beta-0.89.2

[luatex.git] / source / texk / web2c / luatexdir / luafontloader / fontforge / fontforge / splineoverlap.c

/* Copyright (C) 2000-2008 by George Williams */
/*
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:

 * Redistributions of source code must retain the above copyright notice, this
 * list of conditions and the following disclaimer.

 * Redistributions in binary form must reproduce the above copyright notice,
 * this list of conditions and the following disclaimer in the documentation
 * and/or other materials provided with the distribution.

 * The name of the author may not be used to endorse or promote products
 * derived from this software without specific prior written permission.

 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR IMPLIED
 * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
 * EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
 * OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
 * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
 * OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
 * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
#include "pfaedit.h"
#include "splinefont.h"
#include "edgelist2.h"
#include <math.h>
#ifdef HAVE_IEEEFP_H
# include <ieeefp.h>            /* Solaris defines isnan in ieeefp rather than math.h */
#endif
#include <stdarg.h>

/* First thing we do is divide each spline into a set of sub-splines each of */
/*  which is monotonic in both x and y (always increasing or decreasing)     */
/* Then we compare each monotonic spline with every other one and see if they*/
/*  intersect.  If they do, split each up into sub-sub-segments and create an*/
/*  intersection point (note we need to be a little careful if an intersec-  */
/*  tion happens at an end point. We don't need to create a intersection for */
/*  two adjacent splines, there isn't a real intersection... but if a third  */
/*  spline crosses that point (or ends there) then all three (four) splines  */
/*  need to be joined into an intersection point)                            */
/* Nasty things happen if splines are coincident. They will almost never be  */
/*  perfectly coincident and will keep crossing and recrossing as rounding   */
/*  errors suggest one is before the other. Look for coincident splines and  */
/*  treat the places they start and stop being coincident as intersections   */
/*  then when we find needed splines below look for these guys and ignore    */
/*  recrossings of splines which are close together                          */
/* Figure out if each monotonic sub-spline is needed or not                  */
/*  (Note: It was tempting to split the bits up into real splines rather     */
/*   than keeping them as sub-sections of the original. Unfortunately this   */
/*   splitting introduced rounding errors which meant that we got more       */
/*   intersections, which meant that splines could be both needed and un.    */
/*   so I don't do that until later)                                         */
/*  if the spline hasn't been tagged yet:                                    */
/*   does the spline change greater in x or y?                               */
/*   draw a line parallel to the OTHER axis which hits our spline and doesn't*/
/*    hit any endpoints (or intersections, which are end points too now)     */
/*   count the winding number (as we do this we can mark other splines as    */
/*    needed or not) and figure out if our spline is needed                  */
/*  So run through the list of intersections                                 */
/*      At an intersection there should be an even number of needed monos.   */
/*      Use this as the basis of a new splineset, trace it around until      */
/*        we get back to the start intersection (should happen)              */
/*        (Note: We may need to reverse a monotonic sub-spline or two)       */
/*        As we go, mark each monotonic as having been used                  */
/*  Keep doing this until all needed exits from all intersections have been  */
/*      used.                                                                */
/*  The free up our temporary data structures, merge in any open splinesets  */
/*      free the old closed splinesets                                       */

typedef struct mlist {
    Spline *s;
    Monotonic *m;                       /* May get slightly munched but will */
                        /* always have right spline. we fix when we need it */
    extended t;
    int isend;
    BasePoint unit;
    struct mlist *next;
} MList;

typedef struct intersection {
    MList *monos;
    BasePoint inter;
    struct intersection *next;
} Intersection;

static char *glyphname=NULL;

static void SOError(char *format,...) {
    va_list ap;
    va_start(ap,format);
    if ( glyphname==NULL )
        fprintf(stderr, "Internal Error: " );
    else
        fprintf(stderr, "Internal Error in %s: ", glyphname );
    vfprintf(stderr,format,ap);
}

static Monotonic *SplineToMonotonic(Spline *s,extended startt,extended endt,
        Monotonic *last,int exclude) {
    Monotonic *m;
    BasePoint start, end;

    start.x = ((s->splines[0].a*startt+s->splines[0].b)*startt+s->splines[0].c)*startt
                + s->splines[0].d;
    start.y = ((s->splines[1].a*startt+s->splines[1].b)*startt+s->splines[1].c)*startt
                + s->splines[1].d;
    end.x = ((s->splines[0].a*endt+s->splines[0].b)*endt+s->splines[0].c)*endt
                + s->splines[0].d;
    end.y = ((s->splines[1].a*endt+s->splines[1].b)*endt+s->splines[1].c)*endt
                + s->splines[1].d;
    if ( (real) (((start.x+end.x)/2)==start.x || (real) ((start.x+end.x)/2)==end.x) &&
            (real) (((start.y+end.y)/2)==start.y || (real) ((start.y+end.y)/2)==end.y) ) {
        /* The distance between the two extrema is so small */
        /*  as to be unobservable. In other words we'd end up with a zero*/
        /*  length spline */
        if ( endt==1.0 && last!=NULL && last->s==s )
            last->tend = endt;
return( last );
    }

    m = chunkalloc(sizeof(Monotonic));
    m->s = s;
    m->tstart = startt;
    m->tend = endt;
    m->exclude = exclude;

    if ( end.x>start.x ) {
        m->xup = true;
        m->b.minx = start.x;
        m->b.maxx = end.x;
    } else {
        m->b.minx = end.x;
        m->b.maxx = start.x;
    }
    if ( end.y>start.y ) {
        m->yup = true;
        m->b.miny = start.y;
        m->b.maxy = end.y;
    } else {
        m->b.miny = end.y;
        m->b.maxy = start.y;
    }

    if ( last!=NULL ) {
        last->next = m;
        last->linked = m;
        m->prev = last;
    }
return( m );
}

static int SSIsSelected(SplineSet *spl) {
    SplinePoint *sp;

    for ( sp=spl->first; ; ) {
        if ( sp->selected )
return( true );
        if ( sp->next==NULL )
return( false );
        sp = sp->next->to;
        if ( sp==spl->first )
return( false );
    }
}

static int BpSame(BasePoint *bp1, BasePoint *bp2) {
    BasePoint mid;

    mid.x = (bp1->x+bp2->x)/2; mid.y = (bp1->y+bp2->y)/2;
    if ( (bp1->x==mid.x || bp2->x==mid.x) &&
            (bp1->y==mid.y || bp2->y==mid.y))
return( true );

return( false );
}

static int SSRmNullSplines(SplineSet *spl) {
    Spline *s, *first, *next;

    first = NULL;
    for ( s=spl->first->next ; s!=first; s=next ) {
        next = s->to->next;
        if ( ((s->splines[0].a>-.01 && s->splines[0].a<.01 &&
                s->splines[0].b>-.01 && s->splines[0].b<.01 &&
                s->splines[1].a>-.01 && s->splines[1].a<.01 &&
                s->splines[1].b>-.01 && s->splines[1].b<.01) ||
                /* That describes a null spline (a line between the same end-point) */
               RealNear((s->from->nextcp.x-s->from->me.x)*(s->to->me.y-s->to->prevcp.y)-
                        (s->from->nextcp.y-s->from->me.y)*(s->to->me.x-s->to->prevcp.x),0)) &&
                /* And the above describes a point with a spline between it */
                /*  and itself where the spline covers no area (the two cps */
                /*  point in the same direction) */
                BpSame(&s->from->me,&s->to->me)) {
            if ( next==s )
return( true );
            if ( next->from->selected ) s->from->selected = true;
            s->from->next = next;
            s->from->nextcp = next->from->nextcp;
            s->from->nonextcp = next->from->nonextcp;
            s->from->nextcpdef = next->from->nextcpdef;
            SplinePointFree(next->from);
            if ( spl->first==next->from )
                spl->last = spl->first = s->from;
            next->from = s->from;
            SplineFree(s);
        } else {
            if ( first==NULL )
                first = s;
        }
    }
return( false );
}

static Monotonic *SSToMContour(SplineSet *spl, Monotonic *start,
        Monotonic **end, enum overlap_type ot) {
    extended ts[4];
    Spline *first, *s;
    Monotonic *head=NULL, *last=NULL;
    int cnt, i, selected = false;
    extended lastt;

    if ( spl->first->prev==NULL )
return( start );                /* Open contours have no interior, ignore 'em */
    if ( spl->first->prev->from==spl->first &&
            spl->first->noprevcp && spl->first->nonextcp )
return( start );                /* Let's just remove single points */

    if ( ot==over_rmselected || ot==over_intersel || ot==over_fisel || ot==over_exclude ) {
        selected = SSIsSelected(spl);
        if ( ot==over_rmselected || ot==over_intersel || ot==over_fisel ) {
            if ( !selected )
return( start );
            selected = false;
        }
    }

    /* We blow up on zero length splines. And a zero length contour is nasty */
    if ( SSRmNullSplines(spl))
return( start );

    first = NULL;
    for ( s=spl->first->next; s!=first; s=s->to->next ) {
        if ( first==NULL ) first = s;
        cnt = Spline2DFindExtrema(s,ts);
        lastt = 0;
        for ( i=0; i<cnt; ++i ) {
            last = SplineToMonotonic(s,lastt,ts[i],last,selected);
            if ( head==NULL ) head = last;
            lastt=ts[i];
        }
        if ( lastt!=1.0 ) {
            last = SplineToMonotonic(s,lastt,1.0,last,selected);
            if ( head==NULL ) head = last;
        }
    }
    head->prev = last;
    last->next = head;
    if ( start==NULL )
        start = head;
    else
        (*end)->linked = head;
    *end = last;
return( start );
}

static Monotonic *SSsToMContours(SplineSet *spl, enum overlap_type ot) {
    Monotonic *head=NULL, *last = NULL;

    while ( spl!=NULL ) {
        if ( spl->first->prev!=NULL )
            head = SSToMContour(spl,head,&last,ot);
        spl = spl->next;
    }
return( head );
}

static void _AddSpline(Intersection *il,Monotonic *m,extended t,int isend) {
    MList *ml;

    for ( ml=il->monos; ml!=NULL; ml=ml->next ) {
        if ( ml->s==m->s && RealNear( ml->t,t ) && ml->isend==isend )
return;
    }

    ml = chunkalloc(sizeof(MList));
    ml->next = il->monos;
    il->monos = ml;
    ml->s = m->s;
    ml->m = m;                  /* This may change. We'll fix it up later */
    ml->t = t;
    ml->isend = isend;
    if ( isend ) {
        if ( m->end!=NULL && m->end!=il )
            SOError("Resetting end.\n");
        m->end = il;
    } else {
        if ( m->start!=NULL && m->start!=il )
            SOError("Resetting start.\n");
        m->start = il;
    }
return;
}

static void AddSpline(Intersection *il,Monotonic *m,extended t) {
    MList *ml;

    if ( m->start==il || m->end==il )
return;

    for ( ml=il->monos; ml!=NULL; ml=ml->next ) {
        if ( ml->s==m->s && RealWithin( ml->t,t,.0001 ))
return;
    }

