ortho.c

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/*************************************************************************
 * 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
 * https://www.eclipse.org/legal/epl-v10.html
 *
 * Contributors: Details at https://graphviz.org
 *************************************************************************/
 
 
/* TODO:
 * In dot, prefer bottom or top routing
 * In general, prefer closest side to closest side routing.
 * Edge labels
 * Ports/compass points
 * ordering attribute
 * Weights on edges in nodes
 * Edge concentrators?
 */
 
#include "config.h"
 
#define DEBUG
#include <assert.h>
#include <float.h>
#include <math.h>
#include <stdbool.h>
#include <stddef.h>
#include <ortho/maze.h>
#include <ortho/fPQ.h>
#include <ortho/ortho.h>
#include <common/geomprocs.h>
#include <common/globals.h>
#include <common/render.h>
#include <common/pointset.h>
#include <util/alloc.h>
#include <util/exit.h>
#include <util/gv_math.h>
#include <util/list.h>
#include <util/unused.h>
 
typedef struct {
    int d;
    Agedge_t* e;
} epair_t;
 
static UNUSED void emitSearchGraph(FILE *fp, sgraph *sg);
static UNUSED void emitGraph(FILE *fp, maze *mp, size_t n_edges,
                             route *route_list, epair_t[]);
#ifdef DEBUG
int odb_flags;
#endif
 
#define CELL(n) ((cell*)ND_alg(n))
 
static double MID(double a, double b) {
  return (a + b) / 2.0;
}
 
/* cellOf:
 * Given 2 snodes sharing a cell, return the cell.
 */
static cell*
cellOf (snode* p, snode* q)
{
    cell* cp = p->cells[0];
    if (cp == q->cells[0] || cp == q->cells[1]) return cp;
    return p->cells[1];
}
 
static pointf midPt(const cell *cp) {
  return mid_pointf(cp->bb.LL, cp->bb.UR);
}
 
/* sidePt:
 * Given a cell and an snode on one of its sides, return the
 * midpoint of the side.
 */
static pointf sidePt(const snode ptr, const cell* cp) {
    if (cp == ptr.cells[1]) {
        if (ptr.isVert) {
            return (pointf){.x = cp->bb.LL.x, .y = MID(cp->bb.LL.y, cp->bb.UR.y)};
        }
        return (pointf){.x = MID(cp->bb.LL.x, cp->bb.UR.x), .y = cp->bb.LL.y};
    }
    if (ptr.isVert) {
        return (pointf){.x = cp->bb.UR.x, .y = MID(cp->bb.LL.y, cp->bb.UR.y)};
    }
    return (pointf){.x = MID(cp->bb.LL.x, cp->bb.UR.x), .y = cp->bb.UR.y};
}
 
/* setSet:
 * Initialize and normalize segments.
 * p1 stores smaller value
 * Assume b1 != b2
 */
static void
setSeg (segment* sp, bool dir, double fix, double b1, double b2, int l1, int l2)
{
    sp->isVert = dir;
    sp->comm_coord = fix;
    if (b1 < b2) {
        sp->p.p1 = b1;
        sp->p.p2 = b2;
        sp->l1 = l1;
        sp->l2 = l2;
    }
    else {
        sp->p.p2 = b1;
        sp->p.p1 = b2;
        sp->l2 = l1;
        sp->l1 = l2;
    }
}
 
/* Convert route in shortest path graph to route
 * of segments. This records the first and last cells,
 * plus cells where the path bends.
 * Note that the shortest path will always have at least 4 nodes:
 * the two dummy nodes representing the center of the two real nodes,
 * and the two nodes on the boundary of the two real nodes.
 */
static route
convertSPtoRoute (sgraph* g, snode* fst, snode* lst)
{
    snode* ptr;
    snode* next;
    snode* prev;  /* node in shortest path just previous to next */
    cell* cp;
    cell* ncp;
    segment seg;
    double fix, b1, b2;
    int l1, l2;
    pointf bp1, prevbp = {0.0,0.0};  /* bend points */
 
    LIST(segment) rte = {0};
 
    seg.prev = seg.next = 0;
    ptr = prev = N_DAD(fst);
    next = N_DAD(ptr);
    if (IsNode(ptr->cells[0]))
        cp = ptr->cells[1];
    else
        cp = ptr->cells[0];
    bp1 = sidePt(*ptr, cp);
    while (N_DAD(next)!=NULL) {
        ncp = cellOf (prev, next);
        updateWts (g, ncp, N_EDGE(ptr));
 
        /* add seg if path bends or at end */
        if (ptr->isVert != next->isVert || N_DAD(next) == lst) {
            const pointf bp2 = ptr->isVert != next->isVert ? midPt (ncp) : sidePt(*next, ncp);
            if (ptr->isVert) {   /* horizontal segment */
                if (ptr == N_DAD(fst)) l1 = B_NODE;
                else if (prevbp.y > bp1.y) l1 = B_UP;
                else l1 = B_DOWN; 
                if (ptr->isVert != next->isVert) {
                    if (next->cells[0] == ncp) l2 = B_UP;
                    else l2 = B_DOWN;
                }
                else l2 = B_NODE;
                fix = cp->bb.LL.y;
                b1 = cp->bb.LL.x;
                b2 = ncp->bb.LL.x;
            }
            else {   /* vertical segment */
                if (ptr == N_DAD(fst)) l1 = B_NODE;
                else if (prevbp.x > bp1.x) l1 = B_RIGHT;
                else l1 = B_LEFT; 
                if (ptr->isVert != next->isVert) {
                    if (next->cells[0] == ncp) l2 = B_RIGHT;
                    else l2 = B_LEFT;
                }
                else l2 = B_NODE;
                fix = cp->bb.LL.x;
                b1 = cp->bb.LL.y;
                b2 = ncp->bb.LL.y;
            }
            setSeg (&seg, !ptr->isVert, fix, b1, b2, l1, l2);
            LIST_APPEND(&rte, seg);
            cp = ncp;
            prevbp = bp1;
            bp1 = bp2;
            if (ptr->isVert != next->isVert && N_DAD(next) == lst) {
                l2 = B_NODE;
                if (next->isVert) {   /* horizontal segment */
                    if (prevbp.y > bp1.y) l1 = B_UP;
                    else l1 = B_DOWN; 
                    fix = cp->bb.LL.y;
                    b1 = cp->bb.LL.x;
                    b2 = ncp->bb.LL.x;
                }
                else {
                    if (prevbp.x > bp1.x) l1 = B_RIGHT;
                    else l1 = B_LEFT; 
                    fix = cp->bb.LL.x;
                    b1 = cp->bb.LL.y;
                    b2 = ncp->bb.LL.y;
                }
                setSeg (&seg, !next->isVert, fix, b1, b2, l1, l2);
                LIST_APPEND(&rte, seg);
            }
            ptr = next;
        }
        prev = next;
        next = N_DAD(next);
    }
 
