beta-0.89.2

[luatex.git] / source / texk / web2c / luatexdir / luafontloader / fontforge / fontforge / splineutil2.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 "ustring.h"
#include "chardata.h"
#include <unistd.h>
#include <time.h>
#include <stdlib.h>

int new_em_size = 1000;
int new_fonts_are_order2 = false;
int loaded_fonts_same_as_new = false;
int default_fv_row_count = 4;
int default_fv_col_count = 16;
int default_fv_font_size = 24;
int default_fv_antialias=true;
int default_fv_bbsized=true;
int snaptoint=0;

/*#define DEBUG 1*/

int RealNear(real a,real b) {
    real d;

#if 0 /* def FONTFORGE_CONFIG_USE_DOUBLE*/
    if ( a==0 )
return( b>-1e-8 && b<1e-8 );
    if ( b==0 )
return( a>-1e-8 && a<1e-8 );

    d = a/(1024*1024.);
    if ( d<0 ) d = -d;
return( b>a-d && b<a+d );
#else           /* For floats */
    if ( a==0 )
return( b>-1e-5 && b<1e-5 );
    if ( b==0 )
return( a>-1e-5 && a<1e-5 );

    d = a/(1024*64.);
    if ( d<0 ) d = -d;
return( b>a-d && b<a+d );
#endif
}

int RealNearish(real a,real b) {

    if ( a-b<.001 && a-b>-.001 )
return( true );
return( false );
}

int RealApprox(real a,real b) {

    if ( a==0 ) {
        if ( b<.0001 && b>-.0001 )
return( true );
    } else if ( b==0 ) {
        if ( a<.0001 && a>-.0001 )
return( true );
    } else {
        a /= b;
        if ( a>=.95 && a<=1.05 )
return( true );
    }
return( false );
}

int RealWithin(real a,real b,real fudge) {

return( b>=a-fudge && b<=a+fudge );
}

int RealRatio(real a,real b,real fudge) {

    if ( b==0 )
return( RealWithin(a,b,fudge));

return( RealWithin(a/b,1.0,fudge));
}

static int MinMaxWithin(Spline *spline) {
    extended dx, dy;
    int which;
    extended t1, t2;
    extended w;
    /* We know that this "spline" is basically one dimensional. As long as its*/
    /*  extrema are between the start and end points on that line then we can */
    /*  treat it as a line. If the extrema are way outside the line segment */
    /*  then it's a line that backtracks on itself */

    if ( (dx = spline->to->me.x - spline->from->me.x)<0 ) dx = -dx;
    if ( (dy = spline->to->me.y - spline->from->me.y)<0 ) dy = -dy;
    which = dx<dy;
    SplineFindExtrema(&spline->splines[which],&t1,&t2);
    if ( t1==-1 )
return( true );
    w = ((spline->splines[which].a*t1 + spline->splines[which].b)*t1
             + spline->splines[which].c)*t1 + spline->splines[which].d;
    if ( RealNear(w, (&spline->to->me.x)[which]) || RealNear(w, (&spline->from->me.x)[which]) )
        /* Close enough */;
    else if ( (w<(&spline->to->me.x)[which] && w<(&spline->from->me.x)[which]) ||
            (w>(&spline->to->me.x)[which] && w>(&spline->from->me.x)[which]) )
return( false );                /* Outside */

    w = ((spline->splines[which].a*t2 + spline->splines[which].b)*t2
             + spline->splines[which].c)*t2 + spline->splines[which].d;
    if ( RealNear(w, (&spline->to->me.x)[which]) || RealNear(w, (&spline->from->me.x)[which]) )
        /* Close enough */;
    else if ( (w<(&spline->to->me.x)[which] && w<(&spline->from->me.x)[which]) ||
            (w>(&spline->to->me.x)[which] && w>(&spline->from->me.x)[which]) )
return( false );                /* Outside */

return( true );
}

int SplineIsLinear(Spline *spline) {
    double t1,t2, t3,t4;
    int ret;

    if ( spline->knownlinear )
return( true );
    if ( spline->knowncurved )
return( false );

    if ( spline->splines[0].a==0 && spline->splines[0].b==0 &&
            spline->splines[1].a==0 && spline->splines[1].b==0 )
return( true );

    /* Something is linear if the control points lie on the line between the */
    /*  two base points */

    /* Vertical lines */
    if ( RealNear(spline->from->me.x,spline->to->me.x) ) {
        ret = RealNear(spline->from->me.x,spline->from->nextcp.x) &&
            RealNear(spline->from->me.x,spline->to->prevcp.x);
        if ( ! ((spline->from->nextcp.y >= spline->from->me.y &&
                  spline->from->nextcp.y <= spline->to->me.y &&
                  spline->to->prevcp.y >= spline->from->me.y &&
                  spline->to->prevcp.y <= spline->to->me.y ) ||
                 (spline->from->nextcp.y <= spline->from->me.y &&
                  spline->from->nextcp.y >= spline->to->me.y &&
                  spline->to->prevcp.y <= spline->from->me.y &&
                  spline->to->prevcp.y >= spline->to->me.y )) )
            ret = MinMaxWithin(spline);
    /* Horizontal lines */
    } else if ( RealNear(spline->from->me.y,spline->to->me.y) ) {
        ret = RealNear(spline->from->me.y,spline->from->nextcp.y) &&
            RealNear(spline->from->me.y,spline->to->prevcp.y);
        if ( ! ((spline->from->nextcp.x >= spline->from->me.x &&
                  spline->from->nextcp.x <= spline->to->me.x &&
                  spline->to->prevcp.x >= spline->from->me.x &&
                  spline->to->prevcp.x <= spline->to->me.x) ||
                 (spline->from->nextcp.x <= spline->from->me.x &&
                  spline->from->nextcp.x >= spline->to->me.x &&
                  spline->to->prevcp.x <= spline->from->me.x &&
                  spline->to->prevcp.x >= spline->to->me.x)) )
            ret = MinMaxWithin(spline);
    } else {
        ret = true;
        t1 = (spline->from->nextcp.y-spline->from->me.y)/(spline->to->me.y-spline->from->me.y);
        t2 = (spline->from->nextcp.x-spline->from->me.x)/(spline->to->me.x-spline->from->me.x);
        t3 = (spline->to->me.y-spline->to->prevcp.y)/(spline->to->me.y-spline->from->me.y);
        t4 = (spline->to->me.x-spline->to->prevcp.x)/(spline->to->me.x-spline->from->me.x);
        ret = (RealApprox(t1,t2) || (RealApprox(t1,0) && RealApprox(t2,0))) &&
                (RealApprox(t3,t4) || (RealApprox(t3,0) && RealApprox(t4,0)));
        if ( ret ) {
            if ( t1<0 || t2<0 || t3<0 || t4<0 ||
                    t1>1 || t2>1 || t3>1 || t4>1 )
                ret = MinMaxWithin(spline);
        }
    }
    spline->knowncurved = !ret;
    spline->knownlinear = ret;
    if ( ret ) {
        /* A few places that if the spline is knownlinear then its splines[?] */
        /*  are linear. So give the linear version and not that suggested by */
        /*  the control points */
        spline->splines[0].a = spline->splines[0].b = 0;
        spline->splines[0].d = spline->from->me.x;
        spline->splines[0].c = spline->to->me.x-spline->from->me.x;
        spline->splines[1].a = spline->splines[1].b = 0;
        spline->splines[1].d = spline->from->me.y;
        spline->splines[1].c = spline->to->me.y-spline->from->me.y;
    }
return( ret );
}

int SplineIsLinearMake(Spline *spline) {

    if ( spline->islinear )
return( true );
    if ( SplineIsLinear(spline)) {
        spline->islinear = spline->from->nonextcp = spline->to->noprevcp = true;
        spline->from->nextcp = spline->from->me;
        if ( spline->from->nonextcp && spline->from->noprevcp )
            spline->from->pointtype = pt_corner;
        else if ( spline->from->pointtype == pt_curve || spline->from->pointtype == pt_hvcurve )
            spline->from->pointtype = pt_tangent;
        spline->to->prevcp = spline->to->me;
        if ( spline->to->nonextcp && spline->to->noprevcp )
            spline->to->pointtype = pt_corner;
        else if ( spline->to->pointtype == pt_curve || spline->to->pointtype == pt_hvcurve )
            spline->to->pointtype = pt_tangent;
        SplineRefigure(spline);
    }
return( spline->islinear );
}

static Spline *IsLinearApprox(SplinePoint *from, SplinePoint *to,
        TPoint *mid, int cnt, int order2) {
    double vx, vy, slope;
    int i;

    vx = to->me.x-from->me.x; vy = to->me.y-from->me.y;
    if ( vx==0 && vy==0 ) {
        for ( i=0; i<cnt; ++i )
            if ( mid[i].x != from->me.x || mid[i].y != from->me.y )
return( NULL );
    } else if ( fabs(vx)>fabs(vy) ) {
        slope = vy/vx;
        for ( i=0; i<cnt; ++i )
            if ( !RealWithin(mid[i].y,from->me.y+slope*(mid[i].x-from->me.x),.7) )
return( NULL );
    } else {
        slope = vx/vy; 
        for ( i=0; i<cnt; ++i )
            if ( !RealWithin(mid[i].x,from->me.x+slope*(mid[i].y-from->me.y),.7) )
return( NULL );
    }
    from->nonextcp = to->noprevcp = true;
return( SplineMake(from,to,order2) );
}

/* Least squares tells us that:
        | S(xi*ti^3) |   | S(ti^6) S(ti^5) S(ti^4) S(ti^3) |   | a |
        | S(xi*ti^2) | = | S(ti^5) S(ti^4) S(ti^3) S(ti^2) | * | b |
        | S(xi*ti)   |   | S(ti^4) S(ti^3) S(ti^2) S(ti)   |   | c |
        | S(xi)      |   | S(ti^3) S(ti^2) S(ti)   n       |   | d |
 and the definition of a spline tells us:
        | x1         | = |   1        1       1       1    | * (a b c d)
        | x0         | = |   0        0       0       1    | * (a b c d)
So we're a bit over specified. Let's use the last two lines of least squares
and the 2 from the spline defn. So d==x0. Now we've got three unknowns
and only three equations...

For order2 splines we've got
        | S(xi*ti^2) |   | S(ti^4) S(ti^3) S(ti^2) |   | b |
        | S(xi*ti)   | = | S(ti^3) S(ti^2) S(ti)   | * | c |
        | S(xi)      |   | S(ti^2) S(ti)   n       |   | d |
 and the definition of a spline tells us:
        | x1         | = |   1       1       1    | * (b c d)
        | x0         | = |   0       0       1    | * (b c d)
=>
    d = x0
    b+c = x1-x0
    S(ti^2)*b + S(ti)*c = S(xi)-n*x0
    S(ti^2)*b + S(ti)*(x1-x0-b) = S(xi)-n*x0
    [ S(ti^2)-S(ti) ]*b = S(xi)-S(ti)*(x1-x0) - n*x0
*/
static int _ApproximateSplineFromPoints(SplinePoint *from, SplinePoint *to,
        TPoint *mid, int cnt, BasePoint *nextcp, BasePoint *prevcp,
        int order2) {
    double tt, ttn;
    int i, j, ret;
    double vx[3], vy[3], m[3][3];
    double ts[7], xts[4], yts[4];
    BasePoint nres, pres;
    int nrescnt=0, prescnt=0;
    double nmin, nmax, pmin, pmax, test, ptest;
    double bx, by, cx, cy;

    memset(&nres,0,sizeof(nres)); memset(&pres,0,sizeof(pres));