    ml = chunkalloc(sizeof(MList));
    ml->next = il->monos;
    il->monos = ml;
    ml->s = m->s;
    ml->m = m;                  /* This may change. We'll fix it up later */
    ml->t = t;
    ml->isend = true;
    if ( t-m->tstart < m->tend-t && RealNear(m->tstart,t) ) {
        if ( m->start!=NULL && m->start!=il )
            SOError("Resetting start.\n");
        m->start = il;
        ml->t = m->tstart;
        ml->isend = false;
        _AddSpline(il,m->prev,m->prev->tend,true);
    } else if ( RealNear(m->tend,t)) {
        if ( m->end!=NULL && m->end!=il )
            SOError("Resetting end.\n");
        m->end = il;
        ml->t = m->tend;
        _AddSpline(il,m->next,m->next->tstart,false);
    } else {
        /* Ok, if we've got a new intersection on this spline then break up */
        /*  the monotonic into two bits which end and start at this inter */
        if ( t<m->tstart || t>m->tend )
            SOError( "Attempt to subset monotonic rejoin inappropriately: %g should be [%g,%g]\n",
                    t, m->tstart, m->tend );
        else {
            /* It is monotonic, so a subset of it must also be */
            Monotonic *m2 = chunkalloc(sizeof(Monotonic));
            BasePoint pt;
            *m2 = *m;
            m->next = m2;
            m2->prev = m;
            m2->next->prev = m2;
            m->linked = m2;
            m->tend = t;
            m->end = il;
            m2->start = il;
            m2->tstart = t;
            pt.x = ((m->s->splines[0].a*m->tstart+m->s->splines[0].b)*m->tstart+
                    m->s->splines[0].c)*m->tstart+m->s->splines[0].d;
            pt.y = ((m->s->splines[1].a*m->tstart+m->s->splines[1].b)*m->tstart+
                    m->s->splines[1].c)*m->tstart+m->s->splines[1].d;
            if ( pt.x>il->inter.x ) {
                m->b.minx = il->inter.x;
                m->b.maxx = pt.x;
            } else {
                m->b.minx = pt.x;
                m->b.maxx = il->inter.x;
            }
            if ( pt.y>il->inter.y ) {
                m->b.miny = il->inter.y;
                m->b.maxy = pt.y;
            } else {
                m->b.miny = pt.y;
                m->b.maxy = il->inter.y;
            }
            pt.x = ((m2->s->splines[0].a*m2->tend+m2->s->splines[0].b)*m2->tend+
                    m2->s->splines[0].c)*m2->tend+m2->s->splines[0].d;
            pt.y = ((m2->s->splines[1].a*m2->tend+m2->s->splines[1].b)*m2->tend+
                    m2->s->splines[1].c)*m2->tend+m2->s->splines[1].d;
            if ( pt.x>il->inter.x ) {
                m2->b.minx = il->inter.x;
                m2->b.maxx = pt.x;
            } else {
                m2->b.minx = pt.x;
                m2->b.maxx = il->inter.x;
            }
            if ( pt.y>il->inter.y ) {
                m2->b.miny = il->inter.y;
                m2->b.maxy = pt.y;
            } else {
                m2->b.miny = pt.y;
                m2->b.maxy = il->inter.y;
            }
            _AddSpline(il,m2,t,false);
        }
    }
}

static void SetStartPoint(BasePoint *pt,Monotonic *m) {
    if ( m->tstart==0 )
        *pt = m->s->from->me;
    else if ( m->start!=NULL )
        *pt = m->start->inter;
    else {
        pt->x = ((m->s->splines[0].a*m->tstart+m->s->splines[0].b)*m->tstart +
                m->s->splines[0].c)*m->tstart + m->s->splines[0].d;
        pt->y = ((m->s->splines[1].a*m->tstart+m->s->splines[1].b)*m->tstart +
                m->s->splines[1].c)*m->tstart + m->s->splines[1].d;
    }
}

static void SetEndPoint(BasePoint *pt,Monotonic *m) {
    if ( m->tend==1.0 )
        *pt = m->s->to->me;
    else if ( m->end!=NULL )
        *pt = m->end->inter;
    else {
        pt->x = ((m->s->splines[0].a*m->tend+m->s->splines[0].b)*m->tend +
                m->s->splines[0].c)*m->tend + m->s->splines[0].d;
        pt->y = ((m->s->splines[1].a*m->tend+m->s->splines[1].b)*m->tend +
                m->s->splines[1].c)*m->tend + m->s->splines[1].d;
    }
}

static extended RoundToEndpoints(Monotonic *m,extended t,BasePoint *inter) {
    BasePoint end;
    extended bound;

    if ( t==0 || t==1 ) {
        if ( t==0 )
            *inter = m->s->from->me;
        else
            *inter = m->s->to->me;
return( t );
    }

    if ( t-m->tstart < m->tend-t ) {
        bound = m->tstart;
        SetStartPoint(&end,m);
    } else {
        bound = m->tend;
        SetEndPoint(&end,m);
    }
    if ( BpSame(&end,inter) || RealWithin(t,bound,.00001)) {
        *inter = end;
return( bound );
    }

return( t );
}

static extended Grad1(Spline1D *s1, Spline1D *s2,
        extended t1,extended t2 ) {
    /* d/dt[12] (m1(t1).x-m2(t2).x)^2 + (m1(t1).y-m2(t2).y)^2 */
    /* d/dt[12] (m1(t1).x^2 -2m1(t1).x*m2(t2).x + m2(t2).x^2) + (m1(t1).y^2 -2m1(t1).y*m2(t2).y + m2(t2).y^2) */
    extended val2 = ((s2->a*t2+s2->b)*t2+s2->c)*t2+s2->d;

return( ((((6*(extended)s1->a*s1->a*t1 +
            5*2*(extended)s1->a*s1->b)*t1 +
            4*(s1->b*(extended)s1->b+2*s1->a*(extended)s1->c))*t1 +
            3*2*(s1->a*(extended)s1->d+s1->b*(extended)s1->c))*t1 +
            2*(s1->c*(extended)s1->c+2*s1->b*(extended)s1->d))*t1 +
            2*s1->c*(extended)s1->d  -
             2*val2 * ((3*s1->a*t1 + 2*s1->b)*t1 + s1->c) );
}

static void GradImproveInter(Monotonic *m1, Monotonic *m2,
        extended *_t1,extended *_t2,BasePoint *inter) {
    Spline *s1 = m1->s, *s2 = m2->s;
    extended x1, x2, y1, y2;
    extended gt1=0, gt2=0, glen=1;
    extended error, olderr=1e10;
    extended factor = 4096;
    extended t1=*_t1, t2=*_t2;
    extended off, off2, yoff;
    int cnt=0;
    /* We want to find (t1,t2) so that (m1(t1)-m2(t2))^2==0 */
    /* Find the gradiant and move in the reverse direction */
    /* We know that the current values of (t1,t2) are close to an intersection*/
    /* so the grad should point correctly */
    /* d/dt[12] (m1(t1).x-m2(t2).x)^2 + (m1(t1).y-m2(t2).y)^2 */
    /* d/dt[12] (m1(t1).x^2 -2m1(t1).x*m2(t2).x + m2(t2).x^2) + (m1(t1).y^2 -2m1(t1).y*m2(t2).y + m2(t2).y^2) */

    forever {
        x1 = ((s1->splines[0].a*t1 + s1->splines[0].b)*t1 + s1->splines[0].c)*t1 + s1->splines[0].d;
        x2 = ((s2->splines[0].a*t2 + s2->splines[0].b)*t2 + s2->splines[0].c)*t2 + s2->splines[0].d;
        y1 = ((s1->splines[1].a*t1 + s1->splines[1].b)*t1 + s1->splines[1].c)*t1 + s1->splines[1].d;
        y2 = ((s2->splines[1].a*t2 + s2->splines[1].b)*t2 + s2->splines[1].c)*t2 + s2->splines[1].d;
        error = (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2);
        if ( error>olderr ) {
            if ( olderr==1e10 )
    break;
            factor *= 2;
            if ( factor>4096*4096 )
    break;
            glen *= 2;
            t1 += gt1/glen;
            t2 += gt2/glen;
    continue;
        } else
            factor /= 1.4;
        if ( error<1e-11 )      /* Error is actually the square of the error */
    break;                      /* So this isn't as constraining as it looks */

        gt1 = Grad1(&s1->splines[0],&s2->splines[0],t1,t2) + Grad1(&s1->splines[1],&s2->splines[1],t1,t2);
        gt2 = Grad1(&s2->splines[0],&s1->splines[0],t2,t1) + Grad1(&s2->splines[1],&s1->splines[1],t2,t1);
        glen = esqrt(gt1*gt1 + gt2*gt2) * factor;
        if ( glen==0 )
    break;
        *_t1 = t1; *_t2 = t2;
        t1 -= gt1/glen;
        t2 -= gt2/glen;
        if ( isnan(t1) || isnan(t2)) {
            IError( "Nan in grad" );
    break;
        }
        olderr = error;
        ++cnt;
        if ( cnt>1000 )
    break;
    }
#if 0
    if ( cnt<=1 && error>=1e-11 )
        fprintf(stderr,"No Improvement\n" );
    else if ( cnt>1 )
        fprintf(stderr,"Improvement\n" );
#endif
    t1 = *_t1; t2 = *_t2;
    if ( t1<0 && t1>-.00001 ) *_t1 = t1 = 0;
    else if ( t1>1 && t1<1.00001 ) *_t1 = t1 = 1.0;
    if ( t2<0 && t2>-.00001 ) *_t2 = t2 = 0;
    else if ( t2>1 && t2<1.00001 ) *_t2 = t2 = 1.0;
    x1 = ((s1->splines[0].a*t1 + s1->splines[0].b)*t1 + s1->splines[0].c)*t1 + s1->splines[0].d;
    x2 = ((s2->splines[0].a*t2 + s2->splines[0].b)*t2 + s2->splines[0].c)*t2 + s2->splines[0].d;
    y1 = ((s1->splines[1].a*t1 + s1->splines[1].b)*t1 + s1->splines[1].c)*t1 + s1->splines[1].d;
    y2 = ((s2->splines[1].a*t2 + s2->splines[1].b)*t2 + s2->splines[1].c)*t2 + s2->splines[1].d;
    inter->x = (x1+x2)/2; inter->y = (y1+y2)/2;

    if ( (off=x1-x2)<0 ) off = -off;
    if ( (yoff=y1-y2)<0 ) yoff = -yoff;
    off += yoff;

    if ( t1<.0001 ) {
        t1 = 0;
        x1 = s1->splines[0].d;
        y1 = s1->splines[1].d;
    } else if ( t1>.9999 ) {
        t1 = 1.0;
        x1 = s1->splines[0].a+s1->splines[0].b+s1->splines[0].c+s1->splines[0].d;
        y1 = s1->splines[1].a+s1->splines[1].b+s1->splines[1].c+s1->splines[1].d;
    }
    if ( t2<.0001 ) {
        t2=0;
        x2 = s2->splines[0].d;
        y2 = s2->splines[1].d;
    } else if ( t2>.9999 ) {
        t2=1.0;
        x2 = s2->splines[0].a+s2->splines[0].b+s2->splines[0].c+s2->splines[0].d;
        y2 = s2->splines[1].a+s2->splines[1].b+s2->splines[1].c+s2->splines[1].d;
    }
    if ( (off2=x1-x2)<0 ) off2 = -off2;
    if ( (yoff=y1-y2)<0 ) yoff = -yoff;
    off2 += yoff;
    if ( off2<=off ) {
        *_t1 = t1; *_t2 = t2;
        inter->x = (x1+x2)/2; inter->y = (y1+y2)/2;
    }
}

static Intersection *AddIntersection(Intersection *ilist,Monotonic *m1,
        Monotonic *m2,extended t1,extended t2,BasePoint *inter) {
    Intersection *il;
    extended ot1 = t1, ot2 = t2;

    /* Fixup some rounding errors */
    GradImproveInter(m1,m2,&t1,&t2,inter);
    if ( t1<m1->tstart || t1>m1->tend || t2<m2->tstart || t2>m2->tend )
return( ilist );

        t1 = RoundToEndpoints(m1,t1,inter);
        t2 = RoundToEndpoints(m2,t2,inter);
        t1 = RoundToEndpoints(m1,t1,inter);     /* Do it twice. rounding t2 can mean we now need to round t1 */

    if (( m1->s->to == m2->s->from && RealWithin(t1,1.0,.01) && RealWithin(t2,0,.01)) ||
            ( m1->s->from == m2->s->to && RealWithin(t1,0,.01) && RealWithin(t2,1.0,.01)))
return( ilist );

    if (( t1==m1->tstart && m1->start!=NULL &&
            (inter->x!=m1->start->inter.x || inter->y!=m1->start->inter.y)) ||
        ( t1==m1->tend && m1->end!=NULL &&
            (inter->x!=m1->end->inter.x || inter->y!=m1->end->inter.y)))
        t1 = ot1;
    if (( t2==m2->tstart && m2->start!=NULL &&
            (inter->x!=m2->start->inter.x || inter->y!=m2->start->inter.y)) ||
        ( t2==m2->tend && m2->end!=NULL &&
            (inter->x!=m2->end->inter.x || inter->y!=m2->end->inter.y)))
        t2 = ot2;