    route ret = {0};
    LIST_DETACH(&rte, &ret.segs, &ret.n);
    for (size_t i = 0; i < ret.n; i++) {
        if (i > 0)
            ret.segs[i].prev = ret.segs + (i - 1);
        if (i < ret.n - 1)
            ret.segs[i].next = ret.segs + (i + 1);
    }
 
    return ret;
}
 
typedef struct {
    Dtlink_t  link;
    double    v;
    Dt_t*     chans;
} chanItem;
 
static void freeChannel(void *chan) {
    channel *cp = chan;
    free_graph (cp->G);
    LIST_FREE(&cp->seg_list);
    free (cp);
}
 
static void freeChanItem(void *item) {
    chanItem *cp = item;
    dtclose (cp->chans);
    free (cp);
}
 
/* chancmpid:
 * Compare intervals. Two intervals are equal if one contains
 * the other. Otherwise, the one with the smaller p1 value is
 * less. 
 * This combines two separate functions into one. Channels are
 * disjoint, so we really only need to key on p1.
 * When searching for a channel containing a segment, we rely on
 * interval containment to return the correct channel.
 */
static int chancmpid(void *k1, void *k2) {
  const paird *key1 = k1;
  const paird *key2 = k2;
  if (key1->p1 > key2->p1) {
    if (key1->p2 <= key2->p2) return 0;
    return 1;
  }
  if (key1->p1 < key2->p1) {
    if (key1->p2 >= key2->p2) return 0;
    return -1;
  }
  return 0;
}   
 
static int dcmpid(void *k1, void *k2) {
  const double *key1 = k1;
  const double *key2 = k2;
  return fcmp(*key1, *key2);
}   
 
static Dtdisc_t chanDisc = {
    offsetof(channel,p),
    sizeof(paird),
    offsetof(channel,link),
    0,
    freeChannel,
    chancmpid,
};
 
static Dtdisc_t chanItemDisc = {
    offsetof(chanItem,v),
    sizeof(double),
    offsetof(chanItem,link),
    0,
    freeChanItem,
    dcmpid,
};
 
static void
addChan (Dt_t* chdict, channel* cp, double j)
{
    chanItem* subd = dtmatch (chdict, &j);
 
    if (!subd) {
        subd = gv_alloc(sizeof(chanItem));
        subd->v = j;
        subd->chans = dtopen (&chanDisc, Dtoset);
        dtinsert (chdict, subd);
    }
    if (dtinsert(subd->chans, cp) != cp) {
        free(cp);
    }
}
 
static Dt_t*
extractHChans (maze* mp)
{
    snode* np;
    Dt_t* hchans = dtopen (&chanItemDisc, Dtoset);
 
    for (size_t i = 0; i < mp->ncells; i++) {
        channel* chp;
        cell* cp = mp->cells+i;
        cell* nextcp;
        if (IsHScan(cp)) continue;
 
        /* move left */
        while ((np = cp->sides[M_LEFT]) && (nextcp = np->cells[0]) &&
            !IsNode(nextcp)) {
            cp = nextcp;
        }
 
        chp = gv_alloc(sizeof(channel));
        chp->cp = cp;
        chp->p.p1 = cp->bb.LL.x;
 
        /* move right */
        cp->flags |= MZ_HSCAN;
        while ((np = cp->sides[M_RIGHT]) && (nextcp = np->cells[1]) &&
            !IsNode(nextcp)) {
            cp = nextcp;
            cp->flags |= MZ_HSCAN;
        }
 
        chp->p.p2 = cp->bb.UR.x;
        addChan (hchans, chp, chp->cp->bb.LL.y);
    }
    return hchans;
}
 
static Dt_t*
extractVChans (maze* mp)
{
    snode* np;
    Dt_t* vchans = dtopen (&chanItemDisc, Dtoset);
 
    for (size_t i = 0; i < mp->ncells; i++) {
        channel* chp;
        cell* cp = mp->cells+i;
        cell* nextcp;
        if (IsVScan(cp)) continue;
 
        /* move down */
        while ((np = cp->sides[M_BOTTOM]) && (nextcp = np->cells[0]) &&
            !IsNode(nextcp)) {
            cp = nextcp;
        }
 
        chp = gv_alloc(sizeof(channel));
        chp->cp = cp;
        chp->p.p1 = cp->bb.LL.y;
 
        /* move up */
        cp->flags |= MZ_VSCAN;
        while ((np = cp->sides[M_TOP]) && (nextcp = np->cells[1]) &&
            !IsNode(nextcp)) {
            cp = nextcp;
            cp->flags |= MZ_VSCAN;
        }
 
        chp->p.p2 = cp->bb.UR.y;
        addChan (vchans, chp, chp->cp->bb.LL.x);
    }
    return vchans;
}
 
static void
insertChan (channel* chan, segment* seg)
{
    seg->ind_no = LIST_SIZE(&chan->seg_list);
    LIST_APPEND(&chan->seg_list, seg);
}
 
static channel*
chanSearch (Dt_t* chans, segment* seg)
{
  channel* cp;
  chanItem* chani = dtmatch (chans, &seg->comm_coord);
  assert (chani);
  cp = dtmatch (chani->chans, &seg->p);
  assert (cp);
  return cp;
}
 
static void
assignSegs (size_t nrtes, route* route_list, maze* mp)
{
    channel* chan;
 
    for (size_t i=0;i<nrtes;i++) {
        route rte = route_list[i];
        for (size_t j=0;j<rte.n;j++) {
            segment* seg = rte.segs+j;
            if (seg->isVert)
                chan = chanSearch(mp->vchans, seg);
            else
                chan = chanSearch(mp->hchans, seg);
            insertChan (chan, seg);
        }
    }
}
 