    /* Add the initial and end points */
    ts[0] = 2; for ( i=1; i<7; ++i ) ts[i] = 1;
    xts[0] = from->me.x+to->me.x; yts[0] = from->me.y+to->me.y;
    xts[3] = xts[2] = xts[1] = to->me.x; yts[3] = yts[2] = yts[1] = to->me.y;
    nmin = pmin = 0; nmax = pmax = (to->me.x-from->me.x)*(to->me.x-from->me.x)+(to->me.y-from->me.y)*(to->me.y-from->me.y);
    for ( i=0; i<cnt; ++i ) {
        xts[0] += mid[i].x;
        yts[0] += mid[i].y;
        ++ts[0];
        tt = mid[i].t;
        xts[1] += tt*mid[i].x;
        yts[1] += tt*mid[i].y;
        ts[1] += tt;
        ts[2] += (ttn=tt*tt);
        xts[2] += ttn*mid[i].x;
        yts[2] += ttn*mid[i].y;
        ts[3] += (ttn*=tt);
        xts[3] += ttn*mid[i].x;
        yts[3] += ttn*mid[i].y;
        ts[4] += (ttn*=tt);
        ts[5] += (ttn*=tt);
        ts[6] += (ttn*=tt);

        test = (mid[i].x-from->me.x)*(to->me.x-from->me.x) + (mid[i].y-from->me.y)*(to->me.y-from->me.y);
        if ( test<nmin ) nmin=test;
        if ( test>nmax ) nmax=test;
        test = (mid[i].x-to->me.x)*(from->me.x-to->me.x) + (mid[i].y-to->me.y)*(from->me.y-to->me.y);
        if ( test<pmin ) pmin=test;
        if ( test>pmax ) pmax=test;
    }
    pmin *= 1.2; pmax *= 1.2; nmin *= 1.2; nmax *= 1.2;

    for ( j=0; j<3; ++j ) {
        if ( order2 ) {
            if ( RealNear(ts[j+2],ts[j+1]) )
    continue;
            /* This produces really bad results!!!! But I don't see what I can do to improve it */
            bx = (xts[j]-ts[j+1]*(to->me.x-from->me.x) - ts[j]*from->me.x) / (ts[j+2]-ts[j+1]);
            by = (yts[j]-ts[j+1]*(to->me.y-from->me.y) - ts[j]*from->me.y) / (ts[j+2]-ts[j+1]);
            cx = to->me.x-from->me.x-bx;
            cy = to->me.y-from->me.y-by;

            nextcp->x = from->me.x + cx/2;
            nextcp->y = from->me.y + cy/2;
            *prevcp = *nextcp;
        } else {
            vx[0] = xts[j+1]-ts[j+1]*from->me.x;
            vx[1] = xts[j]-ts[j]*from->me.x;
            vx[2] = to->me.x-from->me.x;                /* always use the defn of spline */

            vy[0] = yts[j+1]-ts[j+1]*from->me.y;
            vy[1] = yts[j]-ts[j]*from->me.y;
            vy[2] = to->me.y-from->me.y;

            m[0][0] = ts[j+4]; m[0][1] = ts[j+3]; m[0][2] = ts[j+2];
            m[1][0] = ts[j+3]; m[1][1] = ts[j+2]; m[1][2] = ts[j+1];
            m[2][0] = 1;  m[2][1] = 1;  m[2][2] = 1;

            /* Remove a terms from rows 0 and 1 */
            vx[0] -= ts[j+4]*vx[2];
            vy[0] -= ts[j+4]*vy[2];
            m[0][0] = 0; m[0][1] -= ts[j+4]; m[0][2] -= ts[j+4];
            vx[1] -= ts[j+3]*vx[2];
            vy[1] -= ts[j+3]*vy[2];
            m[1][0] = 0; m[1][1] -= ts[j+3]; m[1][2] -= ts[j+3];

            if ( fabs(m[1][1])<fabs(m[0][1]) ) {
                double temp;
                temp = vx[1]; vx[1] = vx[0]; vx[0] = temp;
                temp = vy[1]; vy[1] = vy[0]; vy[0] = temp;
                temp = m[1][1]; m[1][1] = m[0][1]; m[0][1] = temp;
                temp = m[1][2]; m[1][2] = m[0][2]; m[0][2] = temp;
            }
            /* remove b terms from rows 0 and 2 (first normalize row 1 so m[1][1] is 1*/
            vx[1] /= m[1][1];
            vy[1] /= m[1][1];
            m[1][2] /= m[1][1];
            m[1][1] = 1;
            vx[0] -= m[0][1]*vx[1];
            vy[0] -= m[0][1]*vy[1];
            m[0][2] -= m[0][1]*m[1][2]; m[0][1] = 0;
            vx[2] -= m[2][1]*vx[1];
            vy[2] -= m[2][1]*vy[1];
            m[2][2] -= m[2][1]*m[1][2]; m[2][1] = 0; 

            vx[0] /= m[0][2];                   /* This is cx */
            vy[0] /= m[0][2];                   /* This is cy */
            /*m[0][2] = 1;*/

            vx[1] -= m[1][2]*vx[0];             /* This is bx */
            vy[1] -= m[1][2]*vy[0];             /* This is by */
            /* m[1][2] = 0; */
            vx[2] -= m[2][2]*vx[0];             /* This is ax */
            vy[2] -= m[2][2]*vy[0];             /* This is ay */
            /* m[2][2] = 0; */

            nextcp->x = from->me.x + vx[0]/3;
            nextcp->y = from->me.y + vy[0]/3;
            prevcp->x = nextcp->x + (vx[0]+vx[1])/3;
            prevcp->y = nextcp->y + (vy[0]+vy[1])/3;
        }

        test = (nextcp->x-from->me.x)*(to->me.x-from->me.x) +
                (nextcp->y-from->me.y)*(to->me.y-from->me.y);
        ptest = (prevcp->x-to->me.x)*(from->me.x-to->me.x) +
                (prevcp->y-to->me.y)*(from->me.y-to->me.y);
        if ( order2 &&
                (test<nmin || test>nmax || ptest<pmin || ptest>pmax))
    continue;
        if ( test>=nmin && test<=nmax ) {
            nres.x += nextcp->x; nres.y += nextcp->y;
            ++nrescnt;
        }
        if ( test>=pmin && test<=pmax ) {
            pres.x += prevcp->x; pres.y += prevcp->y;
            ++prescnt;
        }
        if ( nrescnt==1 && prescnt==1 )
    break;
    }

    ret = 0;
    if ( nrescnt>0 ) {
        ret |= 1;
        nextcp->x = nres.x/nrescnt;
        nextcp->y = nres.y/nrescnt;
    } else
        *nextcp = from->nextcp;
    if ( prescnt>0 ) {
        ret |= 2;
        prevcp->x = pres.x/prescnt;
        prevcp->y = pres.y/prescnt;
    } else
        *prevcp = to->prevcp;
    if ( order2 && ret!=3 ) {
        nextcp->x = (nextcp->x + prevcp->x)/2;
        nextcp->y = (nextcp->y + prevcp->y)/2;
    }
    if ( order2 )
        *prevcp = *nextcp;
return( ret );
}

static void TestForLinear(SplinePoint *from,SplinePoint *to) {
    BasePoint off, cpoff, cpoff2;
    double len, co, co2;

    /* Did we make a line? */
    off.x = to->me.x-from->me.x; off.y = to->me.y-from->me.y;
    len = sqrt(off.x*off.x + off.y*off.y);
    if ( len!=0 ) {
        off.x /= len; off.y /= len;
        cpoff.x = from->nextcp.x-from->me.x; cpoff.y = from->nextcp.y-from->me.y;
        len = sqrt(cpoff.x*cpoff.x + cpoff.y*cpoff.y);
        if ( len!=0 ) {
            cpoff.x /= len; cpoff.y /= len;
        }
        cpoff2.x = to->prevcp.x-from->me.x; cpoff2.y = to->prevcp.y-from->me.y;
        len = sqrt(cpoff2.x*cpoff2.x + cpoff2.y*cpoff2.y);
        if ( len!=0 ) {
            cpoff2.x /= len; cpoff2.y /= len;
        }
        co = cpoff.x*off.y - cpoff.y*off.x; co2 = cpoff2.x*off.y - cpoff2.y*off.x;
        if ( co<.05 && co>-.05 && co2<.05 && co2>-.05 ) {
            from->nextcp = from->me; from->nonextcp = true;
            to->prevcp = to->me; to->noprevcp = true;
        } else {
            Spline temp;
            memset(&temp,0,sizeof(temp));
            temp.from = from; temp.to = to;
            SplineRefigure(&temp);
            if ( SplineIsLinear(&temp)) {
                from->nextcp = from->me; from->nonextcp = true;
                to->prevcp = to->me; to->noprevcp = true;
            }
        }
    }
}

/* Find a spline which best approximates the list of intermediate points we */
/*  are given. No attempt is made to fix the slopes */
Spline *ApproximateSplineFromPoints(SplinePoint *from, SplinePoint *to,
        TPoint *mid, int cnt, int order2) {
    int ret;
    Spline *spline;
    BasePoint nextcp, prevcp;

    if ( (spline = IsLinearApprox(from,to,mid,cnt,order2))!=NULL )
return( spline );

    ret = _ApproximateSplineFromPoints(from,to,mid,cnt,&nextcp,&prevcp,order2);

    if ( ret&1 ) {
        from->nextcp = nextcp;
        from->nonextcp = false;
    } else {
        from->nextcp = from->me;
        from->nonextcp = true;
    }
    if ( ret&2 ) {
        to->prevcp = prevcp;
        to->noprevcp = false;
    } else {
        to->prevcp = to->me;
        to->noprevcp = true;
    }
    TestForLinear(from,to);
    spline = SplineMake(from,to,order2);
return( spline );
}

static double ClosestSplineSolve(Spline1D *sp,double sought,double close_to_t) {
    /* We want to find t so that spline(t) = sought */
    /*  find the value which is closest to close_to_t */
    /* on error return closetot */
    Spline1D temp;
    extended ts[3];
    int i;
    double t, best, test;

    temp = *sp;
    temp.d -= sought;
    CubicSolve(&temp,ts);
    best = 9e20; t= close_to_t;
    for ( i=0; i<3; ++i ) if ( ts[i]!=-1 ) {
        if ( (test=ts[i]-close_to_t)<0 ) test = -test;
        if ( test<best ) {
            best = test;
            t = ts[i];
        }
    }

return( t );
}

struct dotbounds {
    BasePoint unit;
    BasePoint base;
    double len;
    double min,max;             /* If min<0 || max>len the spline extends beyond its endpoints */
};

static double SigmaDeltas(Spline *spline,TPoint *mid, int cnt, DBounds *b, struct dotbounds *db) {
    int i, lasti;
    double xdiff, ydiff, sum, temp, t, lastt;
    SplinePoint *to = spline->to, *from = spline->from;
    extended ts[2], x,y;
    struct dotbounds db2;
    double dot;

    if ( (xdiff = to->me.x-from->me.x)<0 ) xdiff = -xdiff;
    if ( (ydiff = to->me.y-from->me.y)<0 ) ydiff = -ydiff;

    sum = 0; lastt = -1; lasti = -1;
    for ( i=0; i<cnt; ++i ) {
        if ( ydiff>2*xdiff ) {
            t = ClosestSplineSolve(&spline->splines[1],mid[i].y,mid[i].t);
        } else if ( xdiff>2*ydiff ) {
            t = ClosestSplineSolve(&spline->splines[0],mid[i].x,mid[i].t);
        } else {
            t = (ClosestSplineSolve(&spline->splines[1],mid[i].y,mid[i].t) +
                    ClosestSplineSolve(&spline->splines[0],mid[i].x,mid[i].t))/2;
        }
        if ( t==lastt )         /* These last* values appear to be debugging */
            t = lastt + (mid[i].t - mid[lasti].t);
        else {
            lastt = t;
            lasti = i;
        }
        temp = mid[i].x - ( ((spline->splines[0].a*t+spline->splines[0].b)*t+spline->splines[0].c)*t + spline->splines[0].d );
        sum += temp*temp;
        temp = mid[i].y - ( ((spline->splines[1].a*t+spline->splines[1].b)*t+spline->splines[1].c)*t + spline->splines[1].d );
        sum += temp*temp;
    }