    /* The ordinary join of one spline to the next doesn't really count */
    /*  Or one monotonic sub-spline to the next either */
    if (( m1->next==m2 && RealNear(t1,m1->tend) && RealNear(t2,m2->tstart)) ||
            (m2->next==m1 && RealNear(t1,m1->tstart) && RealNear(t2,m2->tend)) )
return( ilist );

    if ( RealWithin(m1->tstart,t1,.01) )
        il = m1->start;
    else if ( RealWithin(m1->tend,t1,.01) )
        il = m1->end;
    else
        il = NULL;
    if ( il!=NULL &&
            ((RealWithin(m2->tstart,t2,.01) && m2->start==il) ||
             (RealWithin(m2->tend,t2,.01) && m2->end==il)) )
return( ilist );

    for ( il = ilist; il!=NULL; il=il->next ) {
        if ( RealWithin(il->inter.x,inter->x,.01) && RealWithin(il->inter.y,inter->y,.01)) {
            AddSpline(il,m1,t1);
            AddSpline(il,m2,t2);
return( ilist );
        }
    }

    il = chunkalloc(sizeof(Intersection));
    il->inter = *inter;
    il->next = ilist;
    AddSpline(il,m1,t1);
    AddSpline(il,m2,t2);
return( il );
}

static extended BoundIterateSplineSolve(Spline1D *sp, extended tmin, extended tmax,
        extended sought,double err) {
    extended t = IterateSplineSolve(sp,tmin,tmax,sought,err);
    if ( t<tmin || t>tmax )
return( -1 );

return( t );
}

static Intersection *FindMonotonicIntersection(Intersection *ilist,Monotonic *m1,Monotonic *m2) {
    /* I believe that two monotonic cubics can still intersect in two points */
    /*  so we can't just check if the splines are on oposite sides of each */
    /*  other at top and bottom */
    DBounds b;
    const double error = .0001;
    BasePoint pt;
    extended t1,t2;

    b.minx = m1->b.minx>m2->b.minx ? m1->b.minx : m2->b.minx;
    b.maxx = m1->b.maxx<m2->b.maxx ? m1->b.maxx : m2->b.maxx;
    b.miny = m1->b.miny>m2->b.miny ? m1->b.miny : m2->b.miny;
    b.maxy = m1->b.maxy<m2->b.maxy ? m1->b.maxy : m2->b.maxy;

    if ( b.maxy==b.miny && b.minx==b.maxx ) {
        extended x1,y1, x2,y2;
        if ( m1->next==m2 || m2->next==m1 )
return( ilist );                /* Not interesting. Only intersection is at an endpoint */
        if ( ((m1->start==m2->start || m1->end==m2->start) && m2->start!=NULL) ||
                ((m1->start==m2->end || m1->end==m2->end ) && m2->end!=NULL ))
return( ilist );
        pt.x = b.minx; pt.y = b.miny;
        if ( m1->b.maxx-m1->b.minx > m1->b.maxy-m1->b.miny )
            t1 = BoundIterateSplineSolve(&m1->s->splines[0],m1->tstart,m1->tend,b.minx,error);
        else
            t1 = BoundIterateSplineSolve(&m1->s->splines[1],m1->tstart,m1->tend,b.miny,error);
        if ( m2->b.maxx-m2->b.minx > m2->b.maxy-m2->b.miny )
            t2 = BoundIterateSplineSolve(&m2->s->splines[0],m2->tstart,m2->tend,b.minx,error);
        else
            t2 = BoundIterateSplineSolve(&m2->s->splines[1],m2->tstart,m2->tend,b.miny,error);
        if ( t1!=-1 && t2!=-1 ) {
            x1 = ((m1->s->splines[0].a*t1+m1->s->splines[0].b)*t1+m1->s->splines[0].c)*t1+m1->s->splines[0].d;
            y1 = ((m1->s->splines[1].a*t1+m1->s->splines[1].b)*t1+m1->s->splines[1].c)*t1+m1->s->splines[1].d;
            x2 = ((m2->s->splines[0].a*t2+m2->s->splines[0].b)*t2+m2->s->splines[0].c)*t2+m2->s->splines[0].d;
            y2 = ((m2->s->splines[1].a*t2+m2->s->splines[1].b)*t2+m2->s->splines[1].c)*t2+m2->s->splines[1].d;
            if ( x1-x2>-.01 && x1-x2<.01 && y1-y2>-.01 && y1-y2<.01 )
                ilist = AddIntersection(ilist,m1,m2,t1,t2,&pt);
        }
    } else if ( b.maxy==b.miny ) {
        extended x1,x2;
        if ( m1->next==m2 || m2->next==m1 )
return( ilist );                /* Not interesting. Only intersection is at an endpoint */
        t1 = BoundIterateSplineSolve(&m1->s->splines[1],m1->tstart,m1->tend,b.miny,error);
        t2 = BoundIterateSplineSolve(&m2->s->splines[1],m2->tstart,m2->tend,b.miny,error);
        if ( t1!=-1 && t2!=-1 ) {
            x1 = ((m1->s->splines[0].a*t1+m1->s->splines[0].b)*t1+m1->s->splines[0].c)*t1+m1->s->splines[0].d;
            x2 = ((m2->s->splines[0].a*t2+m2->s->splines[0].b)*t2+m2->s->splines[0].c)*t2+m2->s->splines[0].d;
            if ( x1-x2>-.01 && x1-x2<.01 ) {
                pt.x = (x1+x2)/2; pt.y = b.miny;
                ilist = AddIntersection(ilist,m1,m2,t1,t2,&pt);
            }
        }
    } else if ( b.maxx==b.minx ) {
        extended y1,y2;
        if ( m1->next==m2 || m2->next==m1 )
return( ilist );                /* Not interesting. Only intersection is at an endpoint */
        t1 = BoundIterateSplineSolve(&m1->s->splines[0],m1->tstart,m1->tend,b.minx,error);
        t2 = BoundIterateSplineSolve(&m2->s->splines[0],m2->tstart,m2->tend,b.minx,error);
        if ( t1!=-1 && t2!=-1 ) {
            y1 = ((m1->s->splines[1].a*t1+m1->s->splines[1].b)*t1+m1->s->splines[1].c)*t1+m1->s->splines[1].d;
            y2 = ((m2->s->splines[1].a*t2+m2->s->splines[1].b)*t2+m2->s->splines[1].c)*t2+m2->s->splines[1].d;
            if ( y1-y2>-.01 && y1-y2<.01 ) {
                pt.x = b.minx; pt.y = (y1+y2)/2;
                ilist = AddIntersection(ilist,m1,m2,t1,t2,&pt);
            }
        }
    } else if ( b.maxy-b.miny > b.maxx-b.minx ) {
        extended diff, y, x1,x2, x1o,x2o;
        extended t1,t2, t1o,t2o ;

        diff = (b.maxy-b.miny)/32;
        y = b.miny;
        x1o = x2o = 0;
        while ( y<b.maxy ) {
            while ( y<b.maxy ) {
                t1o = BoundIterateSplineSolve(&m1->s->splines[1],m1->tstart,m1->tend,b.miny,error);
                t2o = BoundIterateSplineSolve(&m2->s->splines[1],m2->tstart,m2->tend,b.miny,error);
                if ( t1o!=-1 && t2o!=-1 )
            break;
                y += diff;
            }
            x1o = ((m1->s->splines[0].a*t1o+m1->s->splines[0].b)*t1o+m1->s->splines[0].c)*t1o+m1->s->splines[0].d;
            x2o = ((m2->s->splines[0].a*t2o+m2->s->splines[0].b)*t2o+m2->s->splines[0].c)*t2o+m2->s->splines[0].d;
            if ( x1o!=x2o )
        break;
            y += diff;
        }
        for ( y+=diff; ; y += diff ) {
            /* I used to say y<=b.maxy in the above for statement. */
            /*  that seemed to get rounding errors on the mac, so we do it */
            /*  like this now: */
            if ( y>b.maxy ) {
                if ( y<b.maxy+diff/4 ) y = b.maxy;
                else
        break;
            }
            t1 = BoundIterateSplineSolve(&m1->s->splines[1],m1->tstart,m1->tend,y,error);
            t2 = BoundIterateSplineSolve(&m2->s->splines[1],m2->tstart,m2->tend,y,error);
            if ( t1==-1 || t2==-1 )
        continue;
            x1 = ((m1->s->splines[0].a*t1+m1->s->splines[0].b)*t1+m1->s->splines[0].c)*t1+m1->s->splines[0].d;
            x2 = ((m2->s->splines[0].a*t2+m2->s->splines[0].b)*t2+m2->s->splines[0].c)*t2+m2->s->splines[0].d;
            if ( x1o!=x2o && (x1o>x2o) != ( x1>x2 ) ) {
                /* A cross over has occured. (assume we have a small enough */
                /*  region that three cross-overs can't have occurred) */
                /* Use a binary search to track it down */
                extended ytop, ybot;
                ytop = y;
                ybot = y-diff;
                while ( ytop!=ybot ) {
                    extended ytest = (ytop+ybot)/2;
                    extended t1t, t2t;
                    t1t = BoundIterateSplineSolve(&m1->s->splines[1],m1->tstart,m1->tend,ytest,error);
                    t2t = BoundIterateSplineSolve(&m2->s->splines[1],m2->tstart,m2->tend,ytest,error);
                    x1 = ((m1->s->splines[0].a*t1t+m1->s->splines[0].b)*t1t+m1->s->splines[0].c)*t1t+m1->s->splines[0].d;
                    x2 = ((m2->s->splines[0].a*t2t+m2->s->splines[0].b)*t2t+m2->s->splines[0].c)*t2t+m2->s->splines[0].d;
                    if ( t1t==-1 || t2t==-1 ) {
                        SOError( "Can't find something in range.\n" );
                break;
                    } else if (( x1-x2<error && x1-x2>-error ) || ytop==ytest || ybot==ytest ) {
                        pt.y = ytest; pt.x = (x1+x2)/2;
                        ilist = AddIntersection(ilist,m1,m2,t1t,t2t,&pt);
                        b.maxy = m1->b.maxy<m2->b.maxy ? m1->b.maxy : m2->b.maxy;
                break;
                    } else if ( (x1o>x2o) != ( x1>x2 ) ) {
                        ytop = ytest;
                    } else {
                        ybot = ytest;
                    }
                }
                x1 = x1o; x1o = x2o; x2o = x1;
            } else {
                x1o = x1; x2o = x2;
            }
        }
    } else {
        extended diff, x, y1,y2, y1o,y2o;
        extended t1,t2, t1o,t2o ;

        diff = (b.maxx-b.minx)/32;
        x = b.minx;
        y1o = y2o = 0;
        while ( x<b.maxx ) {
            while ( x<b.maxx ) {
                t1o = BoundIterateSplineSolve(&m1->s->splines[0],m1->tstart,m1->tend,b.minx,error);
                t2o = BoundIterateSplineSolve(&m2->s->splines[0],m2->tstart,m2->tend,b.minx,error);
                if ( t1o!=-1 && t2o!=-1 )
            break;
                x += diff;
            }
            y1o = ((m1->s->splines[1].a*t1o+m1->s->splines[1].b)*t1o+m1->s->splines[1].c)*t1o+m1->s->splines[1].d;
            y2o = ((m2->s->splines[1].a*t2o+m2->s->splines[1].b)*t2o+m2->s->splines[1].c)*t2o+m2->s->splines[1].d;
            if ( y1o!=y2o )
        break;
            x += diff;
        }
        y1 = y2 = 0;
        for ( x+=diff; ; x += diff ) {
            if ( x>b.maxx ) {
                if ( x<b.maxx+diff/4 ) x = b.maxx;
                else
        break;
            }
            t1 = BoundIterateSplineSolve(&m1->s->splines[0],m1->tstart,m1->tend,x,error);
            t2 = BoundIterateSplineSolve(&m2->s->splines[0],m2->tstart,m2->tend,x,error);
            if ( t1==-1 || t2==-1 )
        continue;
            y1 = ((m1->s->splines[1].a*t1+m1->s->splines[1].b)*t1+m1->s->splines[1].c)*t1+m1->s->splines[1].d;
            y2 = ((m2->s->splines[1].a*t2+m2->s->splines[1].b)*t2+m2->s->splines[1].c)*t2+m2->s->splines[1].d;
            if ( (y1o>y2o) != ( y1>y2 ) ) {
                /* A cross over has occured. (assume we have a small enough */
                /*  region that three cross-overs can't have occurred) */
                /* Use a binary search to track it down */
                extended xtop, xbot;
                xtop = x;
                xbot = x-diff;
                while ( xtop!=xbot ) {
                    extended xtest = (xtop+xbot)/2;
                    extended t1t, t2t;
                    t1t = BoundIterateSplineSolve(&m1->s->splines[0],m1->tstart,m1->tend,xtest,error);
                    t2t = BoundIterateSplineSolve(&m2->s->splines[0],m2->tstart,m2->tend,xtest,error);
                    y1 = ((m1->s->splines[1].a*t1t+m1->s->splines[1].b)*t1t+m1->s->splines[1].c)*t1t+m1->s->splines[1].d;
                    y2 = ((m2->s->splines[1].a*t2t+m2->s->splines[1].b)*t2t+m2->s->splines[1].c)*t2t+m2->s->splines[1].d;
                    if ( t1t==-1 || t2t==-1 ) {
                        SOError( "Can't find something in range.\n" );
                break;
                    } else if (( y1-y2<error && y1-y2>-error ) || xtop==xtest || xbot==xtest ) {
                        pt.x = xtest; pt.y = (y1+y2)/2;
                        ilist = AddIntersection(ilist,m1,m2,t1t,t2t,&pt);
                        b.maxx = m1->b.maxx<m2->b.maxx ? m1->b.maxx : m2->b.maxx;
                break;
                    } else if ( (y1o>y2o) != ( y1>y2 ) ) {
                        xtop = xtest;
                    } else {
                        xbot = xtest;
                    }
                }
                y1 = y1o; y1o = y2o; y2o = y1;
            } else {
                y1o = y1; y2o = y2;
            }
        }
    }
return( ilist );
}


