beta-0.89.2

[luatex.git] / source / texk / web2c / luatexdir / luafontloader / fontforge / fontforge / splineorder2.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 <math.h>
#include <unistd.h>
#include <time.h>
#include <locale.h>
#include <utype.h>
#include <ustring.h>
#include <chardata.h>
#ifdef HAVE_IEEEFP_H
# include <ieeefp.h>            /* Solaris defines isnan in ieeefp rather than math.h */
#endif

/* This file contains utility routines for second order bezier splines   */
/*  (ie. truetype)                                                       */
/* The most interesting thing                                            */
/*  it does is to figure out a quadratic approximation to the cubic splines */
/*  that postscript uses. We do this by looking at each spline and running */
/*  from the end toward the beginning, checking approximately every emunit */
/*  There is only one quadratic spline possible for any given interval of the */
/*  cubic. The start and end points are the interval end points (obviously) */
/*  the control point is where the two slopes (at start and end) intersect. */
/* If this spline is a close approximation to the cubic spline (doesn't */
/*  deviate from it by more than an emunit or so), then we use this interval */
/*  as one of our quadratic splines. */
/* It may turn out that the "quadratic" spline above is actually linear. Well */
/*  that's ok. It may also turn out that we can't find a good approximation. */
/*  If that's true then just insert a linear segment for an emunit stretch. */
/*  (actually this failure mode may not be possible), but I'm not sure */
/* Then we play the same trick for the rest of the cubic spline (if any) */

/* Does the quadratic spline in ttf approximate the cubic spline in ps */
/*  within one pixel between tmin and tmax (on ps. presumably ttf between 0&1 */
/* dim is the dimension in which there is the greatest change */
static int comparespline(Spline *ps, Spline *ttf, real tmin, real tmax, real err) {
    int dim=0, other;
    real dx, dy, ddim, dt, t;
    real d, o;
    real ttf_t, sq, val;
    DBounds bb;
    extended ts[3];
    int i;

    /* Are all points on ttf near points on ps? */
    /* This doesn't answer that question, but rules out gross errors */
    bb.minx = bb.maxx = ps->from->me.x; bb.miny = bb.maxy = ps->from->me.y;
    if ( ps->from->nextcp.x>bb.maxx ) bb.maxx = ps->from->nextcp.x;
    else bb.minx = ps->from->nextcp.x;
    if ( ps->from->nextcp.y>bb.maxy ) bb.maxy = ps->from->nextcp.y;
    else bb.miny = ps->from->nextcp.y;
    if ( ps->to->prevcp.x>bb.maxx ) bb.maxx = ps->to->prevcp.x;
    else if ( ps->to->prevcp.x<bb.minx ) bb.minx = ps->to->prevcp.x;
    if ( ps->to->prevcp.y>bb.maxy ) bb.maxy = ps->to->prevcp.y;
    else if ( ps->to->prevcp.y<bb.miny ) bb.miny = ps->to->prevcp.y;
    if ( ps->to->me.x>bb.maxx ) bb.maxx = ps->to->me.x;
    else if ( ps->to->me.x<bb.minx ) bb.minx = ps->to->me.x;
    if ( ps->to->me.y>bb.maxy ) bb.maxy = ps->to->me.y;
    else if ( ps->to->me.y<bb.miny ) bb.miny = ps->to->me.y;
    for ( t=.1; t<1; t+= .1 ) {
        d = (ttf->splines[0].b*t+ttf->splines[0].c)*t+ttf->splines[0].d;
        o = (ttf->splines[1].b*t+ttf->splines[1].c)*t+ttf->splines[1].d;
        if ( d<bb.minx || d>bb.maxx || o<bb.miny || o>bb.maxy )
return( false );
    }

    /* Are all points on ps near points on ttf? */
    dx = ((ps->splines[0].a*tmax+ps->splines[0].b)*tmax+ps->splines[0].c)*tmax -
         ((ps->splines[0].a*tmin+ps->splines[0].b)*tmin+ps->splines[0].c)*tmin ;
    dy = ((ps->splines[1].a*tmax+ps->splines[1].b)*tmax+ps->splines[1].c)*tmax -
         ((ps->splines[1].a*tmin+ps->splines[1].b)*tmin+ps->splines[1].c)*tmin ;
    if ( dx<0 ) dx = -dx;
    if ( dy<0 ) dy = -dy;
    if ( dx>dy ) {
        dim = 0;
        ddim = dx;
    } else {
        dim = 1;
        ddim = dy;
    }
    other = !dim;

    t = tmin;
    dt = (tmax-tmin)/ddim;
    for ( t=tmin; t<=tmax; t+= dt ) {
        if ( t>tmax-dt/8. ) t = tmax;           /* Avoid rounding errors */
        d = ((ps->splines[dim].a*t+ps->splines[dim].b)*t+ps->splines[dim].c)*t+ps->splines[dim].d;
        o = ((ps->splines[other].a*t+ps->splines[other].b)*t+ps->splines[other].c)*t+ps->splines[other].d;
        if ( ttf->splines[dim].b == 0 ) {
            ttf_t = (d-ttf->splines[dim].d)/ttf->splines[dim].c;
        } else {
            sq = ttf->splines[dim].c*ttf->splines[dim].c -
                    4*ttf->splines[dim].b*(ttf->splines[dim].d-d);
            if ( sq<0 )
return( false );
            sq = sqrt(sq);
            ttf_t = (-ttf->splines[dim].c-sq)/(2*ttf->splines[dim].b);
            if ( ttf_t>=-0.1 && ttf_t<=1.1 ) {          /* Optimizer gives us rounding errors */
                                    /* And tmin/tmax are no longer exact */
                val = (ttf->splines[other].b*ttf_t+ttf->splines[other].c)*ttf_t+
                            ttf->splines[other].d;
                if ( val>o-err && val<o+err )
    continue;
            }
            ttf_t = (-ttf->splines[dim].c+sq)/(2*ttf->splines[dim].b);
        }
        if ( ttf_t>=-0.1 && ttf_t<=1.1 ) {
            val = (ttf->splines[other].b*ttf_t+ttf->splines[other].c)*ttf_t+
                        ttf->splines[other].d;
            if ( val>o-err && val<o+err )
    continue;
        }
return( false );
    }

    /* Are representative points on ttf near points on ps? */
    for ( t=.125; t<1; t+= .125 ) {
        d = (ttf->splines[dim].b*t+ttf->splines[dim].c)*t+ttf->splines[dim].d;
        o = (ttf->splines[other].b*t+ttf->splines[other].c)*t+ttf->splines[other].d;
        SplineSolveFull(&ps->splines[dim],d,ts);
        for ( i=0; i<3; ++i ) if ( ts[i]!=-1 ) {
            val = ((ps->splines[other].a*ts[i]+ps->splines[other].b)*ts[i]+ps->splines[other].c)*ts[i]+ps->splines[other].d;
            if ( val>o-err && val<o+err )
        break;
        }
        if ( i==3 )
return( false );
    }

return( true );
}

static SplinePoint *MakeQuadSpline(SplinePoint *start,Spline *ttf,real x,
        real y, real tmax,SplinePoint *oldend) {
    Spline *new = chunkalloc(sizeof(Spline));
    SplinePoint *end = chunkalloc(sizeof(SplinePoint));

    if ( tmax==1 ) {
        end->roundx = oldend->roundx; end->roundy = oldend->roundy; end->dontinterpolate = oldend->dontinterpolate;
        x = oldend->me.x; y = oldend->me.y;     /* Want it to compare exactly */
    }
    end->ttfindex = 0xfffe;
    end->nextcpindex = 0xfffe;
    end->me.x = end->nextcp.x = x;
    end->me.y = end->nextcp.y = y;
    end->nonextcp = true;

    *new = *ttf;
    new->from = start;          start->next = new;
    new->to = end;              end->prev = new;
    if ( new->splines[0].b==0 && new->splines[1].b==0 ) {
        end->noprevcp = true;
        end->prevcp.x = x; end->prevcp.y = y;
        new->islinear = new->knownlinear = true;
    } else {
        end->prevcp.x = start->nextcp.x = ttf->splines[0].c/2+ttf->splines[0].d;
        end->prevcp.y = start->nextcp.y = ttf->splines[1].c/2+ttf->splines[1].d;
        start->nonextcp = end->noprevcp = false;
        new->isquadratic = true;
    }
    new->order2 = true;
return( end );
}

static int buildtestquads(Spline *ttf,real xmin,real ymin,real cx,real cy,
        real x,real y,real tmin,real t,real err,Spline *ps, DBounds *psbb) {
    real fudge;