    /* Ok, we've got distances from a set of points on the old spline to the */
    /*  new one. Let's do the reverse: find the extrema of the new and see how*/
    /*  close they get to the bounding box of the old */
    /* And get really unhappy if the spline extends beyond the end-points */
    db2.min = 0; db2.max = db->len;
    SplineFindExtrema(&spline->splines[0],&ts[0],&ts[1]);
    for ( i=0; i<2; ++i ) {
        if ( ts[i]!=-1 ) {
            x = ((spline->splines[0].a*ts[i]+spline->splines[0].b)*ts[i]+spline->splines[0].c)*ts[i] + spline->splines[0].d;
            y = ((spline->splines[1].a*ts[i]+spline->splines[1].b)*ts[i]+spline->splines[1].c)*ts[i] + spline->splines[1].d;
            if ( x<b->minx )
                sum += (x-b->minx)*(x-b->minx);
            else if ( x>b->maxx )
                sum += (x-b->maxx)*(x-b->maxx);
            dot = (x-db->base.x)*db->unit.x + (y-db->base.y)*db->unit.y;
            if ( dot<db2.min ) db2.min = dot;
            if ( dot>db2.max ) db2.max = dot;
        }
    }
    SplineFindExtrema(&spline->splines[1],&ts[0],&ts[1]);
    for ( i=0; i<2; ++i ) {
        if ( ts[i]!=-1 ) {
            x = ((spline->splines[0].a*ts[i]+spline->splines[0].b)*ts[i]+spline->splines[0].c)*ts[i] + spline->splines[0].d;
            y = ((spline->splines[1].a*ts[i]+spline->splines[1].b)*ts[i]+spline->splines[1].c)*ts[i] + spline->splines[1].d;
            if ( y<b->miny )
                sum += (y-b->miny)*(y-b->miny);
            else if ( y>b->maxy )
                sum += (y-b->maxy)*(y-b->maxy);
            dot = (x-db->base.x)*db->unit.x + (y-db->base.y)*db->unit.y;
            if ( dot<db2.min ) db2.min = dot;
            if ( dot>db2.max ) db2.max = dot;
        }
    }

    /* Big penalty for going beyond the range of the desired spline */
    if ( db->min==0 && db2.min<0 )
        sum += 10000 + db2.min*db2.min;
    else if ( db2.min<db->min )
        sum += 100 + (db2.min-db->min)*(db2.min-db->min);
    if ( db->max==db->len && db2.max>db->len )
        sum += 10000 + (db2.max-db->max)*(db2.max-db->max);
    else if ( db2.max>db->max )
        sum += 100 + (db2.max-db->max)*(db2.max-db->max);

return( sum );
}

static void ApproxBounds(DBounds *b,TPoint *mid, int cnt, struct dotbounds *db) {
    int i;
    double dot;

    b->minx = b->maxx = mid[0].x;
    b->miny = b->maxy = mid[0].y;
    db->min = 0; db->max = db->len;
    for ( i=1; i<cnt; ++i ) {
        if ( mid[i].x>b->maxx ) b->maxx = mid[i].x;
        if ( mid[i].x<b->minx ) b->minx = mid[i].x;
        if ( mid[i].y>b->maxy ) b->maxy = mid[i].y;
        if ( mid[i].y<b->miny ) b->miny = mid[i].y;
        dot = (mid[i].x-db->base.x)*db->unit.x + (mid[i].y-db->base.y)*db->unit.y;
        if ( dot<db->min ) db->min = dot;
        if ( dot>db->max ) db->max = dot;
    }
}

static int GoodCurve(SplinePoint *sp, int check_prev ) {
    double dx, dy, lenx, leny;

    if ( sp->pointtype!=pt_curve && sp->pointtype!=pt_hvcurve )
return( false );
    if ( check_prev ) {
        dx = sp->me.x - sp->prevcp.x;
        dy = sp->me.y - sp->prevcp.y;
    } else {
        dx = sp->me.x - sp->nextcp.x;
        dy = sp->me.y - sp->nextcp.y;
    }
    /* If the cp is very close to the base point the point might as well be a corner */
    if ( dx<0 ) dx = -dx;
    if ( dy<0 ) dy = -dy;
    if ( dx+dy<1 )
return( false );

    if ( check_prev ) {
        if ( sp->prev==NULL )
return( true );
        lenx = sp->me.x - sp->prev->from->me.x;
        leny = sp->me.y - sp->prev->from->me.y;
    } else {
        if ( sp->next==NULL )
return( true );
        lenx = sp->me.x - sp->next->to->me.x;
        leny = sp->me.y - sp->next->to->me.y;
    }
    if ( lenx<0 ) lenx = -lenx;
    if ( leny<0 ) leny = -leny;
    if ( 50*(dx+dy) < lenx+leny )
return( false );

return( true );
}

#if 0
static int totcnt_cnt, nocnt_cnt, incr_cnt, curdiff_cnt;
#endif

/* I used to do a least squares aproach adding two more to the above set of equations */
/*  which held the slopes constant. But that didn't work very well. So instead*/
/*  Then I tried doing the approximation, and then forcing the control points */
/*  to be in line (witht the original slopes), getting a better approximation */
/*  to "t" for each data point and then calculating an error array, approximating*/
/*  it, and using that to fix up the final result */
/* Then I tried checking various possible cp lengths in the desired directions*/
/*  finding the best one or two, and doing a 2D binary search using that as a */
/*  starting point. */
/* And sometimes a least squares approach will give us the right answer, so   */
/*  try that too. */
/* This still isn't as good as I'd like it... But I haven't been able to */
/*  improve it further yet */
#define TRY_CNT         2
#define DECIMATION      5
Spline *ApproximateSplineFromPointsSlopes(SplinePoint *from, SplinePoint *to,
        TPoint *mid, int cnt, int order2) {
    BasePoint tounit, fromunit, ftunit;
    double flen,tlen,ftlen;
    Spline *spline, temp;
    BasePoint nextcp;
    int bettern, betterp;
    double offn, offp, incrn, incrp, trylen;
    int nocnt = 0, totcnt;
    double curdiff, bestdiff[TRY_CNT];
    int i,j,besti[TRY_CNT],bestj[TRY_CNT],k,l;
    double fdiff, tdiff, fmax, tmax, fdotft, tdotft;
    DBounds b;
    struct dotbounds db;
    double offn_, offp_, finaldiff;

    /* If all the selected points are at the same spot, and one of the */
    /*  end-points is also at that spot, then just copy the control point */
    /* But our caller seems to have done that for us */
    
    /* If the two end-points are corner points then allow the slope to vary */
    /* Or if one end-point is a tangent but the point defining the tangent's */
    /*  slope is being removed then allow the slope to vary */
    /* Except if the slope is horizontal or vertical then keep it fixed */
    if ( ( !from->nonextcp && ( from->nextcp.x==from->me.x || from->nextcp.y==from->me.y)) ||
            (!to->noprevcp && ( to->prevcp.x==to->me.x || to->prevcp.y==to->me.y)) )
        /* Preserve the slope */;
    else if ( ((from->pointtype == pt_corner && from->nonextcp) ||
                (from->pointtype == pt_tangent &&
                        ((from->nonextcp && from->noprevcp) || !from->noprevcp))) &&
            ((to->pointtype == pt_corner && to->noprevcp) ||
                (to->pointtype == pt_tangent &&
                        ((to->nonextcp && to->noprevcp) || !to->nonextcp))) ) {
        from->pointtype = to->pointtype = pt_corner;
return( ApproximateSplineFromPoints(from,to,mid,cnt,order2) );
    }

    /* If we are going to honour the slopes of a quadratic spline, there is */
    /*  only one possibility */
    if ( order2 ) {
        if ( from->nonextcp )
            from->nextcp = from->next->to->me;
        if ( to->noprevcp )
            to->prevcp = to->prev->from->me;
        from->nonextcp = to->noprevcp = false;
        fromunit.x = from->nextcp.x-from->me.x; fromunit.y = from->nextcp.y-from->me.y;
        tounit.x = to->prevcp.x-to->me.x; tounit.y = to->prevcp.y-to->me.y;

        if ( !IntersectLines(&nextcp,&from->nextcp,&from->me,&to->prevcp,&to->me) ||
                (nextcp.x-from->me.x)*fromunit.x + (nextcp.y-from->me.y)*fromunit.y < 0 ||
                (nextcp.x-to->me.x)*tounit.x + (nextcp.y-to->me.y)*tounit.y < 0 ) {
            /* If the slopes don't intersect then use a line */
            /*  (or if the intersection is patently absurd) */
            from->nonextcp = to->noprevcp = true;
            from->nextcp = from->me;
            to->prevcp = to->me;
            TestForLinear(from,to);
        } else {
            from->nextcp = to->prevcp = nextcp;
            from->nonextcp = to->noprevcp = false;
        }
return( SplineMake2(from,to));
    }
    /* From here down we are only working with cubic splines */

    if ( cnt==0 ) {
        /* Just use what we've got, no data to improve it */
        /* But we do sometimes get some cps which are too big */
        double len = sqrt((to->me.x-from->me.x)*(to->me.x-from->me.x) + (to->me.y-from->me.y)*(to->me.y-from->me.y));
        if ( len==0 ) {
            from->nonextcp = to->noprevcp = true;
            from->nextcp = from->me;
            to->prevcp = to->me;
        } else {
            BasePoint noff, poff;
            double nlen, plen;
            noff.x = from->nextcp.x-from->me.x; noff.y = from->nextcp.y-from->me.y;
            poff.x = to->me.x-to->prevcp.x; poff.y = to->me.y-to->prevcp.y;
            nlen = sqrt(noff.x*noff.x + noff.y+noff.y);
            plen = sqrt(poff.x*poff.x + poff.y+poff.y);
            if ( nlen>len/3 ) {
                noff.x *= len/3/nlen; noff.y *= len/3/nlen;
                from->nextcp.x = from->me.x + noff.x;
                from->nextcp.y = from->me.y + noff.y;
            }
            if ( plen>len/3 ) {
                poff.x *= len/3/plen; poff.y *= len/3/plen;
                to->prevcp.x = to->me.x + poff.x;
                to->prevcp.y = to->me.y + poff.y;
            }
        }
return( SplineMake3(from,to));
    }

    if ( to->prev!=NULL && (( to->noprevcp && to->nonextcp ) || to->prev->knownlinear )) {
        tounit.x = to->prev->from->me.x-to->me.x; tounit.y = to->prev->from->me.y-to->me.y;
    } else if ( !to->noprevcp || to->pointtype == pt_corner ) {
        tounit.x = to->prevcp.x-to->me.x; tounit.y = to->prevcp.y-to->me.y;
    } else {
        tounit.x = to->me.x-to->nextcp.x; tounit.y = to->me.y-to->nextcp.y;
    }
    tlen = sqrt(tounit.x*tounit.x + tounit.y*tounit.y);
    if ( from->next!=NULL && (( from->noprevcp && from->nonextcp ) || from->next->knownlinear) ) {
        fromunit.x = from->next->to->me.x-from->me.x; fromunit.y = from->next->to->me.y-from->me.y;
    } else if ( !from->nonextcp || from->pointtype == pt_corner ) {
        fromunit.x = from->nextcp.x-from->me.x; fromunit.y = from->nextcp.y-from->me.y;
    } else {
        fromunit.x = from->me.x-from->prevcp.x; fromunit.y = from->me.y-from->prevcp.y;
    }
    flen = sqrt(fromunit.x*fromunit.x + fromunit.y*fromunit.y);
    if ( tlen==0 || flen==0 ) {
        if ( from->next!=NULL )
            temp = *from->next;
        else {
            memset(&temp,0,sizeof(temp));
            temp.from = from; temp.to = to;
            SplineRefigure(&temp);
            from->next = to->prev = NULL;
        }
    }
    if ( tlen==0 ) {
        if ( (to->pointtype==pt_curve || to->pointtype==pt_hvcurve) &&
                to->next && !to->nonextcp ) {
            tounit.x = to->me.x-to->nextcp.x; tounit.y = to->me.y-to->nextcp.y;
/* Doesn't work
        } else if ( to->pointtype==pt_tangent && to->next ) {
            tounit.x = to->me.x-to->next->to->me.x; tounit.y = to->me.y-to->next->to->me.y;
*/
        } else {
            tounit.x = -( (3*temp.splines[0].a*.9999+2*temp.splines[0].b)*.9999+temp.splines[0].c );
            tounit.y = -( (3*temp.splines[1].a*.9999+2*temp.splines[1].b)*.9999+temp.splines[1].c );
        }
        tlen = sqrt(tounit.x*tounit.x + tounit.y*tounit.y);
    }
    tounit.x /= tlen; tounit.y /= tlen;

    if ( flen==0 ) {
        if ( (from->pointtype==pt_curve || from->pointtype==pt_hvcurve) &&
                from->prev && !from->noprevcp ) {
            fromunit.x = from->me.x-from->prevcp.x; fromunit.y = from->me.y-from->prevcp.y;
/*
        } else if ( from->pointtype==pt_tangent && from->prev ) {
            fromunit.x = from->me.x-from->prev->from->me.x; fromunit.y = from->me.y-from->prev->from->me.y;
*/
        } else {
            fromunit.x = ( (3*temp.splines[0].a*.0001+2*temp.splines[0].b)*.0001+temp.splines[0].c );
            fromunit.y = ( (3*temp.splines[1].a*.0001+2*temp.splines[1].b)*.0001+temp.splines[1].c );
        }
        flen = sqrt(fromunit.x*fromunit.x + fromunit.y*fromunit.y);
    }
    fromunit.x /= flen; fromunit.y /= flen;