static extended SplineContainsPoint(Monotonic *m,BasePoint *pt) {
    int which, nw;
    extended t;
    BasePoint slope;
    const double error = .0001;

    which = ( m->b.maxx-m->b.minx > m->b.maxy-m->b.miny )? 0 : 1;
    nw = !which;
    t = BoundIterateSplineSolve(&m->s->splines[which],m->tstart,m->tend,(&pt->x)[which],error);
    if ( (slope.x = (3*m->s->splines[0].a*t+2*m->s->splines[0].b)*t+m->s->splines[0].c)<0 )
        slope.x = -slope.x;
    if ( (slope.y = (3*m->s->splines[1].a*t+2*m->s->splines[1].b)*t+m->s->splines[1].c)<0 )
        slope.y = -slope.y;
    if ( t==-1 || (slope.y>slope.x)!=which ) {
        nw = which;
        which = 1-which;
        t = BoundIterateSplineSolve(&m->s->splines[which],m->tstart,m->tend,(&pt->x)[which],error);
    }
    if ( t!=-1 && RealWithin((&pt->x)[nw],
           ((m->s->splines[nw].a*t+m->s->splines[nw].b)*t +
                m->s->splines[nw].c)*t + m->s->splines[nw].d,.1 ))
return( t );

return( -1 );
}

/* If two splines are coincident, then pretend they intersect at both */
/*  end-points and nowhere else */
static int CoincidentIntersect(Monotonic *m1,Monotonic *m2,BasePoint *pts,
        extended *t1s,extended *t2s) {
    const double error = .0001;
    int cnt=0;
    extended t, t2, diff;

    if ( m1==m2 || m1->next==m2 || m1->prev==m2 )
return( false );                /* Can't be coincident. Adjacent */
    /* Actually adjacent splines can double back on themselves */

    if ( (m1->xup==m2->xup && m1->yup==m2->yup) ||
            ((m1->xup!=m2->xup || (m1->b.minx==m1->b.maxx && m2->b.minx==m2->b.maxx)) ||
             (m1->yup!=m2->yup || (m1->b.miny==m1->b.maxy && m2->b.miny==m2->b.maxy))))
        /* A match is possible */;
    else
return( false );

    SetStartPoint(&pts[cnt],m1);
    t1s[cnt] = m1->tstart;
    if ( (t2s[cnt] = SplineContainsPoint(m2,&pts[cnt]))!=-1 )
        ++cnt;

    SetEndPoint(&pts[cnt],m1);
    t1s[cnt] = m1->tend;
    if ( (t2s[cnt] = SplineContainsPoint(m2,&pts[cnt]))!=-1 )
        ++cnt;

    if ( cnt!=2 ) {
        SetStartPoint(&pts[cnt],m2);
        t2s[cnt] = m2->tstart;
        if ( (t1s[cnt] = SplineContainsPoint(m1,&pts[cnt]))!=-1 )
            ++cnt;
    }

    if ( cnt!=2 ) {
        SetEndPoint(&pts[cnt],m2);
        t2s[cnt] = m2->tend;
        if ( (t1s[cnt] = SplineContainsPoint(m1,&pts[cnt]))!=-1 )
            ++cnt;
    }

    if ( cnt!=2 )
return( false );

    if ( RealWithin(t1s[0],t1s[1],.01) )
return( false );

    /* Ok, if we've gotten this far we know that two of the end points are  */
    /*  on both splines.                                                    */
    t1s[2] = t2s[2] = -1;
    if ( !m1->s->knownlinear || !m1->s->knownlinear ) {
        if ( t1s[1]<t1s[0] ) {
            extended temp = t1s[1]; t1s[1] = t1s[0]; t1s[0] = temp;
            temp = t2s[1]; t2s[1] = t2s[0]; t2s[0] = temp;
        }
        diff = (t1s[1]-t1s[0])/16;
        for ( t=t1s[0]+diff; t<t1s[1]-diff/4; t += diff ) {
            BasePoint here, slope;
            here.x = ((m1->s->splines[0].a*t+m1->s->splines[0].b)*t+m1->s->splines[0].c)*t+m1->s->splines[0].d;
            here.y = ((m1->s->splines[1].a*t+m1->s->splines[1].b)*t+m1->s->splines[1].c)*t+m1->s->splines[1].d;
            if ( (slope.x = (3*m1->s->splines[0].a*t+2*m1->s->splines[0].b)*t+m1->s->splines[0].c)<0 )
                slope.x = -slope.x;
            if ( (slope.y = (3*m1->s->splines[1].a*t+2*m1->s->splines[1].b)*t+m1->s->splines[1].c)<0 )
                slope.y = -slope.y;
            if ( slope.y>slope.x ) {
                t2 = BoundIterateSplineSolve(&m2->s->splines[1],t2s[0],t2s[1],here.y,error);
                if ( t2==-1 || !RealWithin(here.x,((m2->s->splines[0].a*t2+m2->s->splines[0].b)*t2+m2->s->splines[0].c)*t2+m2->s->splines[0].d,.1))
return( false );
            } else {
                t2 = BoundIterateSplineSolve(&m2->s->splines[0],t2s[0],t2s[1],here.x,error);
                if ( t2==-1 || !RealWithin(here.y,((m2->s->splines[1].a*t2+m2->s->splines[1].b)*t2+m2->s->splines[1].c)*t2+m2->s->splines[1].d,.1))
return( false );
            }
        }
    }

return( true );
}

static void FigureProperMonotonicsAtIntersections(Intersection *ilist) {
    MList *ml, *ml2, *mlnext, *prev, *p2;

    while ( ilist!=NULL ) {
        for ( ml=ilist->monos; ml!=NULL; ml=ml->next ) {
            if ( (ml->t==ml->m->tstart && !ml->isend) ||
                    (ml->t==ml->m->tend && ml->isend))
                /* It's right */;
            else if ( ml->t>ml->m->tstart ) {
                while ( ml->t>ml->m->tend ) {
                    ml->m = ml->m->next;
                    if ( ml->m->s!=ml->s ) {
                        SOError("we could not find a matching monotonic\n" );
                break;
                    }
                }
            } else {
                while ( ml->t<ml->m->tstart ) {
                    ml->m = ml->m->prev;
                    if ( ml->m->s!=ml->s ) {
                        SOError( "we could not find a matching monotonic\n" );
                break;
                    }
                }
            }
            if ( ml->t==ml->m->tstart && ml->isend )
                ml->m = ml->m->prev;
            else if ( ml->t==ml->m->tend && !ml->isend )
                ml->m = ml->m->next;
            if ( ml->t!=ml->m->tstart && ml->t!=ml->m->tend )
                SOError( "we could not find a matching monotonic time\n" );
        }
        for ( prev=NULL, ml=ilist->monos; ml!=NULL; ml = mlnext ) {
            mlnext = ml->next;
            if ( ml->m->start==ml->m->end ) {
                for ( p2 = ml, ml2=ml->next; ml2!=NULL; p2=ml2, ml2 = ml2->next ) {
                    if ( ml2->m==ml->m )
                break;
                }
                if ( ml2!=NULL ) {
                    if ( ml2==mlnext ) mlnext = ml2->next;
                    p2->next = ml2->next;
                    chunkfree(ml2,sizeof(*ml2));
                }
                if ( prev==NULL )
                    ilist->monos = mlnext;
                else
                    prev->next = mlnext;
                chunkfree(ml,sizeof(*ml));
            }
        }
#if 0
        for ( ml=ilist->monos; ml!=NULL; ml=ml->next ) {
            Monotonic *search;
            MList *ml2;
            extended t;
            if ( ml->m->start == ilist ) {
                search = ml->m->prev;
                t = ( ml->m->tstart==0 ) ? 1.0 : ml->m->tstart;
            } else {
                search = ml->m->next;
                t = ( ml->m->tend==1.0 ) ? 0.0 : ml->m->tend;
            }
            for ( ml2=ilist->monos; ml2!=NULL && ml2->m!=search; ml2=ml2->next );
            if ( ml2==NULL ) {
                ml2 = chunkalloc(sizeof(MList));
                ml2->m = search;
                ml2->s = search->s;
                ml2->t = t;
                ml2->next = ml->next;
                ml->next = ml2;
                ml = ml2;
            }
        }
#endif
        ilist = ilist->next;
    }
}

static void Validate(Monotonic *ms, Intersection *ilist) {
    MList *ml;
    int mcnt;

    while ( ilist!=NULL ) {
        for ( mcnt=0, ml=ilist->monos; ml!=NULL; ml=ml->next ) {
            if ( ml->m->isneeded ) ++mcnt;
            if ( ml->m->start!=ilist && ml->m->end!=ilist )
                SOError( "Intersection (%g,%g) not on a monotonic which should contain it.\n",
                        ilist->inter.x, ilist->inter.y );
        }
        if ( mcnt&1 )
            SOError( "Odd number of needed monotonic sections at intersection. (%g,%g)\n",
                    ilist->inter.x,ilist->inter.y );
        ilist = ilist->next;
    }

    while ( ms!=NULL ) {
        if ( ms->prev->end!=ms->start )
            SOError( "Mismatched intersection.\n");
        ms = ms->linked;
    }
}

static Intersection *FindIntersections(Monotonic *ms, enum overlap_type ot) {
    Monotonic *m1, *m2;
    BasePoint pts[9];
    extended t1s[10], t2s[10];
    Intersection *ilist=NULL;
    int i;
    int wasc;

    for ( m1=ms; m1!=NULL; m1=m1->linked ) {
        for ( m2=m1->linked; m2!=NULL; m2=m2->linked ) {
            if ( m2->b.minx > m1->b.maxx ||
                    m2->b.maxx < m1->b.minx ||
                    m2->b.miny > m1->b.maxy ||
                    m2->b.maxy < m1->b.miny )
        continue;               /* Can't intersect */;
            wasc = CoincidentIntersect(m1,m2,pts,t1s,t2s);
            if ( wasc || m1->s->knownlinear || m2->s->knownlinear ||
                    (m1->s->splines[0].a==0 && m1->s->splines[1].a==0 &&
                     m2->s->splines[0].a==0 && m2->s->splines[1].a==0 )) {
                if ( !wasc && SplinesIntersect(m1->s,m2->s,pts,t1s,t2s)<=0 )
        continue;
                for ( i=0; i<4 && t1s[i]!=-1; ++i ) {
                    if ( t1s[i]>=m1->tstart && t1s[i]<=m1->tend &&
                            t2s[i]>=m2->tstart && t2s[i]<=m2->tend ) {
                        ilist = AddIntersection(ilist,m1,m2,t1s[i],t2s[i],&pts[i]);
                    }
                }
        continue;
            }
            ilist = FindMonotonicIntersection(ilist,m1,m2);
        }
    }

    FigureProperMonotonicsAtIntersections(ilist);