/* addLoop:
 * Add two temporary nodes to sgraph corresponding to two ends of a loop at cell cp, i
 * represented by dp and sp.
 */
static void
addLoop (sgraph* sg, cell* cp, snode* dp, snode* sp)
{
    for (size_t i = 0; i < cp->nsides; i++) {
        snode* onp = cp->sides[i];
 
        if (onp->isVert) continue;
        const bool onTop = onp->cells[0] == cp;
        if (onTop)
            createSEdge (sg, sp, onp, 0);  /* FIX weight */
        else
            createSEdge (sg, dp, onp, 0);  /* FIX weight */
    }
    sg->nnodes += 2;
}
 
/* addNodeEdges:
 * Add temporary node to sgraph corresponding to cell cp, represented
 * by np.
 */
static void
addNodeEdges (sgraph* sg, cell* cp, snode* np)
{
    for (size_t i = 0; i < cp->nsides; i++) {
        snode* onp = cp->sides[i];
 
        createSEdge (sg, np, onp, 0);  /* FIX weight */
    }
    sg->nnodes++;
#ifdef DEBUG
    np->cells[0] = np->cells[1] = cp;
#endif
}
 
static char* bendToStr (bend b)
{
  char* s = NULL;
  switch (b) {
  case B_NODE :
    s = "B_NODE";
    break;
  case B_UP :
    s = "B_UP";
    break;
  case B_LEFT :
    s = "B_LEFT";
    break;
  case B_DOWN :
    s = "B_DOWN";
    break;
  default:
    assert(b == B_RIGHT);
    s = "B_RIGHT";
    break;
  }
  return s;
}
 
static void putSeg (FILE* fp, segment* seg)
{
  if (seg->isVert)
    fprintf (fp, "((%f,%f),(%f,%f)) %s %s", seg->comm_coord, seg->p.p1,
      seg->comm_coord, seg->p.p2, bendToStr (seg->l1), bendToStr (seg->l2));
  else
    fprintf (fp, "((%f,%f),(%f,%f)) %s %s", seg->p.p1,seg->comm_coord, 
      seg->p.p2, seg->comm_coord, bendToStr (seg->l1), bendToStr (seg->l2));
}
 
static UNUSED void dumpChanG(channel *cp, double v) {
  if (LIST_SIZE(&cp->seg_list) < 2) return;
  fprintf (stderr, "channel %.0f (%f,%f)\n", v, cp->p.p1, cp->p.p2);
  for (size_t k = 0; k < LIST_SIZE(&cp->seg_list); ++k) {
    const adj_list_t adj = cp->G->vertices[k].adj_list;
    if (LIST_IS_EMPTY(&adj)) continue;
    putSeg(stderr, LIST_GET(&cp->seg_list, k));
    fputs (" ->\n", stderr);
    for (size_t i = 0; i < LIST_SIZE(&adj); ++i) {
      fputs ("     ", stderr);
      putSeg(stderr, LIST_GET(&cp->seg_list, LIST_GET(&adj, i)));
      fputs ("\n", stderr);
    }
  }
}
 
static void
assignTrackNo (Dt_t* chans)
{
    Dt_t* lp;
    Dtlink_t* l1;
    Dtlink_t* l2;
    channel* cp;
 
    for (l1 = dtflatten (chans); l1; l1 = dtlink(chans,l1)) {
        lp = ((chanItem*)l1)->chans;
        for (l2 = dtflatten (lp); l2; l2 = dtlink(lp,l2)) {
            cp = (channel*)l2;
            if (!LIST_IS_EMPTY(&cp->seg_list)) {
#ifdef DEBUG
    if (odb_flags & ODB_CHANG) dumpChanG (cp, ((chanItem*)l1)->v);
#endif
                top_sort (cp->G);
                for (size_t k = 0; k < LIST_SIZE(&cp->seg_list); ++k)
                    LIST_GET(&cp->seg_list, k)->track_no = cp->G->vertices[k].topsort_order+1;
            }
        }
    }
}
 
static void
create_graphs(Dt_t* chans)
{
    Dt_t* lp;
    Dtlink_t* l1;
    Dtlink_t* l2;
    channel* cp;
 
    for (l1 = dtflatten (chans); l1; l1 = dtlink(chans,l1)) {
        lp = ((chanItem*)l1)->chans;
        for (l2 = dtflatten (lp); l2; l2 = dtlink(lp,l2)) {
            cp = (channel*)l2;
            cp->G = make_graph(LIST_SIZE(&cp->seg_list));
        }
    }
}
 
static int
eqEndSeg (bend S1l2, bend S2l2, bend T1, bend T2)
{
    if ((S1l2==T2 && S2l2!=T2) || (S1l2==B_NODE && S2l2==T1))
        return 0;
    else
        return -1;
}
 
static int
overlapSeg (segment* S1, segment* S2, bend T1, bend T2)
{
        if(S1->p.p2<S2->p.p2) {
                if (S1->l2 == T1 && S2->l1 == T2) return -1;
                if (S1->l2 == T2 && S2->l1 == T1) return 1;
                return 0;
        }
        if (S1->p.p2 > S2->p.p2) {
                if (S2->l1 == T2 && S2->l2 == T2) return -1;
                if (S2->l1 == T1 && S2->l2 == T1) return 1;
                return 0;
        }
        if (S2->l1 == T2) return eqEndSeg (S1->l2, S2->l2, T1, T2);
        return -1 * eqEndSeg(S2->l2, S1->l2, T1, T2);
}
 
static int
ellSeg (bend S1l1, bend S1l2, bend T)
{
    if (S1l1 == T) {
        if (S1l2== T) return -1;
        return 0;
    }
    return 1;
}
 