    trylen = (to->me.x-from->me.x)*fromunit.x + (to->me.y-from->me.y)*fromunit.y;
    if ( trylen>flen ) flen = trylen;
    
    trylen = (from->me.x-to->me.x)*tounit.x + (from->me.y-to->me.y)*tounit.y;
    if ( trylen>tlen ) tlen = trylen;

    ftunit.x = (to->me.x-from->me.x); ftunit.y = (to->me.y-from->me.y);
    ftlen = sqrt(ftunit.x*ftunit.x + ftunit.y*ftunit.y);
    if ( ftlen!=0 ) {
        ftunit.x /= ftlen; ftunit.y /= ftlen;
    }
    fdotft = fromunit.x*ftunit.x + fromunit.y*ftunit.y;
    fmax = fdotft>0 ? ftlen/fdotft : 1e10;
    tdotft = -tounit.x*ftunit.x - tounit.y*ftunit.y;
    tmax = tdotft>0 ? ftlen/tdotft : 1e10;
    /* At fmax, tmax the control points will stretch beyond the other endpoint*/
    /*  when projected along the line between the two endpoints */

    db.base = from->me;
    db.unit.x = (to->me.x-from->me.x); db.unit.y = (to->me.y-from->me.y);
    db.len = sqrt(db.unit.x*db.unit.x + db.unit.y*db.unit.y);
    if ( db.len!=0 ) {
        db.unit.x /= db.len;
        db.unit.y /= db.len;
    }
    ApproxBounds(&b,mid,cnt,&db);

    for ( k=0; k<TRY_CNT; ++k ) {
        bestdiff[k] = 1e20;
        besti[k] = -1; bestj[k] = -1;
    }
    fdiff = flen/DECIMATION;
    tdiff = tlen/DECIMATION;
    from->nextcp = from->me;
    from->nonextcp = false;
    to->noprevcp = false;
    memset(&temp,0,sizeof(Spline));
    temp.from = from; temp.to = to;
    for ( i=1; i<DECIMATION; ++i ) {
        from->nextcp.x += fdiff*fromunit.x; from->nextcp.y += fdiff*fromunit.y;
        to->prevcp = to->me;
        for ( j=1; j<DECIMATION; ++j ) {
            to->prevcp.x += tdiff*tounit.x; to->prevcp.y += tdiff*tounit.y;
            SplineRefigure(&temp);
            curdiff = SigmaDeltas(&temp,mid,cnt,&b,&db);
            for ( k=0; k<TRY_CNT; ++k ) {
                if ( curdiff<bestdiff[k] ) {
                    for ( l=TRY_CNT-1; l>k; --l ) {
                        bestdiff[l] = bestdiff[l-1];
                        besti[l] = besti[l-1];
                        bestj[l] = bestj[l-1];
                    }
                    bestdiff[k] = curdiff;
                    besti[k] = i; bestj[k]=j;
            break;
                }
            }
        }
    }

    finaldiff = 1e20;
    offn_ = offp_ = -1;
    spline = SplineMake(from,to,false);
    for ( k=-1; k<TRY_CNT; ++k ) {
        if ( k<0 ) {
            BasePoint nextcp, prevcp;
            double temp1, temp2;
            int ret = _ApproximateSplineFromPoints(from,to,mid,cnt,&nextcp,&prevcp,false);
            /* sometimes least squares gives us the right answer */
            if ( !(ret&1) || !(ret&2))
    continue;
            temp1 = (prevcp.x-to->me.x)*tounit.x + (prevcp.y-to->me.y)*tounit.y;
            temp2 = (nextcp.x-from->me.x)*fromunit.x + (nextcp.y-from->me.y)*fromunit.y;
            if ( temp1<=0 || temp2<=0 )         /* A nice solution... but the control points are diametrically opposed to what they should be */
    continue;
            tlen = temp1; flen = temp2;
        } else {
            if ( bestj[k]<0 || besti[k]<0 )
    continue;
            tlen = bestj[k]*tdiff; flen = besti[k]*fdiff;
        }
        to->prevcp.x = to->me.x + tlen*tounit.x; to->prevcp.y = to->me.y + tlen*tounit.y;
        from->nextcp.x = from->me.x + flen*fromunit.x; from->nextcp.y = from->me.y + flen*fromunit.y;
        SplineRefigure(spline);

        bettern = betterp = false;
        incrn = tdiff/2.0; incrp = fdiff/2.0;
        offn = flen; offp = tlen;
        nocnt = 0;
        curdiff = SigmaDeltas(spline,mid,cnt,&b,&db);
        totcnt = 0;
        forever {
            double fadiff, fsdiff;
            double tadiff, tsdiff;

            from->nextcp.x = from->me.x + (offn+incrn)*fromunit.x; from->nextcp.y = from->me.y + (offn+incrn)*fromunit.y;
            to->prevcp.x = to->me.x + offp*tounit.x; to->prevcp.y = to->me.y + offp*tounit.y;
            SplineRefigure(spline);
            fadiff = SigmaDeltas(spline,mid,cnt,&b,&db);
            from->nextcp.x = from->me.x + (offn-incrn)*fromunit.x; from->nextcp.y = from->me.y + (offn-incrn)*fromunit.y;
            SplineRefigure(spline);
            fsdiff = SigmaDeltas(spline,mid,cnt,&b,&db);
            from->nextcp.x = from->me.x + offn*fromunit.x; from->nextcp.y = from->me.y + offn*fromunit.y;
            if ( offn-incrn<=0 )
                fsdiff += 1e10;

            to->prevcp.x = to->me.x + (offp+incrp)*tounit.x; to->prevcp.y = to->me.y + (offp+incrp)*tounit.y;
            SplineRefigure(spline);
            tadiff = SigmaDeltas(spline,mid,cnt,&b,&db);
            to->prevcp.x = to->me.x + (offp-incrp)*tounit.x; to->prevcp.y = to->me.y + (offp-incrp)*tounit.y;
            SplineRefigure(spline);
            tsdiff = SigmaDeltas(spline,mid,cnt,&b,&db);
            to->prevcp.x = to->me.x + offp*tounit.x; to->prevcp.y = to->me.y + offp*tounit.y;
            if ( offp-incrp<=0 )
                tsdiff += 1e10;

            if ( offn>=incrn && fsdiff<curdiff &&
                    (fsdiff<fadiff && fsdiff<tsdiff && fsdiff<tadiff)) {
                offn -= incrn;
                if ( bettern>0 )
                    incrn /= 2;
                bettern = -1;
                nocnt = 0;
                curdiff = fsdiff;
            } else if ( offn+incrn<fmax && fadiff<curdiff &&
                    (fadiff<=fsdiff && fadiff<tsdiff && fadiff<tadiff)) {
                offn += incrn;
                if ( bettern<0 )
                    incrn /= 2;
                bettern = 1;
                nocnt = 0;
                curdiff = fadiff;
            } else if ( offp>=incrp && tsdiff<curdiff &&
                    (tsdiff<=fsdiff && tsdiff<=fadiff && tsdiff<tadiff)) {
                offp -= incrp;
                if ( betterp>0 )
                    incrp /= 2;
                betterp = -1;
                nocnt = 0;
                curdiff = tsdiff;
            } else if ( offp+incrp<tmax && tadiff<curdiff &&
                    (tadiff<=fsdiff && tadiff<=fadiff && tadiff<=tsdiff)) {
                offp += incrp;
                if ( betterp<0 )
                    incrp /= 2;
                betterp = 1;
                nocnt = 0;
                curdiff = tadiff;
            } else {
                if ( ++nocnt > 6 )
        break;
                incrn /= 2;
                incrp /= 2;
            }
            if ( curdiff<1 )
        break;
            if ( incrp<tdiff/1024 || incrn<fdiff/1024 )
        break;
            if ( ++totcnt>200 )
        break;
            if ( offn<0 || offp<0 ) {
                IError("Approximation got inverse control points");
        break;
            }
        }
#if 0
 if ( nocnt>6 )
  nocnt_cnt++;
 else if ( curdiff<1 )
  curdiff_cnt++;
 else if ( totcnt>200 )
  totcnt_cnt++;
 else
  incr_cnt++;
#endif
        if ( curdiff<finaldiff ) {
            finaldiff = curdiff;
            offn_ = offn;
            offp_ = offp;
        }
    }

    to->noprevcp = offp_==0;
    from->nonextcp = offn_==0;
    to->prevcp.x = to->me.x + offp_*tounit.x; to->prevcp.y = to->me.y + offp_*tounit.y;
    from->nextcp.x = from->me.x + offn_*fromunit.x; from->nextcp.y = from->me.y + offn_*fromunit.y;
    /* I used to check for a spline very close to linear (and if so, make it */
    /*  linear). But in when stroking a path with an eliptical pen we transform*/
    /*  the coordinate system and our normal definitions of "close to linear" */
    /*  don't apply */
    /*TestForLinear(from,to);*/
    SplineRefigure(spline);

return( spline );
}
#undef TRY_CNT
#undef DECIMATION

    /* calculating the actual length of a spline is hard, this gives a very */
    /*  rough (but quick) approximation */
static double SplineLenApprox(Spline *spline) {
    double len, slen, temp;

    if ( (temp = spline->to->me.x-spline->from->me.x)<0 ) temp = -temp;
    len = temp;
    if ( (temp = spline->to->me.y-spline->from->me.y)<0 ) temp = -temp;
    len += temp;
    if ( !spline->to->noprevcp || !spline->from->nonextcp ) {
        if ( (temp = spline->from->nextcp.x-spline->from->me.x)<0 ) temp = -temp;
        slen = temp;
        if ( (temp = spline->from->nextcp.y-spline->from->me.y)<0 ) temp = -temp;
        slen += temp;
        if ( (temp = spline->to->prevcp.x-spline->from->nextcp.x)<0 ) temp = -temp;
        slen += temp;
        if ( (temp = spline->to->prevcp.y-spline->from->nextcp.y)<0 ) temp = -temp;
        slen += temp;
        if ( (temp = spline->to->me.x-spline->to->prevcp.x)<0 ) temp = -temp;
        slen += temp;
        if ( (temp = spline->to->me.y-spline->to->prevcp.y)<0 ) temp = -temp;
        slen += temp;
        len = (len + slen)/2;
    }
return( len );
}

double SplineLength(Spline *spline) {
    /* I ignore the constant term. It's just an unneeded addition */
    double len, t;
    double lastx = 0, lasty = 0;
    double curx, cury;

    len = 0;
    for ( t=1.0/128; t<=1.0001 ; t+=1.0/128 ) {
        curx = ((spline->splines[0].a*t+spline->splines[0].b)*t+spline->splines[0].c)*t;
        cury = ((spline->splines[1].a*t+spline->splines[1].b)*t+spline->splines[1].c)*t;
        len += sqrt( (curx-lastx)*(curx-lastx) + (cury-lasty)*(cury-lasty) );
        lastx = curx; lasty = cury;
    }
return( len );
}


static TPoint *SplinesFigureTPsBetween(SplinePoint *from, SplinePoint *to,
        int *tot) {
    int cnt, i, j, pcnt;
    double len, slen, lbase;
    SplinePoint *np;
    TPoint *tp;
    double _lens[10], *lens = _lens;
    int _cnts[10], *cnts = _cnts;
    /* I used just to give every spline 10 points. But that gave much more */
    /*  weight to small splines than to big ones */

    cnt = 0;
    for ( np = from->next->to; ; np = np->next->to ) {
        ++cnt;
        if ( np==to )
    break;
    }
    if ( cnt>10 ) {
        lens = galloc(cnt*sizeof(double));
        cnts = galloc(cnt*sizeof(int));
    }
    cnt = 0; len = 0;
    for ( np = from->next->to; ; np = np->next->to ) {
        lens[cnt] = SplineLenApprox(np->prev);
        len += lens[cnt];
        ++cnt;
        if ( np==to )
    break;
    }
    if ( len!=0 ) {
        pcnt = 0;
        for ( i=0; i<cnt; ++i ) {
            int pnts = rint( (10*cnt*lens[i])/len );
            if ( pnts<2 ) pnts = 2;
            cnts[i] = pnts;
            pcnt += pnts;
        }
    } else
        pcnt = 2*cnt;

    tp = galloc((pcnt+1)*sizeof(TPoint)); i = 0;
    if ( len==0 ) {
        for ( i=0; i<=pcnt; ++i ) {
            tp[i].t = i/(pcnt);
            tp[i].x = from->me.x;
            tp[i].y = from->me.y;
        }
    } else {
        lbase = 0;
        for ( i=cnt=0, np = from->next->to; ; np = np->next->to, ++cnt ) {
            slen = SplineLenApprox(np->prev);
            for ( j=0; j<cnts[cnt]; ++j ) {
                double t = j/(double) cnts[cnt];
                tp[i].t = (lbase+ t*slen)/len;
                tp[i].x = ((np->prev->splines[0].a*t+np->prev->splines[0].b)*t+np->prev->splines[0].c)*t + np->prev->splines[0].d;
                tp[i++].y = ((np->prev->splines[1].a*t+np->prev->splines[1].b)*t+np->prev->splines[1].c)*t + np->prev->splines[1].d;
            }
            lbase += slen;
            if ( np==to )
        break;
        }
    }
    if ( cnts!=_cnts ) free(cnts);
    if ( lens!=_lens ) free(lens);

