv, rv, u, v) == ON_CIRCLE)
        {
            du = du->next;
            del_remove_edge(b);
        }
    }
    else
        du = dd;

    assert(du->pair);
    return du;
}

/*
 * validate a link
 */
static auto del_valid_link(halfedge_t *b) -> halfedge_t *
{
    point2d_t *g, *g_p, *d, *d_p;
    halfedge_t *gd, *dd, *new_gd, *new_dd;

    g = b->vertex;
    gd = del_valid_left(b);
    g_p = gd->vertex;

    assert(b->pair);
    d = b->pair->vertex;
    dd = del_valid_right(b);
    d_p = dd->vertex;
    assert(b->pair);

    if (g != g_p && d != d_p)
    {
        int a = in_circle(g, d, g_p, d_p);

        if (a != ON_CIRCLE)
        {
            if (a == INSIDE)
            {
                // cppcheck-suppress unreadVariable
                g_p = g;
                gd = b;
            }
            else
            {
                // cppcheck-suppress unreadVariable
                d_p = d;
                dd = b->pair;
            }
        }
    }

    /* create the 2 halfedges */
    new_gd = halfedge_alloc();
    new_dd = halfedge_alloc();

    /* setup new_gd and new_dd */

    new_gd->vertex = gd->vertex;
    new_gd->pair = new_dd;
    new_gd->prev = gd;
    new_gd->next = gd->next;
    gd->next->prev = new_gd;
    gd->next = new_gd;

    new_dd->vertex = dd->vertex;
    new_dd->pair = new_gd;
    new_dd->prev = dd->prev;
    dd->prev->next = new_dd;
    new_dd->next = dd;
    dd->prev = new_dd;

    return new_gd;
}

/*
 * find the lower tangent between the two delaunay, going from left to right (returns the left half edge)
 */
static auto del_get_lower_tangent(delaunay_t *left, delaunay_t *right) -> halfedge_t *
{
    halfedge_t *right_d, *left_d, *new_ld, *new_rd;
    int sl, sr;

    left_d = left->rightmost_he;
    right_d = right->leftmost_he;

    do
    {
        point2d_t *pl = left_d->prev->pair->vertex;
        point2d_t *pr = right_d->pair->vertex;

        if ((sl = classify_point_seg(left_d->vertex, right_d->vertex, pl)) == ON_RIGHT)
        {
            left_d = left_d->prev->pair;
        }

        if ((sr = classify_point_seg(left_d->vertex, right_d->vertex, pr)) == ON_RIGHT)
        {
            right_d = right_d->pair->next;
        }

    } while (sl == ON_RIGHT || sr == ON_RIGHT);

    /* create the 2 halfedges */
    new_ld = halfedge_alloc();
    new_rd = halfedge_alloc();

    /* setup new_gd and new_dd */
    new_ld->vertex = left_d->vertex;
    new_ld->pair = new_rd;
    new_ld->prev = left_d->prev;
    left_d->prev->next = new_ld;
    new_ld->next = left_d;
    left_d->prev = new_ld;

    new_rd->vertex = right_d->vertex;
    new_rd->pair = new_ld;
    new_rd->prev = right_d->prev;
    right_d->prev->next = new_rd;
    new_rd->next = right_d;
    right_d->prev = new_rd;

    return new_ld;
}

/*
 * link the 2 delaunay together
 */
static void del_link(delaunay_t *result, delaunay_t *left, delaunay_t *right)
{
    point2d_t *u, *v, *ml, *mr;
    halfedge_t *base;

    assert(left->points == right->points);

    /* save the most right point and the most left point */
    ml = left->leftmost_he->vertex;
    mr = right->rightmost_he->vertex;

    base = del_get_lower_tangent(left, right);

    u = base->next->pair->vertex;
    v = base->pair->prev->pair->vertex;

    while (del_classify_point(base, u) == ON_LEFT || del_classify_point(base, v) == ON_LEFT)
    {
        base = del_valid_link(base);
        u = base->next->pair->vertex;
        v = base->pair->prev->pair->vertex;
    }

    right->rightmost_he = mr->he;
    left->leftmost_he = ml->he;

    /* TODO: this part is not needed, and can be optimized */
    while (del_classify_point(right->rightmost_he, right->rightmost_he->prev->pair->vertex) == ON_RIGHT)
        right->rightmost_he = right->rightmost_he->prev;

    while (del_classify_point(left->leftmost_he, left->leftmost_he->prev->pair->vertex) == ON_RIGHT)
        left->leftmost_he = left->leftmost_he->prev;

    result->leftmost_he = left->leftmost_he;
    result->rightmost_he = right->rightmost_he;
    result->points = left->points;
    result->start_point = left->start_point;
    result->end_point = right->end_point;
}

