lib/common/routespl.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/
 *************************************************************************/

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include "render.h"
#include "pathplan.h"
#include <setjmp.h>

#ifdef UNUSED
static box *bs = NULL;
static int bn;
static int maxbn = 0;
#define BINC 300
#endif

#define PINC 300

#ifdef NOTNOW
static edge_t *origedge;
#endif

static int nedges, nboxes; /* total no. of edges and boxes used in routing */

static int routeinit;
/* static data used across multiple edges */
static pointf *ps;             /* final spline points */
static int maxpn;             /* size of ps[] */
static Ppoint_t *polypoints;  /* vertices of polygon defined by boxes */
static int polypointn;        /* size of polypoints[] */
static Pedge_t *edges;        /* polygon edges passed to Proutespline */
static int edgen;             /* size of edges[] */

static int checkpath(int, boxf*, path*);
static int mkspacep(int size);
static void printpath(path * pp);
#ifdef DEBUG
static void printboxes(int boxn, boxf* boxes)
{
    pointf ll, ur;
    int bi;
    char buf[BUFSIZ];
    int newcnt = Show_cnt + boxn;

    Show_boxes = ALLOC(newcnt+2,Show_boxes,char*);
    for (bi = 0; bi < boxn; bi++) {
        ll = boxes[bi].LL, ur = boxes[bi].UR;
        sprintf(buf, "%d %d %d %d pathbox", (int)ll.x, (int)ll.y, (int)ur.x, (int)ur.y);
        Show_boxes[bi+1+Show_cnt] = strdup (buf);
    }
    Show_cnt = newcnt;
    Show_boxes[Show_cnt+1] = NULL;
}

static void psprintpolypts(Ppoint_t * p, int sz)
{
    int i;

    fprintf(stderr, "%%!\n");
    fprintf(stderr, "%% constraint poly\n");
    fprintf(stderr, "newpath\n");
    for (i = 0; i < sz; i++)
        fprintf(stderr, "%f %f %s\n", p[i].x, p[i].y,
                (i == 0 ? "moveto" : "lineto"));
    fprintf(stderr, "closepath stroke\n");
}
static void psprintpoint(point p)
{
    fprintf(stderr, "gsave\n");
    fprintf(stderr,
            "newpath %d %d moveto %d %d 2 0 360 arc closepath fill stroke\n",
            p.x, p.y, p.x, p.y);
    fprintf(stderr, "/Times-Roman findfont 4 scalefont setfont\n");
    fprintf(stderr, "%d %d moveto (\\(%d,%d\\)) show\n", p.x + 5, p.y + 5,
            p.x, p.y);
    fprintf(stderr, "grestore\n");
}
static void psprintpointf(pointf p)
{
    fprintf(stderr, "gsave\n");
    fprintf(stderr,
            "newpath %.5g %.5g moveto %.5g %.5g 2 0 360 arc closepath fill stroke\n",
            p.x, p.y, p.x, p.y);
    fprintf(stderr, "/Times-Roman findfont 4 scalefont setfont\n");
    fprintf(stderr, "%.5g %.5g moveto (\\(%.5g,%.5g\\)) show\n", p.x + 5, p.y + 5,
            p.x, p.y);
    fprintf(stderr, "grestore\n");
}

static void psprintspline(Ppolyline_t spl)
{
    char buf[BUFSIZ];
    int newcnt = Show_cnt + spl.pn + 4;
    int li, i;

    Show_boxes = ALLOC(newcnt+2,Show_boxes,char*);
    li = Show_cnt+1;
    Show_boxes[li++] = strdup ("%%!");
    Show_boxes[li++] = strdup ("%% spline");
    Show_boxes[li++] = strdup ("gsave 1 0 0 setrgbcolor newpath");
    for (i = 0; i < spl.pn; i++) {
        sprintf(buf, "%f %f %s", spl.ps[i].x, spl.ps[i].y,
          (i == 0) ?  "moveto" : ((i % 3 == 0) ? "curveto" : ""));
        Show_boxes[li++] = strdup (buf);
    }
    Show_boxes[li++] = strdup ("stroke grestore");
    Show_cnt = newcnt;
    Show_boxes[Show_cnt+1] = NULL;
}

static void psprintline(Ppolyline_t pl)
{
    char buf[BUFSIZ];
    int newcnt = Show_cnt + pl.pn + 4;
    int i, li;