static int
segCmp (segment* S1, segment* S2, bend T1, bend T2)
{
        /* no overlap */
    if (S1->p.p2 < S2->p.p1 || S1->p.p1 > S2->p.p2) return 0;
        /* left endpoint of S2 inside S1 */
    if(S1->p.p1<S2->p.p1&&S2->p.p1<S1->p.p2)
        return overlapSeg (S1, S2, T1, T2);
        /* left endpoint of S1 inside S2 */
    if (S2->p.p1 < S1->p.p1 && S1->p.p1 < S2->p.p2)
        return -1*overlapSeg (S2, S1, T1, T2);
    if (S1->p.p1 == S2->p.p1) {
        if (S1->p.p2 < S2->p.p2) {
            if(S1->l2==T1)
                return eqEndSeg (S2->l1, S1->l1, T1, T2);
            return -1 * eqEndSeg(S2->l1, S1->l1, T1, T2);
        }
        if (S1->p.p2 > S2->p.p2) {
            if (S2->l2 == T2)
                return eqEndSeg(S1->l1, S2->l1, T1, T2);
            return -1 * eqEndSeg(S1->l1, S2->l1, T1, T2);
        }
        if (S1->l1 == S2->l1 && S1->l2 == S2->l2)
            return 0;
        if (S2->l1 == S2->l2) {
            if (S2->l1 == T1) return 1;
            if (S2->l1 == T2) return -1;
            if (S1->l1 != T1 && S1->l2 != T1) return 1;
            if (S1->l1 != T2 && S1->l2 != T2) return -1;
            return 0;
        }
        if (S2->l1 == T1 && S2->l2 == T2) {
            if (S1->l1 != T1 && S1->l2 == T2) return 1;
            if (S1->l1 == T1 && S1->l2 != T2) return -1;
            return 0;
        }
        if (S2->l2 == T1 && S2->l1 == T2) {
            if (S1->l2 != T1 && S1->l1 == T2) return 1;
            if (S1->l2 == T1 && S1->l1 != T2) return -1;
            return 0;
        }
        if (S2->l1 == B_NODE && S2->l2 == T1) {
            return ellSeg (S1->l1, S1->l2, T1);
        }
        if (S2->l1 == B_NODE && S2->l2 == T2) {
            return -1*ellSeg (S1->l1, S1->l2, T2);
        }
        if (S2->l1 == T1 && S2->l2 == B_NODE) {
            return ellSeg (S1->l2, S1->l1, T1);
        }
        /* ((S2->l1==T2)&&(S2->l2==B_NODE)) */
        return -1 * ellSeg(S1->l2, S1->l1, T2);
    }
    if (S1->p.p2 == S2->p.p1) {
        if (S1->l2 == S2->l1) return 0;
        if (S1->l2 == T2) return 1;
        return -1;
    }
    /* S1->p.p1==S2->p.p2 */
    if (S1->l1 == S2->l2) return 0;
    if (S1->l1 == T2) return 1;
    return -1;
}
 
/* Function seg_cmp returns
 *  -1 if S1 HAS TO BE to the right/below S2 to avoid a crossing, 
 *   0 if a crossing is unavoidable or there is no crossing at all or 
 *     the segments are parallel,
 *   1 if S1 HAS TO BE to the left/above S2 to avoid a crossing
 *  -2 if S1 and S2 are incomparable
 *
 * Note: This definition means horizontal segments have track numbers
 * increasing as y decreases, while vertical segments have track numbers
 * increasing as x increases. It would be good to make this consistent,
 * with horizontal track numbers increasing with y. This can be done by
 * switching B_DOWN and B_UP in the first call to segCmp. At present,
 * though, I'm not sure what assumptions are made in handling parallel
 * segments, so we leave the code alone for the time being.
 */
static int
seg_cmp(segment* S1, segment* S2)               
{
    if(S1->isVert!=S2->isVert||S1->comm_coord!=S2->comm_coord) {
        agerrorf("incomparable segments !! -- Aborting\n");
        return -2;
    }
    if(S1->isVert)
        return segCmp (S1, S2, B_RIGHT, B_LEFT);
    else
        return segCmp (S1, S2, B_DOWN, B_UP);
}
 
static int
add_edges_in_G(channel* cp)
{
    seg_list_t *seg_list = &cp->seg_list;
    const size_t size = LIST_SIZE(&cp->seg_list);
    rawgraph* G = cp->G;
 
    for (size_t x = 0; x + 1 < size; ++x) {
        for (size_t y = x + 1; y < size; ++y) {
            const int cmp = seg_cmp(LIST_GET(seg_list, x), LIST_GET(seg_list, y));
            if (cmp == -2) {
                return -1;
            } else if (cmp > 0) {
                insert_edge(G,x,y);
            } else if (cmp == -1) {
                insert_edge(G,y,x);
            }
        }
    }
 
    return 0;
}
 
static int
add_np_edges (Dt_t* chans)
{
    for (Dtlink_t *l1 = dtflatten(chans); l1; l1 = dtlink(chans, l1)) {
        Dt_t *const lp = ((chanItem*)l1)->chans;
        for (Dtlink_t *l2 = dtflatten(lp); l2; l2 = dtlink(lp, l2)) {
            channel *const cp = (channel*)l2;
            if (!LIST_IS_EMPTY(&cp->seg_list))
                if (add_edges_in_G(cp)) {
                  return -1;
                }
        }
    }
 
    return 0;
}
 
static segment*
next_seg(segment* seg, int dir)
{
    assert(seg);
    if (!dir)
        return seg->prev;
    else
        return seg->next;
}
 
/* propagate_prec propagates the precedence relationship along 
 * a series of parallel segments on 2 edges
 */
static int
propagate_prec(segment* seg, int prec, int hops, int dir)
{
    int x;
    int ans=prec;
    segment* next;
    segment* current;
 
    current = seg;
    for(x=1;x<=hops;x++) {
        next = next_seg(current, dir);
        if(!current->isVert) {
            if(next->comm_coord==current->p.p1) {
                if(current->l1==B_UP) ans *= -1;
            }
            else {
                if(current->l2==B_DOWN) ans *= -1;
            }
        }
        else {
            if(next->comm_coord==current->p.p1) {
                if(current->l1==B_RIGHT) ans *= -1;
            }
            else {
                if(current->l2==B_LEFT) ans *= -1;
            }
        }
        current = next;
    }
    return ans;
}
 
static bool
is_parallel(segment* s1, segment* s2)
{
    assert (s1->comm_coord==s2->comm_coord);
    return s1->p.p1 == s2->p.p1 &&
           s1->p.p2 == s2->p.p2 &&
           s1->l1 == s2->l1 &&
           s1->l2 == s2->l2;
}
 