    *tot = i;
        
return( tp );
}

static void SplinePointReCatagorize(SplinePoint *sp,int oldpt) {
    SplinePointCatagorize(sp);
    if ( sp->pointtype!=oldpt ) {
        if ( sp->pointtype==pt_curve && oldpt==pt_hvcurve &&
                ((sp->nextcp.x == sp->me.x && sp->nextcp.y != sp->me.y ) ||
                 (sp->nextcp.y == sp->me.y && sp->nextcp.x != sp->me.x )))
            sp->pointtype = pt_hvcurve;
    }
}

void SplinesRemoveBetween(SplineChar *sc, SplinePoint *from, SplinePoint *to,int type) {
    int tot;
    TPoint *tp;
    SplinePoint *np, oldfrom;
    int oldfpt = from->pointtype, oldtpt = to->pointtype;
    Spline *sp;
    int order2 = from->next->order2;

    oldfrom = *from;
    tp = SplinesFigureTPsBetween(from,to,&tot);

    if ( type==1 )
        ApproximateSplineFromPointsSlopes(from,to,tp,tot-1,order2);
    else
        ApproximateSplineFromPoints(from,to,tp,tot-1,order2);

    /* Have to do the frees after the approximation because the approx */
    /*  uses the splines to determine slopes */
    for ( sp = oldfrom.next; ; ) {
        np = sp->to;
        SplineFree(sp);
        if ( np==to )
    break;
        sp = np->next;
        SplinePointMDFree(sc,np);
    }
    
    free(tp);

    SplinePointReCatagorize(from,oldfpt);
    SplinePointReCatagorize(to,oldtpt);
}


static void RemoveStupidControlPoints(SplineSet *spl) {
    double len, normal, dir;
    Spline *s, *first;
    BasePoint unit, off;

    /* Also remove really stupid control points: Tiny offsets pointing in */
    /*  totally the wrong direction. Some of the TeX fonts we get have these */
    /* We get equally bad results with a control point that points beyond the */
    /*  other end point */
    first = NULL;
    for ( s = spl->first->next; s!=NULL && s!=first; s=s->to->next ) {
        unit.x = s->to->me.x-s->from->me.x;
        unit.y = s->to->me.y-s->from->me.y;
        len = sqrt(unit.x*unit.x+unit.y*unit.y);
        if ( len!=0 ) {
            int refigure = false;
            unit.x /= len; unit.y /= len;
            if ( !s->from->nonextcp ) {
                off.x = s->from->nextcp.x-s->from->me.x;
                off.y = s->from->nextcp.y-s->from->me.y;
                if ((normal = off.x*unit.y - off.y*unit.x)<0 ) normal = -normal;
                dir = off.x*unit.x + off.y*unit.y;
                if (( normal<dir && normal<1 && dir<0 ) || (normal<.5 && dir<-.5) ||
                        (normal<.1 && dir>len)) {
                    s->from->nextcp = s->from->me;
                    s->from->nonextcp = true;
                    refigure = true;
                }
            }
            if ( !s->to->noprevcp ) {
                off.x = s->to->me.x - s->to->prevcp.x;
                off.y = s->to->me.y - s->to->prevcp.y;
                if ((normal = off.x*unit.y - off.y*unit.x)<0 ) normal = -normal;
                dir = off.x*unit.x + off.y*unit.y;
                if (( normal<-dir && normal<1 && dir<0 ) || (normal<.5 && dir>-.5 && dir<0) ||
                        (normal<.1 && dir>len)) {
                    s->to->prevcp = s->to->me;
                    s->to->noprevcp = true;
                    refigure = true;
                }
            }
            if ( refigure )
                SplineRefigure(s);
        }
        if ( first==NULL ) first = s;
    }
}

void SSRemoveStupidControlPoints(SplineSet *base) {
    SplineSet *spl;

    for (spl=base; spl!=NULL; spl=spl->next )
        RemoveStupidControlPoints(spl);
}

static void OverlapClusterCpAngles(SplineSet *spl,double within) {
    double len, nlen, plen;
    double startoff, endoff;
    SplinePoint *sp, *nsp, *psp;
    BasePoint *nbp, *pbp;
    BasePoint pdir, ndir, fpdir, fndir;
    int nbad, pbad;

    /* If we have a junction point (right mid of 3) where the two splines */
    /*  are almost, but not quite moving in the same direction as they go */
    /*  away from the point, and if there is a tiny overlap because of this */
    /*  "almost" same, then we will probably get a bit confused in remove */
    /*  overlap */

    for ( sp = spl->first; ; ) {
        if ( sp->next==NULL )
    break;
        nsp = sp->next->to;
        if (( !sp->nonextcp || !sp->noprevcp ) && sp->prev!=NULL ) {
            psp = sp->prev->from; 
            nbp = !sp->nonextcp ? &sp->nextcp : !nsp->noprevcp ? &nsp->prevcp : &nsp->me;
            pbp = !sp->noprevcp ? &sp->prevcp : !psp->nonextcp ? &psp->nextcp : &psp->me;

            pdir.x = pbp->x-sp->me.x; pdir.y = pbp->y-sp->me.y;
            ndir.x = nbp->x-sp->me.x; ndir.y = nbp->y-sp->me.y;
            fpdir.x = psp->me.x-sp->me.x; fpdir.y = psp->me.y-sp->me.y;
            fndir.x = nsp->me.x-sp->me.x; fndir.y = nsp->me.y-sp->me.y;

            plen = sqrt(pdir.x*pdir.x+pdir.y*pdir.y);
            if ( plen!=0 ) {
                pdir.x /= plen; pdir.y /= plen;
            }

            nlen = sqrt(ndir.x*ndir.x+ndir.y*ndir.y);
            if ( nlen!=0 ) {
                ndir.x /= nlen; ndir.y /= nlen;
            }

            nbad = pbad = false;
            if ( !sp->nonextcp && plen!=0 && nlen!=0 ) {
                len = sqrt(fndir.x*fndir.x+fndir.y*fndir.y);
                if ( len!=0 ) {
                    fndir.x /= len; fndir.y /= len;
                    startoff = ndir.x*pdir.y - ndir.y*pdir.x;
                    endoff = fndir.x*pdir.y - fndir.y*pdir.x;
                    if (( (startoff<0 && endoff>0) || (startoff>0 && endoff<0)) &&
                            startoff > -within && startoff < within )
                        nbad = true;
                }
            }
            if ( !sp->noprevcp && plen!=0 && nlen!=0 ) {
                len = sqrt(fpdir.x*fpdir.x+fpdir.y*fpdir.y);
                if ( len!=0 ) {
                    fpdir.x /= len; fpdir.y /= len;
                    startoff = pdir.x*ndir.y - pdir.y*ndir.x;
                    endoff = fpdir.x*ndir.y - fpdir.y*ndir.x;
                    if (( (startoff<0 && endoff>0) || (startoff>0 && endoff<0)) &&
                            startoff > -within && startoff < within )
                        pbad = true;
                }
            }
            if ( nbad && pbad ) {
                if ( ndir.x==0 || ndir.y==0 )
                    nbad = false;
                else if ( pdir.x==0 || pdir.y==0 )
                    pbad = false;
            }
            if ( nbad && pbad ) {
                if ( ndir.x*pdir.x + ndir.y*pdir.y > 0 ) {
                    ndir.x = pdir.x = (ndir.x + pdir.x)/2;
                    ndir.y = pdir.y = (ndir.x + pdir.x)/2;
                } else {
                    ndir.x = (ndir.x - pdir.x)/2;
                    ndir.y = (ndir.y - pdir.y)/2;
                    pdir.x = -ndir.x; pdir.y = -ndir.y;
                }
                sp->nextcp.x = sp->me.x + nlen*ndir.x;
                sp->nextcp.y = sp->me.y + nlen*ndir.y;
                sp->prevcp.x = sp->me.x + plen*pdir.x;
                sp->prevcp.y = sp->me.y + plen*pdir.y;
                SplineRefigure(sp->next); SplineRefigure(sp->prev);
            } else if ( nbad ) {
                if ( ndir.x*pdir.x + ndir.y*pdir.y < 0 ) {
                    pdir.x = -pdir.x;
                    pdir.y = -pdir.y;
                }
                sp->nextcp.x = sp->me.x + nlen*pdir.x;
                sp->nextcp.y = sp->me.y + nlen*pdir.y;
                SplineRefigure(sp->next);
            } else if ( pbad ) {
                if ( ndir.x*pdir.x + ndir.y*pdir.y < 0 ) {
                    ndir.x = -ndir.x;
                    ndir.y = -ndir.y;
                }
                sp->prevcp.x = sp->me.x + plen*ndir.x;
                sp->prevcp.y = sp->me.y + plen*ndir.y;
                SplineRefigure(sp->prev);
            }
        }
        if ( nsp==spl->first )
    break;
        sp = nsp;
    }
}

void SSOverlapClusterCpAngles(SplineSet *base,double within) {
    SplineSet *spl;

    for (spl=base; spl!=NULL; spl=spl->next )
        OverlapClusterCpAngles(spl,within);
}


Spline *SplineAddExtrema(Spline *s,int always,real lenbound, real offsetbound,
        DBounds *b) {
    /* First find the extrema, if any */
    bigreal t[4], min;
    uint8 rmfrom[4], rmto[4];
    int p, i,j, p_s, mini;
    SplinePoint *sp;
    real len = 0; /* Init variable to silence compiler warnings */

    if ( !always ) {
        real xlen, ylen;
        xlen = (s->from->me.x-s->to->me.x);
        ylen = (s->from->me.y-s->to->me.y);
        len = xlen*xlen + ylen*ylen;
        lenbound *= lenbound;
        if ( len < lenbound ) {
            len = SplineLength(s);
            len *= len;
        }
    }

    memset(rmfrom,0,sizeof(rmfrom));
    memset(rmto,0,sizeof(rmto));

    forever {
        if ( s->knownlinear )
return(s);
        p = 0;
        if ( s->splines[0].a!=0 ) {
            double d = 4*s->splines[0].b*s->splines[0].b-4*3*s->splines[0].a*s->splines[0].c;
            if ( d>0 ) {
                d = sqrt(d);
                t[p++] = CheckExtremaForSingleBitErrors(&s->splines[0],(-2*s->splines[0].b+d)/(2*3*s->splines[0].a));
                t[p++] = CheckExtremaForSingleBitErrors(&s->splines[0],(-2*s->splines[0].b-d)/(2*3*s->splines[0].a));
            }
        } else if ( s->splines[0].b!=0 )
            t[p++] = -s->splines[0].c/(2*s->splines[0].b);
        if ( !always ) {
            /* Generally we are only interested in extrema on long splines, or */
            /* extrema which are extrema for the entire contour, not just this */
            /* spline */
            /* Also extrema which are very close to one of the end-points can */
            /*  be ignored. */
            /* No they can't. But we need to remove the original point in this*/
            /*  case */
            for ( i=0; i<p; ++i ) {
                real x = ((s->splines[0].a*t[i]+s->splines[0].b)*t[i]+s->splines[0].c)*t[i]+s->splines[0].d;
                real y = ((s->splines[1].a*t[i]+s->splines[1].b)*t[i]+s->splines[1].c)*t[i]+s->splines[1].d;
                int close_from = ( x-s->from->me.x<offsetbound && x-s->from->me.x>-offsetbound) &&
                                ( y-s->from->me.y<10*offsetbound && y-s->from->me.y>-10*offsetbound );
                int close_to = ( x-s->to->me.x<offsetbound && x-s->to->me.x>-offsetbound) &&
                                ( y-s->to->me.y<10*offsetbound && y-s->to->me.y>-10*offsetbound );
                int remove_from = close_from  && GoodCurve(s->from,true);
                int remove_to = close_to  && GoodCurve(s->to,false);
                if (( x>b->minx && x<b->maxx  && len<lenbound ) ||
                        (close_from && !remove_from) || (close_to && !remove_to) ) {
                    --p;
                    for ( j=i; j<p; ++j )
                        t[j] = t[j+1];
                    --i;
                } else {
                    rmfrom[i] = remove_from;
                    rmto[i] = remove_to;
                }
            }
        }