    /* test the control points are reasonable */
    fudge = (psbb->maxx-psbb->minx) + (psbb->maxy-psbb->miny);
    if ( cx<psbb->minx-fudge || cx>psbb->maxx+fudge )
return( false );
    if ( cy<psbb->miny-fudge || cy>psbb->maxy+fudge )
return( false );

    ttf->splines[0].d = xmin;
    ttf->splines[0].c = 2*(cx-xmin);
    ttf->splines[0].b = xmin+x-2*cx;
    ttf->splines[1].d = ymin;
    ttf->splines[1].c = 2*(cy-ymin);
    ttf->splines[1].b = ymin+y-2*cy;
    if ( comparespline(ps,ttf,tmin,t,err) )
return( true );

#if 0
    /* In a few cases, the following code will find a match when the above */
    /*  would not. We move the control point slightly along a vector normal */
    /*  to the vector between the end-points. What I really want is along */
    /*  a vector midway between the two slopes, but that's too hard to figure */
    sq = sqrt((x-xmin)*(x-xmin) + (y-ymin)*(y-ymin));
    norm.x = (ymin-y)/sq; norm.y = (x-xmin)/sq;

    ttf->splines[0].c += err*norm.x;
    ttf->splines[0].b -= err*norm.x;
    ttf->splines[1].c += err*norm.y;
    ttf->splines[1].b -= err*norm.y;
    if ( comparespline(ps,ttf,tmin,t,err) )
return( true );

    ttf->splines[0].c -= 2*err*norm.x;
    ttf->splines[0].b += 2*err*norm.x;
    ttf->splines[1].c -= 2*err*norm.y;
    ttf->splines[1].b += 2*err*norm.y;
    if ( comparespline(ps,ttf,tmin,t,err) )
return( true );

    ttf->splines[0].c = 2*(cx-xmin);
    ttf->splines[0].b = xmin+x-2*cx;
    ttf->splines[1].c = 2*(cy-ymin);
    ttf->splines[1].b = ymin+y-2*cy;
#endif
return( false );
}

static SplinePoint *LinearSpline(Spline *ps,SplinePoint *start, real tmax) {
    real x,y;
    Spline *new = chunkalloc(sizeof(Spline));
    SplinePoint *end = chunkalloc(sizeof(SplinePoint));

    x = ((ps->splines[0].a*tmax+ps->splines[0].b)*tmax+ps->splines[0].c)*tmax+ps->splines[0].d;
    y = ((ps->splines[1].a*tmax+ps->splines[1].b)*tmax+ps->splines[1].c)*tmax+ps->splines[1].d;
    if ( tmax==1 ) {
        SplinePoint *oldend = ps->to;
        end->roundx = oldend->roundx; end->roundy = oldend->roundy; end->dontinterpolate = oldend->dontinterpolate;
        x = oldend->me.x; y = oldend->me.y;     /* Want it to compare exactly */
    }
    end->ttfindex = 0xfffe;
    end->nextcpindex = 0xfffe;
    end->me.x = end->nextcp.x = end->prevcp.x = x;
    end->me.y = end->nextcp.y = end->prevcp.y = y;
    end->nonextcp = end->noprevcp = start->nonextcp = true;
    new->from = start;          start->next = new;
    new->to = end;              end->prev = new;
    new->splines[0].d = start->me.x;
    new->splines[0].c = (x-start->me.x);
    new->splines[1].d = start->me.y;
    new->splines[1].c = (y-start->me.y);
    new->order2 = true;
    new->islinear = new->knownlinear = true;
return( end );
}

static SplinePoint *_ttfapprox(Spline *ps,real tmin, real tmax, SplinePoint *start) {
    int dim=0;
    real dx, dy, ddim, dt, t, err;
    real x,y, xmin, ymin;
    real dxdtmin, dydtmin, dxdt, dydt;
    SplinePoint *sp;
    real cx, cy;
    Spline ttf;
    int cnt = -1, forceit, unforceable;
    BasePoint end, rend, dend;
    DBounds bb;

    rend.x = ((ps->splines[0].a*tmax+ps->splines[0].b)*tmax+ps->splines[0].c)*tmax + ps->splines[0].d;
    rend.y = ((ps->splines[1].a*tmax+ps->splines[1].b)*tmax+ps->splines[1].c)*tmax + ps->splines[1].d;
    end.x = rint( rend.x );
    end.y = rint( rend.y );
    dend.x = (3*ps->splines[0].a*tmax+2*ps->splines[0].b)*tmax+ps->splines[0].c;
    dend.y = (3*ps->splines[1].a*tmax+2*ps->splines[1].b)*tmax+ps->splines[1].c;
    memset(&ttf,'\0',sizeof(ttf));

    bb.minx = bb.maxx = ps->from->me.x;
    if ( ps->from->nextcp.x > bb.maxx ) bb.maxx = ps->from->nextcp.x;
    else if ( ps->from->nextcp.x < bb.minx ) bb.minx = ps->from->nextcp.x;
    if ( ps->to->prevcp.x > bb.maxx ) bb.maxx = ps->to->prevcp.x;
    else if ( ps->to->prevcp.x < bb.minx ) bb.minx = ps->to->prevcp.x;
    if ( ps->to->me.x > bb.maxx ) bb.maxx = ps->to->me.x;
    else if ( ps->to->me.x < bb.minx ) bb.minx = ps->to->me.x;
    bb.miny = bb.maxy = ps->from->me.y;
    if ( ps->from->nextcp.y > bb.maxy ) bb.maxy = ps->from->nextcp.y;
    else if ( ps->from->nextcp.y < bb.miny ) bb.miny = ps->from->nextcp.y;
    if ( ps->to->prevcp.y > bb.maxy ) bb.maxy = ps->to->prevcp.y;
    else if ( ps->to->prevcp.y < bb.miny ) bb.miny = ps->to->prevcp.y;
    if ( ps->to->me.y > bb.maxy ) bb.maxy = ps->to->me.y;
    else if ( ps->to->me.y < bb.miny ) bb.miny = ps->to->me.y;

  tail_recursion:
    ++cnt;

    xmin = start->me.x;
    ymin = start->me.y;
    dxdtmin = (3*ps->splines[0].a*tmin+2*ps->splines[0].b)*tmin + ps->splines[0].c;
    dydtmin = (3*ps->splines[1].a*tmin+2*ps->splines[1].b)*tmin + ps->splines[1].c;

    dx = ((ps->splines[0].a*tmax+ps->splines[0].b)*tmax+ps->splines[0].c)*tmax -
         ((ps->splines[0].a*tmin+ps->splines[0].b)*tmin+ps->splines[0].c)*tmin ;
    dy = ((ps->splines[1].a*tmax+ps->splines[1].b)*tmax+ps->splines[1].c)*tmax -
         ((ps->splines[1].a*tmin+ps->splines[1].b)*tmin+ps->splines[1].c)*tmin ;
    if ( dx<0 ) dx = -dx;
    if ( dy<0 ) dy = -dy;
    if ( dx>dy ) {
        dim = 0;
        ddim = dx;
    } else {
        dim = 1;
        ddim = dy;
    }
    if (( err = ddim/3000 )<1 ) err = 1;

    if ( ddim<2 ||
            (dend.x==0 && rint(start->me.x)==end.x && dy<=10 && cnt!=0) ||
            (dend.y==0 && rint(start->me.y)==end.y && dx<=10 && cnt!=0) ) {
        if ( cnt==0 || start->noprevcp )
return( LinearSpline(ps,start,tmax));
        /* If the end point is very close to where we want to be, then just */
        /*  pretend it's right */
        start->prev->splines[0].b += ps->to->me.x-start->me.x;
        start->prev->splines[1].b += ps->to->me.y-start->me.y;
        start->prevcp.x += rend.x-start->me.x;
        start->prevcp.y += rend.y-start->me.y;
        if ( start->prev!=NULL && !start->prev->from->nonextcp )
            start->prev->from->nextcp = start->prevcp;
        start->me = rend;
return( start );
    }

    dt = (tmax-tmin)/ddim;
    forceit = false;
 force_end:
    unforceable = false;
    for ( t=tmax; t>tmin+dt/128; t-= dt ) {             /* dt/128 is a hack to avoid rounding errors */
        x = ((ps->splines[0].a*t+ps->splines[0].b)*t+ps->splines[0].c)*t+ps->splines[0].d;
        y = ((ps->splines[1].a*t+ps->splines[1].b)*t+ps->splines[1].c)*t+ps->splines[1].d;
        dxdt = (3*ps->splines[0].a*t+2*ps->splines[0].b)*t + ps->splines[0].c;
        dydt = (3*ps->splines[1].a*t+2*ps->splines[1].b)*t + ps->splines[1].c;
        /* if the slopes are parallel at the ends there can be no bezier quadratic */
        /*  (control point is where the splines intersect. But if they are */
        /*  parallel and colinear then there is a line between 'em */
        if ( ( dxdtmin==0 && dxdt==0 ) || (dydtmin==0 && dydt==0) ||
                ( dxdt!=0 && dxdtmin!=0 &&
                    RealNearish(dydt/dxdt,dydtmin/dxdtmin)) )
    continue;