/* decide_point returns (through ret) the number of hops needed in the given
 * directions along the 2 edges to get to a deciding point (or NODES) and also
 * puts into prec the appropriate dependency (follows same convention as
 * seg_cmp)
 */
static int
decide_point(pair *ret, segment* si, segment* sj, int dir1, int dir2)
{
    int prec = 0, ans = 0, temp;
    segment* np1;
    segment *np2 = NULL;
    
    while ((np1 = next_seg(si,dir1)) && (np2 = next_seg(sj,dir2)) &&
        is_parallel(np1, np2)) {
        ans++;
        si = np1;
        sj = np2;
    }
    if (!np1)
        prec = 0;
    else if (!np2)
        assert(0); /* FIXME */
    else {
        temp = seg_cmp(np1, np2);
        if (temp == -2) {
            return -1;
        }
        prec = propagate_prec(np1, temp, ans+1, 1-dir1);
    }
                
    ret->a = ans;
    ret->b = prec;
    return 0;
}
 
/* sets the edges for a series of parallel segments along two edges starting 
 * from segment i, segment j. It is assumed that the edge should be from 
 * segment i to segment j - the dependency is appropriately propagated
 */
static void
set_parallel_edges (segment* seg1, segment* seg2, int dir1, int dir2, int hops,
    maze* mp)
{
    int x;
    channel* chan;
    channel* nchan;
    segment* prev1;
    segment* prev2;
 
    if (seg1->isVert)
        chan = chanSearch(mp->vchans, seg1);
    else
        chan = chanSearch(mp->hchans, seg1);
    insert_edge(chan->G, seg1->ind_no, seg2->ind_no);
 
    for (x=1;x<=hops;x++) {
        prev1 = next_seg(seg1, dir1);
        prev2 = next_seg(seg2, dir2);
        if(!seg1->isVert) {
            nchan = chanSearch(mp->vchans, prev1);
            if(prev1->comm_coord==seg1->p.p1) {
                if(seg1->l1==B_UP) {
                    if(edge_exists(chan->G, seg1->ind_no, seg2->ind_no))
                        insert_edge(nchan->G, prev2->ind_no, prev1->ind_no);
                    else
                        insert_edge(nchan->G, prev1->ind_no, prev2->ind_no);
                }
                else {
                    if(edge_exists(chan->G, seg1->ind_no, seg2->ind_no))
                        insert_edge(nchan->G, prev1->ind_no, prev2->ind_no);
                    else
                        insert_edge(nchan->G, prev2->ind_no, prev1->ind_no);
                }
            }
            else {
                if(seg1->l2==B_UP) {
                    if(edge_exists(chan->G, seg1->ind_no, seg2->ind_no))
                        insert_edge(nchan->G,prev1->ind_no, prev2->ind_no);
                    else
                        insert_edge(nchan->G,prev2->ind_no, prev1->ind_no);
                }
                else {
                    if(edge_exists(chan->G, seg1->ind_no, seg2->ind_no))
                        insert_edge(nchan->G, prev2->ind_no, prev1->ind_no);
                    else
                        insert_edge(nchan->G, prev1->ind_no, prev2->ind_no);
                }
            }
        }
        else {
            nchan = chanSearch(mp->hchans, prev1);
            if(prev1->comm_coord==seg1->p.p1) {
                if(seg1->l1==B_LEFT) {
                    if(edge_exists(chan->G, seg1->ind_no, seg2->ind_no))
                        insert_edge(nchan->G, prev1->ind_no, prev2->ind_no);
                    else
                        insert_edge(nchan->G, prev2->ind_no, prev1->ind_no);
                }
                else {
                    if(edge_exists(chan->G, seg1->ind_no, seg2->ind_no))
                        insert_edge(nchan->G, prev2->ind_no, prev1->ind_no);
                    else
                        insert_edge(nchan->G, prev1->ind_no, prev2->ind_no);
                }
            }
            else {
                if(seg1->l2==B_LEFT) {
                    if(edge_exists(chan->G, seg1->ind_no, seg2->ind_no))
                        insert_edge(nchan->G, prev2->ind_no, prev1->ind_no);
                    else
                        insert_edge(nchan->G, prev1->ind_no, prev2->ind_no);
                }
                else {
                    if(edge_exists(chan->G, seg1->ind_no, seg2->ind_no))
                        insert_edge(nchan->G, prev1->ind_no, prev2->ind_no);
                    else
                        insert_edge(nchan->G, prev2->ind_no, prev1->ind_no);
                }
            }
        }
        chan = nchan;
        seg1 = prev1;
        seg2 = prev2;
    }
}
 
/* removes the edge between segments after the resolution of a conflict
 */
static void
removeEdge(segment* seg1, segment* seg2, int dir, maze* mp)
{
    segment* ptr1;
    segment* ptr2;
    channel* chan;
 
    ptr1 = seg1;
    ptr2 = seg2;
    while(is_parallel(ptr1, ptr2)) {
        ptr1 = next_seg(ptr1, 1);
        ptr2 = next_seg(ptr2, dir);
    }
    if(ptr1->isVert)
        chan = chanSearch(mp->vchans, ptr1);
    else
        chan = chanSearch(mp->hchans, ptr1);
    remove_redge (chan->G, ptr1->ind_no, ptr2->ind_no);
}
 
static int
addPEdges (channel* cp, maze* mp)
{
    /* dir[1,2] are used to figure out whether we should use prev 
     * pointers or next pointers -- 0 : decrease, 1 : increase
     */
    int dir;
    /* number of hops along the route to get to the deciding points */
    pair hops;
    /* precedences of the deciding points : same convention as 
     * seg_cmp function 
     */
    int prec1, prec2;
    pair p;
    rawgraph* G = cp->G;
    seg_list_t *segs = &cp->seg_list;
 
    for(size_t i = 0; i + 1 < LIST_SIZE(&cp->seg_list); ++i) {
        for(size_t j = i + 1; j < LIST_SIZE(&cp->seg_list); ++j) {
            if (!edge_exists(G,i,j) && !edge_exists(G,j,i)) {
                if (is_parallel(LIST_GET(segs, i), LIST_GET(segs, j))) {
                /* get_directions */
                    if (LIST_GET(segs, i)->prev == 0) {
                        if (LIST_GET(segs, j)->prev == 0)
                            dir = 0;
                        else
                            dir = 1;
                    }
                    else if (LIST_GET(segs, j)->prev == 0) {
                        dir = 1;
                    }
                    else {
                        if (LIST_GET(segs, i)->prev->comm_coord ==
                            LIST_GET(segs, j)->prev->comm_coord)
                            dir = 0;
                        else
                            dir = 1;
                    }
 