    /* Now suppose we have a contour which intersects nothing? */
    /* with no intersections we lose track of it and it will vanish */
    /* That's not a good idea. Make sure each contour has at least one inter */
    if ( ot!=over_findinter && ot!=over_fisel ) {
        for ( m1=ms; m1!=NULL; m1=m2->linked ) {
            if ( m1->start==NULL && m1->end==NULL ) {
                Intersection *il;
                il = chunkalloc(sizeof(Intersection));
                il->inter = m1->s->from->me;
                il->next = ilist;
                AddSpline(il,m1,0);
                AddSpline(il,m1->prev,1.0);
                ilist = il;
            }
            for ( m2=m1; m2->linked==m2->next; m2=m2->linked );
        }
    }

return( ilist );
}

static int dcmp(const void *_p1, const void *_p2) {
    const extended *dpt1 = _p1, *dpt2 = _p2;
    if ( *dpt1>*dpt2 )
return( 1 );
    else if ( *dpt1<*dpt2 )
return( -1 );

return( 0 );
}

static extended *FindOrderedEndpoints(Monotonic *ms,int which) {
    int cnt;
    Monotonic *m;
    extended *ends;
    int i,j,k;

    for ( m=ms, cnt=0; m!=NULL; m=m->linked, ++cnt );
    ends = galloc((2*cnt+1)*sizeof(extended));
    for ( m=ms, cnt=0; m!=NULL; m=m->linked, cnt+=2 ) {
        if ( m->start!=NULL )
            ends[cnt] = (&m->start->inter.x)[which];
        else if ( m->tstart==0 )
            ends[cnt] = (&m->s->from->me.x)[which];
        else
            ends[cnt] = ((m->s->splines[which].a*m->tstart+m->s->splines[which].b)*m->tstart+
                    m->s->splines[which].c)*m->tstart+m->s->splines[which].d;
        if ( m->end!=NULL )
            ends[cnt+1] = (&m->end->inter.x)[which];
        else if ( m->tend==1.0 )
            ends[cnt+1] = (&m->s->to->me.x)[which];
        else
            ends[cnt+1] = ((m->s->splines[which].a*m->tend+m->s->splines[which].b)*m->tend+
                    m->s->splines[which].c)*m->tend+m->s->splines[which].d;
    }

    qsort(ends,cnt,sizeof(extended),dcmp);
    for ( i=0; i<cnt; ++i ) {
        for ( j=i; j<cnt && ends[i]==ends[j]; ++j );
        if ( j>i+1 ) {
            for ( k=i+1; j<cnt; ends[k++] = ends[j++]);
            cnt-= j-k;
        }
    }
    ends[cnt] = 1e10;
return( ends );
}

static int mcmp(const void *_p1, const void *_p2) {
    const Monotonic * const *mpt1 = _p1, * const *mpt2 = _p2;
    if ( (*mpt1)->other>(*mpt2)->other )
return( 1 );
    else if ( (*mpt1)->other<(*mpt2)->other )
return( -1 );

return( 0 );
}

static int MonotonicFindAt(Monotonic *ms,int which, extended test, Monotonic **space ) {
    /* Find all monotonic sections which intersect the line (x,y)[which] == test */
    /*  find the value of the other coord on that line */
    /*  Order them (by the other coord) */
    /*  then run along that line figuring out which monotonics are needed */
    extended t;
    Monotonic *m, *mm;
    int i, j, k, cnt;
    const double error = .0001;
    int nw = !which;

    for ( m=ms, i=0; m!=NULL; m=m->linked ) {
        if (( which==0 && test >= m->b.minx && test <= m->b.maxx ) ||
                ( which==1 && test >= m->b.miny && test <= m->b.maxy )) {
            /* Lines parallel to the direction we are testing just get in the */
            /*  way and don't add any useful info */
            if ( m->s->knownlinear &&
                    (( which==1 && m->s->from->me.y==m->s->to->me.y ) ||
                        (which==0 && m->s->from->me.x==m->s->to->me.x)))
    continue;
            t = BoundIterateSplineSolve(&m->s->splines[which],m->tstart,m->tend,test,error);
            if ( t==-1 )
    continue;
            m->t = t;
            if ( t==m->tend ) t -= (m->tend-m->tstart)/100;
            else if ( t==m->tstart ) t += (m->tend-m->tstart)/100;
            m->other = ((m->s->splines[nw].a*t+m->s->splines[nw].b)*t+
                    m->s->splines[nw].c)*t+m->s->splines[nw].d;
            space[i++] = m;
        }
    }
    cnt = i;

    /* Things get a little tricky at end-points */
    for ( i=0; i<cnt; ++i ) {
        m = space[i];
        if ( m->t==m->tend ) {
            /* Ignore horizontal/vertical lines (as appropriate) */
            for ( mm=m->next; mm!=m; mm=mm->next ) {
                if ( !mm->s->knownlinear )
            break;
                if (( which==1 && mm->s->from->me.y!=m->s->to->me.y ) ||
                        (which==0 && mm->s->from->me.x!=m->s->to->me.x))
            break;
            }
        } else if ( m->t==m->tstart ) {
            for ( mm=m->prev; mm!=m; mm=mm->prev ) {
                if ( !mm->s->knownlinear )
            break;
                if (( which==1 && mm->s->from->me.y!=m->s->to->me.y ) ||
                        (which==0 && mm->s->from->me.x!=m->s->to->me.x))
            break;
            }
        } else
    break;
        /* If the next monotonic continues in the same direction, and we found*/
        /*  it too, then don't count both. They represent the same intersect */
        /* If they are in oposite directions then they cancel each other out */
        /*  and that is correct */
        if ( mm!=m &&   /* Should always be true */
                (&mm->xup)[which]==(&m->xup)[which] ) {
            for ( j=cnt-1; j>=0; --j )
                if ( space[j]==mm )
            break;
            if ( j!=-1 ) {
                /* remove mm */
                for ( k=j+1; k<cnt; ++k )
                    space[k-1] = space[k];
                --cnt;
                if ( i>j ) --i;
            }
        }
    }

    space[cnt] = NULL; space[cnt+1] = NULL;
    qsort(space,cnt,sizeof(Monotonic *),mcmp);
return(cnt);
}

static void FigureNeeds(Monotonic *ms,int which, extended test, Monotonic **space,
        enum overlap_type ot, int ignore_close) {
    /* Find all monotonic sections which intersect the line (x,y)[which] == test */
    /*  find the value of the other coord on that line */
    /*  Order them (by the other coord) */
    /*  then run along that line figuring out which monotonics are needed */
    int i, j, winding, ew, was_close, close;

    MonotonicFindAt(ms,which,test,space);

    winding = 0; ew = 0; was_close = false;
    for ( i=0; space[i]!=NULL; ++i ) {
        int needed, unneeded, inverted=false;
        Monotonic *m;
        int new;
        int nwinding;
      retry:
        needed = false, unneeded = false;
        nwinding=winding;
        new=ew;
        m = space[i];
        if ( m->exclude )
            new += ( (&m->xup)[which] ? 1 : -1 );
        else
            nwinding += ( (&m->xup)[which] ? 1 : -1 );
        if ( ot==over_remove || ot==over_rmselected ) {
            if ( winding==0 || nwinding==0 )
                needed = true;
            else
                unneeded = true;
        } else if ( ot==over_intersect || ot==over_intersel ) {
            if ( (winding>-2 && winding<2 && nwinding>-2 && nwinding<2) ||
                    ((winding<=-2 || winding>=2) && (nwinding<=-2 && nwinding>=2)))
                unneeded = true;
            else
                needed = true;
        } else if ( ot == over_exclude ) {
            if ( (( winding==0 || nwinding==0 ) && ew==0 && new==0 ) ||
                    (winding!=0 && (( ew!=0 && new==0 ) || ( ew==0 && new!=0))) )
                needed = true;
            else
                unneeded = true;
        }
        if ( space[i+1]!=NULL )
            close = space[i+1]->other-space[i]->other < 1;
        else
            close = false;
        if (( !close && !was_close ) || ignore_close ) {
            if (( m->isneeded || m->isunneeded ) && m->isneeded!=needed ) {
                for ( j=i+1; space[j]!=NULL && space[j]->other-m->other<.5; ++j ) {
                    if ( space[j]->start==m->start && space[j]->end==m->end &&
                            (space[j]->isneeded == needed ||
                             (!space[j]->isneeded && !space[j]->isunneeded))) {
                        space[i] = space[j];
                        space[j] = m;
                        m = space[i];
                break;
                    } else if ( !inverted && space[j]->other-m->other<.001 &&
                            (((&space[j]->xup)[which] == (&m->xup)[which] &&
                              (space[j]->isneeded == needed ||
                               (!space[j]->isneeded && !space[j]->isunneeded))) ||
                             ((&space[j]->xup)[which] != (&m->xup)[which] &&
                              (space[j]->isneeded != needed ||
                               (!space[j]->isneeded && !space[j]->isunneeded)))) ) {
                        space[i] = space[j];
                        space[j] = m;
                        inverted = true;
                  goto retry;
                    }
                }
            }
            if ( !m->isneeded && !m->isunneeded ) {
                m->isneeded = needed; m->isunneeded = unneeded;
                m->when_set = test;             /* Debugging */
            } else if ( m->isneeded!=needed || m->isunneeded!=unneeded )
                SOError( "monotonic is both needed and unneeded.\n" );
        }
        winding = nwinding;
        ew = new;
        was_close = close;
    }
    if ( winding!=0 )
        SOError( "Winding number did not return to 0 when %s=%g\n",
                which ? "y" : "x", test );
}

struct gaps { extended test, len; int which; };

static int gcmp(const void *_p1, const void *_p2) {
    const struct gaps *gpt1 = _p1, *gpt2 = _p2;
    if ( gpt1->len > gpt2->len )
return( 1 );
    else if ( gpt1->len < gpt2->len )
return( -1 );

return( 0 );
}

static void FindNeeded(Monotonic *ms,enum overlap_type ot) {
    extended *ends[2];
    Monotonic *m, **space;
    extended top, bottom, test;
    int t,b,i,j,k,cnt,which;
    struct gaps *gaps;
    extended min_gap;

    if ( ms==NULL )
return;

    ends[0] = FindOrderedEndpoints(ms,0);
    ends[1] = FindOrderedEndpoints(ms,1);

    for ( m=ms, cnt=0; m!=NULL; m=m->linked, ++cnt );
    space = galloc((cnt+2)*sizeof(Monotonic*));
    gaps = galloc(2*cnt*sizeof(struct gaps));