        p_s = p;
        if ( s->splines[1].a!=0 ) {
            double d = 4*s->splines[1].b*s->splines[1].b-4*3*s->splines[1].a*s->splines[1].c;
            if ( d>0 ) {
                d = sqrt(d);
                t[p++] = CheckExtremaForSingleBitErrors(&s->splines[1],(-2*s->splines[1].b+d)/(2*3*s->splines[1].a));
                t[p++] = CheckExtremaForSingleBitErrors(&s->splines[1],(-2*s->splines[1].b-d)/(2*3*s->splines[1].a));
            }
        } else if ( s->splines[1].b!=0 )
            t[p++] = -s->splines[1].c/(2*s->splines[1].b);
        if ( !always ) {
            for ( i=p_s; i<p; ++i ) {
                real x = ((s->splines[0].a*t[i]+s->splines[0].b)*t[i]+s->splines[0].c)*t[i]+s->splines[0].d;
                real y = ((s->splines[1].a*t[i]+s->splines[1].b)*t[i]+s->splines[1].c)*t[i]+s->splines[1].d;
                int close_from =( y-s->from->me.y<offsetbound && y-s->from->me.y>-offsetbound ) &&
                        ( x-s->from->me.x<offsetbound && x-s->from->me.x>-offsetbound);
                int close_to = ( y-s->to->me.y<offsetbound && y-s->to->me.y>-offsetbound ) &&
                        ( x-s->to->me.x<offsetbound && x-s->to->me.x>-offsetbound);
                int remove_from = close_from  && GoodCurve(s->from,true);
                int remove_to = close_to  && GoodCurve(s->to,false);
                if (( y>b->miny && y<b->maxy && len<lenbound ) ||
                        (close_from && !remove_from) || (close_to && !remove_to) ) {
                    --p;
                    for ( j=i; j<p; ++j )
                        t[j] = t[j+1];
                    --i;
                } else {
                    rmfrom[i] = remove_from;
                    rmto[i] = remove_to;
                }
            }
        }

        /* Throw out any t values which are not between 0 and 1 */
        /*  (we do a little fudging near the endpoints so we don't get confused */
        /*   by rounding errors) */
        for ( i=0; i<p; ++i ) {
            if ( t[i]>0 && t[i]<.05 ) {
                BasePoint test;
                /* Expand strong gets very confused on zero-length splines so */
                /*  don't let that happen */
                test.x = ((s->splines[0].a*t[i]+s->splines[0].b)*t[i]+s->splines[0].c)*t[i]+s->splines[0].d;
                test.y = ((s->splines[1].a*t[i]+s->splines[1].b)*t[i]+s->splines[1].c)*t[i]+s->splines[1].d;
                if ( test.x== s->from->me.x && test.y==s->from->me.y )
                    t[i] = 0;           /* Throw it out */
            }
            if ( t[i]<1 && t[i]>.95 ) {
                BasePoint test;
                test.x = ((s->splines[0].a*t[i]+s->splines[0].b)*t[i]+s->splines[0].c)*t[i]+s->splines[0].d;
                test.y = ((s->splines[1].a*t[i]+s->splines[1].b)*t[i]+s->splines[1].c)*t[i]+s->splines[1].d;
                if ( test.x== s->to->me.x && test.y==s->to->me.y )
                    t[i] = 1.0;         /* Throw it out */
            }
                
            if ( t[i]<.0001 || t[i]>.9999 ) {
                --p;
                for ( j=i; j<p; ++j ) {
                    t[j] = t[j+1];
                    rmfrom[j] = rmfrom[j+1];
                    rmto[j] = rmto[j+1];
                }
                --i;
            }
        }

        if ( p==0 )
return(s);

        /* Find the smallest of all the interesting points */
        min = t[0]; mini = 0;
        for ( i=1; i<p; ++i ) {
            if ( t[i]<min ) {
                min=t[i];
                mini = i;
            }
        }
        sp = SplineBisect(s,min);
/* On the mac we get rounding errors in the bisect routine */
        { double dx, dy;
            if ( (dx = sp->me.x - sp->prevcp.x)<0 ) dx=-dx;
            if ( (dy = sp->me.y - sp->prevcp.y)<0 ) dy=-dy;
            if ( dx!=0 && dy!=0 ) {
                if ( dx<dy )
                    sp->prevcp.x = sp->me.x;
                else
                    sp->prevcp.y = sp->me.y;
            }
            if ( (dx = sp->me.x - sp->nextcp.x)<0 ) dx=-dx;
            if ( (dy = sp->me.y - sp->nextcp.y)<0 ) dy=-dy;
            if ( dx!=0 && dy!=0 ) {
                if ( dx<dy )
                    sp->nextcp.x = sp->me.x;
                else
                    sp->nextcp.y = sp->me.y;
            }
        }

        if ( rmfrom[mini] ) sp->prev->from->ticked = true;
        if ( rmto[mini] ) sp->next->to->ticked = true;
        s = sp->next;
        if ( p==1 )
return( s );
        /* Don't try to use any other computed t values, it is easier to */
        /*  recompute them than to try and figure out what they map to on the */
        /*  new spline */
    }
}

void SplineSetAddExtrema(SplineChar *sc, SplineSet *ss,enum ae_type between_selected, int emsize) {
    Spline *s, *first;
    DBounds b;
    int always = true;
    real lenbound = 0;
    real offsetbound=0;
    SplinePoint *sp, *nextp;

    if ( between_selected==ae_only_good ) {
        SplineSetQuickBounds(ss,&b);
        lenbound = (emsize)/32.0;
        always = false;
        offsetbound = .5;
        between_selected = ae_only_good_rm_later;
        for ( sp = ss->first; ; ) {
            sp->ticked = false;
            if ( sp->next==NULL )
        break;
            sp = sp->next->to;
            if ( sp==ss->first )
        break;
        }
    }

    first = NULL;
    for ( s = ss->first->next; s!=NULL && s!=first; s = s->to->next ) {
        if ( between_selected!=ae_between_selected ||
                (s->from->selected && s->to->selected))
            s = SplineAddExtrema(s,always,lenbound,offsetbound,&b);
        if ( first==NULL ) first = s;
    }
    if ( between_selected == ae_only_good_rm_later ) {
        for ( sp = ss->first; ; ) {
            if ( sp->next==NULL )
        break;
            nextp = sp->next->to;
            if ( sp->ticked ) {
                if ( sp==ss->first )
                    ss->first = ss->last = nextp;
                SplinesRemoveBetween(sc,sp->prev->from,nextp,1);
            }
            sp = nextp;
            if ( sp==ss->first )
        break;
        }
    }
}


char *GetNextUntitledName(void) {
    static int untitled_cnt=1;
    char buffer[80];

    sprintf( buffer, "Untitled%d", untitled_cnt++ );
return( copy(buffer));
}

SplineFont *SplineFontEmpty(void) {
    extern int default_fv_row_count, default_fv_col_count;
    time_t now;
    SplineFont *sf;

    sf = gcalloc(1,sizeof(SplineFont));
    sf->pfminfo.fstype = -1;
    sf->top_enc = -1;
    sf->macstyle = -1;
    sf->desired_row_cnt = default_fv_row_count; sf->desired_col_cnt = default_fv_col_count;
    sf->display_antialias = default_fv_antialias;
    sf->display_bbsized = default_fv_bbsized;
    sf->display_size = -default_fv_font_size;
    sf->display_layer = ly_fore;
    sf->pfminfo.winascent_add = sf->pfminfo.windescent_add = true;
    sf->pfminfo.hheadascent_add = sf->pfminfo.hheaddescent_add = true;
    sf->pfminfo.typoascent_add = sf->pfminfo.typodescent_add = true;
    if ( TTFFoundry!=NULL )
        strncpy(sf->pfminfo.os2_vendor,TTFFoundry,4);
    else
        memcpy(sf->pfminfo.os2_vendor,"PfEd",4);
    sf->for_new_glyphs = DefaultNameListForNewFonts();
    time(&now);
    sf->creationtime = sf->modificationtime = now;

    sf->layer_cnt = 2;
    sf->layers = gcalloc(2,sizeof(LayerInfo));
    sf->layers[0].name = copy(_("Back"));
    sf->layers[0].background = true;
    sf->layers[1].name = copy(_("Fore"));
    sf->layers[1].background = false;
    sf->grid.background = true;

return( sf );
}


static void SFChangeXUID(SplineFont *sf, int random) {
    char *pt, *new, *npt;
    int val;

    if ( sf->xuid==NULL )
return;
    pt = strrchr(sf->xuid,' ');
    if ( pt==NULL )
        pt = strchr(sf->xuid,'[');
    if ( pt==NULL )
        pt = sf->xuid;
    else
        ++pt;
    if ( random )
        val = rand()&0xffffff;
    else {
        val = strtol(pt,NULL,10);
        val = (val+1)&0xffffff;
    }

    new = galloc(pt-sf->xuid+12);
    strncpy(new,sf->xuid,pt-sf->xuid);
    npt = new + (pt-sf->xuid);
    if ( npt==new ) *npt++ = '[';
    sprintf(npt, "%d]", val );
    free(sf->xuid); sf->xuid = new;
    sf->changed = true;
    sf->changed_since_xuidchanged = false;
}

void SFIncrementXUID(SplineFont *sf) {
    SFChangeXUID(sf,false);
}

void SFRandomChangeXUID(SplineFont *sf) {
    SFChangeXUID(sf,true);
}

void SPWeightedAverageCps(SplinePoint *sp) {
    double pangle, nangle, angle, plen, nlen, c, s;
    if ( sp->noprevcp || sp->nonextcp )
        /*SPAverageCps(sp)*/;           /* Expand Stroke wants this case to hold still */
    else if (( sp->pointtype==pt_curve || sp->pointtype==pt_hvcurve) &&
            sp->prev && sp->next ) {
        pangle = atan2(sp->me.y-sp->prevcp.y,sp->me.x-sp->prevcp.x);
        nangle = atan2(sp->nextcp.y-sp->me.y,sp->nextcp.x-sp->me.x);
        if ( pangle<0 && nangle>0 && nangle-pangle>=3.1415926 )
            pangle += 2*3.1415926535897932;
        else if ( pangle>0 && nangle<0 && pangle-nangle>=3.1415926 )
            nangle += 2*3.1415926535897932;
        plen = sqrt((sp->me.y-sp->prevcp.y)*(sp->me.y-sp->prevcp.y) +
                (sp->me.x-sp->prevcp.x)*(sp->me.x-sp->prevcp.x));
        nlen = sqrt((sp->nextcp.y-sp->me.y)*(sp->nextcp.y-sp->me.y) +
                (sp->nextcp.x-sp->me.x)*(sp->nextcp.x-sp->me.x));
        if ( plen+nlen==0 )
            angle = (nangle+pangle)/2;
        else
            angle = (plen*pangle + nlen*nangle)/(plen+nlen);
        plen = -plen;
        c = cos(angle); s=sin(angle);
        sp->nextcp.x = c*nlen + sp->me.x;
        sp->nextcp.y = s*nlen + sp->me.y;
        sp->prevcp.x = c*plen + sp->me.x;
        sp->prevcp.y = s*plen + sp->me.y;
        SplineRefigure(sp->prev);
        SplineRefigure(sp->next);
    } else
        SPAverageCps(sp);
}