/*
 * divide and conquer delaunay
 */
void del_divide_and_conquer(delaunay_t *del, int start, int end);
void del_divide_and_conquer(delaunay_t *del, int start, int end)
{
    delaunay_t left, right;

    int n = (end - start + 1);

    if (n > 3)
    {
        int i = (n / 2) + (n & 1);
        left.points = del->points;
        right.points = del->points;
        del_divide_and_conquer(&left, start, start + i - 1);
        del_divide_and_conquer(&right, start + i, end);
        del_link(del, &left, &right);
    }
    else if (n == 3)
        del_init_tri(del, start);
    else if (n == 2)
        del_init_seg(del, start);
}

static void build_halfedge_face(delaunay_t *del, halfedge_t *d)
{
    halfedge_t *curr;

    /* test if the halfedge has already a pointing face */
    if (d->face != nullptr)
        return;

    del->faces = (face_t *)realloc(del->faces, (del->num_faces + 1) * sizeof(face_t));

    face_t *f = &(del->faces[del->num_faces]);
    curr = d;
    f->he = d;
    f->num_verts = 0;
    do
    {
        curr->face = f;
        (f->num_verts)++;
        curr = curr->pair->prev;
    } while (curr != d);

    (del->num_faces)++;

    /*	if( d->face.radius < 0.0 )
        {
            d->face.p[0]	= d->vertex;
            d->face.p[1]	= d->pair->vertex;
            d->face.p[2]	= d->pair->prev->pair->vertex;

            if( classify_point_seg( d->face.p[0], d->face.p[1], d->face.p[2] ) == ON_LEFT )
            {
                compute_circle(d->face.p[0], d->face.p[1], d->face.p[2], &(d->face.cx), &(d->face.cy),
       &(d->face.radius));
            }
        }
    */
}

/*
 * build the faces for all the halfedge
 */
void del_build_faces(delaunay_t *del);
void del_build_faces(delaunay_t *del)
{
    quint32 i;
    halfedge_t *curr;

    del->num_faces = 0;
    del->faces = nullptr;

    /* build external face first */
    build_halfedge_face(del, del->rightmost_he->pair);

    for (i = del->start_point; i <= del->end_point; i++)
    {
        curr = del->points[i]->he;

        do
        {
            build_halfedge_face(del, curr);
            curr = curr->next;
        } while (curr != del->points[i]->he);
    }
}

/*
 */
auto delaunay2d_from(del_point2d_t *points, quint32 num_points) -> delaunay2d_t *
{
    delaunay2d_t *res = nullptr;
    delaunay_t del;
    quint32 i;
    quint32 *faces = nullptr;

    del.num_faces = 0; // Warning using uninitialized value

#if PREDICATE == EXACT_PREDICATE
    exactinit();
#endif

    /* allocate the points */
    del.points = (point2d_t **)malloc(num_points * sizeof(point2d_t *));
    assert(del.points != nullptr);
    memset(del.points, 0, num_points * sizeof(point2d_t *));

    /* copy the points */
    for (i = 0; i < num_points; i++)
    {
        del.points[i] = point_alloc();
        del.points[i]->idx = i;
        del.points[i]->x = points[i].x;
        del.points[i]->y = points[i].y;
    }

    qsort(del.points, num_points, sizeof(point2d_t *), cmp_points);

    if (num_points >= 3)
    {
        quint32 fbuff_size = 0;
        quint32 j = 0;

        del_divide_and_conquer(&del, 0, static_cast<int>(num_points - 1));
        del_build_faces(&del);

        for (i = 0; i < del.num_faces; i++)
            fbuff_size += del.faces[i].num_verts + 1;

        faces = (quint32 *)malloc(sizeof(quint32) * fbuff_size);

        for (i = 0; i < del.num_faces; i++)
        {
            halfedge_t *curr;

            faces[j] = del.faces[i].num_verts;
            j++;

            curr = del.faces[i].he;
            do
            {
                faces[j] = curr->vertex->idx;
                j++;
                curr = curr->pair->prev;
            } while (curr != del.faces[i].he);
        }

        del_free_halfedges(&del);

        free(del.faces);
        for (i = 0; i < num_points; i++)
            point_free(del.points[i]);

        free(del.points);
    }

    res = (delaunay2d_t *)malloc(sizeof(delaunay2d_t));
    res->num_points = num_points;
    res->points = (del_point2d_t *)malloc(sizeof(del_point2d_t) * num_points);
    memcpy(res->points, points, sizeof(del_point2d_t) * num_points);
    res->num_faces = del.num_faces;
    res->faces = faces;

    return res;
}

void delaunay2d_release(delaunay2d_t *del)
{
    free(del->faces);
    free(del->points);
    free(del);
}

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