    /* Look for the longest splines without interruptions first. These are */
    /* least likely to cause problems and will give us a good basis from which*/
    /* to make guesses should rounding errors occur later */
    for ( j=k=0; j<2; ++j )
        for ( i=0; ends[j][i+1]!=1e10; ++i ) {
            gaps[k].which = j;
            gaps[k].len = (ends[j][i+1]-ends[j][i]);
            gaps[k++].test = (ends[j][i+1]+ends[j][i])/2;
        }
    qsort(gaps,k,sizeof(struct gaps),gcmp);
    min_gap = 1e10;
    for ( m=ms; m!=NULL; m=m->linked ) {
        if ( m->b.maxx-m->b.minx > m->b.maxy-m->b.miny ) {
            if ( min_gap > m->b.maxx-m->b.minx ) min_gap = m->b.maxx-m->b.minx;
        } else {
            if ( m->b.maxy-m->b.miny==0 )
                fprintf( stderr, "Foo\n");
            if ( min_gap > m->b.maxy-m->b.miny ) min_gap = m->b.maxy-m->b.miny;
        }
    }
    if ( min_gap<.5 ) min_gap = .5;
    for ( i=0; i<k && gaps[i].len>=min_gap; ++i )
        FigureNeeds(ms,gaps[i].which,gaps[i].test,space,ot,0);

    for ( m=ms; m!=NULL; m=m->linked ) if ( !m->isneeded && !m->isunneeded ) {
        if ( m->b.maxx-m->b.minx > m->b.maxy-m->b.miny ) {
            top = m->b.maxx;
            bottom = m->b.minx;
            which = 0;
        } else {
            top = m->b.maxy;
            bottom = m->b.miny;
            which = 1;
        }
        for ( b=0; ends[which][b]<=bottom; ++b );
        for ( t=b; ends[which][t]<top; ++t );
        --t;
        /* b points to an endpoint which is greater than bottom */
        /* t points to an endpoint which is less than top */
        test = (top+bottom)/2;
        for ( i=b; i<=t; ++i ) {
            if ( RealNearish(test,ends[which][i]) ) {
                if ( i==b )
                    test = (bottom+ends[which][i])/2;
                else
                    test = (ends[which][i-1]+ends[which][i])/2;
        break;
            }
        }
        FigureNeeds(ms,which,test,space,ot,1);
    }
    free(ends[0]);
    free(ends[1]);
    free(space);
    free(gaps);
}

static void FindUnitVectors(Intersection *ilist) {
    MList *ml;
    Intersection *il;
    BasePoint u;
    double len;

    for ( il=ilist; il!=NULL; il=il->next ) {
        for ( ml=il->monos; ml!=NULL; ml=ml->next ) {
            if ( ml->m->isneeded ) {
                Spline *s = ml->m->s;
                double t1, t2;
                t1 = ml->t;
                if ( ml->isend )
                    t2 = ml->t - (ml->t-ml->m->tstart)/20.0;
                else
                    t2 = ml->t + (ml->m->tend-ml->t)/20.0;
                u.x = ((s->splines[0].a*t1 + s->splines[0].b)*t1 + s->splines[0].c)*t1 -
                        ((s->splines[0].a*t2 + s->splines[0].b)*t2 + s->splines[0].c)*t2;
                u.y = ((s->splines[1].a*t1 + s->splines[1].b)*t1 + s->splines[1].c)*t1 -
                        ((s->splines[1].a*t2 + s->splines[1].b)*t2 + s->splines[1].c)*t2;
                len = u.x*u.x + u.y*u.y;
                if ( len!=0 ) {
                    len = sqrt(len);
                    u.x /= len;
                    u.y /= len;
                }
                ml->unit = u;
            }
        }
    }
}

static void TestForBadDirections(Intersection *ilist) {
    /* If we have a glyph with at least two contours one drawn clockwise, */
    /*  one counter, and these two intersect, then our algorithm will */
    /*  not remove what appears to the user to be an overlap. Warn about */
    /*  this. */
    /* I think it happens iff all exits from an intersection are needed */
    MList *ml, *ml2;
    int cnt, ncnt;
    Intersection *il;

    /* If we have two splines one going from a->b and the other from b->a */
    /*  tracing exactly the same route, then they should cancel each other */
    /*  out. But depending on the order we hit them they may both be marked */
    /*  needed */  /* OverlapBugs.sfd: asciicircumflex */
    for ( il=ilist; il!=NULL; il=il->next ) {
        for ( ml=il->monos; ml!=NULL; ml=ml->next ) {
            if ( ml->m->isneeded && ml->m->s->knownlinear &&
                    ml->m->start!=NULL && ml->m->end!=NULL ) {
                for ( ml2 = ml->next; ml2!=NULL; ml2=ml2->next ) {
                    if ( ml2->m->isneeded && ml2->m->s->knownlinear &&
                            ml2->m->start == ml->m->end &&
                            ml2->m->end == ml->m->start ) {
                        ml2->m->isneeded = false;
                        ml->m->isneeded = false;
                        ml2->m->isunneeded = true;
                        ml->m->isunneeded = true;
                break;
                    }
                }
            }
        }
    }

    while ( ilist!=NULL ) {
        cnt = ncnt = 0;
        for ( ml = ilist->monos; ml!=NULL; ml=ml->next ) {
            ++cnt;
            if ( ml->m->isneeded ) ++ncnt;
        }
        ilist = ilist->next;
    }
}

static void MonoFigure(Spline *s,extended firstt,extended endt, SplinePoint *first,
        SplinePoint *end) {
    extended f;
    Spline1D temp;

    f = endt - firstt;
    /*temp.d = first->me.x;*/
    /*temp.a = s->splines[0].a*f*f*f;*/
    temp.b = (s->splines[0].b + 3*s->splines[0].a*firstt) *f*f;
    temp.c = (s->splines[0].c + 2*s->splines[0].b*firstt + 3*s->splines[0].a*firstt*firstt) * f;
    first->nextcp.x = first->me.x + temp.c/3;
    end->prevcp.x = first->nextcp.x + (temp.b+temp.c)/3;
    if ( temp.c>-.01 && temp.c<.01 ) first->nextcp.x = first->me.x;
    if ( (temp.b+temp.c)>-.01 && (temp.b+temp.c)<.01 ) end->prevcp.x = end->me.x;

    temp.b = (s->splines[1].b + 3*s->splines[1].a*firstt) *f*f;
    temp.c = (s->splines[1].c + 2*s->splines[1].b*firstt + 3*s->splines[1].a*firstt*firstt) * f;
    first->nextcp.y = first->me.y + temp.c/3;
    end->prevcp.y = first->nextcp.y + (temp.b+temp.c)/3;
    if ( temp.c>-.01 && temp.c<.01 ) first->nextcp.y = first->me.y;
    if ( (temp.b+temp.c)>-.01 && (temp.b+temp.c)<.01 ) end->prevcp.y = end->me.y;
    first->nonextcp = false; end->noprevcp = false;
    SplineMake3(first,end);
    if ( SplineIsLinear(first->next)) {
        first->nextcp = first->me;
        end->prevcp = end->me;
        first->nonextcp = end->noprevcp = true;
        SplineRefigure(first->next);
    }
}

static Intersection *MonoFollow(Intersection *curil, Monotonic *m) {
    Monotonic *mstart=m;

    if ( m->start==curil ) {
        while ( m!=NULL && m->end==NULL ) {
            m=m->next;
            if ( m==mstart )
        break;
        }
        if ( m==NULL )
return( NULL );

return( m->end );
    } else {
        while ( m!=NULL && m->start==NULL ) {
            m=m->prev;
            if ( m==mstart )
        break;
        }
        if ( m==NULL )
return( NULL );

return( m->start );
    }
}

static int MonoGoesSomewhereUseful(Intersection *curil, Monotonic *m) {
    Intersection *nextil = MonoFollow(curil,m);
    MList *ml;
    int cnt;

    if ( nextil==NULL )
return( false );
    cnt = 0;
    for ( ml=nextil->monos; ml!=NULL ; ml=ml->next )
        if ( ml->m->isneeded )
            ++cnt;
    if ( cnt>=2 )       /* One for the mono that one in, one for another going out... */
return( true );

return( false );
}

static MList *FindMLOfM(Intersection *curil,Monotonic *finalm) {
    MList *ml;

    for ( ml=curil->monos; ml!=NULL; ml=ml->next ) {
        if ( ml->m==finalm )
return( ml );
    }
return( NULL );
}

static SplinePoint *MonoFollowForward(Intersection **curil, MList *ml,
        SplinePoint *last, Monotonic **finalm) {
    SplinePoint *mid;
    Monotonic *m = ml->m, *mstart;

    forever {
        for ( mstart = m; m->s==mstart->s; m=m->next) {
            if ( !m->isneeded )
                SOError( "Expected needed monotonic.\n" );
            m->isneeded = false;                /* Mark as used */
            if ( m->end!=NULL )
        break;
        }
        if ( m->s==mstart->s ) {
            if ( m->end==NULL ) SOError( "Invariant condition does not hold.\n" );
            mid = SplinePointCreate(m->end->inter.x,m->end->inter.y);
        } else {
            m = m->prev;
            mid = SplinePointCreate(m->s->to->me.x,m->s->to->me.y);
        }
        if ( mstart->tstart==0 && m->tend==1.0 ) {
            /* I check for this special case to avoid rounding errors */
            last->nextcp = m->s->from->nextcp;
            last->nonextcp = m->s->from->nonextcp;
            mid->prevcp = m->s->to->prevcp;
            mid->noprevcp = m->s->to->noprevcp;
            SplineMake3(last,mid);
        } else {
            MonoFigure(m->s,mstart->tstart,m->tend,last,mid);
        }
        last = mid;
        if ( m->end!=NULL ) {
            *curil = m->end;
            *finalm = m;
return( last );
        }
        m = m->next;
    }
}

static SplinePoint *MonoFollowBackward(Intersection **curil, MList *ml,
        SplinePoint *last, Monotonic **finalm) {
    SplinePoint *mid;
    Monotonic *m = ml->m, *mstart;

    forever {
        for ( mstart=m; m->s==mstart->s; m=m->prev) {
            if ( !m->isneeded )
                SOError( "Expected needed monotonic.\n" );
            m->isneeded = false;                /* Mark as used */
            if ( m->start!=NULL )
        break;
        }
        if ( m->s==mstart->s ) {
            if ( m->start==NULL ) SOError( "Invariant condition does not hold.\n" );
            mid = SplinePointCreate(m->start->inter.x,m->start->inter.y);
        } else {
            m = m->next;
            mid = SplinePointCreate(m->s->from->me.x,m->s->from->me.y);
        }
        if ( m->s->knownlinear ) mid->pointtype = pt_corner;
        if ( mstart->tend==1.0 && m->tstart==0 ) {
            /* I check for this special case to avoid rounding errors */
            last->nextcp = m->s->to->prevcp;
            last->nonextcp = m->s->to->noprevcp;
            mid->prevcp = m->s->from->nextcp;
            mid->noprevcp = m->s->from->nonextcp;
            SplineMake3(last,mid);
        } else {
            MonoFigure(m->s,mstart->tend,m->tstart,last,mid);
        }
        last = mid;
        if ( m->start!=NULL ) {
            *curil = m->start;
            *finalm = m;
return( last );
        }
        m = m->prev;
    }
}

static SplineSet *JoinAContour(Intersection *startil,MList *ml) {
    SplineSet *ss = chunkalloc(sizeof(SplineSet));
    SplinePoint *last;
    Intersection *curil;
    int allexclude = ml->m->exclude;
    Monotonic *finalm;
    MList *lastml;

    ss->first = last = SplinePointCreate(startil->inter.x,startil->inter.y);
    curil = startil;
    forever {
        if ( allexclude && !ml->m->exclude ) allexclude = false;
        finalm = NULL;
        if ( ml->m->start==curil ) {
            last = MonoFollowForward(&curil,ml,last,&finalm);
        } else if ( ml->m->end==curil ) {
            last = MonoFollowBackward(&curil,ml,last,&finalm);
        } else {
            SOError( "Couldn't find endpoint (%g,%g).\n",
                    curil->inter.x, curil->inter.y );
            ml->m->isneeded = false;            /* Prevent infinite loops */
            ss->last = last;
    break;
        }
        if ( curil==startil ) {
            ss->first->prev = last->prev;
            ss->first->prevcp = last->prevcp;
            ss->first->noprevcp = last->noprevcp;
            last->prev->to = ss->first;
            SplinePointFree(last);
            ss->last = ss->first;
    break;
        }
        lastml = FindMLOfM(curil,finalm);
        if ( lastml==NULL ) {
            IError("Could not find finalm");
            /* Try to preserve direction */
            for ( ml=curil->monos; ml!=NULL && (!ml->m->isneeded || ml->m->end==curil); ml=ml->next );
            if ( ml==NULL )
                for ( ml=curil->monos; ml!=NULL && !ml->m->isneeded; ml=ml->next );
        } else {
            int k; MList *bestml; double bestdot;
            for ( k=0; k<2; ++k ) {
                bestml = NULL; bestdot = -2;
                for ( ml=curil->monos; ml!=NULL ; ml=ml->next ) {
                    if ( ml->m->isneeded && (ml->m->start==curil || k) ) {
                        double dot = lastml->unit.x*ml->unit.x + lastml->unit.y*ml->unit.y;
                        if ( dot>bestdot ) {
                            bestml = ml;
                            bestdot = dot;
                        }
                    }
                }
                if ( bestml!=NULL )
            break;
            }
            ml = bestml;
        }
        if ( ml==NULL ) {
            for ( ml=curil->monos; ml!=NULL ; ml=ml->next )
                if ( ml->m->isunneeded && ml->m->start==curil &&
                        MonoFollow(curil,ml->m)==startil )
            break;
            if ( ml==NULL )
                for ( ml=curil->monos; ml!=NULL ; ml=ml->next )
                    if ( ml->m->isunneeded && ml->m->end==curil &&
                            MonoFollow(curil,ml->m)==startil )
                break;
            if ( ml!=NULL ) {
                SOError("Closing contour with unneeded path\n" );
                ml->m->isneeded = true;
            }
        }
        if ( ml==NULL ) {
            SOError( "couldn't find a needed exit from an intersection\n" );
            ss->last = last;
    break;
        }
    }
    SPLCatagorizePoints(ss);
    if ( allexclude && SplinePointListIsClockwise(ss))
        SplineSetReverse(ss);
return( ss );
}