        if ( dxdt==0 )
            cx=x;
        else if ( dxdtmin==0 )
            cx=xmin;
        else
            cx = -(ymin-(dydtmin/dxdtmin)*xmin-y+(dydt/dxdt)*x)/(dydtmin/dxdtmin-dydt/dxdt);
        if ( dydt==0 )
            cy=y;
        else if ( dydtmin==0 )
            cy=ymin;
        else
            cy = -(xmin-(dxdtmin/dydtmin)*ymin-x+(dxdt/dydt)*y)/(dxdtmin/dydtmin-dxdt/dydt);
        if ( t==tmax && ((cy==y && cx==x) || (cy==ymin && cx==xmin)) )
            unforceable = true;
        /* Make the quadratic spline from (xmin,ymin) through (cx,cy) to (x,y)*/
        if ( forceit || buildtestquads(&ttf,xmin,ymin,cx,cy,x,y,tmin,t,err,ps,&bb)) {
            if ( !forceit && !unforceable && (rend.x-x)*(rend.x-x)+(rend.y-y)*(rend.y-y)<4*4 ) {
                forceit = true;
 goto force_end;
            }
            sp = MakeQuadSpline(start,&ttf,x,y,t,ps->to);
            forceit = false;
            if ( t==tmax )
return( sp );
            tmin = t;
            start = sp;
  goto tail_recursion;
        }
        ttf.splines[0].d = xmin;
        ttf.splines[0].c = x-xmin;
        ttf.splines[0].b = 0;
        ttf.splines[1].d = ymin;
        ttf.splines[1].c = y-ymin;
        ttf.splines[1].b = 0;
        if ( comparespline(ps,&ttf,tmin,t,err) ) {
            sp = LinearSpline(ps,start,t);
            if ( t==tmax )
return( sp );
            tmin = t;
            start = sp;
  goto tail_recursion;
        }
    }
    tmin += dt;
    start = LinearSpline(ps,start,tmin);
  goto tail_recursion;
}

static SplinePoint *__ttfApprox(Spline *ps,real tmin, real tmax, SplinePoint *start) {
    extended inflect[2];
    int i=0;
#if 1
    SplinePoint *end;
    Spline *s, *next;

    end = _ttfapprox(ps,tmin,tmax,start);
    if ( ps->knownlinear )
return( end );
    for ( s=start->next; s!=NULL && !s->islinear; s=s->to->next );
    if ( s==NULL )
return( end );
    for ( s=start->next; s!=NULL ; s=next ) {
        next = s->to->next;
        SplinePointFree(s->to);
        SplineFree(s);
    }
#endif
/* Hmm. With my algorithem, checking for points of inflection actually makes */
/*  things worse. It uses more points and the splines don't join as nicely */
/* However if we get a bad match (a line) in the normal approx, then check */
/*  Err... I was computing POI incorrectly. Above statement might not be correct*/
    /* no points of inflection in quad splines */

    i = Spline2DFindPointsOfInflection(ps, inflect);
    if ( i==2 ) {
        if ( RealNearish(inflect[0],inflect[1]) )
            --i;
        else if ( inflect[0]>inflect[1] ) {
            real temp = inflect[0];
            inflect[0] = inflect[1];
            inflect[1] = temp;
        }
    }
    if ( i!=0 ) {
        start = _ttfapprox(ps,tmin,inflect[0],start);
        tmin = inflect[0];
        if ( i==2 ) {
            start = _ttfapprox(ps,tmin,inflect[1],start);
            tmin = inflect[1];
        }
    }
return( _ttfapprox(ps,tmin,tmax,start));
}

#if !defined(FONTFORGE_CONFIG_NON_SYMMETRIC_QUADRATIC_CONVERSION)
typedef struct qpoint {
    BasePoint bp;
    BasePoint cp;
    double t;
} QPoint;

static int comparedata(Spline *ps,QPoint *data,int qfirst,int qlast,
        int round_to_int ) {
    Spline ttf;
    int i;
    double err = round_to_int ? 1.5 : 1;

    if ( qfirst==qlast )                /* happened (was a bug) */
return( false );

    /* Control points diametrically opposed */
    if ( (data[qlast-2].cp.x-ps->to->me.x)*(ps->to->prevcp.x-ps->to->me.x) +
            (data[qlast-2].cp.y-ps->to->me.y)*(ps->to->prevcp.y-ps->to->me.y)<0 )
return( false );
    if ( (data[qfirst-1].cp.x-ps->from->me.x)*(ps->from->nextcp.x-ps->from->me.x) +
            (data[qfirst-1].cp.y-ps->from->me.y)*(ps->from->nextcp.y-ps->from->me.y)<0 )
return( false );

    memset(&ttf,0,sizeof(ttf));
    for ( i=qfirst; i<qlast; ++i ) {
        ttf.splines[0].d = data[i-1].bp.x;
        ttf.splines[0].c = 2*(data[i-1].cp.x-data[i-1].bp.x);
        ttf.splines[0].b = data[i-1].bp.x+data[i].bp.x-2*data[i-1].cp.x;
        ttf.splines[1].d = data[i-1].bp.y;
        ttf.splines[1].c = 2*(data[i-1].cp.y-data[i-1].bp.y);
        ttf.splines[1].b = data[i-1].bp.y+data[i].bp.y-2*data[i-1].cp.y;
        if ( !comparespline(ps,&ttf,data[i-1].t,data[i].t,err) )
return( false );
    }
return( true );
}

static SplinePoint *CvtDataToSplines(QPoint *data,int qfirst,int qlast,SplinePoint *start) {
    SplinePoint *end;
    int i;

    for ( i=qfirst; i<qlast; ++i ) {
        end = SplinePointCreate(data[i].bp.x,data[i].bp.y);
        start->nextcp = end->prevcp = data[i-1].cp;
        start->nonextcp = end->noprevcp = false;
        if (( data[i-1].cp.x == data[i].bp.x && data[i-1].cp.y == data[i].bp.y ) ||
                ( data[i-1].cp.x == start->me.x && data[i-1].cp.y == start->me.y ))
            start->nonextcp = end->noprevcp = true;
        SplineMake2(start,end);
        start = end;
    }
return( start );
}

static int SplineWithWellBehavedControlPoints(Spline *ps) {
    BasePoint splineunit;
    double splinelen, npos, ppos;

    splineunit.x = ps->to->me.x - ps->from->me.x;
    splineunit.y = ps->to->me.y - ps->from->me.y;
    splinelen = sqrt(splineunit.x*splineunit.x + splineunit.y*splineunit.y);
    if ( splinelen!=0 ) {
        splineunit.x /= splinelen;
        splineunit.y /= splinelen;
    }

    npos = (ps->from->nextcp.x-ps->from->me.x) * splineunit.x +
            (ps->from->nextcp.y-ps->from->me.y) * splineunit.y;
    ppos = (ps->to->prevcp.x-ps->from->me.x) * splineunit.x +
            (ps->to->prevcp.y-ps->from->me.y) * splineunit.y;
return( npos>=0 && /* npos<=ppos &&*/ ppos<=splinelen );
}

static int PrettyApprox(Spline *ps,double tmin, double tmax,
        QPoint *data, int qcnt, int round_to_int ) {
    int ptcnt, q, i;
    double distance, dx, dy, tstart;
    BasePoint end, mid, slopemin, slopemid, slopeend;
    BasePoint splineunit, start;
    double splinelen, midpos, lastpos, lastpos2, cppos;
    int do_good_spline_check;
    QPoint data2[12];

    if ( qcnt==-1 )
return( -1 );

    slopemin.x = (3*ps->splines[0].a*tmin+2*ps->splines[0].b)*tmin+ps->splines[0].c;
    slopemin.y = (3*ps->splines[1].a*tmin+2*ps->splines[1].b)*tmin+ps->splines[1].c;
    if ( slopemin.x==0 && slopemin.y==0 ) {
        double t = tmin + (tmax-tmin)/256;
        /* If there is no control point for this end point, then the slope is */
        /*  0/0 at the end point. Which isn't useful, it leads to a quadratic */
        /*  control point at the end point, but this one is real because it   */
        /*  is used to interpolate the next point, but we get all confused    */
        /*  because we don't expect a real cp to be on the base point.        */
        slopemin.x = (3*ps->splines[0].a*t+2*ps->splines[0].b)*t+ps->splines[0].c;
        slopemin.y = (3*ps->splines[1].a*t+2*ps->splines[1].b)*t+ps->splines[1].c;
    }