    Show_boxes = ALLOC(newcnt+2,Show_boxes,char*);
    li = Show_cnt+1;
    Show_boxes[li++] = strdup ("%%!");
    Show_boxes[li++] = strdup ("%% line");
    Show_boxes[li++] = strdup ("gsave 0 0 1 setrgbcolor newpath");
    for (i = 0; i < pl.pn; i++) {
        sprintf(buf, "%f %f %s", pl.ps[i].x, pl.ps[i].y,
                (i == 0 ? "moveto" : "lineto"));
        Show_boxes[li++] = strdup (buf);
    }
    Show_boxes[li++] = strdup ("stroke grestore");
    Show_cnt = newcnt;
    Show_boxes[Show_cnt+1] = NULL;
}

static void psprintpoly(Ppoly_t p)
{
    char buf[BUFSIZ];
    int newcnt = Show_cnt + p.pn + 3;
    point tl, hd;
    int bi, li;
    char*  pfx;

    Show_boxes = ALLOC(newcnt+2,Show_boxes,char*);
    li = Show_cnt+1;
    Show_boxes[li++] = strdup ("%% poly list");
    Show_boxes[li++] = strdup ("gsave 0 1 0 setrgbcolor");
    for (bi = 0; bi < p.pn; bi++) {
        tl.x = (int)p.ps[bi].x;
        tl.y = (int)p.ps[bi].y;
        hd.x = (int)p.ps[(bi+1) % p.pn].x;
        hd.y = (int)p.ps[(bi+1) % p.pn].y;
        if ((tl.x == hd.x) && (tl.y == hd.y)) pfx = "%%";
        else pfx ="";
        sprintf(buf, "%s%d %d %d %d makevec", pfx, tl.x, tl.y, hd.x, hd.y);
        Show_boxes[li++] = strdup (buf);
    }
    Show_boxes[li++] = strdup ("grestore");

    Show_cnt = newcnt;
    Show_boxes[Show_cnt+1] = NULL;
}

static void psprintboxes(int boxn, boxf* boxes)
{
    char buf[BUFSIZ];
    int newcnt = Show_cnt + 5*boxn + 3;
    pointf ll, ur;
    int bi, li;

    Show_boxes = ALLOC(newcnt+2,Show_boxes,char*);
    li = Show_cnt+1;
    Show_boxes[li++] = strdup ("%% box list");
    Show_boxes[li++] = strdup ("gsave 0 1 0 setrgbcolor");
    for (bi = 0; bi < boxn; bi++) {
        ll = boxes[bi].LL, ur = boxes[bi].UR;
        sprintf(buf, "newpath\n%d %d moveto", (int)ll.x, (int)ll.y);
        Show_boxes[li++] = strdup (buf);
        sprintf(buf, "%d %d lineto", (int)ll.x, (int)ur.y);
        Show_boxes[li++] = strdup (buf);
        sprintf(buf, "%d %d lineto", (int)ur.x, (int)ur.y);
        Show_boxes[li++] = strdup (buf);
        sprintf(buf, "%d %d lineto", (int)ur.x, (int)ll.y);
        Show_boxes[li++] = strdup (buf);
        Show_boxes[li++] = strdup ("closepath stroke");
    }
    Show_boxes[li++] = strdup ("grestore");

    Show_cnt = newcnt;
    Show_boxes[Show_cnt+1] = NULL;
}

static void psprintinit (int begin)
{
    int newcnt = Show_cnt + 1;

    Show_boxes = ALLOC(newcnt+2,Show_boxes,char*);
    if (begin)
        Show_boxes[1+Show_cnt] = strdup ("dbgstart");
    else
        Show_boxes[1+Show_cnt] = strdup ("grestore");
    Show_cnt = newcnt;
    Show_boxes[Show_cnt+1] = NULL;
}

static int debugleveln(edge_t* realedge, int i)
{
    return (GD_showboxes(realedge->head->graph) == i ||
            GD_showboxes(realedge->tail->graph) == i ||
            ED_showboxes(realedge) == i ||
            ND_showboxes(realedge->head) == i ||
            ND_showboxes(realedge->tail) == i);
}
#endif  /* DEBUG */