static SplineSet *FindMatchingContour(SplineSet *head,SplineSet *cur) {
    SplineSet *test;

    for ( test=head; test!=NULL; test=test->next ) {
        if ( test->first->prev==NULL &&
                test->first->me.x==cur->last->me.x && test->first->me.y==cur->last->me.y &&
                test->last->me.x==cur->first->me.x && test->last->me.y==cur->first->me.y )
    break;
    }
    if ( test==NULL ) {
        for ( test=head; test!=NULL; test=test->next ) {
            if ( test->first->prev==NULL &&
                    test->last->me.x==cur->last->me.x && test->last->me.y==cur->last->me.y &&
                    test->first->me.x==cur->first->me.x && test->first->me.y==cur->first->me.y ) {
                SplineSetReverse(cur);
        break;
            }
        }
    }
    if ( test==NULL ) {
        for ( test=head; test!=NULL; test=test->next ) {
            if ( test->first->prev==NULL &&
                    ((test->first->me.x==cur->last->me.x && test->first->me.y==cur->last->me.y) ||
                     (test->last->me.x==cur->first->me.x && test->last->me.y==cur->first->me.y )))
        break;
        }
    }
    if ( test==NULL ) {
        for ( test=head; test!=NULL; test=test->next ) {
            if ( test->first->prev==NULL &&
                    ((test->last->me.x==cur->last->me.x && test->last->me.y==cur->last->me.y) ||
                     (test->first->me.x==cur->first->me.x && test->first->me.y==cur->first->me.y ))) {
                SplineSetReverse(cur);
        break;
            }
        }
    }
return( test );
}

static SplineSet *JoinAllNeeded(Intersection *ilist) {
    Intersection *il;
    SplineSet *head=NULL, *last=NULL, *cur, *test;
    MList *ml;

    for ( il=ilist; il!=NULL; il=il->next ) {
        /* Try to preserve direction */
        forever {
            for ( ml=il->monos; ml!=NULL && (!ml->m->isneeded || ml->m->end==il); ml=ml->next );
            if ( ml==NULL )
                for ( ml=il->monos; ml!=NULL && !ml->m->isneeded; ml=ml->next );
            if ( ml==NULL )
        break;
            if ( !MonoGoesSomewhereUseful(il,ml->m)) {
                SOError("Humph. This monotonic leads nowhere.\n" );
        /* break; */
            }
            cur = JoinAContour(il,ml);
            if ( head==NULL )
                head = cur;
            else {
                if ( cur->first->prev==NULL ) {
                    /* Open contours are errors. See if we had an earlier error */
                    /*  to which we can join this */
                    test = FindMatchingContour(head,cur);
                    if ( test!=NULL ) {
                        if ( test->first->me.x==cur->last->me.x && test->first->me.y==cur->last->me.y ) {
                            test->first->prev = cur->last->prev;
                            cur->last->prev->to = test->first;
                            SplinePointFree(cur->last);
                            if ( test->last->me.x==cur->first->me.x && test->last->me.y==cur->first->me.y ) {
                                test->last->next = cur->first->next;
                                cur->first->next->from = test->last;
                                SplinePointFree(cur->first);
                                test->last = test->first;
                            } else
                                test->first = cur->first;
                        } else {
                            if ( test->last->me.x!=cur->first->me.x || test->last->me.y!=cur->first->me.y )
                                SOError( "Join failed");
                            else {
                                test->last->next = cur->first->next;
                                cur->first->next->from = test->last;
                                SplinePointFree(cur->first);
                                test->last = test->first;
                            }
                        }
                        cur->first = cur->last = NULL;
                        SplinePointListFree(cur);
                        cur=NULL;
                    }
                }
                if ( cur!=NULL )
                    last->next = cur;
            }
            if ( cur!=NULL )
                last = cur;
        }
    }
return( head );
}

static SplineSet *MergeOpenAndFreeClosed(SplineSet *new,SplineSet *old,
        enum overlap_type ot) {
    SplineSet *next;

    while ( old!=NULL ) {
        next = old->next;
        if ( old->first->prev==NULL ||
                (( ot==over_rmselected || ot==over_intersel || ot==over_fisel) &&
                  !SSIsSelected(old)) ) {
            old->next = new;
            new = old;
        } else {
            old->next = NULL;
            SplinePointListFree(old);
        }
        old = next;
    }
return(new);
}

static void FreeMonotonics(Monotonic *m) {
    Monotonic *next;

    while ( m!=NULL ) {
        next = m->linked;
        chunkfree(m,sizeof(*m));
        m = next;
    }
}

static void FreeMList(MList *ml) {
    MList *next;

    while ( ml!=NULL ) {
        next = ml->next;
        chunkfree(ml,sizeof(*ml));
        ml = next;
    }
}

static void FreeIntersections(Intersection *ilist) {
    Intersection *next;

    while ( ilist!=NULL ) {
        next = ilist->next;
        FreeMList(ilist->monos);
        chunkfree(ilist,sizeof(*ilist));
        ilist = next;
    }
}

static void MonoSplit(Monotonic *m) {
    Spline *s = m->s;
    SplinePoint *last = s->from;
    SplinePoint *final = s->to;
    extended lastt = 0;

    last->next = NULL;
    final->prev = NULL;
    while ( m!=NULL && m->s==s && m->tend<1 ) {
        if ( m->end!=NULL ) {
            SplinePoint *mid = SplinePointCreate(m->end->inter.x,m->end->inter.y);
            if ( m->s->knownlinear ) mid->pointtype = pt_corner;
            MonoFigure(s,lastt,m->tend,last,mid);
            lastt = m->tend;
            last = mid;
        }
        m = m->linked;
    }
    MonoFigure(s,lastt,1.0,last,final);
    SplineFree(s);
}

static void FixupIntersectedSplines(Monotonic *ms) {
    /* If all we want is intersections, then the contours are already correct */
    /*  all we need to do is run through the Monotonic list and when we find */
    /*  an intersection, make sure it has real splines around it */
    Monotonic *m;
    int needs_split;

    while ( ms!=NULL ) {
        needs_split = false;
        for ( m=ms; m!=NULL && m->s==ms->s; m=m->linked ) {
            if ( (m->tstart!=0 && m->start!=NULL) || (m->tend!=1 && m->end!=NULL))
                needs_split = true;
        }
        if ( needs_split )
            MonoSplit(ms);
        ms = m;
    }
}

static int BpClose(BasePoint *here, BasePoint *there, double error) {
    extended dx, dy;

    if ( (dx = here->x-there->x)<0 ) dx= -dx;
    if ( (dy = here->y-there->y)<0 ) dy= -dy;
    if ( dx<error && dy<error )
return( true );

return( false );
}

static SplineSet *SSRemoveTiny(SplineSet *base) {
    DBounds b;
    double error;
    extended test, dx, dy;
    SplineSet *prev = NULL, *head = base, *ssnext;
    SplinePoint *sp, *nsp;

    SplineSetQuickBounds(base,&b);
    error = b.maxy-b.miny;
    test = b.maxx-b.minx;
    if ( test>error ) error = test;
    if ( (test = b.maxy)<0 ) test = -test;
    if ( test>error ) error = test;
    if ( (test = b.maxx)<0 ) test = -test;
    if ( test>error ) error = test;
    error /= 30000;

    while ( base!=NULL ) {
        ssnext = base->next;
        for ( sp=base->first; ; ) {
            if ( sp->next==NULL )
        break;
            nsp = sp->next->to;
            if ( BpClose(&sp->me,&nsp->me,error) ) {
                if ( BpClose(&sp->me,&sp->nextcp,2*error) &&
                        BpClose(&nsp->me,&nsp->prevcp,2*error)) {
                    /* Remove the spline */
                    if ( nsp==sp ) {
                        /* Only this spline in the contour, so remove the contour */
                        base->next = NULL;
                        SplinePointListFree(base);
                        if ( prev==NULL )
                            head = ssnext;
                        else
                            prev->next = ssnext;
                        base = NULL;
        break;
                    }
                    SplineFree(sp->next);
                    if ( nsp->nonextcp ) {
                        sp->nextcp = sp->me;
                        sp->nonextcp = true;
                    } else {
                        sp->nextcp = nsp->nextcp;
                        sp->nonextcp = false;
                    }
                    sp->nextcpdef = nsp->nextcpdef;
                    sp->next = nsp->next;
                    if ( nsp->next!=NULL ) {
                        nsp->next->from = sp;
                        SplineRefigure(sp->next);
                    }
                    if ( nsp==base->last )
                        base->last = sp;
                    if ( nsp==base->first )
                        base->first = sp;
                    SplinePointFree(nsp);
                    if ( sp->next==NULL )
        break;
                    nsp = sp->next->to;
                } else {
                    /* Leave the spline, but move the two points together */
                    BasePoint new;
                    new.x = (sp->me.x+nsp->me.x)/2;
                    new.y = (sp->me.y+nsp->me.y)/2;
                    dx = new.x-sp->me.x; dy = new.y-sp->me.y;
                    sp->me = new;
                    sp->nextcp.x += dx; sp->nextcp.y += dy;
                    sp->prevcp.x += dx; sp->prevcp.y += dy;
                    dx = new.x-nsp->me.x; dy = new.y-nsp->me.y;
                    nsp->me = new;
                    nsp->nextcp.x += dx; nsp->nextcp.y += dy;
                    nsp->prevcp.x += dx; nsp->prevcp.y += dy;
                    SplineRefigure(sp->next);
                    if ( sp->prev ) SplineRefigure(sp->prev);
                    if ( nsp->next ) SplineRefigure(nsp->next);
                }
            }
            sp = nsp;
            if ( sp==base->first )
        break;
        }
        if ( sp->prev!=NULL && !sp->noprevcp ) {
            int refigure = false;
            if ( sp->me.x-sp->prevcp.x>-error && sp->me.x-sp->prevcp.x<error ) {
                sp->prevcp.x = sp->me.x;
                refigure = true;
            }
            if ( sp->me.y-sp->prevcp.y>-error && sp->me.y-sp->prevcp.y<error ) {
                sp->prevcp.y = sp->me.y;
                refigure = true;
            }
            if ( sp->me.x==sp->prevcp.x && sp->me.y==sp->prevcp.y )
                sp->noprevcp = true;
            if ( refigure )
                SplineRefigure(sp->prev);
        }
        if ( sp->next!=NULL && !sp->nonextcp ) {
            int refigure = false;
            if ( sp->me.x-sp->nextcp.x>-error && sp->me.x-sp->nextcp.x<error ) {
                sp->nextcp.x = sp->me.x;
                refigure = true;
            }
            if ( sp->me.y-sp->nextcp.y>-error && sp->me.y-sp->nextcp.y<error ) {
                sp->nextcp.y = sp->me.y;
                refigure = true;
            }
            if ( sp->me.x==sp->nextcp.x && sp->me.y==sp->nextcp.y )
                sp->nonextcp = true;
            if ( refigure )
                SplineRefigure(sp->next);
        }
        if ( base!=NULL )
            prev = base;
        base = ssnext;
    }

return( head );
}

static void RemoveNextSP(SplinePoint *psp,SplinePoint *sp,SplinePoint *nsp,
        SplineSet *base) {
    if ( psp==nsp ) {
        SplineFree(psp->next);
        psp->next = psp->prev;
        psp->next->from = psp;
        SplinePointFree(sp);
        SplineRefigure(psp->prev);
    } else {
        psp->next = nsp->next;
        psp->next->from = psp;
        psp->nextcp = nsp->nextcp;
        psp->nonextcp = nsp->nonextcp;
        psp->nextcpdef = nsp->nextcpdef;
        SplineFree(sp->prev);
        SplineFree(sp->next);
        SplinePointFree(sp);
        SplinePointFree(nsp);
        SplineRefigure(psp->next);
    }
    if ( base->first==sp || base->first==nsp )
        base->first = psp;
    if ( base->last==sp || base->last==nsp )
        base->last = psp;
}