    end.x = ((ps->splines[0].a*tmax+ps->splines[0].b)*tmax+ps->splines[0].c)*tmax+ps->splines[0].d;
    end.y = ((ps->splines[1].a*tmax+ps->splines[1].b)*tmax+ps->splines[1].c)*tmax+ps->splines[1].d;
    slopeend.x = (3*ps->splines[0].a*tmax+2*ps->splines[0].b)*tmax+ps->splines[0].c;
    slopeend.y = (3*ps->splines[1].a*tmax+2*ps->splines[1].b)*tmax+ps->splines[1].c;
    if ( slopemin.x==0 && slopemin.y==0 ) {
        double t = tmax - (tmax-tmin)/256;
        /* Same problem as above, except at the other end */
        slopeend.x = (3*ps->splines[0].a*t+2*ps->splines[0].b)*t+ps->splines[0].c;
        slopeend.y = (3*ps->splines[1].a*t+2*ps->splines[1].b)*t+ps->splines[1].c;
    }

    start.x = data[qcnt-1].bp.x;
    start.y = data[qcnt-1].bp.y;
    splineunit.x = end.x - start.x;
    splineunit.y = end.y - start.y;
    splinelen = sqrt(splineunit.x*splineunit.x + splineunit.y*splineunit.y);
    if ( splinelen!=0 ) {
        splineunit.x /= splinelen;
        splineunit.y /= splinelen;
    }
    do_good_spline_check = SplineWithWellBehavedControlPoints(ps);

    if ( round_to_int && tmax!=1 ) {
        end.x = rint( end.x );
        end.y = rint( end.y );
    }

    dx = end.x-data[qcnt-1].bp.x; dy = end.y-data[qcnt-1].bp.y;
    distance = dx*dx + dy*dy;

    if ( distance<.3 ) {
        /* This is meaningless in truetype, use a line */
        data[qcnt-1].cp = data[qcnt-1].bp;
        data[qcnt].bp = end;
        data[qcnt].t = 1;
return( qcnt+1 );
    }

    for ( ptcnt=0; ptcnt<10; ++ptcnt ) {
        if ( ptcnt>1 && distance/(ptcnt*ptcnt)<100 )
return( -1 );                   /* Points too close for a good approx */
        q = qcnt;
        data2[ptcnt+1].bp = end;
        lastpos=0; lastpos2 = splinelen;
        for ( i=0; i<=ptcnt; ++i ) {
            tstart = (tmin*(ptcnt-i) + tmax*(i+1))/(ptcnt+1);
            mid.x = ((ps->splines[0].a*tstart+ps->splines[0].b)*tstart+ps->splines[0].c)*tstart+ps->splines[0].d;
            mid.y = ((ps->splines[1].a*tstart+ps->splines[1].b)*tstart+ps->splines[1].c)*tstart+ps->splines[1].d;
            if ( i==0 ) {
                slopemid.x = (3*ps->splines[0].a*tstart+2*ps->splines[0].b)*tstart+ps->splines[0].c;
                slopemid.y = (3*ps->splines[1].a*tstart+2*ps->splines[1].b)*tstart+ps->splines[1].c;
                if ( slopemid.x==0 )
                    data[q-1].cp.x=mid.x;
                else if ( slopemin.x==0 )
                    data[q-1].cp.x=data[q-1].bp.x;
                else if ( RealNear(slopemin.y/slopemin.x,slopemid.y/slopemid.x) )
        break;
                else
                    data[q-1].cp.x = -(data[q-1].bp.y-(slopemin.y/slopemin.x)*data[q-1].bp.x-mid.y+(slopemid.y/slopemid.x)*mid.x)/(slopemin.y/slopemin.x-slopemid.y/slopemid.x);
                if ( slopemid.y==0 )
                    data[q-1].cp.y=mid.y;
                else if ( slopemin.y==0 )
                    data[q-1].cp.y=data[q-1].bp.y;
                else if ( RealNear(slopemin.x/slopemin.y,slopemid.x/slopemid.y) )
        break;
                else
                    data[q-1].cp.y = -(data[q-1].bp.x-(slopemin.x/slopemin.y)*data[q-1].bp.y-mid.x+(slopemid.x/slopemid.y)*mid.y)/(slopemin.x/slopemin.y-slopemid.x/slopemid.y);
            } else {
                data[q-1].cp.x = 2*data[q-1].bp.x - data[q-2].cp.x;
                data[q-1].cp.y = 2*data[q-1].bp.y - data[q-2].cp.y;
            }

            midpos = (mid.x-start.x)*splineunit.x + (mid.y-start.y)*splineunit.y;
            cppos  = (data[q-1].cp.x-start.x)*splineunit.x + (data[q-1].cp.y-start.y)*splineunit.y;

            if ( ((do_good_spline_check || i!=0 ) &&  cppos<lastpos) || cppos>midpos ) {
                i = 0;          /* Means we failed */
        break;
            }
            lastpos = midpos;

            data[q].bp = mid;
            data[q++].t = tstart;

            tstart = (tmax*(ptcnt-i) + tmin*(i+1))/(ptcnt+1);
            mid.x = ((ps->splines[0].a*tstart+ps->splines[0].b)*tstart+ps->splines[0].c)*tstart+ps->splines[0].d;
            mid.y = ((ps->splines[1].a*tstart+ps->splines[1].b)*tstart+ps->splines[1].c)*tstart+ps->splines[1].d;
            if ( i==0 ) {
                slopemid.x = (3*ps->splines[0].a*tstart+2*ps->splines[0].b)*tstart+ps->splines[0].c;
                slopemid.y = (3*ps->splines[1].a*tstart+2*ps->splines[1].b)*tstart+ps->splines[1].c;
                if ( slopemid.x==0 )
                    data2[ptcnt-i].cp.x=mid.x;
                else if ( slopeend.x==0 )
                    data2[ptcnt-i].cp.x=data2[ptcnt-i+1].bp.x;
                else if ( RealNear(slopeend.y/slopeend.x,slopemid.y/slopemid.x) )
        break;
                else
                    data2[ptcnt-i].cp.x = -(data2[ptcnt-i+1].bp.y-(slopeend.y/slopeend.x)*data2[ptcnt-i+1].bp.x-mid.y+(slopemid.y/slopemid.x)*mid.x)/(slopeend.y/slopeend.x-slopemid.y/slopemid.x);
                if ( slopemid.y==0 )
                    data2[ptcnt-i].cp.y=mid.y;
                else if ( slopeend.y==0 )
                    data2[ptcnt-i].cp.y=data2[ptcnt-i+1].bp.y;
                else if ( RealNear(slopeend.x/slopeend.y,slopemid.x/slopemid.y) )
        break;
                else
                    data2[ptcnt-i].cp.y = -(data2[ptcnt-i+1].bp.x-(slopeend.x/slopeend.y)*data2[ptcnt-i+1].bp.y-mid.x+(slopemid.x/slopemid.y)*mid.y)/(slopeend.x/slopeend.y-slopemid.x/slopemid.y);
            } else {
                data2[ptcnt-i].cp.x = 2*data2[ptcnt-i+1].bp.x - data2[ptcnt-i+1].cp.x;
                data2[ptcnt-i].cp.y = 2*data2[ptcnt-i+1].bp.y - data2[ptcnt-i+1].cp.y;
            }
            data2[ptcnt-i].bp = mid;

            midpos = (mid.x-start.x)*splineunit.x + (mid.y-start.y)*splineunit.y;
            cppos  = (data2[ptcnt-i].cp.x-start.x)*splineunit.x + (data2[ptcnt-i].cp.y-start.y)*splineunit.y;
            if ( ((do_good_spline_check || i!=0 ) && cppos>lastpos2) || cppos<midpos ) {
                i = 0;          /* Means we failed */
        break;
            }
            lastpos2 = midpos;