void SPAverageCps(SplinePoint *sp) {
    double pangle, nangle, angle, plen, nlen, c, s;
    if (( sp->pointtype==pt_curve || sp->pointtype==pt_hvcurve) &&
            sp->prev && sp->next ) {
        if ( sp->noprevcp )
            pangle = atan2(sp->me.y-sp->prev->from->me.y,sp->me.x-sp->prev->from->me.x);
        else
            pangle = atan2(sp->me.y-sp->prevcp.y,sp->me.x-sp->prevcp.x);
        if ( sp->nonextcp )
            nangle = atan2(sp->next->to->me.y-sp->me.y,sp->next->to->me.x-sp->me.x);
        else
            nangle = atan2(sp->nextcp.y-sp->me.y,sp->nextcp.x-sp->me.x);
        if ( pangle<0 && nangle>0 && nangle-pangle>=3.1415926 )
            pangle += 2*3.1415926535897932;
        else if ( pangle>0 && nangle<0 && pangle-nangle>=3.1415926 )
            nangle += 2*3.1415926535897932;
        angle = (nangle+pangle)/2;
        plen = -sqrt((sp->me.y-sp->prevcp.y)*(sp->me.y-sp->prevcp.y) +
                (sp->me.x-sp->prevcp.x)*(sp->me.x-sp->prevcp.x));
        nlen = sqrt((sp->nextcp.y-sp->me.y)*(sp->nextcp.y-sp->me.y) +
                (sp->nextcp.x-sp->me.x)*(sp->nextcp.x-sp->me.x));
        c = cos(angle); s=sin(angle);
        sp->nextcp.x = c*nlen + sp->me.x;
        sp->nextcp.y = s*nlen + sp->me.y;
        sp->prevcp.x = c*plen + sp->me.x;
        sp->prevcp.y = s*plen + sp->me.y;
        SplineRefigure(sp->prev);
        SplineRefigure(sp->next);
    } else if ( sp->pointtype==pt_tangent && sp->prev && sp->next ) {
        if ( !sp->noprevcp ) {
            nangle = atan2(sp->next->to->me.y-sp->me.y,sp->next->to->me.x-sp->me.x);
            plen = -sqrt((sp->me.y-sp->prevcp.y)*(sp->me.y-sp->prevcp.y) +
                    (sp->me.x-sp->prevcp.x)*(sp->me.x-sp->prevcp.x));
            c = cos(nangle); s=sin(nangle);
            sp->prevcp.x = c*plen + sp->me.x;
            sp->prevcp.y = s*plen + sp->me.y;
        SplineRefigure(sp->prev);
        }
        if ( !sp->nonextcp ) {
            pangle = atan2(sp->me.y-sp->prev->from->me.y,sp->me.x-sp->prev->from->me.x);
            nlen = sqrt((sp->nextcp.y-sp->me.y)*(sp->nextcp.y-sp->me.y) +
                    (sp->nextcp.x-sp->me.x)*(sp->nextcp.x-sp->me.x));
            c = cos(pangle); s=sin(pangle);
            sp->nextcp.x = c*nlen + sp->me.x;
            sp->nextcp.y = s*nlen + sp->me.y;
            SplineRefigure(sp->next);
        }
    }
}


void SplineCharTangentNextCP(SplinePoint *sp) {
    double len;
    BasePoint *bp, unit;
    extern int snaptoint;

    if ( sp->prev==NULL )
return;
    bp = &sp->prev->from->me;

    unit.y = sp->me.y-bp->y; unit.x = sp->me.x-bp->x;
    len = sqrt( unit.x*unit.x + unit.y*unit.y );
    if ( len!=0 ) {
        unit.x /= len;
        unit.y /= len;
    }
    len = sqrt((sp->nextcp.y-sp->me.y)*(sp->nextcp.y-sp->me.y) + (sp->nextcp.x-sp->me.x)*(sp->nextcp.x-sp->me.x));
    sp->nextcp.x = sp->me.x + len*unit.x;
    sp->nextcp.y = sp->me.y + len*unit.y;
    if ( snaptoint ) {
        sp->nextcp.x = rint(sp->nextcp.x);
        sp->nextcp.y = rint(sp->nextcp.y);
    } else {
        sp->nextcp.x = rint(sp->nextcp.x*1024)/1024;
        sp->nextcp.y = rint(sp->nextcp.y*1024)/1024;
    }
    if ( sp->next!=NULL && sp->next->order2 )
        sp->next->to->prevcp = sp->nextcp;
}

void SplineCharTangentPrevCP(SplinePoint *sp) {
    double len;
    BasePoint *bp, unit;
    extern int snaptoint;

    if ( sp->next==NULL )
return;
    bp = &sp->next->to->me;

    unit.y = sp->me.y-bp->y; unit.x = sp->me.x-bp->x;
    len = sqrt( unit.x*unit.x + unit.y*unit.y );
    if ( len!=0 ) {
        unit.x /= len;
        unit.y /= len;
    }
    len = sqrt((sp->prevcp.y-sp->me.y)*(sp->prevcp.y-sp->me.y) + (sp->prevcp.x-sp->me.x)*(sp->prevcp.x-sp->me.x));
    sp->prevcp.x = sp->me.x + len*unit.x;
    sp->prevcp.y = sp->me.y + len*unit.y;
    if ( snaptoint ) {
        sp->prevcp.x = rint(sp->prevcp.x);
        sp->prevcp.y = rint(sp->prevcp.y);
    } else {
        sp->prevcp.x = rint(sp->prevcp.x*1024)/1024;
        sp->prevcp.y = rint(sp->prevcp.y*1024)/1024;
    }
    if ( sp->prev!=NULL && sp->prev->order2 )
        sp->prev->from->nextcp = sp->prevcp;
}

static void BP_HVForce(BasePoint *vector) {
    /* Force vector to be horizontal/vertical */
    double dx, dy, len;

    if ( (dx= vector->x)<0 ) dx = -dx;
    if ( (dy= vector->y)<0 ) dy = -dy;
    if ( dx==0 || dy==0 )
return;
    len = sqrt(dx*dx + dy*dy);
    if ( dx>dy ) {
        vector->x = vector->x<0 ? -len : len;
        vector->y = 0;
    } else {
        vector->y = vector->y<0 ? -len : len;
        vector->x = 0;
    }
}
    
#define NICE_PROPORTION .39
void SplineCharDefaultNextCP(SplinePoint *base) {
    SplinePoint *prev=NULL, *next;
    double len, plen, ulen;
    BasePoint unit;
    extern int snaptoint;

    if ( base->next==NULL )
return;
    if ( base->next->order2 ) {
        SplineRefigureFixup(base->next);
return;
    }
    if ( !base->nextcpdef ) {
        if ( base->pointtype==pt_tangent )
            SplineCharTangentNextCP(base);
return;
    }
    next = base->next->to;
    if ( base->prev!=NULL )
        prev = base->prev->from;

    len = NICE_PROPORTION * sqrt((base->me.x-next->me.x)*(base->me.x-next->me.x) +
            (base->me.y-next->me.y)*(base->me.y-next->me.y));
    unit.x = next->me.x - base->me.x;
    unit.y = next->me.y - base->me.y;
    ulen = sqrt(unit.x*unit.x + unit.y*unit.y);
    if ( ulen!=0 )
        unit.x /= ulen, unit.y /= ulen;
    base->nonextcp = false;

    if ( base->pointtype == pt_curve || base->pointtype == pt_hvcurve ) {
        if ( prev!=NULL && (base->prevcpdef || base->noprevcp)) {
            unit.x = next->me.x - prev->me.x;
            unit.y = next->me.y - prev->me.y;
            ulen = sqrt(unit.x*unit.x + unit.y*unit.y);
            if ( ulen!=0 )
                unit.x /= ulen, unit.y /= ulen;
            if ( base->pointtype == pt_hvcurve )
                BP_HVForce(&unit);
            plen = sqrt((base->prevcp.x-base->me.x)*(base->prevcp.x-base->me.x) +
                    (base->prevcp.y-base->me.y)*(base->prevcp.y-base->me.y));
            base->prevcp.x = base->me.x - plen*unit.x;
            base->prevcp.y = base->me.y - plen*unit.y;
            if ( snaptoint ) {
                base->prevcp.x = rint(base->prevcp.x);
                base->prevcp.y = rint(base->prevcp.y);
            }
            SplineRefigureFixup(base->prev);
        } else if ( prev!=NULL ) {
            /* The prev control point is fixed. So we've got to use the same */
            /*  angle it uses */
            unit.x = base->me.x-base->prevcp.x;
            unit.y = base->me.y-base->prevcp.y;
            ulen = sqrt(unit.x*unit.x + unit.y*unit.y);
            if ( ulen!=0 )
                unit.x /= ulen, unit.y /= ulen;
        } else {
            base->prevcp = base->me;
            base->noprevcp = true;
            base->prevcpdef = true;
        }
        if ( base->pointtype == pt_hvcurve )
            BP_HVForce(&unit);
    } else if ( base->pointtype == pt_corner ) {
        if ( next->pointtype != pt_curve && next->pointtype != pt_hvcurve ) {
            base->nonextcp = true;
        }
    } else /* tangent */ {
        if ( next->pointtype != pt_curve ) {
            base->nonextcp = true;
        } else {
            if ( prev!=NULL ) {
                if ( !base->noprevcp ) {
                    plen = sqrt((base->prevcp.x-base->me.x)*(base->prevcp.x-base->me.x) +
                            (base->prevcp.y-base->me.y)*(base->prevcp.y-base->me.y));
                    base->prevcp.x = base->me.x - plen*unit.x;
                    base->prevcp.y = base->me.y - plen*unit.y;
                    SplineRefigureFixup(base->prev);
                }
                unit.x = base->me.x-prev->me.x;
                unit.y = base->me.y-prev->me.y;
                ulen = sqrt(unit.x*unit.x + unit.y*unit.y);
                if ( ulen!=0 )
                    unit.x /= ulen, unit.y /= ulen;
            }
        }
    }
    if ( base->nonextcp )
        base->nextcp = base->me;
    else {
        base->nextcp.x = base->me.x + len*unit.x;
        base->nextcp.y = base->me.y + len*unit.y;
        if ( snaptoint ) {
            base->nextcp.x = rint(base->nextcp.x);
            base->nextcp.y = rint(base->nextcp.y);
        } else {
            base->nextcp.x = rint(base->nextcp.x*1024)/1024;
            base->nextcp.y = rint(base->nextcp.y*1024)/1024;
        }
        if ( base->next != NULL )
            SplineRefigureFixup(base->next);
    }
}

void SplineCharDefaultPrevCP(SplinePoint *base) {
    SplinePoint *next=NULL, *prev;
    double len, nlen, ulen;
    BasePoint unit;
    extern int snaptoint;

    if ( base->prev==NULL )
return;
    if ( base->prev->order2 ) {
        SplineRefigureFixup(base->prev);
return;
    }
    if ( !base->prevcpdef ) {
        if ( base->pointtype==pt_tangent )
            SplineCharTangentPrevCP(base);
return;
    }
    prev = base->prev->from;
    if ( base->next!=NULL )
        next = base->next->to;

    len = NICE_PROPORTION * sqrt((base->me.x-prev->me.x)*(base->me.x-prev->me.x) +
            (base->me.y-prev->me.y)*(base->me.y-prev->me.y));
    unit.x = prev->me.x - base->me.x;
    unit.y = prev->me.y - base->me.y;
    ulen = sqrt(unit.x*unit.x + unit.y*unit.y);
    if ( ulen!=0 )
        unit.x /= ulen, unit.y /= ulen;
    base->noprevcp = false;