static void RemovePrevSP(SplinePoint *psp,SplinePoint *sp,SplinePoint *nsp,
        SplineSet *base) {
    if ( psp==nsp ) {
        SplineFree(nsp->prev);
        nsp->prev = nsp->next;
        nsp->prev->to = nsp;
        SplinePointFree(sp);
        SplineRefigure(nsp->next);
    } else {
        nsp->prev = psp->prev;
        nsp->prev->to = nsp;
        nsp->prevcp = nsp->me;
        nsp->noprevcp = true;
        nsp->prevcpdef = psp->prevcpdef;
        SplineFree(sp->prev);
        SplineFree(sp->next);
        SplinePointFree(sp);
        SplinePointFree(psp);
        SplineRefigure(nsp->prev);
    }
    if ( base->first==sp || base->first==psp )
        base->first = nsp;
    if ( base->last==sp || base->last==psp )
        base->last = nsp;
}

static SplinePoint *SameLine(SplinePoint *psp, SplinePoint *sp, SplinePoint *nsp) {
    BasePoint noff, poff;
    real nlen, plen, normal;

    noff.x = nsp->me.x-sp->me.x; noff.y = nsp->me.y-sp->me.y;
    poff.x = psp->me.x-sp->me.x; poff.y = psp->me.y-sp->me.y;
    nlen = esqrt(noff.x*noff.x + noff.y*noff.y);
    plen = esqrt(poff.x*poff.x + poff.y*poff.y);
    if ( nlen==0 )
return( nsp );
    if ( plen==0 )
return( psp );
    normal = (noff.x*poff.y - noff.y*poff.x)/nlen/plen;
    if ( normal<-.0001 || normal>.0001 )
return( NULL );

    if ( noff.x*poff.x < 0 || noff.y*poff.y < 0 )
return( NULL );         /* Same line, but different directions */
    if ( (noff.x>0 && noff.x>poff.x) ||
            (noff.x<0 && noff.x<poff.x) ||
            (noff.y>0 && noff.y>poff.y) ||
            (noff.y<0 && noff.y<poff.y))
return( nsp );

return( psp );
}

static double AdjacentSplinesMatch(Spline *s1,Spline *s2,int s2forward) {
    /* Is every point on s2 close to a point on s1 */
    double t, tdiff, t1 = -1;
    double xoff, yoff;
    double t1start, t1end;
    extended ts[2];
    int i;

    if ( (xoff = s2->to->me.x-s2->from->me.x)<0 ) xoff = -xoff;
    if ( (yoff = s2->to->me.y-s2->from->me.y)<0 ) yoff = -yoff;
    if ( xoff>yoff )
        SplineFindExtrema(&s1->splines[0],&ts[0],&ts[1]);
    else
        SplineFindExtrema(&s1->splines[1],&ts[0],&ts[1]);
    if ( s2forward ) {
        t = 0;
        tdiff = 1/16.0;
        t1end = 1;
        for ( i=1; i>=0 && ts[i]==-1; --i );
        t1start = i<0 ? 0 : ts[i];
    } else {
        t = 1;
        tdiff = -1/16.0;
        t1start = 0;
        t1end = ( ts[0]==-1 ) ? 1.0 : ts[0];
    }

    for ( ; (s2forward && t<=1) || (!s2forward && t>=0 ); t += tdiff ) {
        double x1, y1, xo, yo;
        double x = ((s2->splines[0].a*t+s2->splines[0].b)*t+s2->splines[0].c)*t+s2->splines[0].d;
        double y = ((s2->splines[1].a*t+s2->splines[1].b)*t+s2->splines[1].c)*t+s2->splines[1].d;
        if ( xoff>yoff )
            t1 = IterateSplineSolve(&s1->splines[0],t1start,t1end,x,.001);
        else
            t1 = IterateSplineSolve(&s1->splines[1],t1start,t1end,y,.001);
        if ( t1<0 || t1>1 )
return( -1 );
        x1 = ((s1->splines[0].a*t1+s1->splines[0].b)*t1+s1->splines[0].c)*t1+s1->splines[0].d;
        y1 = ((s1->splines[1].a*t1+s1->splines[1].b)*t1+s1->splines[1].c)*t1+s1->splines[1].d;
        if ( (xo = (x-x1))<0 ) xo = -xo;
        if ( (yo = (y-y1))<0 ) yo = -yo;
        if ( xo+yo>.5 )
return( -1 );
    }
return( t1 );
}
        
static void SSRemoveBacktracks(SplineSet *ss) {
    SplinePoint *sp;

    if ( ss==NULL )
return;
    for ( sp=ss->first; ; ) {
        if ( sp->next!=NULL && sp->prev!=NULL ) {
            SplinePoint *nsp = sp->next->to, *psp = sp->prev->from, *isp;
            BasePoint ndir, pdir;
            double dot, pdot, nlen, plen, t = -1;

            ndir.x = (nsp->me.x - sp->me.x); ndir.y = (nsp->me.y - sp->me.y);
            pdir.x = (psp->me.x - sp->me.x); pdir.y = (psp->me.y - sp->me.y);
            nlen = ndir.x*ndir.x + ndir.y*ndir.y; plen = pdir.x*pdir.x + pdir.y*pdir.y;
            dot = ndir.x*pdir.x + ndir.y*pdir.y;
            if ( (pdot = ndir.x*pdir.y - ndir.y*pdir.x)<0 ) pdot = -pdot;
            if ( dot>0 && dot>pdot ) {
                if ( nlen>plen && (t=AdjacentSplinesMatch(sp->next,sp->prev,false))!=-1 ) {
                    isp = SplineBisect(sp->next,t);
                    psp->nextcp.x = psp->me.x + (isp->nextcp.x-isp->me.x);
                    psp->nextcp.y = psp->me.y + (isp->nextcp.y-isp->me.y);
                    psp->nonextcp = isp->nonextcp;
                    psp->next = isp->next;
                    isp->next->from = psp;
                    SplineFree(isp->prev);
                    SplineFree(sp->prev);
                    SplinePointFree(isp);
                    SplinePointFree(sp);
                    if ( psp->next->order2 ) {
                        psp->nextcp.x = nsp->prevcp.x = (psp->nextcp.x+nsp->prevcp.x)/2;
                        psp->nextcp.y = nsp->prevcp.y = (psp->nextcp.y+nsp->prevcp.y)/2;
                        if ( psp->nonextcp || nsp->noprevcp )
                            psp->nonextcp = nsp->noprevcp = true;
                    }
                    SplineRefigure(psp->next);
                    if ( ss->first==sp )
                        ss->first = psp;
                    if ( ss->last==sp )
                        ss->last = psp;
                    sp=psp;
                } else if ( nlen<plen && (t=AdjacentSplinesMatch(sp->prev,sp->next,true))!=-1 ) {
                    isp = SplineBisect(sp->prev,t);
                    nsp->prevcp.x = nsp->me.x + (isp->prevcp.x-isp->me.x);
                    nsp->prevcp.y = nsp->me.y + (isp->prevcp.y-isp->me.y);
                    nsp->noprevcp = isp->noprevcp;
                    nsp->prev = isp->prev;
                    isp->prev->to = nsp;
                    SplineFree(isp->next);
                    SplineFree(sp->next);
                    SplinePointFree(isp);
                    SplinePointFree(sp);
                    if ( psp->next->order2 ) {
                        psp->nextcp.x = nsp->prevcp.x = (psp->nextcp.x+nsp->prevcp.x)/2;
                        psp->nextcp.y = nsp->prevcp.y = (psp->nextcp.y+nsp->prevcp.y)/2;
                        if ( psp->nonextcp || nsp->noprevcp )
                            psp->nonextcp = nsp->noprevcp = true;
                    }
                    SplineRefigure(nsp->prev);
                    if ( ss->first==sp )
                        ss->first = psp;
                    if ( ss->last==sp )
                        ss->last = psp;
                    sp=psp;
                }
            }
        }
        if ( sp->next==NULL )
    break;
        sp=sp->next->to;
        if ( sp==ss->first )
    break;
    }
}

/* If we have a contour with no width, say a line from A to B and then from B */
/*  to A, then it will be ambiguous, depending on how we hit the contour, as  */
/*  to whether it is needed or not. Which will cause us to complain. Since    */
/*  they contain no area, they achieve nothing, so we might as well say they  */
/*  overlap themselves and remove them here */
static SplineSet *SSRemoveReversals(SplineSet *base) {
    SplineSet *head = base, *prev=NULL, *next;
    SplinePoint *sp;
    int changed;

    while ( base!=NULL ) {
        next = base->next;
        changed = true;
        while ( changed ) {
            changed = false;
            if ( base->first->next==NULL ||
                    (base->first->next->to==base->first &&
                     base->first->nextcp.x==base->first->prevcp.x &&
                     base->first->nextcp.y==base->first->prevcp.y)) {
                /* remove single points */
                if ( prev==NULL )
                    head = next;
                else
                    prev->next = next;
                base->next = NULL;
                SplinePointListFree(base);
                base = prev;
        break;
            }
            for ( sp=base->first; ; ) {
                if ( sp->next!=NULL && sp->prev!=NULL &&
                        sp->nextcp.x==sp->prevcp.x && sp->nextcp.y==sp->prevcp.y ) {
                    SplinePoint *nsp = sp->next->to, *psp = sp->prev->from, *isp;
                    if ( psp->me.x==nsp->me.x && psp->me.y==nsp->me.y &&
                            psp->nextcp.x==nsp->prevcp.x && psp->nextcp.y==nsp->prevcp.y ) {
                        /* We wish to remove sp, sp->next, sp->prev & one of nsp/psp */
                        RemoveNextSP(psp,sp,nsp,base);
                        changed = true;
            break;
                    } else if ( sp->nonextcp /* which implies sp->noprevcp */ &&
                            psp->nonextcp && nsp->noprevcp &&
                            (isp = SameLine(psp,sp,nsp))!=NULL ) {
                        /* We have a line that backtracks, but doesn't cover */
                        /*  the entire spline, so we intersect */
                        /* We want to remove sp, the shorter of sp->next, sp->prev */
                        /*  and a bit of the other one. Also reomve one of nsp,psp */
                        if ( isp==psp ) {
                            RemoveNextSP(psp,sp,nsp,base);
                            psp->nextcp = psp->me;
                            psp->nonextcp = true;
                        } else {
                            RemovePrevSP(psp,sp,nsp,base);
                        }
                        changed = true;
            break;
                    }
                }
                if ( sp->next==NULL )
            break;
                sp = sp->next->to;
                if ( sp==base->first )
            break;
            }
        }
        SSRemoveBacktracks(base);
        prev = base;
        base = next;
    }
return( head );
}

SplineSet *SplineSetRemoveOverlap(SplineChar *sc, SplineSet *base,enum overlap_type ot) {
    Monotonic *ms;
    Intersection *ilist;
    SplineSet *ret;
    SplineSet *order3 = NULL;
    int is_o2 = false;
    SplineSet *ss;

    for ( ss=base; ss!=NULL; ss=ss->next )
        if ( ss->first->next!=NULL ) {
            is_o2 = ss->first->next->order2;
    break;
        }
    if ( is_o2 ) {
        order3 = SplineSetsPSApprox(base);
        SplinePointListsFree(base);
        base = order3;
    }

    if ( sc!=NULL )
        glyphname = sc->name;

    base = SSRemoveTiny(base);
    SSRemoveStupidControlPoints(base);
    SplineSetsRemoveAnnoyingExtrema(base,.3);
    SSOverlapClusterCpAngles(base,.01);
    base = SSRemoveReversals(base);
    ms = SSsToMContours(base,ot);
    ilist = FindIntersections(ms,ot);
    Validate(ms,ilist);
    if ( ot==over_findinter || ot==over_fisel ) {
        FixupIntersectedSplines(ms);
        ret = base;
    } else {
        FindNeeded(ms,ot);
        FindUnitVectors(ilist);
        if ( ot==over_remove || ot == over_rmselected )
            TestForBadDirections(ilist);
        ret = JoinAllNeeded(ilist);
        ret = MergeOpenAndFreeClosed(ret,base,ot);
    }
    FreeMonotonics(ms);
    FreeIntersections(ilist);
    glyphname = NULL;
    if ( order3!=NULL ) {
        ss = SplineSetsTTFApprox(ret);
        SplinePointListsFree(ret);
        ret = ss;
    }
return( ret );
}