        }
        if ( i==0 )
    continue;
        if ( (data2[ptcnt+1].bp.x-data2[ptcnt].bp.x)*(data2[ptcnt].cp.x-data2[ptcnt].bp.x)<0 ||
                (data2[ptcnt+1].bp.y-data2[ptcnt].bp.y)*(data2[ptcnt].cp.y-data2[ptcnt].bp.y)<0 ) {
            /* data2 are bad ... don't use them */;
        } else if ( (data[qcnt-1].bp.x-data[qcnt].bp.x)*(data[qcnt-1].cp.x-data[qcnt].bp.x)<0 ||
                (data[qcnt-1].bp.y-data[qcnt].bp.y)*(data[qcnt-1].cp.y-data[qcnt].bp.y)<0 ) {
            /* data are bad */;
            for ( i=0; i<=ptcnt; ++i ) {
                data[qcnt+i-1].cp = data2[i].cp;
                data[qcnt+i-1].bp = data2[i].bp;
            }
        } else {
            for ( i=0; i<=ptcnt; ++i ) {
                if ( ptcnt!=0 ) {
                    data[qcnt+i-1].cp.x = (data[qcnt+i-1].cp.x*(ptcnt-i) + data2[i].cp.x*i)/ptcnt;
                    data[qcnt+i-1].cp.y = (data[qcnt+i-1].cp.y*(ptcnt-i) + data2[i].cp.y*i)/ptcnt;
                }
            }
        }
        if ( round_to_int ) {
            for ( i=0; i<=ptcnt; ++i ) {
                data[qcnt+i-1].cp.x = rint( data[qcnt+i-1].cp.x );
                data[qcnt+i-1].cp.y = rint( data[qcnt+i-1].cp.y );
            }
        }
        for ( i=0; i<ptcnt; ++i ) {
            data[qcnt+i].bp.x = (data[qcnt+i].cp.x + data[qcnt+i-1].cp.x)/2;
            data[qcnt+i].bp.y = (data[qcnt+i].cp.y + data[qcnt+i-1].cp.y)/2;
        }
        if ( comparedata(ps,data,qcnt,q,round_to_int))
return( q );
    }
return( -1 );
}
#endif

static SplinePoint *AlreadyQuadraticCheck(Spline *ps, SplinePoint *start) {
    SplinePoint *sp;

    if ( (RealNearish(ps->splines[0].a,0) && RealNearish(ps->splines[1].a,0)) ||
            ((ps->splines[0].b!=0 && RealNearish(ps->splines[0].a/ps->splines[0].b,0)) &&
             (ps->splines[1].b!=0 && RealNearish(ps->splines[1].a/ps->splines[1].b,0))) ) {
        /* Already Quadratic, just need to find the control point */
        /* Or linear, in which case we don't need to do much of anything */
        Spline *spline;
        sp = chunkalloc(sizeof(SplinePoint));
        sp->me.x = ps->to->me.x; sp->me.y = ps->to->me.y;
        sp->roundx = ps->to->roundx; sp->roundy = ps->to->roundy; sp->dontinterpolate = ps->to->dontinterpolate;
        sp->ttfindex = 0xfffe;
        sp->nextcpindex = 0xfffe;
        sp->nonextcp = true;
        spline = chunkalloc(sizeof(Spline));
        spline->order2 = true;
        spline->from = start;
        spline->to = sp;
        spline->splines[0] = ps->splines[0]; spline->splines[1] = ps->splines[1];
        start->next = sp->prev = spline;
        if ( ps->knownlinear ) {
            spline->islinear = spline->knownlinear = true;
            start->nonextcp = sp->noprevcp = true;
            start->nextcp = start->me;
            sp->prevcp = sp->me;
        } else {
            start->nonextcp = sp->noprevcp = false;
            start->nextcp.x = sp->prevcp.x = (ps->splines[0].c+2*ps->splines[0].d)/2;
            start->nextcp.y = sp->prevcp.y = (ps->splines[1].c+2*ps->splines[1].d)/2;
        }
return( sp );
    }
return( NULL );
}

static SplinePoint *ttfApprox(Spline *ps, SplinePoint *start) {
#if !defined(FONTFORGE_CONFIG_NON_SYMMETRIC_QUADRATIC_CONVERSION)
    extended magicpoints[6], last;
    int cnt, i, j, qcnt;
    QPoint data[8*10];
    int round_to_int =
    /* The end points are at integer points, or one coord is at half while */
    /*  the other is at an integer (ie. condition for ttf interpolated point)*/
            ((ps->from->me.x==rint(ps->from->me.x) &&
              ps->from->me.y==rint(ps->from->me.y)) ||
             (ps->from->me.x==rint(ps->from->me.x) &&
              ps->from->me.x==ps->from->nextcp.x &&
              ps->from->me.y!=ps->from->nextcp.y &&
              2*ps->from->me.y==rint(2*ps->from->me.y)) ||
             (ps->from->me.y==rint(ps->from->me.y) &&
              ps->from->me.y==ps->from->nextcp.y &&
              ps->from->me.x!=ps->from->nextcp.x &&
              2*ps->from->me.x==rint(2*ps->from->me.x)) ) &&
            ((ps->to->me.x == rint(ps->to->me.x) &&
              ps->to->me.y == rint(ps->to->me.y)) ||
             (ps->to->me.x==rint(ps->to->me.x) &&
              ps->to->me.x==ps->to->prevcp.x &&
              ps->to->me.y!=ps->to->prevcp.y &&
              2*ps->to->me.y==rint(2*ps->to->me.y)) ||
             (ps->to->me.y==rint(ps->to->me.y) &&
              ps->to->me.y==ps->to->prevcp.y &&
              ps->to->me.x!=ps->to->prevcp.x &&
              2*ps->to->me.x==rint(2*ps->to->me.x)) );
#endif
    SplinePoint *ret;
/* Divide the spline up at extrema and points of inflection. The first  */
/*  because ttf splines should have points at their extrema, the second */
/*  because quadratic splines can't have points of inflection.          */
/* Let's not do the first (extrema) AddExtrema does this better and we  */
/*  don't want unneeded extrema.                                        */
/* And sometimes we don't want to look at the points of inflection either*/

    if (( ret = AlreadyQuadraticCheck(ps,start))!=NULL )
return( ret );

#if !defined(FONTFORGE_CONFIG_NON_SYMMETRIC_QUADRATIC_CONVERSION)
    qcnt = 1;
    data[0].bp = ps->from->me;
    data[0].t = 0;
    qcnt = PrettyApprox(ps,0,1,data,qcnt,round_to_int);
    if ( qcnt!=-1 )
return( CvtDataToSplines(data,1,qcnt,start));

    cnt = 0;
    /* cnt = Spline2DFindExtrema(ps,magicpoints);*/

    cnt += Spline2DFindPointsOfInflection(ps,magicpoints+cnt);

    /* remove points outside range */
    for ( i=0; i<cnt; ++i ) {
        if ( magicpoints[i]<=0 || magicpoints[i]>=1 ) {
            for ( j=i+1; j<cnt; ++j )
                magicpoints[j-1] = magicpoints[j];
            --cnt;
            --i;
        }
    }
    /* sort points */
    for ( i=0; i<cnt; ++i ) for ( j=i+1; j<cnt; ++j ) {
        if ( magicpoints[i]>magicpoints[j] ) {
            double temp = magicpoints[i];
            magicpoints[i] = magicpoints[j];
            magicpoints[j] = temp;
        }
    }
    /* Remove duplicates */
    for ( i=1; i<cnt; ++i ) {
        while ( i<cnt && RealNear(magicpoints[i-1],magicpoints[i])) {
            --cnt;
            for ( j=i ; j<cnt; ++j )
                magicpoints[j] = magicpoints[j+1];
            magicpoints[cnt] = -1;
        }
    }

    qcnt = 1;
    last = 0;
    for ( i=0; i<cnt; ++i ) {
        qcnt = PrettyApprox(ps,last,magicpoints[i],data,qcnt,round_to_int);
        last = magicpoints[i];
    }
    qcnt = PrettyApprox(ps,last,1,data,qcnt,round_to_int);
    if ( qcnt!=-1 )
return( CvtDataToSplines(data,1,qcnt,start));
#endif

return( __ttfApprox(ps,0,1,start));
}

static void ttfCleanup(SplinePoint *from) {
    SplinePoint *test, *next;

    for ( test = from; test->next!=NULL; test = next ) {
        next = test->next->to;
        /* Too close together to be meaningful when output as ttf */
        if ( rint(test->me.x) == rint(next->me.x) &&
                rint(test->me.y) == rint(next->me.y) ) {
            if ( next->next==NULL || next==from ) {
                if ( test==from )
    break;
                next->prevcp = test->prevcp;
                next->noprevcp = test->noprevcp;
                next->prev = test->prev;
                next->prev->to = next;
                SplineFree(test->next);
                SplinePointFree(test);
            } else {
                test->nextcp = next->nextcp;
                test->nonextcp = next->nonextcp;
                test->next = next->next;
                test->next->from = test;
                SplineFree(next->prev);
                SplinePointFree(next);
                next = test->next->to;
            }
        }
        if ( next==from )
    break;
    }
}

SplinePoint *SplineTtfApprox(Spline *ps) {
    SplinePoint *from;
    from = chunkalloc(sizeof(SplinePoint));
    *from = *ps->from;
    from->hintmask = NULL;
    ttfApprox(ps,from);
return( from );
}