/* simpleSplineRoute:
 * Given a simple (ccw) polygon, route an edge from tp to hp.
 */
pointf*
simpleSplineRoute (pointf tp, pointf hp, Ppoly_t poly, int* n_spl_pts,
    int polyline)
{
    Ppolyline_t pl, spl;
    Ppoint_t eps[2];
    Pvector_t evs[2];
    int i;

    eps[0].x = tp.x;
    eps[0].y = tp.y;
    eps[1].x = hp.x;
    eps[1].y = hp.y;
    if (Pshortestpath(&poly, eps, &pl) < 0)
        return NULL;

    if (polyline)
        make_polyline (pl, &spl);
    else {
        if (poly.pn > edgen) {
            edges = ALLOC(poly.pn, edges, Pedge_t);
            edgen = poly.pn;
        }
        for (i = 0; i < poly.pn; i++) {
            edges[i].a = poly.ps[i];
            edges[i].b = poly.ps[(i + 1) % poly.pn];
        }
#if 0
        if (pp->start.constrained) {
            evs[0].x = cos(pp->start.theta);
            evs[0].y = sin(pp->start.theta);
        } else
#endif
            evs[0].x = evs[0].y = 0;
#if 0
        if (pp->end.constrained) {
            evs[1].x = -cos(pp->end.theta);
            evs[1].y = -sin(pp->end.theta);
        } else
#endif
            evs[1].x = evs[1].y = 0;
        if (Proutespline(edges, poly.pn, pl, evs, &spl) < 0)
            return NULL;
    }

    if (mkspacep(spl.pn))
        return NULL;
    for (i = 0; i < spl.pn; i++) {
        ps[i] = spl.ps[i];
    }
    *n_spl_pts = spl.pn;
    return ps;
}

/* routesplinesinit:
 * Data initialized once until matching call to routeplineterm
 * Allows recursive calls to dot
 */
int
routesplinesinit()
{
    if (++routeinit > 1) return 0;
    if (!(ps = N_GNEW(PINC, pointf))) {
        agerr(AGERR, "routesplinesinit: cannot allocate ps\n");
        return 1;
    }
    maxpn = PINC;
#ifdef DEBUG
    if (Show_boxes) {
        int i;
        for (i = 0; Show_boxes[i]; i++)
            free (Show_boxes[i]);
        free (Show_boxes);
        Show_boxes = NULL;
        Show_cnt = 0;
    }
#endif
    nedges = 0;
    nboxes = 0;
    if (Verbose)
        start_timer();
    return 0;
}

void routesplinesterm()
{
    if (--routeinit > 0) return;
    free(ps);
#ifdef UNUSED
    free(bs), bs = NULL /*, maxbn = bn = 0 */ ;
#endif
    if (Verbose)
        fprintf(stderr,
                "routesplines: %d edges, %d boxes %.2f sec\n",
                nedges, nboxes, elapsed_sec());
}

static void
limitBoxes (boxf* boxes, int boxn, pointf *pps, int pn, int delta)
{
    int bi, si, splinepi;
    double t;
    pointf sp[4];
    int num_div = delta * boxn;

    for (splinepi = 0; splinepi + 3 < pn; splinepi += 3) {
        for (si = 0; si <= num_div; si++) {
            t = si / (double)num_div;
            sp[0] = pps[splinepi];
            sp[1] = pps[splinepi + 1];
            sp[2] = pps[splinepi + 2];
            sp[3] = pps[splinepi + 3];
            sp[0].x = sp[0].x + t * (sp[1].x - sp[0].x);
            sp[0].y = sp[0].y + t * (sp[1].y - sp[0].y);
            sp[1].x = sp[1].x + t * (sp[2].x - sp[1].x);
            sp[1].y = sp[1].y + t * (sp[2].y - sp[1].y);
            sp[2].x = sp[2].x + t * (sp[3].x - sp[2].x);
            sp[2].y = sp[2].y + t * (sp[3].y - sp[2].y);
            sp[0].x = sp[0].x + t * (sp[1].x - sp[0].x);
            sp[0].y = sp[0].y + t * (sp[1].y - sp[0].y);
            sp[1].x = sp[1].x + t * (sp[2].x - sp[1].x);
            sp[1].y = sp[1].y + t * (sp[2].y - sp[1].y);
            sp[0].x = sp[0].x + t * (sp[1].x - sp[0].x);
            sp[0].y = sp[0].y + t * (sp[1].y - sp[0].y);
            for (bi = 0; bi < boxn; bi++) {
/* this tested ok on 64bit machines, but on 32bit we need this FUDGE
 *     or graphs/directed/records.gv fails */
#define FUDGE .0001
                if (sp[0].y <= boxes[bi].UR.y+FUDGE && sp[0].y >= boxes[bi].LL.y-FUDGE) {
                    if (boxes[bi].LL.x > sp[0].x)
                        boxes[bi].LL.x = sp[0].x;
                    if (boxes[bi].UR.x < sp[0].x)
                        boxes[bi].UR.x = sp[0].x;
                }
            }
        }
    }
}

