legal.c

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/* $Id$ $Revision$ */
/* vim:set shiftwidth=4 ts=8: */

/*************************************************************************
 * Copyright (c) 2011 AT&T Intellectual Property 
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * http://www.eclipse.org/legal/epl-v10.html
 *
 * Contributors: See CVS logs. Details at http://www.graphviz.org/
 *************************************************************************/

#include "neato.h"
#include "pathutil.h"
#include <setjmp.h>

static jmp_buf jbuf;

#define MAXINTS  10000          /* modify this line to reflect the max no. of 
                                   intersections you want reported -- 50000 seems to break the program */

#define SLOPE(p,q) ( ( ( p.y ) - ( q.y ) ) / ( ( p.x ) - ( q.x ) ) )

#define EQ_PT(v,w) (((v).x == (w).x) && ((v).y == (w).y))

#define after(v) (((v)==((v)->poly->finish))?((v)->poly->start):((v)+1))
#define prior(v) (((v)==((v)->poly->start))?((v)->poly->finish):((v)-1))

typedef struct active_edge active_edge;
typedef struct polygon polygon;

    typedef struct {
        pointf pos;
        polygon *poly;
        active_edge *active;
    } vertex ;

    struct polygon {
        vertex *start, *finish;
        boxf bb;
    };

    typedef struct {
        vertex *firstv, *secondv;
#ifdef RECORD_INTERSECTS
        polygon *firstp, *secondp;
#endif
        double x, y;
    } intersection ;

    struct active_edge {
        vertex *name;
        struct active_edge *next, *last;
    };
    typedef struct active_edge_list {
        active_edge *first, *final;
        int number;
    } active_edge_list ;
    typedef struct {
        int nvertices, npolygons, ninters;
    } data ;


/* find the sign of the area of each of the triangles
    formed by adding a vertex of m to l  
    also find the sign of their product  */
static void sgnarea(vertex *l, vertex *m, int i[])
{
    double a, b, c, d, e, f, g, h, t;
    a = l->pos.x;
    b = l->pos.y;
    c = after(l)->pos.x - a;
    d = after(l)->pos.y - b;
    e = m->pos.x - a;
    f = m->pos.y - b;
    g = after(m)->pos.x - a;
    h = after(m)->pos.y - b;
    t = (c * f) - (d * e);
    i[0] = ((t == 0) ? 0 : (t > 0 ? 1 : -1));
    t = (c * h) - (d * g);
    i[1] = ((t == 0) ? 0 : (t > 0 ? 1 : -1));
    i[2] = i[0] * i[1];
}

/* determine if g lies between f and h      */
static int between(double f, double g, double h)
{
    if ((f == g) || (g == h))
        return (0);
    return ((f < g) ? (g < h ? 1 : -1) : (h < g ? 1 : -1));
}

/* determine if vertex i of line m is on line l     */
static int online(vertex *l, vertex *m, int i)
{
    pointf a, b, c;
    a = l->pos;
    b = after(l)->pos;
    c = (i == 0) ? m->pos : after(m)->pos;
    return ((a.x == b.x) ? ((a.x == c.x)
                            && (-1 !=
                                between(a.y, c.y, b.y))) : between(a.x,
                                                                   c.x,
                                                                   b.x));
}

/* determine point of detected intersections  */
static int intpoint(vertex *l, vertex *m, double *x, double *y, int cond)
{
    pointf ls, le, ms, me, pt1, pt2;
    double m1, m2, c1, c2;

    if (cond <= 0)
        return (0);
    ls = l->pos;
    le = after(l)->pos;
    ms = m->pos;
    me = after(m)->pos;

    switch (cond) {

    case 3:                     /* a simple intersection        */
        if (ls.x == le.x) {
            *x = ls.x;
            *y = me.y + SLOPE(ms, me) * (*x - me.x);
        } else if (ms.x == me.x) {
            *x = ms.x;
            *y = le.y + SLOPE(ls, le) * (*x - le.x);
        } else {
            m1 = SLOPE(ms, me);
            m2 = SLOPE(ls, le);
            c1 = ms.y - (m1 * ms.x);
            c2 = ls.y - (m2 * ls.x);
            *x = (c2 - c1) / (m1 - m2);
            *y = ((m1 * c2) - (c1 * m2)) / (m1 - m2);
        }
        break;

    case 2:                     /*     the two lines  have a common segment  */
        if (online(l, m, 0) == -1) {    /* ms between ls and le */
            pt1 = ms;
            pt2 =
                (online(m, l, 1) ==
                 -1) ? ((online(m, l, 0) == -1) ? le : ls) : me;
        } else if (online(l, m, 1) == -1) {     /* me between ls and le */
            pt1 = me;
            pt2 =
                (online(l, m, 0) ==
                 -1) ? ((online(m, l, 0) == -1) ? le : ls) : ms;
        } else {
            /* may be degenerate? */
            if (online(m, l, 0) != -1)
                return 0;
            pt1 = ls;
            pt2 = le;
        }