SplineSet *SSttfApprox(SplineSet *ss) {
    SplineSet *ret = chunkalloc(sizeof(SplineSet));
    Spline *spline, *first;

    ret->first = chunkalloc(sizeof(SplinePoint));
    *ret->first = *ss->first;
    if ( ret->first->hintmask != NULL ) {
        ret->first->hintmask = chunkalloc(sizeof(HintMask));
        memcpy(ret->first->hintmask,ss->first->hintmask,sizeof(HintMask));
    }
    ret->last = ret->first;

    first = NULL;
    for ( spline=ss->first->next; spline!=NULL && spline!=first; spline=spline->to->next ) {
        ret->last = ttfApprox(spline,ret->last);
        ret->last->ptindex = spline->to->ptindex;
        ret->last->ttfindex = spline->to->ttfindex;
        ret->last->nextcpindex = spline->to->nextcpindex;
        if ( spline->to->hintmask != NULL ) {
            ret->last->hintmask = chunkalloc(sizeof(HintMask));
            memcpy(ret->last->hintmask,spline->to->hintmask,sizeof(HintMask));
        }
        if ( first==NULL ) first = spline;
    }
    if ( ss->first==ss->last ) {
        if ( ret->last!=ret->first ) {
            ret->first->prevcp = ret->last->prevcp;
            ret->first->noprevcp = ret->last->noprevcp;
            ret->first->prev = ret->last->prev;
            ret->last->prev->to = ret->first;
            SplinePointFree(ret->last);
            ret->last = ret->first;
        }
    }
    ttfCleanup(ret->first);
    SPLCatagorizePoints(ret);
return( ret );
}

SplineSet *SplineSetsTTFApprox(SplineSet *ss) {
    SplineSet *head=NULL, *last, *cur;

    while ( ss!=NULL ) {
        cur = SSttfApprox(ss);
        if ( head==NULL )
            head = cur;
        else
            last->next = cur;
        last = cur;
        ss = ss->next;
    }
return( head );
}

SplineSet *SSPSApprox(SplineSet *ss) {
    SplineSet *ret = chunkalloc(sizeof(SplineSet));
    Spline *spline, *first;
    SplinePoint *to;

    ret->first = chunkalloc(sizeof(SplinePoint));
    *ret->first = *ss->first;
    if ( ret->first->hintmask != NULL ) {
        ret->first->hintmask = chunkalloc(sizeof(HintMask));
        memcpy(ret->first->hintmask,ss->first->hintmask,sizeof(HintMask));
    }
    ret->last = ret->first;

    first = NULL;
    for ( spline=ss->first->next; spline!=NULL && spline!=first; spline=spline->to->next ) {
        to = chunkalloc(sizeof(SplinePoint));
        *to = *spline->to;
        if ( to->hintmask != NULL ) {
            to->hintmask = chunkalloc(sizeof(HintMask));
            memcpy(to->hintmask,spline->to->hintmask,sizeof(HintMask));
        }
        if ( !spline->knownlinear ) {
            ret->last->nextcp.x = spline->splines[0].c/3 + ret->last->me.x;
            ret->last->nextcp.y = spline->splines[1].c/3 + ret->last->me.y;
            to->prevcp.x = ret->last->nextcp.x+ (spline->splines[0].b+spline->splines[0].c)/3;
            to->prevcp.y = ret->last->nextcp.y+ (spline->splines[1].b+spline->splines[1].c)/3;
        }
        SplineMake3(ret->last,to);
        ret->last = to;
        if ( first==NULL ) first = spline;
    }
    if ( ss->first==ss->last ) {
        if ( ret->last!=ret->first ) {
            ret->first->prevcp = ret->last->prevcp;
            ret->first->noprevcp = ret->last->noprevcp;
            ret->first->prev = ret->last->prev;
            ret->last->prev->to = ret->first;
            SplinePointFree(ret->last);
            ret->last = ret->first;
        }
    }
    ret->is_clip_path = ss->is_clip_path;
return( ret );
}

SplineSet *SplineSetsPSApprox(SplineSet *ss) {
    SplineSet *head=NULL, *last, *cur;

    while ( ss!=NULL ) {
        cur = SSPSApprox(ss);
        if ( head==NULL )
            head = cur;
        else
            last->next = cur;
        last = cur;
        ss = ss->next;
    }
return( head );
}

void SCConvertLayerToOrder2(SplineChar *sc,int layer) {
    SplineSet *new;

    if ( sc==NULL )
return;

    new = SplineSetsTTFApprox(sc->layers[layer].splines);
    SplinePointListsFree(sc->layers[layer].splines);
    sc->layers[layer].splines = new;

    UndoesFree(sc->layers[layer].undoes);
    UndoesFree(sc->layers[layer].redoes);
    sc->layers[layer].undoes = NULL;
    sc->layers[layer].redoes = NULL;
    sc->layers[layer].order2 = true;

    MinimumDistancesFree(sc->md); sc->md = NULL;
}

void SCConvertToOrder2(SplineChar *sc) {
    int layer;

    if ( sc==NULL )
return;

    for ( layer=ly_back; layer<sc->layer_cnt; ++layer )
        SCConvertLayerToOrder2(sc,layer);
}


/* ************************************************************************** */

void SplineRefigure2(Spline *spline) {
    SplinePoint *from = spline->from, *to = spline->to;
    Spline1D *xsp = &spline->splines[0], *ysp = &spline->splines[1];
    Spline old;

#ifdef DEBUG
    if ( RealNear(from->me.x,to->me.x) && RealNear(from->me.y,to->me.y))
        IError("Zero length spline created");
#endif
    if ( spline->acceptableextrema )
        old = *spline;

    if ( from->nonextcp || to->noprevcp ||
            ( from->nextcp.x==from->me.x && from->nextcp.y == from->me.y ) ||
            ( to->prevcp.x==to->me.x && to->prevcp.y == to->me.y )) {
        from->nonextcp = to->noprevcp = true;
        from->nextcp = from->me;
        to->prevcp = to->me;
    }

    if ( from->nonextcp && to->noprevcp )
        /* Ok */;
    else if ( from->nonextcp || to->noprevcp || from->nextcp.x!=to->prevcp.x ||
            from->nextcp.y!=to->prevcp.y ) {
        if ( RealNear(from->nextcp.x,to->prevcp.x) &&
                RealNear(from->nextcp.y,to->prevcp.y)) {
            from->nextcp.x = to->prevcp.x = (from->nextcp.x+to->prevcp.x)/2;
            from->nextcp.y = to->prevcp.y = (from->nextcp.y+to->prevcp.y)/2;
        } else {
            IError("Invalid 2nd order spline in SplineRefigure2" );
#ifndef GWW_TEST
            /* I don't want these to go away when I'm debugging. I want to */
            /*  know how I got them */
            from->nextcp.x = to->prevcp.x = (from->nextcp.x+to->prevcp.x)/2;
            from->nextcp.y = to->prevcp.y = (from->nextcp.y+to->prevcp.y)/2;
#endif
        }
    }

    xsp->d = from->me.x; ysp->d = from->me.y;
    if ( from->nonextcp && to->noprevcp ) {
        spline->islinear = true;
        xsp->c = to->me.x-from->me.x;
        ysp->c = to->me.y-from->me.y;
        xsp->a = xsp->b = 0;
        ysp->a = ysp->b = 0;
    } else {
        /* from p. 393 (Operator Details, curveto) Postscript Lang. Ref. Man. (Red book) */
        xsp->c = 2*(from->nextcp.x-from->me.x);
        ysp->c = 2*(from->nextcp.y-from->me.y);
        xsp->b = to->me.x-from->me.x-xsp->c;
        ysp->b = to->me.y-from->me.y-ysp->c;
        xsp->a = 0;
        ysp->a = 0;
        if ( RealNear(xsp->c,0)) xsp->c=0;
        if ( RealNear(ysp->c,0)) ysp->c=0;
        if ( RealNear(xsp->b,0)) xsp->b=0;
        if ( RealNear(ysp->b,0)) ysp->b=0;
        spline->islinear = false;
        if ( ysp->b==0 && xsp->b==0 )
            spline->islinear = true;    /* This seems extremely unlikely... */
    }
    if ( isnan(ysp->b) || isnan(xsp->b) )
        IError("NaN value in spline creation");
    LinearApproxFree(spline->approx);
    spline->approx = NULL;
    spline->knowncurved = false;
    spline->knownlinear = spline->islinear;
    SplineIsLinear(spline);
    spline->isquadratic = !spline->knownlinear;
    spline->order2 = true;

    if ( spline->acceptableextrema ) {
        /* I don't check "d", because changes to that reflect simple */
        /*  translations which will not affect the shape of the spline */
        /* (I don't check "a" because it is always 0 in a quadratic spline) */
        if ( !RealNear(old.splines[0].b,spline->splines[0].b) ||
                !RealNear(old.splines[0].c,spline->splines[0].c) ||
                !RealNear(old.splines[1].b,spline->splines[1].b) ||
                !RealNear(old.splines[1].c,spline->splines[1].c) )
            spline->acceptableextrema = false;
    }
}

void SplineRefigure(Spline *spline) {
    if ( spline==NULL )
return;
    if ( spline->order2 )
        SplineRefigure2(spline);
    else
        SplineRefigure3(spline);
}

static int IsHV(Spline *spline, int isfrom) {
    SplinePoint *sp;

    if ( spline==NULL )
return( false );