    if ( base->pointtype == pt_curve || base->pointtype == pt_hvcurve ) {
        if ( next!=NULL && (base->nextcpdef || base->nonextcp)) {
            unit.x = prev->me.x - next->me.x;
            unit.y = prev->me.y - next->me.y;
            ulen = sqrt(unit.x*unit.x + unit.y*unit.y);
            if ( ulen!=0 ) 
                unit.x /= ulen, unit.y /= ulen;
            if ( base->pointtype == pt_hvcurve )
                BP_HVForce(&unit);
            nlen = sqrt((base->nextcp.x-base->me.x)*(base->nextcp.x-base->me.x) +
                    (base->nextcp.y-base->me.y)*(base->nextcp.y-base->me.y));
            base->nextcp.x = base->me.x - nlen*unit.x;
            base->nextcp.y = base->me.y - nlen*unit.y;
            if ( snaptoint ) {
                base->nextcp.x = rint(base->nextcp.x);
                base->nextcp.y = rint(base->nextcp.y);
            }
            SplineRefigureFixup(base->next);
        } else if ( next!=NULL ) {
            /* The next control point is fixed. So we got to use the same */
            /*  angle it uses */
            unit.x = base->me.x-base->nextcp.x;
            unit.y = base->me.y-base->nextcp.y;
            ulen = sqrt(unit.x*unit.x + unit.y*unit.y);
            if ( ulen!=0 )
                unit.x /= ulen, unit.y /= ulen;
        } else {
            base->nextcp = base->me;
            base->nonextcp = true;
            base->nextcpdef = true;
        }
        if ( base->pointtype == pt_hvcurve )
            BP_HVForce(&unit);
    } else if ( base->pointtype == pt_corner ) {
        if ( prev->pointtype != pt_curve && prev->pointtype != pt_hvcurve ) {
            base->noprevcp = true;
        }
    } else /* tangent */ {
        if ( prev->pointtype != pt_curve ) {
            base->noprevcp = true;
        } else {
            if ( next!=NULL ) {
                if ( !base->nonextcp ) {
                    nlen = sqrt((base->nextcp.x-base->me.x)*(base->nextcp.x-base->me.x) +
                            (base->nextcp.y-base->me.y)*(base->nextcp.y-base->me.y));
                    base->nextcp.x = base->me.x - nlen*unit.x;
                    base->nextcp.y = base->me.y - nlen*unit.y;
                    SplineRefigureFixup(base->next);
                }
                unit.x = base->me.x-next->me.x;
                unit.y = base->me.y-next->me.y;
                ulen = sqrt(unit.x*unit.x + unit.y*unit.y);
                if ( ulen!=0 )
                    unit.x /= ulen, unit.y /= ulen;
            }
        }
    }
    if ( base->noprevcp )
        base->prevcp = base->me;
    else {
        base->prevcp.x = base->me.x + len*unit.x;
        base->prevcp.y = base->me.y + len*unit.y;
        if ( snaptoint ) {
            base->prevcp.x = rint(base->prevcp.x);
            base->prevcp.y = rint(base->prevcp.y);
        } else {
            base->prevcp.x = rint(base->prevcp.x*1024)/1024;
            base->prevcp.y = rint(base->prevcp.y*1024)/1024;
        }
        if ( base->prev!=NULL )
            SplineRefigureFixup(base->prev);
    }
}


SplineSet *SplineSetReverse(SplineSet *spl) {
    Spline *spline, *first, *next;
    BasePoint tp;
    SplinePoint *temp;
    int bool;
    /* reverse the splineset so that what was the start point becomes the end */
    /*  and vice versa. This entails reversing every individual spline, and */
    /*  each point */

    first = NULL;
    spline = spl->first->next;
    if ( spline==NULL )
return( spl );                  /* Only one point, reversal is meaningless */

    tp = spline->from->nextcp;
    spline->from->nextcp = spline->from->prevcp;
    spline->from->prevcp = tp;
    bool = spline->from->nonextcp;
    spline->from->nonextcp = spline->from->noprevcp;
    spline->from->noprevcp = bool;
    bool = spline->from->nextcpdef;
    spline->from->nextcpdef = spline->from->prevcpdef;
    spline->from->prevcpdef = bool;

    for ( ; spline!=NULL && spline!=first; spline=next ) {
        next = spline->to->next;

        if ( spline->to!=spl->first ) {         /* On a closed spline don't want to reverse the first point twice */
            tp = spline->to->nextcp;
            spline->to->nextcp = spline->to->prevcp;
            spline->to->prevcp = tp;
            bool = spline->to->nonextcp;
            spline->to->nonextcp = spline->to->noprevcp;
            spline->to->noprevcp = bool;
            bool = spline->to->nextcpdef;
            spline->to->nextcpdef = spline->to->prevcpdef;
            spline->to->prevcpdef = bool;
        }

        temp = spline->to;
        spline->to = spline->from;
        spline->from = temp;
        spline->from->next = spline;
        spline->to->prev = spline;
        SplineRefigure(spline);
        if ( first==NULL ) first = spline;
    }

    if ( spl->first!=spl->last ) {
        temp = spl->first;
        spl->first = spl->last;
        spl->last = temp;
        spl->first->prev = NULL;
        spl->last->next = NULL;
    }

return( spl );
}

static void SplineSetsUntick(SplineSet *spl) {
    Spline *spline, *first;
    
    while ( spl!=NULL ) {
        first = NULL;
        spl->first->isintersection = false;
        for ( spline=spl->first->next; spline!=first && spline!=NULL; spline = spline->to->next ) {
            spline->isticked = false;
            spline->isneeded = false;
            spline->isunneeded = false;
            spline->ishorvert = false;
            spline->to->isintersection = false;
            if ( first==NULL ) first = spline;
        }
        spl = spl->next;
    }
}

static void SplineSetTick(SplineSet *spl) {
    Spline *spline, *first;
    
    first = NULL;
    for ( spline=spl->first->next; spline!=first && spline!=NULL; spline = spline->to->next ) {
        spline->isticked = true;
        if ( first==NULL ) first = spline;
    }
}

static SplineSet *SplineSetOfSpline(SplineSet *spl,Spline *search) {
    Spline *spline, *first;
    
    while ( spl!=NULL ) {
        first = NULL;
        for ( spline=spl->first->next; spline!=first && spline!=NULL; spline = spline->to->next ) {
            if ( spline==search )
return( spl );
            if ( first==NULL ) first = spline;
        }
        spl = spl->next;
    }
return( NULL );
}

static int SplineInSplineSet(Spline *spline, SplineSet *spl) {
    Spline *first, *s;

    first = NULL;
    for ( s = spl->first->next; s!=NULL && s!=first; s = s->to->next ) {
        if ( s==spline )
return( true );
        if ( first==NULL ) first = s;
    }
return( false );
}

#include "edgelist.h"

static void EdgeListReverse(EdgeList *es, SplineSet *spl) {
    int i;

    if ( es->edges!=NULL ) {
        for ( i=0; i<es->cnt; ++i ) {
            Edge *e;
            for ( e = es->edges[i]; e!=NULL; e = e->esnext ) {
                if ( SplineInSplineSet(e->spline,spl)) {
                    e->up = !e->up;
                    e->t_mmin = 1-e->t_mmin;
                    e->t_mmax = 1-e->t_mmax;
                    e->t_cur = 1-e->t_cur;
                }
            }
        }
    }
}

static int SSCheck(SplineSet *base,Edge *active, int up, EdgeList *es,int *changed) {
    SplineSet *spl;
    if ( active->spline->isticked )
return( 0 );
    spl = SplineSetOfSpline(base,active->spline);
    if ( active->up!=up ) {
        SplineSetReverse(spl);
        *changed = true;
        EdgeListReverse(es,spl);
    }
    SplineSetTick(spl);
return( 1 );
}


/* The idea behind SplineSetsCorrect is simple. However there are many splinesets */
/*  where it is impossible, so bear in mind that this only works for nice */
/*  splines. Figure 8's, interesecting splines all cause problems */
/* The outermost spline should be clockwise (up), the next splineset we find */
/*  should be down, if it isn't reverse it (if it's already been dealt with */
/*  then ignore it) */
SplineSet *SplineSetsCorrect(SplineSet *base,int *changed) {
    SplineSet *spl;
    int sscnt, check_cnt;
    EdgeList es;
    DBounds b;
    Edge *active=NULL, *apt, *pr, *e;
    int i, winding;

    *changed = false;

    SplineSetsUntick(base);
    for (sscnt=0,spl=base; spl!=NULL; spl=spl->next, ++sscnt );

    SplineSetFindBounds(base,&b);
    memset(&es,'\0',sizeof(es));
    es.scale = 1.0;
    es.mmin = floor(b.miny*es.scale);
    es.mmax = ceil(b.maxy*es.scale);
    es.omin = b.minx*es.scale;
    es.omax = b.maxx*es.scale;
    es.layer = ly_fore;         /* Not meaningful */

/* Give up if we are given unreasonable values (ie. if rounding errors might screw us up) */
    if ( es.mmin<1e5 && es.mmax>-1e5 && es.omin<1e5 && es.omax>-1e5 ) {
        es.cnt = (int) (es.mmax-es.mmin) + 1;
        es.edges = gcalloc(es.cnt,sizeof(Edge *));
        es.interesting = gcalloc(es.cnt,sizeof(char));
        es.sc = NULL;
        es.major = 1; es.other = 0;
        FindEdgesSplineSet(base,&es,false);

        check_cnt = 0;
        for ( i=0; i<es.cnt && check_cnt<sscnt; ++i ) {
            active = ActiveEdgesRefigure(&es,active,i);
            if ( es.edges[i]!=NULL )
        continue;                       /* Just too hard to get the edges sorted when we are at a start vertex */
            if ( /*es.edges[i]==NULL &&*/ !es.interesting[i] &&
                    !(i>0 && es.interesting[i-1]) && !(i>0 && es.edges[i-1]!=NULL) &&
                    !(i<es.cnt-1 && es.edges[i+1]!=NULL) &&
                    !(i<es.cnt-1 && es.interesting[i+1]))       /* interesting things happen when we add (or remove) entries */
        continue;                       /* and where we have extrema */
            for ( apt=active; apt!=NULL; apt = e) {
                check_cnt += SSCheck(base,apt,true,&es,changed);
                winding = apt->up?1:-1;
                for ( pr=apt, e=apt->aenext; e!=NULL && winding!=0; pr=e, e=e->aenext ) {
                    if ( !e->spline->isticked )
                        check_cnt += SSCheck(base,e,winding<0,&es,changed);
                    if ( pr->up!=e->up )
                        winding += (e->up?1:-1);
                    else if ( (pr->before==e || pr->after==e ) &&
                            (( pr->mmax==i && e->mmin==i ) ||
                             ( pr->mmin==i && e->mmax==i )) )
                        /* This just continues the line and doesn't change count */;
                    else
                        winding += (e->up?1:-1);
                }
                /* color a horizontal line that comes out of the last vertex */
                if ( e!=NULL && (e->before==pr || e->after==pr) &&
                            (( pr->mmax==i && e->mmin==i ) ||
                             ( pr->mmin==i && e->mmax==i )) ) {
                    pr = e;
                    e = e->aenext;
                }
            }
        }
        FreeEdges(&es);
    }
return( base );
}


int SplinePointListIsClockwise(const SplineSet *spl) {
    EIList el;
    EI *active=NULL, *apt, *e;
    int i, change,waschange;
    SplineChar dummy;
    SplineSet *next;
    int ret = -1, maybe=-1;
    Layer layers[2];

    if ( spl->first!=spl->last || spl->first->next == NULL )
return( -1 );           /* Open paths, (open paths with only one point are a special case) */

    memset(&el,'\0',sizeof(el));
    memset(&dummy,'\0',sizeof(dummy));
    memset(layers,0,sizeof(layers));
    el.layer = ly_fore;
    dummy.layers = layers;
    dummy.layer_cnt = 2;
    dummy.layers[ly_fore].splines = (SplineSet *) spl;
    next = spl->next; ((SplineSet *) spl)->next = NULL;
    ELFindEdges(&dummy,&el);
    if ( el.coordmax[1]-el.coordmin[1] > 1.e6 ) {
        LogError( _("Warning: Unreasonably big splines. They will be ignored.\n") );
return( -1 );
    }
    el.major = 1;
    ELOrder(&el,el.major);

    waschange = false;
    for ( i=0; i<el.cnt && ret==-1; ++i ) {
        active = EIActiveEdgesRefigure(&el,active,i,1,&change);
        if ( el.ordered[i]!=NULL || el.ends[i] || waschange || change ) {
            waschange = change;
            if ( active!=NULL )
                maybe = active->up;
    continue;                   /* Just too hard to get the edges sorted when we are at a start vertex */
        }
        waschange = change;
        for ( apt=active; apt!=NULL && ret==-1; apt = e) {
            if ( EISkipExtremum(apt,i+el.low,1)) {
                e = apt->aenext->aenext;
        continue;
            }
            ret = apt->up;
        break;
        }
    }
    free(el.ordered);
    free(el.ends);
    ElFreeEI(&el);
    ((SplineSet *) spl)->next = next;
    if ( ret==-1 )
        ret = maybe;
return( ret );
}