        *x = (pt1.x + pt2.x) / 2;
        *y = (pt1.y + pt2.y) / 2;
        break;

    case 1:                     /* a vertex of line m is on line l */
        if ((ls.x - le.x) * (ms.y - ls.y) == (ls.y - le.y) * (ms.x - ls.x)) {
            *x = ms.x;
            *y = ms.y;
        } else {
            *x = me.x;
            *y = me.y;
        }
    }                           /* end switch  */
    return (1);
}

static void
putSeg (int i, vertex* v)
{
    fprintf(stderr, "seg#%d : (%.3f, %.3f) (%.3f, %.3f)\n",
        i, v->pos.x, v->pos.y, after(v)->pos.x, after(v)->pos.y);
}

/* realIntersect:
 * Return 1 if a real inatersection has been found
 */
static int
realIntersect (vertex *firstv, vertex *secondv, pointf p)
{
    pointf vft, vsd, avft, avsd;

    vft = firstv->pos;
    avft = after(firstv)->pos;
    vsd = secondv->pos;
    avsd = after(secondv)->pos;

    if (((vft.x != avft.x) && (vsd.x != avsd.x)) ||
        ((vft.x == avft.x) &&
         !EQ_PT(vft, p) &&
         !EQ_PT(avft, p)) ||
        ((vsd.x == avsd.x) &&
         !EQ_PT(vsd, p) && !EQ_PT(avsd, p))) 
    {
        if (Verbose > 1) {
                fprintf(stderr, "\nintersection at %.3f %.3f\n",
                        p.x, p.y);
                putSeg (1, firstv);
                putSeg (2, secondv);
        }
        return 1;
    }
    else return 0;
}

/* find_intersection:
 * detect whether segments l and m intersect      
 * Return 1 if found; 0 otherwise;
 */
static int find_intersection(vertex *l,
                  vertex *m,
                  intersection* ilist, data *input)
{
    double x, y;
    pointf p;
        int i[3];
    sgnarea(l, m, i);

    if (i[2] > 0)
        return 0;

    if (i[2] < 0) {
        sgnarea(m, l, i);
        if (i[2] > 0)
            return 0;
        if (!intpoint
            (l, m, &x, &y, (i[2] < 0) ? 3 : online(m, l, ABS(i[0]))))
            return 0;
    }

    else if (!intpoint(l, m, &x, &y, (i[0] == i[1]) ?
                       2 * MAX(online(l, m, 0),
                               online(l, m, 1)) : online(l, m, ABS(i[0]))))
        return 0;

#ifdef RECORD_INTERSECTS
    if (input->ninters >= MAXINTS) {
        agerr(AGERR, "using too many intersections\n");
        exit(1);
    }

    ilist[input->ninters].firstv = l;
    ilist[input->ninters].secondv = m;
    ilist[input->ninters].firstp = l->poly;
    ilist[input->ninters].secondp = m->poly;
    ilist[input->ninters].x = x;
    ilist[input->ninters].y = y;
    input->ninters++;
#endif
    p.x = x;
    p.y = y;
    return realIntersect(l, m, p);
}

static int gt(vertex **i, vertex **j)
{
    /* i > j if i.x > j.x or i.x = j.x and i.y > j.y  */
    double t;
    if ((t = (*i)->pos.x - (*j)->pos.x) != 0.)
        return ((t > 0.) ? 1 : -1);
    if ((t = (*i)->pos.y - (*j)->pos.y) == 0.)
        return (0);
    else
        return ((t > 0.) ? 1 : -1);
}

/* find_ints:
 * Check for pairwise intersection of polygon sides
 * Return 1 if intersection found, 0 otherwise.
 */
static int
find_ints(vertex vertex_list[],
          polygon polygon_list[],
          data *input, intersection ilist[])
{
    int i, j, k, found = 0;
    active_edge_list all;
    active_edge *new, *tempa;
    vertex *pt1, *pt2, *templ, **pvertex;

    input->ninters = 0;
    all.first = all.final = 0;
    all.number = 0;

    pvertex = N_GNEW(input->nvertices, vertex *);

    for (i = 0; i < input->nvertices; i++)
        pvertex[i] = vertex_list + i;

/* sort vertices by x coordinate        */
    qsort(pvertex, input->nvertices, sizeof(vertex *),
          (int (*)(const void *, const void *))gt);