    if ( !isfrom ) {
        sp = spline->to;
        if ( sp->noprevcp )
return( false );
        if ( sp->me.x == sp->prevcp.x )
return( 2 );    /* Vertical */
        else if ( sp->me.y == sp->prevcp.y )
return( 1 );    /* Horizontal */
        else
return( 0 );    /* Neither */
    } else {
        sp = spline->from;
        if ( sp->nonextcp )
return( false );
        if ( sp->me.x == sp->nextcp.x )
return( 2 );    /* Vertical */
        else if ( sp->me.y == sp->nextcp.y )
return( 1 );    /* Horizontal */
        else
return( 0 );    /* Neither */
    }
}

void SplineRefigureFixup(Spline *spline) {
    SplinePoint *from, *to, *prev, *next;
    BasePoint foff, toff, unit, new;
    double len;
    enum pointtype fpt, tpt;
    int done = false;
    extern int snaptoint;

    if ( !spline->order2 ) {
        SplineRefigure3(spline);
return;
    }
    from = spline->from; to = spline->to;
    if ( from->pointtype==pt_hvcurve && to->pointtype==pt_hvcurve ) {
        done = true;
        if ( !IsHV(from->prev,0) && !IsHV(to->next,1) ) {
            if ( to->me.x == from->me.x ) {
                from->nextcp.x = to->prevcp.x = to->me.x;
                from->nextcp.y = to->prevcp.y = (from->me.y+from->me.y)/2;
            } else if ( to->me.y==from->me.y ) {
                from->nextcp.y = to->prevcp.y = to->me.y;
                from->nextcp.x = to->prevcp.x = (from->me.x+from->me.x)/2;
            /* Assume they are drawing clockwise */
            } else if (( to->me.x>from->me.x && to->me.y>=from->me.y ) ||
                        (to->me.x<from->me.x && to->me.y<=from->me.y )) {
                from->nextcp.x = to->prevcp.x = from->me.x;
                from->nextcp.y = to->prevcp.y = to->me.y;
            } else {
                from->nextcp.x = to->prevcp.x = to->me.x;
                from->nextcp.y = to->prevcp.y = from->me.y;
            }
        } else if ( !IsHV(to->next,1)) {
            if ( IsHV(from->prev,0)==1 ) {
                from->nextcp.x = to->prevcp.x = to->me.x;
                from->nextcp.y = to->prevcp.y = from->me.y;
            } else {
                from->nextcp.x = to->prevcp.x = from->me.x;
                from->nextcp.y = to->prevcp.y = to->me.y;
            }
        } else if ( !IsHV(from->prev,0)) {
            if ( IsHV(to->next,1)==1 ) {
                from->nextcp.x = to->prevcp.x = from->me.x;
                from->nextcp.y = to->prevcp.y = to->me.y;
            } else {
                from->nextcp.x = to->prevcp.x = to->me.x;
                from->nextcp.y = to->prevcp.y = from->me.y;
            }
        } else {
            if ( IsHV(from->prev,0)==1 && IsHV(to->next,1)==2 ) {
                from->nextcp.x = to->prevcp.x = to->me.x;
                from->nextcp.y = to->prevcp.y = from->me.y;
            } else if ( IsHV(from->prev,0)==2 && IsHV(to->next,1)==1 ) {
                from->nextcp.x = to->prevcp.x = from->me.x;
                from->nextcp.y = to->prevcp.y = to->me.y;
            } else
                done = false;
        }
        if ( done )
            to->noprevcp = from->nonextcp = false;
    }

  if ( !done ) {
    unit.x = from->nextcp.x-from->me.x;
    unit.y = from->nextcp.y-from->me.y;
    len = sqrt(unit.x*unit.x + unit.y*unit.y);
    if ( len!=0 )
        unit.x /= len; unit.y /= len;