#define INIT_DELTA 10 
#define LOOP_TRIES 15  /* number of times to try to limiting boxes to regain space, using smaller divisions */

/* routesplines:
 * Route a path using the path info in pp. This includes start and end points
 * plus a collection of contiguous boxes contain the terminal points. The boxes
 * are converted into a containing polygon. A shortest path is constructed within
 * the polygon from between the terminal points. If polyline is true, this path
 * is converted to a spline representation. Otherwise, we call the path planner to
 * convert the polyline into a smooth spline staying within the polygon. In both
 * cases, the function returns an array of the computed control points. The number
 * of these points is given in npoints.
 *
 * Note that the returned points are stored in a single array, so the points must be
 * used before another call to this function.
 *
 * During cleanup, the function determines the x-extent of the spline in the box, so
 * the box can be shrunk to the minimum width. The extra space can then be used by other
 * edges. 
 *
 * If a catastrophic error, return NULL.
 */
static pointf *_routesplines(path * pp, int *npoints, int polyline)
{
    Ppoly_t poly;
    Ppolyline_t pl, spl;
    int splinepi;
    Ppoint_t eps[2];
    Pvector_t evs[2];
    int edgei, prev, next;
    int pi, bi;
    boxf *boxes;
    int boxn;
    edge_t* realedge;
    int flip;
    int loopcnt, delta = INIT_DELTA;
    boolean unbounded;

    nedges++;
    nboxes += pp->nbox;

    for (realedge = (edge_t *) pp->data;
#ifdef NOTNOW
         origedge = realedge;
#endif
         realedge && ED_edge_type(realedge) != NORMAL;
         realedge = ED_to_orig(realedge));
    if (!realedge) {
        agerr(AGERR, "in routesplines, cannot find NORMAL edge\n");
        return NULL;
    }

    boxes = pp->boxes;
    boxn = pp->nbox;

    if (checkpath(boxn, boxes, pp))
        return NULL;

#ifdef DEBUG
    if (debugleveln(realedge, 1))
        printboxes(boxn, boxes);
    if (debugleveln(realedge, 3)) {
        psprintinit(1);
        psprintboxes(boxn, boxes);
    }
#endif

    if (boxn * 8 > polypointn) {
        polypoints = ALLOC(boxn * 8, polypoints, Ppoint_t);
        polypointn = boxn * 8;
    }

    if ((boxn > 1) && (boxes[0].LL.y > boxes[1].LL.y)) {
        flip = 1;
        for (bi = 0; bi < boxn; bi++) {
            double v = boxes[bi].UR.y;
            boxes[bi].UR.y = -1*boxes[bi].LL.y;
            boxes[bi].LL.y = -v;
        }
    }
    else flip = 0;