                    if (decide_point(&p, LIST_GET(segs, i), LIST_GET(segs, j), 0, dir)
                        != 0) {
                        return -1;
                    }
                    hops.a = p.a;
                    prec1 = p.b;
                    if (decide_point(&p, LIST_GET(segs, i), LIST_GET(segs, j), 1,
                                     1 - dir) != 0) {
                        return -1;
                    }
                    hops.b = p.a;
                    prec2 = p.b;
 
                    if (prec1 == -1) {
                        set_parallel_edges(LIST_GET(segs, j), LIST_GET(segs, i), dir, 0,
                                           hops.a, mp);
                        set_parallel_edges(LIST_GET(segs, j), LIST_GET(segs, i), 1 - dir, 1,
                                           hops.b, mp);
                        if(prec2==1)
                            removeEdge(LIST_GET(segs, i), LIST_GET(segs, j), 1 - dir, mp);
                    } else if (prec1 == 0) {
                        if (prec2 == -1) {
                            set_parallel_edges(LIST_GET(segs, j), LIST_GET(segs, i), dir, 0,
                                               hops.a, mp);
                            set_parallel_edges(LIST_GET(segs, j), LIST_GET(segs, i), 1 - dir,
                                               1, hops.b, mp);
                        } else if (prec2 == 0) {
                            set_parallel_edges(LIST_GET(segs, i), LIST_GET(segs, j), 0, dir,
                                               hops.a, mp);
                            set_parallel_edges(LIST_GET(segs, i), LIST_GET(segs, j), 1,
                                               1 - dir, hops.b, mp);
                        } else if (prec2 == 1) {
                            set_parallel_edges(LIST_GET(segs, i), LIST_GET(segs, j), 0, dir,
                                               hops.a, mp);
                            set_parallel_edges(LIST_GET(segs, i), LIST_GET(segs, j), 1,
                                               1 - dir, hops.b, mp);
                        }
                    } else if (prec1 == 1) {
                        set_parallel_edges(LIST_GET(segs, i), LIST_GET(segs, j), 0, dir,
                                           hops.a, mp);
                        set_parallel_edges(LIST_GET(segs, i), LIST_GET(segs, j), 1, 1 - dir,
                                           hops.b, mp);
                        if(prec2==-1)
                            removeEdge(LIST_GET(segs, i), LIST_GET(segs, j), 1 - dir, mp);
                    }
                }
            }
        }
    }
 
    return 0;
}
 
static int
add_p_edges (Dt_t* chans, maze* mp)
{
    for (Dtlink_t *l1 = dtflatten(chans); l1; l1 = dtlink(chans, l1)) {
        Dt_t *const lp = ((chanItem*)l1)->chans;
        for (Dtlink_t *l2 = dtflatten(lp); l2; l2 = dtlink(lp, l2)) {
            if (addPEdges((channel*)l2, mp) != 0) {
                return -1;
            }
        }
    }
 
    return 0;
}
 
static int
assignTracks (maze* mp)
{
    /* Create the graphs for each channel */
    create_graphs(mp->hchans);
    create_graphs(mp->vchans);
 
    /* add edges between non-parallel segments */
    if (add_np_edges(mp->hchans) != 0) {
        return -1;
    }
    if (add_np_edges(mp->vchans) != 0) {
        return -1;
    }
 
    /* add edges between parallel segments + remove appropriate edges */
    if (add_p_edges(mp->hchans, mp) != 0) {
        return -1;
    }
    if (add_p_edges(mp->vchans, mp) != 0) {
        return -1;
    }
 
    /* Assign the tracks after a top sort */
    assignTrackNo (mp->hchans);
    assignTrackNo (mp->vchans);
 
    return 0;
}
 
static double
vtrack (segment* seg, maze* m)
{
  channel* chp = chanSearch(m->vchans, seg);
  const double f = seg->track_no / ((double)LIST_SIZE(&chp->seg_list) + 1);
  const pointf interp = interpolate_pointf(f, chp->cp->bb.LL, chp->cp->bb.UR);
  return interp.x;
}
 
static double htrack(segment *seg, maze *m) {
  channel* chp = chanSearch(m->hchans, seg);
  double f = 1.0 - seg->track_no / ((double)LIST_SIZE(&chp->seg_list) + 1);
  double lo = chp->cp->bb.LL.y;
  double hi = chp->cp->bb.UR.y;
  return round(lo + f * (hi - lo));
}
 
static void attachOrthoEdges(maze *mp, size_t n_edges, route* route_list,
                             splineInfo *sinfo, epair_t es[], bool doLbls) {
    LIST(pointf) ispline = {0};
    textlabel_t* lbl;
 
    for (size_t irte = 0; irte < n_edges; irte++) {
        Agedge_t *const e = es[irte].e;
        const pointf p1 = add_pointf(ND_coord(agtail(e)), ED_tail_port(e).p);
        const pointf q1 = add_pointf(ND_coord(aghead(e)), ED_head_port(e).p);
 
        route rte = route_list[irte];
        size_t npts = 1 + 3*rte.n;
        LIST_RESERVE(&ispline, npts);
            
        segment *seg = rte.segs;
        if (seg == NULL) {
                continue;
        }
        pointf p;
        if (seg->isVert) {
                p = (pointf){.x = vtrack(seg, mp), .y = p1.y};
        }
        else {
                p = (pointf){.x = p1.x, .y = htrack(seg, mp)};
        }
        LIST_APPEND(&ispline, p);
        LIST_APPEND(&ispline, p);
 
        for (size_t i = 1;i<rte.n;i++) {
                seg = rte.segs+i;
                if (seg->isVert)
                    p.x = vtrack(seg, mp);
                else
                    p.y = htrack(seg, mp);
                LIST_APPEND(&ispline, p);
                LIST_APPEND(&ispline, p);
                LIST_APPEND(&ispline, p);
        }
 