    if ( (fpt = from->pointtype)==pt_hvcurve ) fpt = pt_curve;
    if ( (tpt =   to->pointtype)==pt_hvcurve ) tpt = pt_curve;
    if ( from->nextcpdef && to->prevcpdef ) switch ( fpt*3+tpt ) {
      case pt_corner*3+pt_corner:
      case pt_corner*3+pt_tangent:
      case pt_tangent*3+pt_corner:
      case pt_tangent*3+pt_tangent:
        from->nonextcp = to->noprevcp = true;
        from->nextcp = from->me;
        to->prevcp = to->me;
      break;
      case pt_curve*3+pt_curve:
      case pt_curve*3+pt_corner:
      case pt_corner*3+pt_curve:
      case pt_tangent*3+pt_curve:
      case pt_curve*3+pt_tangent:
        if ( from->prev!=NULL && (from->pointtype==pt_tangent || from->pointtype==pt_hvcurve)) {
            prev = from->prev->from;
            foff.x = prev->me.x;
            foff.y = prev->me.y;
        } else if ( from->prev!=NULL ) {
            prev = from->prev->from;
            foff.x = to->me.x-prev->me.x  + from->me.x;
            foff.y = to->me.y-prev->me.y  + from->me.y;
        } else {
            foff.x = from->me.x + (to->me.x-from->me.x)-(to->me.y-from->me.y);
            foff.y = from->me.y + (to->me.x-from->me.x)+(to->me.y-from->me.y);
            prev = NULL;
        }
        if ( to->next!=NULL && (to->pointtype==pt_tangent || to->pointtype==pt_hvcurve)) {
            next = to->next->to;
            toff.x = next->me.x;
            toff.y = next->me.y;
        } else if ( to->next!=NULL ) {
            next = to->next->to;
            toff.x = next->me.x-from->me.x  + to->me.x;
            toff.y = next->me.y-from->me.y  + to->me.y;
        } else {
            toff.x = to->me.x + (to->me.x-from->me.x)+(to->me.y-from->me.y);
            toff.y = to->me.y - (to->me.x-from->me.x)+(to->me.y-from->me.y);
            next = NULL;
        }
        if (( from->pointtype==pt_hvcurve && foff.x!=from->me.x && foff.y!=from->me.y ) ||
                ( to->pointtype==pt_hvcurve && toff.x!=to->me.x && toff.y!=to->me.y )) {
            if ( from->me.x == to->me.x ) {
                if ( from->pointtype==pt_hvcurve )
                    foff.x = from->me.x;
                if ( to->pointtype==pt_hvcurve )
                    toff.x = to->me.x;
            } else if ( from->me.y == to->me.y ) {
                if ( from->pointtype==pt_hvcurve )
                    foff.y = from->me.y;
                if ( to->pointtype==pt_hvcurve )
                    toff.y = to->me.y;
            } else {
                if ( from->pointtype==pt_hvcurve && foff.x!=from->me.x && foff.y!=from->me.y ) {
                    if ( fabs(foff.x-from->me.x) > fabs(foff.y-from->me.y) )
                        foff.y = from->me.y;
                    else
                        foff.x = from->me.x;
                }
                if ( to->pointtype==pt_hvcurve && toff.x!=to->me.x && toff.y!=to->me.y ) {
                    if ( from->pointtype==pt_hvcurve ) {
                        if ( from->me.x==foff.x )
                            toff.y = to->me.y;
                        else
                            toff.x = to->me.x;
                    } else if ( fabs(toff.x-to->me.x) > fabs(toff.y-to->me.y) )
                        toff.y = to->me.y;
                    else
                        toff.x = to->me.x;
                }
            }
        }
        if ( IntersectLinesClip(&from->nextcp,&foff,&from->me,&toff,&to->me)) {
            from->nonextcp = to->noprevcp = false;
            to->prevcp = from->nextcp;
            if ( (from->pointtype==pt_curve || from->pointtype==pt_hvcurve ) &&
                    !from->noprevcp && from->prev!=NULL ) {
                prev = from->prev->from;
                if ( IntersectLinesClip(&from->prevcp,&from->nextcp,&from->me,&prev->nextcp,&prev->me)) {
                    prev->nextcp = from->prevcp;
                    SplineRefigure2(from->prev);
                }
            }
            if ( (to->pointtype==pt_curve || to->pointtype==pt_hvcurve) &&
                    !to->nonextcp && to->next!=NULL ) {
                next = to->next->to;
                if ( IntersectLinesClip(&to->nextcp,&to->prevcp,&to->me,&next->prevcp,&next->me)) {
                    next->prevcp = to->nextcp;
                    SplineRefigure(to->next);
                }
            }
        }
      break;
    } else {
        /* Can't set things arbetrarily here, but make sure they are consistant */
        if ( (from->pointtype==pt_curve || from->pointtype==pt_hvcurve ) &&
                !from->noprevcp && !from->nonextcp ) {
            unit.x = from->nextcp.x-from->me.x;
            unit.y = from->nextcp.y-from->me.y;
            len = sqrt(unit.x*unit.x + unit.y*unit.y);
            if ( len!=0 ) {
                unit.x /= len; unit.y /= len;
                len = sqrt((from->prevcp.x-from->me.x)*(from->prevcp.x-from->me.x) + (from->prevcp.y-from->me.y)*(from->prevcp.y-from->me.y));
                new.x = -len*unit.x + from->me.x; new.y = -len*unit.y + from->me.y;
                if ( new.x-from->prevcp.x<-1 || new.x-from->prevcp.x>1 ||
                         new.y-from->prevcp.y<-1 || new.y-from->prevcp.y>1 ) {
                    prev = NULL;
                    if ( from->prev!=NULL && (prev = from->prev->from)!=NULL &&
                            IntersectLinesClip(&from->prevcp,&new,&from->me,&prev->nextcp,&prev->me)) {
                        prev->nextcp = from->prevcp;
                        SplineRefigure2(from->prev);
                    } else {
                        from->prevcp = new;
                        if ( prev!=NULL )
                            prev->nextcp = new;
                    }
                }
            }
        } else if ( from->pointtype==pt_tangent ) {
            if ( from->prev!=NULL ) {
                prev = from->prev->from;
                if ( !from->noprevcp && !prev->nonextcp &&
                        IntersectLinesClip(&from->prevcp,&to->me,&from->me,&prev->nextcp,&prev->me)) {
                    prev->nextcp = from->prevcp;
                    SplineRefigure2(from->prev);
                }
                if ( !from->nonextcp && !to->noprevcp &&
                        IntersectLinesClip(&from->nextcp,&prev->me,&from->me,&to->prevcp,&to->me))
                    to->prevcp = from->nextcp;
            }
        }
        if ( (to->pointtype==pt_curve || to->pointtype==pt_hvcurve ) &&
                !to->noprevcp && !to->nonextcp ) {
            unit.x = to->prevcp.x-to->nextcp.x;
            unit.y = to->prevcp.y-to->nextcp.y;
            len = sqrt(unit.x*unit.x + unit.y*unit.y);
            if ( len!=0 ) {
                unit.x /= len; unit.y /= len;
                len = sqrt((to->nextcp.x-to->me.x)*(to->nextcp.x-to->me.x) + (to->nextcp.y-to->me.y)*(to->nextcp.y-to->me.y));
                new.x = -len*unit.x + to->me.x; new.y = -len*unit.y + to->me.y;
                if ( new.x-to->nextcp.x<-1 || new.x-to->nextcp.x>1 ||
                        new.y-to->nextcp.y<-1 || new.y-to->nextcp.y>1 ) {
                    if ( to->next!=NULL && (next = to->next->to)!=NULL &&
                            IntersectLinesClip(&to->nextcp,&new,&to->me,&next->prevcp,&next->me)) {
                        next->prevcp = to->nextcp;
                        SplineRefigure2(to->next);
                    } else {
                        to->nextcp = new;
                        if ( to->next!=NULL ) {
                            to->next->to->prevcp = new;
                            SplineRefigure(to->next);
                        }
                    }
                }
            }
        } else if ( to->pointtype==pt_tangent ) {
            if ( to->next!=NULL ) {
                next = to->next->to;
                if ( !to->nonextcp && !next->noprevcp &&
                        IntersectLinesClip(&to->nextcp,&from->me,&to->me,&next->prevcp,&next->me)) {
                    next->prevcp = to->nextcp;
                    SplineRefigure2(to->next);
                }
                if ( !from->nonextcp && !to->noprevcp &&
                        IntersectLinesClip(&from->nextcp,&next->me,&to->me,&from->nextcp,&from->me))
                    to->prevcp = from->nextcp;
            }
        }
    }
    if ( from->nonextcp && to->noprevcp )
        /* Ok */;
    else if ( from->nonextcp || to->noprevcp ) {
        from->nonextcp = to->noprevcp = true;
    } else if (( from->nextcp.x==from->me.x && from->nextcp.y==from->me.y ) ||
                ( to->prevcp.x==to->me.x && to->prevcp.y==to->me.y ) ) {
        from->nonextcp = to->noprevcp = true;
    } else if ( from->nonextcp || to->noprevcp || from->nextcp.x!=to->prevcp.x ||
            from->nextcp.y!=to->prevcp.y ) {
        if ( !IntersectLinesClip(&from->nextcp,
                (from->pointtype==pt_tangent && from->prev!=NULL)?&from->prev->from->me:&from->nextcp, &from->me,
                (to->pointtype==pt_tangent && to->next!=NULL)?&to->next->to->me:&to->prevcp, &to->me)) {
            from->nextcp.x = (from->me.x+to->me.x)/2;
            from->nextcp.y = (from->me.y+to->me.y)/2;
        }
        to->prevcp = from->nextcp;
        if (( from->nextcp.x==from->me.x && from->nextcp.y==from->me.y ) ||
                ( to->prevcp.x==to->me.x && to->prevcp.y==to->me.y ) ) {
            from->nonextcp = to->noprevcp = true;
            from->nextcp = from->me;
            to->prevcp = to->me;
        }
    }
  }
    if ( snaptoint && !from->nonextcp ) {
        from->nextcp.x = to->prevcp.x = rint(from->nextcp.x);
        from->nextcp.y = to->prevcp.y = rint(from->nextcp.y);
    }
    SplineRefigure2(spline);

    /* Now in order2 splines it is possible to request combinations that are */
    /*  mathematically impossible -- two adjacent hv points often don't work */
    if ( to->pointtype==pt_hvcurve &&
                !(to->prevcp.x == to->me.x && to->prevcp.y != to->me.y ) &&
                !(to->prevcp.y == to->me.y && to->prevcp.x != to->me.x ) )
        to->pointtype = pt_curve;
    if ( from->pointtype==pt_hvcurve &&
                !(from->nextcp.x == from->me.x && from->nextcp.y != from->me.y ) &&
                !(from->nextcp.y == from->me.y && from->nextcp.x != from->me.x ) )
        from->pointtype = pt_curve;
}

Spline *SplineMake2(SplinePoint *from, SplinePoint *to) {
    Spline *spline = chunkalloc(sizeof(Spline));

    spline->from = from; spline->to = to;
    from->next = to->prev = spline;
    spline->order2 = true;
    SplineRefigure2(spline);
return( spline );
}

Spline *SplineMake(SplinePoint *from, SplinePoint *to, int order2) {
    if ( order2 )
return( SplineMake2(from,to));
    else
return( SplineMake3(from,to));
}

int IntersectLines(BasePoint *inter,
        BasePoint *line1_1, BasePoint *line1_2,
        BasePoint *line2_1, BasePoint *line2_2) {
    double s1, s2;

    if ( line1_1->x == line1_2->x ) {
        inter->x = line1_1->x;
        if ( line2_1->x == line2_2->x ) {
            if ( line2_1->x!=line1_1->x )
return( false );                /* Parallel vertical lines */
            inter->y = (line1_1->y+line2_1->y)/2;
        } else
            inter->y = line2_1->y + (inter->x-line2_1->x) * (line2_2->y - line2_1->y)/(line2_2->x - line2_1->x);
return( true );
    } else if ( line2_1->x == line2_2->x ) {
        inter->x = line2_1->x;
        inter->y = line1_1->y + (inter->x-line1_1->x) * (line1_2->y - line1_1->y)/(line1_2->x - line1_1->x);
return( true );
    } else {
        s1 = (line1_2->y - line1_1->y)/(line1_2->x - line1_1->x);
        s2 = (line2_2->y - line2_1->y)/(line2_2->x - line2_1->x);
        if ( RealNear(s1,s2)) {
            if ( !RealNear(line1_1->y + (line2_1->x-line1_1->x) * s1,line2_1->y))
return( false );
            inter->x = (line1_2->x+line2_2->x)/2;
            inter->y = (line1_2->y+line2_2->y)/2;
        } else {
            inter->x = (s1*line1_1->x - s2*line2_1->x - line1_1->y + line2_1->y)/(s1-s2);
            inter->y = line1_1->y + (inter->x-line1_1->x) * s1;
        }
return( true );
    }
}

int IntersectLinesClip(BasePoint *inter,
        BasePoint *line1_1, BasePoint *line1_2,
        BasePoint *line2_1, BasePoint *line2_2) {
    BasePoint old = *inter, unit;
    double len, val;

    if ( !IntersectLines(inter,line1_1,line1_2,line2_1,line2_2))
return( false );
    else {
        unit.x = line2_2->x-line1_2->x;
        unit.y = line2_2->y-line1_2->y;
        len = sqrt(unit.x*unit.x + unit.y*unit.y);
        if ( len==0 )
return( false );
        else {
            unit.x /= len; unit.y /= len;
            val = unit.x*(inter->x-line1_2->x) + unit.y*(inter->y-line1_2->y);
            if ( val<=0 || val>=len ) {
                *inter = old;
return( false );
            }
        }
    }
return( true );
}