    if (agtail(realedge) != aghead(realedge)) {
        /* I assume that the path goes either down only or
           up - right - down */
        for (bi = 0, pi = 0; bi < boxn; bi++) {
            next = prev = 0;
            if (bi > 0)
                prev = (boxes[bi].LL.y > boxes[bi - 1].LL.y) ? -1 : 1;
            if (bi < boxn - 1)
                next = (boxes[bi + 1].LL.y > boxes[bi].LL.y) ? 1 : -1;
            if (prev != next) {
                if (next == -1 || prev == 1) {
                    polypoints[pi].x = boxes[bi].LL.x;
                    polypoints[pi++].y = boxes[bi].UR.y;
                    polypoints[pi].x = boxes[bi].LL.x;
                    polypoints[pi++].y = boxes[bi].LL.y;
                } else {
                    polypoints[pi].x = boxes[bi].UR.x;
                    polypoints[pi++].y = boxes[bi].LL.y;
                    polypoints[pi].x = boxes[bi].UR.x;
                    polypoints[pi++].y = boxes[bi].UR.y;
                }
            }
            else if (prev == 0) { /* single box */
                polypoints[pi].x = boxes[bi].LL.x;
                polypoints[pi++].y = boxes[bi].UR.y;
                polypoints[pi].x = boxes[bi].LL.x;
                polypoints[pi++].y = boxes[bi].LL.y;
            } 
            else {
                if (!(prev == -1 && next == -1)) {
                    agerr(AGERR, "in routesplines, illegal values of prev %d and next %d, line %d\n", prev, next, __LINE__);
                    return NULL;
                }
            }
        }
        for (bi = boxn - 1; bi >= 0; bi--) {
            next = prev = 0;
            if (bi < boxn - 1)
                prev = (boxes[bi].LL.y > boxes[bi + 1].LL.y) ? -1 : 1;
            if (bi > 0)
                next = (boxes[bi - 1].LL.y > boxes[bi].LL.y) ? 1 : -1;
            if (prev != next) {
                if (next == -1 || prev == 1 ) {
                    polypoints[pi].x = boxes[bi].LL.x;
                    polypoints[pi++].y = boxes[bi].UR.y;
                    polypoints[pi].x = boxes[bi].LL.x;
                    polypoints[pi++].y = boxes[bi].LL.y;
                } else {
                    polypoints[pi].x = boxes[bi].UR.x;
                    polypoints[pi++].y = boxes[bi].LL.y;
                    polypoints[pi].x = boxes[bi].UR.x;
                    polypoints[pi++].y = boxes[bi].UR.y;
                }
            } 
            else if (prev == 0) { /* single box */
                polypoints[pi].x = boxes[bi].UR.x;
                polypoints[pi++].y = boxes[bi].LL.y;
                polypoints[pi].x = boxes[bi].UR.x;
                polypoints[pi++].y = boxes[bi].UR.y;
            }
            else {
                if (!(prev == -1 && next == -1)) {
                    /* it went badly, e.g. degenerate box in boxlist */
                    agerr(AGERR, "in routesplines, illegal values of prev %d and next %d, line %d\n", prev, next, __LINE__);
                    return NULL; /* for correctness sake, it's best to just stop */
                }
                polypoints[pi].x = boxes[bi].UR.x;
                polypoints[pi++].y = boxes[bi].LL.y;
                polypoints[pi].x = boxes[bi].UR.x;
                polypoints[pi++].y = boxes[bi].UR.y;
                polypoints[pi].x = boxes[bi].LL.x;
                polypoints[pi++].y = boxes[bi].UR.y;
                polypoints[pi].x = boxes[bi].LL.x;
                polypoints[pi++].y = boxes[bi].LL.y;
            }
        }
    }
    else {
        agerr(AGERR, "in routesplines, edge is a loop at %s\n", agnameof(aghead(realedge)));
        return NULL;
    }

    if (flip) {
        int i;
        for (bi = 0; bi < boxn; bi++) {
            int v = boxes[bi].UR.y;
            boxes[bi].UR.y = -1*boxes[bi].LL.y;
            boxes[bi].LL.y = -v;
        }
        for (i = 0; i < pi; i++)
            polypoints[i].y *= -1;
    }

    for (bi = 0; bi < boxn; bi++)
        boxes[bi].LL.x = INT_MAX, boxes[bi].UR.x = INT_MIN;
    poly.ps = polypoints, poly.pn = pi;
    eps[0].x = pp->start.p.x, eps[0].y = pp->start.p.y;
    eps[1].x = pp->end.p.x, eps[1].y = pp->end.p.y;
    if (Pshortestpath(&poly, eps, &pl) < 0) {
        agerr(AGERR, "in routesplines, Pshortestpath failed\n");
        return NULL;
    }
#ifdef DEBUG
    if (debugleveln(realedge, 3)) {
        psprintpoly(poly);
        psprintline(pl);
    }
#endif