        if (seg->isVert) {
                p = (pointf){.x = vtrack(seg, mp), .y = q1.y};
        }
        else {
                p = (pointf){.x = q1.x, .y = htrack(seg, mp)};
        }
        LIST_APPEND(&ispline, p);
        LIST_APPEND(&ispline, p);
        if (Verbose > 1)
            fprintf(stderr, "ortho %s %s\n", agnameof(agtail(e)),agnameof(aghead(e)));
        clip_and_install(e, aghead(e), LIST_FRONT(&ispline), LIST_SIZE(&ispline),
                         sinfo);
        if (doLbls && (lbl = ED_label(e)) && !lbl->set)
            addEdgeLabels(e);
        LIST_CLEAR(&ispline);
    }
    LIST_FREE(&ispline);
}
 
static int
edgeLen (Agedge_t* e)
{
    pointf p = ND_coord(agtail(e));
    pointf q = ND_coord(aghead(e));
    return (int)DIST2(p,q);
}
 
static int edgecmp(const void *x, const void *y) {
  const epair_t *e0 = x;
  const epair_t *e1 = y;
  if (e0->d > e1->d) {
    return 1;
  }
  if (e0->d < e1->d) {
    return -1;
  }
  return 0;
}
 
static bool spline_merge(node_t * n)
{
    (void)n;
    return false;
}
 
static bool swap_ends_p(edge_t * e)
{
    (void)e;
    return false;
}
 
static splineInfo sinfo = { swap_ends_p, spline_merge, true, true };
 
/* orthoEdges:
 * For edges without position information, construct an orthogonal routing.
 * If useLbls is true, use edge label info when available to guide routing, 
 * and set label pos for those edges for which this info is not available.
 */
void orthoEdges(Agraph_t *g, bool useLbls) {
    epair_t* es = gv_calloc(agnedges(g), sizeof(epair_t));
    PointSet* ps = NULL;
    textlabel_t* lbl;
 
    if (Concentrate) 
        ps = newPS();
 
#ifdef DEBUG
    {
        char* s = agget(g, "odb");
        char c;
        odb_flags = 0;
        if (s && *s != '\0') {
            while ((c = *s++)) {
                switch (c) {
                case 'c' :
                    odb_flags |= ODB_CHANG;     // emit channel graph 
                    break;
                case 'i' :
                    odb_flags |= (ODB_SGRAPH|ODB_IGRAPH);  // emit search graphs
                    break;
                case 'm' :
                    odb_flags |= ODB_MAZE;      // emit maze
                    break;
                case 'r' :
                    odb_flags |= ODB_ROUTE;     // emit routes in maze
                    break;
                case 's' :
                    odb_flags |= ODB_SGRAPH;    // emit search graph 
                    break;
                default:
                    break;
                }
            }
        }
    }
#endif
    if (useLbls) {
        agwarningf("Orthogonal edges do not currently handle edge labels. Try using xlabels.\n");
        useLbls = false;
    }
    maze *const mp = mkMaze(g);
    sgraph *const sg = mp->sg;
#ifdef DEBUG
    if (odb_flags & ODB_SGRAPH) emitSearchGraph (stderr, sg);
#endif
 
    /* store edges to be routed in es, along with their lengths */
    size_t n_edges = 0;
    for (Agnode_t *n = agfstnode (g); n; n = agnxtnode(g, n)) {
        for (Agedge_t *e = agfstout(g, n); e; e = agnxtout(g,e)) {
            if (Nop == 2 && ED_spl(e)) continue;
            if (Concentrate) {
                int ti = AGSEQ(agtail(e));
                int hi = AGSEQ(aghead(e));
                if (ti <= hi) {
                    if (isInPS (ps,ti,hi)) continue;
                    addPS(ps,ti,hi);
                }
                else {
                    if (isInPS (ps,hi,ti)) continue;
                    addPS(ps,hi,ti);
                }
            }
            es[n_edges].e = e;
            es[n_edges].d = edgeLen (e);
            n_edges++;
        }
    }
 
    route *const route_list = gv_calloc(n_edges, sizeof(route));
 
    qsort(es, n_edges, sizeof(epair_t), edgecmp);
 
    const int gstart = sg->nnodes;
    PQgen (sg->nnodes+2);
    snode *const sn = &sg->nodes[gstart];
    snode *const dn = &sg->nodes[gstart+1];
    for (size_t i = 0; i < n_edges; i++) {
#ifdef DEBUG
        if (i > 0 && (odb_flags & ODB_IGRAPH)) emitSearchGraph (stderr, sg);
#endif
        Agedge_t *const e = es[i].e;
        cell *const start = CELL(agtail(e));
        cell *const dest = CELL(aghead(e));
 
        if (useLbls && (lbl = ED_label(e)) && lbl->set) {
        }
        else {
            if (start == dest)
                addLoop (sg, start, dn, sn);
            else {
                addNodeEdges (sg, dest, dn);
                addNodeEdges (sg, start, sn);
            }
            if (shortPath (sg, dn, sn)) goto orthofinish;
        }
            
        route_list[i] = convertSPtoRoute(sg, sn, dn);
        reset (sg);
    }
    PQfree ();
 
    mp->hchans = extractHChans (mp);
    mp->vchans = extractVChans (mp);
    assignSegs (n_edges, route_list, mp);
    if (assignTracks(mp) != 0)
        goto orthofinish;
#ifdef DEBUG
    if (odb_flags & ODB_ROUTE) emitGraph (stderr, mp, n_edges, route_list, es);
#endif
    attachOrthoEdges(mp, n_edges, route_list, &sinfo, es, useLbls);
 
orthofinish:
    if (Concentrate)
        freePS (ps);
 
    for (size_t i=0; i < n_edges; i++)
        free (route_list[i].segs);
    free (route_list);
    freeMaze (mp);
    free (es);
}
 