/* walk through the vertices in order of increasing x coordinate        */
    for (i = 0; i < input->nvertices; i++) {
        pt1 = pvertex[i];
        templ = pt2 = prior(pvertex[i]);
        for (k = 0; k < 2; k++) {       /* each vertex has 2 edges */
            switch (gt(&pt1, &pt2)) {

            case -1:            /* forward edge, test and insert      */

                 /* test */
                for (tempa = all.first, j = 0; j < all.number;
                     j++, tempa = tempa->next) {
                    found = find_intersection(tempa->name, templ, ilist, input);
                    if (found)
                        goto finish;
                }

                new = GNEW(active_edge);
                if (all.number == 0) {
                    all.first = new;
                    new->last = 0;
                } /* insert */
                else {
                    all.final->next = new;
                    new->last = all.final;
                }

                new->name = templ;
                new->next = 0;
                templ->active = new;
                all.final = new;
                all.number++;

                break;          /* end of case -1       */

            case 1:             /* backward edge, delete        */

                if ((tempa = templ->active) == 0) {
                    agerr(AGERR, "trying to delete a non-line\n");
                    longjmp(jbuf, 1);
                }
                if (all.number == 1)
                    all.final = all.first = 0;  /* delete the line */
                else if (tempa == all.first) {
                    all.first = all.first->next;
                    all.first->last = 0;
                } else if (tempa == all.final) {
                    all.final = all.final->last;
                    all.final->next = 0;
                } else {
                    tempa->last->next = tempa->next;
                    tempa->next->last = tempa->last;
                }
                free((char *) tempa);
                all.number--;
                templ->active = 0;
                break;          /* end of case 1        */

            }                   /* end switch   */

            pt2 = after(pvertex[i]);
            templ = pvertex[i]; /*second neighbor */
        }                       /* end k for loop       */
    }                           /* end i for loop       */

finish :
    for (tempa = all.first, j = 0; j < all.number;
                     j++, tempa = new) {
        new = tempa->next;
        free (tempa);
    }
    free (pvertex);
    return found;
}

#define INBOX(p,bb) ((p.x <= bb.UR.x) && (p.x >= bb.LL.x) && (p.y <= bb.UR.y) && (p.y >= bb.LL.y))
#define NESTED(a,b) (INBOX(a.LL,b) && INBOX(a.UR,b))

/* findInside:
 * Check if one polygon is inside another. We know that each
 * pair is either disjoint or one is inside the other.
 * Return 1 if an intersection is found, 0 otherwise.
 */
static int
findInside(Ppoly_t ** polys, int n_polys, polygon* polygon_list)
{
    int i, j;
    pointf pt;
    Ppoly_t* p1;
    Ppoly_t* p2;

    for (i = 0; i < n_polys; i++) {
        p1 = polys[i];
        pt = p1->ps[0];
        for (j = i+1; j < n_polys; j++) {
            p2 = polys[j];
            if (NESTED(polygon_list[i].bb,polygon_list[j].bb)) {
                if (in_poly(*p2, pt)) return 1;
            }
            else if (NESTED(polygon_list[j].bb,polygon_list[i].bb)) {
                if (in_poly(*p1, p2->ps[0])) return 1;
            }
        }
    }
    return 0;
}

/* Plegal_arrangement:
 * Check that none of the polygons overlap.
 * Return 1 if okay; 0 otherwise.
 */
int Plegal_arrangement(Ppoly_t ** polys, int n_polys)
{
    int i, j, vno, nverts, found;
    vertex *vertex_list;
    polygon *polygon_list;
    data input;
    intersection ilist[MAXINTS];
    boxf bb;
    double x, y;

    polygon_list = N_GNEW(n_polys, polygon);

    for (i = nverts = 0; i < n_polys; i++)
        nverts += polys[i]->pn;

    vertex_list = N_GNEW(nverts, vertex);

    for (i = vno = 0; i < n_polys; i++) {
        polygon_list[i].start = &vertex_list[vno];
        bb.LL.x = bb.LL.y = MAXDOUBLE;
        bb.UR.x = bb.UR.y = -MAXDOUBLE;
        for (j = 0; j < polys[i]->pn; j++) {
            x = polys[i]->ps[j].x;
            y = polys[i]->ps[j].y;
            bb.LL.x = MIN(bb.LL.x,x);
            bb.LL.y = MIN(bb.LL.y,y);
            bb.UR.x = MAX(bb.UR.x,x);
            bb.UR.y = MAX(bb.UR.y,y);
            vertex_list[vno].pos.x = x;
            vertex_list[vno].pos.y = y;
            vertex_list[vno].poly = &polygon_list[i];
            vertex_list[vno].active = 0;
            vno++;
        }
        polygon_list[i].finish = &vertex_list[vno - 1];
        polygon_list[i].bb = bb;
    }

    input.nvertices = nverts;
    input.npolygons = n_polys;

    if (setjmp(jbuf)) {
        free(polygon_list);
        free(vertex_list);
        return 0;
    }
    found = find_ints(vertex_list, polygon_list, &input, ilist);

    if (!found) {
        found = findInside(polys, n_polys, polygon_list);
    }
    free(polygon_list);
    free(vertex_list);

    return !found;
}