    if (polyline) {
        make_polyline (pl, &spl);
    }
    else {
        if (poly.pn > edgen) {
            edges = ALLOC(poly.pn, edges, Pedge_t);
            edgen = poly.pn;
        }
        for (edgei = 0; edgei < poly.pn; edgei++) {
            edges[edgei].a = polypoints[edgei];
            edges[edgei].b = polypoints[(edgei + 1) % poly.pn];
        }
        if (pp->start.constrained) {
            evs[0].x = cos(pp->start.theta);
            evs[0].y = sin(pp->start.theta);
        } else
            evs[0].x = evs[0].y = 0;
        if (pp->end.constrained) {
            evs[1].x = -cos(pp->end.theta);
            evs[1].y = -sin(pp->end.theta);
        } else
            evs[1].x = evs[1].y = 0;

        if (Proutespline(edges, poly.pn, pl, evs, &spl) < 0) {
            agerr(AGERR, "in routesplines, Proutespline failed\n");
            return NULL;
        }
#ifdef DEBUG
        if (debugleveln(realedge, 3)) {
            psprintspline(spl);
            psprintinit(0);
        }
#endif
    }
    if (mkspacep(spl.pn))
        return NULL;  /* Bailout if no memory left */

    for (bi = 0; bi < boxn; bi++) {
        boxes[bi].LL.x = INT_MAX;
        boxes[bi].UR.x = INT_MIN;
    }
    unbounded = TRUE;
    for (splinepi = 0; splinepi < spl.pn; splinepi++) {
        ps[splinepi] = spl.ps[splinepi];
    }

    for (loopcnt = 0; unbounded && (loopcnt < LOOP_TRIES); loopcnt++) {
        limitBoxes (boxes, boxn, ps, spl.pn, delta);

    /* The following check is necessary because if a box is not very 
     * high, it is possible that the sampling above might miss it.
     * Therefore, we make the sample finer until all boxes have
     * valid values. cf. bug 456. Would making sp[] pointfs help?
     */
        for (bi = 0; bi < boxn; bi++) {
        /* these fp equality tests are used only to detect if the
         * values have been changed since initialization - ok */
            if ((boxes[bi].LL.x == INT_MAX) || (boxes[bi].UR.x == INT_MIN)) {
                delta *= 2; /* try again with a finer interval */
                if (delta > INT_MAX/boxn) /* in limitBoxes, boxn*delta must fit in an int, so give up */
                    loopcnt = LOOP_TRIES;
                break;
            }
        }
        if (bi == boxn)
            unbounded = FALSE;
    }
    if (unbounded) {  
        /* Either an extremely short, even degenerate, box, or some failure with the path
         * planner causing the spline to miss some boxes. In any case, use the shortest path 
         * to bound the boxes. This will probably mean a bad edge, but we avoid an infinite
         * loop and we can see the bad edge, and even use the showboxes scaffolding.
         */
        Ppolyline_t polyspl;
        agerr(AGWARN, "Unable to reclaim box space in spline routing for edge \"%s\" -> \"%s\". Something is probably seriously wrong.\n", agnameof(agtail(realedge)), agnameof(aghead(realedge)));
        make_polyline (pl, &polyspl);
        limitBoxes (boxes, boxn, polyspl.ps, polyspl.pn, INIT_DELTA);
        free (polyspl.ps);
    }

    *npoints = spl.pn;

#ifdef DEBUG
    if (GD_showboxes(realedge->head->graph) == 2 ||
        GD_showboxes(realedge->tail->graph) == 2 ||
        ED_showboxes(realedge) == 2 ||
        ND_showboxes(realedge->head) == 2 ||
        ND_showboxes(realedge->tail) == 2)
        printboxes(boxn, boxes);
#endif

    return ps;
}

pointf *routesplines(path * pp, int *npoints)
{
    return _routesplines (pp, npoints, 0);
}

pointf *routepolylines(path * pp, int *npoints)
{
    return _routesplines (pp, npoints, 1);
}

static int overlap(int i0, int i1, int j0, int j1)
{
    /* i'll bet there's an elegant way to do this */
    if (i1 <= j0)
        return 0;
    if (i0 >= j1)
        return 0;
    if ((j0 <= i0) && (i0 <= j1))
        return (j1 - i0);
    if ((j0 <= i1) && (i1 <= j1))
        return (i1 - j0);
    return MIN(i1 - i0, j1 - j0);
}