#include <common/arith.h>
#define TRANS 10
 
static char* prolog2 =
"%%!PS-Adobe-2.0\n\
%%%%BoundingBox: (atend)\n\
/point {\n\
  /Y exch def\n\
  /X exch def\n\
  newpath\n\
  X Y 3 0 360 arc fill\n\
} def\n\
/cell {\n\
  /Y exch def\n\
  /X exch def\n\
  /y exch def\n\
  /x exch def\n\
  newpath\n\
  x y moveto\n\
  x Y lineto\n\
  X Y lineto\n\
  X y lineto\n\
  closepath stroke\n\
} def\n\
/node {\n\
 /u exch def\n\
 /r exch def\n\
 /d exch def\n\
 /l exch def\n\
 newpath l d moveto\n\
 r d lineto r u lineto l u lineto\n\
 closepath fill\n\
} def\n\
\n";
 
static char* epilog2 =
"showpage\n\
%%%%Trailer\n\
%%%%BoundingBox: %.f %.f %.f %.f\n";
 
static pointf coordOf(cell *cp, snode *np) {
    if (cp->sides[M_TOP] == np) {
        return (pointf){.x = (cp->bb.LL.x + cp->bb.UR.x) / 2, .y = cp->bb.UR.y};
    }
    if (cp->sides[M_BOTTOM] == np) {
        return (pointf){.x = (cp->bb.LL.x + cp->bb.UR.x) / 2, .y = cp->bb.LL.y};
    }
    if (cp->sides[M_LEFT] == np) {
        return (pointf){.x = cp->bb.LL.x, .y = (cp->bb.LL.y + cp->bb.UR.y) / 2};
    }
    if (cp->sides[M_RIGHT] == np) {
        return (pointf){.x = cp->bb.UR.x, .y = (cp->bb.LL.y + cp->bb.UR.y) / 2};
    }
    agerrorf("Node not adjacent to cell -- Aborting\n");
    graphviz_exit(EXIT_FAILURE);
}
 
static boxf
emitEdge (FILE* fp, Agedge_t* e, route rte, maze* m, boxf bb)
{
    double x, y;
    boxf n = CELL(agtail(e))->bb;
    segment* seg = rte.segs;
    if (seg->isVert) {
        x = vtrack(seg, m);
        y = (n.UR.y + n.LL.y)/2;
    }
    else {
        y = htrack(seg, m);
        x = (n.UR.x + n.LL.x)/2;
    }
    bb.LL.x = fmin(bb.LL.x, x);
    bb.LL.y = fmin(bb.LL.y, y);
    bb.UR.x = fmax(bb.UR.x, x);
    bb.UR.y = fmax(bb.UR.y, y);
    fprintf(fp, "newpath %.0f %.0f moveto\n", x, y);
 
    for (size_t i = 1;i<rte.n;i++) {
        seg = rte.segs+i;
        if (seg->isVert) {
            x = vtrack(seg, m);
        }
        else {
            y = htrack(seg, m);
        }
        bb.LL.x = fmin(bb.LL.x, x);
        bb.LL.y = fmin(bb.LL.y, y);
        bb.UR.x = fmax(bb.UR.x, x);
        bb.UR.y = fmax(bb.UR.y, y);
        fprintf(fp, "%.0f %.0f lineto\n", x, y);
    }
 
    n = CELL(aghead(e))->bb;
    if (seg->isVert) {
        x = vtrack(seg, m);
        y = (n.UR.y + n.LL.y)/2;
    }
    else {
        y = htrack(seg, m);
        x = (n.LL.x + n.UR.x)/2;
    }
    bb.LL.x = fmin(bb.LL.x, x);
    bb.LL.y = fmin(bb.LL.y, y);
    bb.UR.x = fmax(bb.UR.x, x);
    bb.UR.y = fmax(bb.UR.y, y);
    fprintf(fp, "%.0f %.0f lineto stroke\n", x, y);
 
    return bb;
}
 
static UNUSED void emitSearchGraph(FILE *fp, sgraph *sg) {
    pointf p;
    fputs ("graph G {\n", fp);
    fputs (" node[shape=point]\n", fp);
    fputs (" layout=neato\n", fp);
    for (int i = 0; i < sg->nnodes; i++) {
        snode *const np = sg->nodes+i;
        cell *cp = np->cells[0];
        if (cp == np->cells[1]) {
            p = midPt(cp);
        }
        else {
            if (IsNode(cp)) cp = np->cells[1];
            p = coordOf (cp, np);
        }
        fprintf (fp, "  %d [pos=\"%.0f,%.0f!\"]\n", i, p.x, p.y);
    }
    for (int i = 0; i < sg->nedges; i++) {
        sedge *const ep = sg->edges+i;
        fprintf (fp, "  %d -- %d[label=\"%f\"]\n", ep->v1, ep->v2, ep->weight);
    }
    fputs ("}\n", fp);
}
 
static UNUSED void emitGraph(FILE *fp, maze *mp, size_t n_edges,
                             route *route_list, epair_t es[]) {
    boxf absbb = {.LL = {.x = DBL_MAX, .y = DBL_MAX},
                  .UR = {.x = -DBL_MAX, .y = -DBL_MAX}};
 
    fprintf (fp, "%s", prolog2);
    fprintf (fp, "%d %d translate\n", TRANS, TRANS);
 
    fputs ("0 0 1 setrgbcolor\n", fp);
    for (size_t i = 0; i < mp->ngcells; i++) {
      const boxf bb = mp->gcells[i].bb;
      fprintf (fp, "%f %f %f %f node\n", bb.LL.x, bb.LL.y, bb.UR.x, bb.UR.y);
    }
 
    for (size_t i = 0; i < n_edges; i++) {
        absbb = emitEdge (fp, es[i].e, route_list[i], mp, absbb);
    }
    
    fputs ("0.8 0.8 0.8 setrgbcolor\n", fp);
    for (size_t i = 0; i < mp->ncells; i++) {
      const boxf bb = mp->cells[i].bb;
      fprintf (fp, "%f %f %f %f cell\n", bb.LL.x, bb.LL.y, bb.UR.x, bb.UR.y);
      absbb.LL.x = fmin(absbb.LL.x, bb.LL.x);
      absbb.LL.y = fmin(absbb.LL.y, bb.LL.y);
      absbb.UR.x = fmax(absbb.UR.x, bb.UR.x);
      absbb.UR.y = fmax(absbb.UR.y, bb.UR.y);
    }
 
    const boxf bbox = {
      .LL = {.x = absbb.LL.x + TRANS,
             .y = absbb.LL.y + TRANS},
      .UR = {.x = absbb.UR.x + TRANS,
             .y = absbb.UR.y + TRANS}};
    fprintf (fp, epilog2, bbox.LL.x, bbox.LL.y,  bbox.UR.x, bbox.UR.y);
}