/*
 * repairs minor errors in the boxpath, such as boxes not joining
 * or slightly intersecting.  it's sort of the equivalent of the
 * audit process in the 5E control program - if you've given up on
 * fixing all the bugs, at least try to engineer around them!
 * in postmodern CS, we could call this "self-healing code."
 *
 * Return 1 on failure; 0 on success.
 */
static int checkpath(int boxn, boxf* boxes, path* thepath)
{
    boxf *ba, *bb;
    int bi, i, errs, l, r, d, u;
    int xoverlap, yoverlap;

#ifndef DONTFIXPATH
    /* remove degenerate boxes. */
    i = 0;
    for (bi = 0; bi < boxn; bi++) {
        if (ABS(boxes[bi].LL.y - boxes[bi].UR.y) < .01)
            continue;
        if (ABS(boxes[bi].LL.x - boxes[bi].UR.x) < .01)
            continue;
        if (i != bi)
            boxes[i] = boxes[bi];
        i++;
    }
    boxn = i;
#endif                          /* DONTFIXPATH */

    ba = &boxes[0];
    if (ba->LL.x > ba->UR.x || ba->LL.y > ba->UR.y) {
        agerr(AGERR, "in checkpath, box 0 has LL coord > UR coord\n");
        printpath(thepath);
        return 1;
    }
    for (bi = 0; bi < boxn - 1; bi++) {
        ba = &boxes[bi], bb = &boxes[bi + 1];
        if (bb->LL.x > bb->UR.x || bb->LL.y > bb->UR.y) {
            agerr(AGERR, "in checkpath, box %d has LL coord > UR coord\n",
                  bi + 1);
            printpath(thepath);
            return 1;
        }
        l = (ba->UR.x < bb->LL.x) ? 1 : 0;
        r = (ba->LL.x > bb->UR.x) ? 1 : 0;
        d = (ba->UR.y < bb->LL.y) ? 1 : 0;
        u = (ba->LL.y > bb->UR.y) ? 1 : 0;
        errs = l + r + d + u;
        if (errs > 0 && Verbose) {
            fprintf(stderr, "in checkpath, boxes %d and %d don't touch\n",
                    bi, bi + 1);
            printpath(thepath);
        }
#ifndef DONTFIXPATH
        if (errs > 0) {
            int xy;

            if (l == 1)
                xy = ba->UR.x, ba->UR.x = bb->LL.x, bb->LL.x = xy, l = 0;
            else if (r == 1)
                xy = ba->LL.x, ba->LL.x = bb->UR.x, bb->UR.x = xy, r = 0;
            else if (d == 1)
                xy = ba->UR.y, ba->UR.y = bb->LL.y, bb->LL.y = xy, d = 0;
            else if (u == 1)
                xy = ba->LL.y, ba->LL.y = bb->UR.y, bb->UR.y = xy, u = 0;
            for (i = 0; i < errs - 1; i++) {
                if (l == 1)
                    xy = (ba->UR.x + bb->LL.x) / 2.0 + 0.5, ba->UR.x =
                        bb->LL.x = xy, l = 0;
                else if (r == 1)
                    xy = (ba->LL.x + bb->UR.x) / 2.0 + 0.5, ba->LL.x =
                        bb->UR.x = xy, r = 0;
                else if (d == 1)
                    xy = (ba->UR.y + bb->LL.y) / 2.0 + 0.5, ba->UR.y =
                        bb->LL.y = xy, d = 0;
                else if (u == 1)
                    xy = (ba->LL.y + bb->UR.y) / 2.0 + 0.5, ba->LL.y =
                        bb->UR.y = xy, u = 0;
            }
        }
#else
        abort();
#endif
#ifndef DONTFIXPATH
        /* check for overlapping boxes */
        xoverlap = overlap(ba->LL.x, ba->UR.x, bb->LL.x, bb->UR.x);
        yoverlap = overlap(ba->LL.y, ba->UR.y, bb->LL.y, bb->UR.y);
        if (xoverlap && yoverlap) {
            if (xoverlap < yoverlap) {
                if (ba->UR.x - ba->LL.x > bb->UR.x - bb->LL.x) {
                    /* take space from ba */
                    if (ba->UR.x < bb->UR.x)
                        ba->UR.x = bb->LL.x;
                    else
                        ba->LL.x = bb->UR.x;
                } else {
                    /* take space from bb */
                    if (ba->UR.x < bb->UR.x)
                        bb->LL.x = ba->UR.x;
                    else
                        bb->UR.x = ba->LL.x;
                }
            } else {            /* symmetric for y coords */
                if (ba->UR.y - ba->LL.y > bb->UR.y - bb->LL.y) {
                    /* take space from ba */
                    if (ba->UR.y < bb->UR.y)
                        ba->UR.y = bb->LL.y;
                    else
                        ba->LL.y = bb->UR.y;
                } else {
                    /* take space from bb */
                    if (ba->UR.y < bb->UR.y)
                        bb->LL.y = ba->UR.y;
                    else
                        bb->UR.y = ba->LL.y;
                }
            }
        }
    }
#endif                          /* DONTFIXPATH */

    if (thepath->start.p.x < boxes[0].LL.x
        || thepath->start.p.x > boxes[0].UR.x
        || thepath->start.p.y < boxes[0].LL.y
        || thepath->start.p.y > boxes[0].UR.y) {
        if (Verbose) {
            fprintf(stderr, "in checkpath, start port not in first box\n");
            printpath(thepath);
        }
#ifndef DONTFIXPATH
        if (thepath->start.p.x < boxes[0].LL.x)
            thepath->start.p.x = boxes[0].LL.x;
        if (thepath->start.p.x > boxes[0].UR.x)
            thepath->start.p.x = boxes[0].UR.x;
        if (thepath->start.p.y < boxes[0].LL.y)
            thepath->start.p.y = boxes[0].LL.y;
        if (thepath->start.p.y > boxes[0].UR.y)
            thepath->start.p.y = boxes[0].UR.y;
#else
        abort();
#endif
    }
    if (thepath->end.p.x < boxes[boxn - 1].LL.x
        || thepath->end.p.x > boxes[boxn - 1].UR.x
        || thepath->end.p.y < boxes[boxn - 1].LL.y
        || thepath->end.p.y > boxes[boxn - 1].UR.y) {
        if (Verbose) {
            fprintf(stderr, "in checkpath, end port not in last box\n");
            printpath(thepath);
        }
#ifndef DONTFIXPATH
        if (thepath->end.p.x < boxes[boxn - 1].LL.x)
            thepath->end.p.x = boxes[boxn - 1].LL.x;
        if (thepath->end.p.x > boxes[boxn - 1].UR.x)
            thepath->end.p.x = boxes[boxn - 1].UR.x;
        if (thepath->end.p.y < boxes[boxn - 1].LL.y)
            thepath->end.p.y = boxes[boxn - 1].LL.y;
        if (thepath->end.p.y > boxes[boxn - 1].UR.y)
            thepath->end.p.y = boxes[boxn - 1].UR.y;
#else
        abort();
#endif
    }
    return 0;
}

static int mkspacep(int size)
{
    if (size > maxpn) {
        int newmax = maxpn + (size / PINC + 1) * PINC;
        ps = RALLOC(newmax, ps, pointf);
        if (!ps) {
            agerr(AGERR, "cannot re-allocate ps\n");
            return 1;
        }
        maxpn = newmax;
    }
    return 0;
}

static void printpath(path * pp)
{
    int bi;

#ifdef NOTNOW
    fprintf(stderr, "edge %d from %s to %s\n", nedges,
            realedge->tail->name, realedge->head->name);
    if (ED_count(origedge) > 1)
        fprintf(stderr, "    (it's part of a concentrator edge)\n");
#endif
    fprintf(stderr, "%d boxes:\n", pp->nbox);
    for (bi = 0; bi < pp->nbox; bi++)
        fprintf(stderr, "%d (%.5g, %.5g), (%.5g, %.5g)\n", bi,
                pp->boxes[bi].LL.x, pp->boxes[bi].LL.y,
                pp->boxes[bi].UR.x, pp->boxes[bi].UR.y);
    fprintf(stderr, "start port: (%.5g, %.5g), tangent angle: %.5g, %s\n",
            pp->start.p.x, pp->start.p.y, pp->start.theta,
            pp->start.constrained ? "constrained" : "not constrained");
    fprintf(stderr, "end port: (%.5g, %.5g), tangent angle: %.5g, %s\n",
            pp->end.p.x, pp->end.p.y, pp->end.theta,
            pp->end.constrained ? "constrained" : "not constrained");
}