plfill.c

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//      Polygon pattern fill.
//
// Copyright (C) 2004-2015 Alan W. Irwin
// Copyright (C) 2005, 2006, 2007, 2008, 2009  Arjen Markus
//
// This file is part of PLplot.
//
// PLplot is free software; you can redistribute it and/or modify
// it under the terms of the GNU Library General Public License as published
// by the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// PLplot is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Library General Public License for more details.
//
// You should have received a copy of the GNU Library General Public License
// along with PLplot; if not, write to the Free Software
// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
//
//

#include "plplotP.h"

#define INSIDE( ix, iy )    ( BETW( ix, xmin, xmax ) && BETW( iy, ymin, ymax ) )

#define DTOR       ( PI / 180. )
#define BINC       50
// Near-border comparison criterion (NBCC).
#define PL_NBCC    2
// Variant of BETW that returns true if between or within PL_NBCC of it.
#define BETW_NBCC( ix, ia, ib )    ( ( ( ix ) <= ( ia + PL_NBCC ) && ( ix ) >= ( ib - PL_NBCC ) ) || ( ( ix ) >= ( ia - PL_NBCC ) && ( ix ) <= ( ib + PL_NBCC ) ) )

// Status codes ORed together in the return from notcrossed.
// PL_NOT_CROSSED is set whenever the two line segments definitely
// (i.e., intersection not near the ends or completely apart)
// do not cross each other.
//
// PL_NEAR_A1 is set if the intersect is near (+/- PL_NBCC) the first
// end of line segment A.
//
// PL_NEAR_A2 is set if the intersect is near (+/- PL_NBCC) the second
// end of line segment A.
//
// PL_NEAR_B1 is set if the intersect is near (+/- PL_NBCC) the first
// end of line segment B.
//
// PL_NEAR_B2 is set if the intersect is near (+/- PL_NBCC) the second
// end of line segment B.
//
// PL_NEAR_PARALLEL is set if the two line segments are nearly parallel
// with each other, i.e., a change in one of the coordinates of up to
// (+/- PL_NBCC) would render them exactly parallel.
//
// PL_PARALLEL is set if the two line segments are exactly parallel
// with each other.
//
enum PL_CrossedStatus
{
    PL_NOT_CROSSED   = 0x1,
    PL_NEAR_A1       = 0x2,
    PL_NEAR_A2       = 0x4,
    PL_NEAR_B1       = 0x8,
    PL_NEAR_B2       = 0x10,
    PL_NEAR_PARALLEL = 0x20,
    PL_PARALLEL      = 0x40
};

struct point
{
    PLINT x, y;
};
static PLINT bufferleng, buffersize, *buffer;

// Static function prototypes

static int
compar( const void *, const void * );

static void
addcoord( PLINT, PLINT );

static void
tran( PLINT *, PLINT *, PLFLT, PLFLT );

static void
buildlist( PLINT, PLINT, PLINT, PLINT, PLINT, PLINT, PLINT );

static int
notpointinpolygon( PLINT n, PLINT_VECTOR x, PLINT_VECTOR y, PLINT xp, PLINT yp );

static int
circulation( PLINT *x, PLINT *y, PLINT npts );

#ifdef USE_FILL_INTERSECTION_POLYGON
static void
fill_intersection_polygon( PLINT recursion_depth, PLINT ifextrapolygon,
                           PLINT fill_status,
                           void ( *fill )( short *, short *, PLINT ),
                           PLINT_VECTOR x1, PLINT_VECTOR y1,
                           PLINT i1start, PLINT n1,
                           PLINT_VECTOR x2, PLINT_VECTOR y2,
                           PLINT_VECTOR if2, PLINT n2 );

static int
positive_orientation( PLINT n, PLINT_VECTOR x, PLINT_VECTOR y );

static int
number_crossings( PLINT *xcross, PLINT *ycross, PLINT *i2cross, PLINT ncross,
                  PLINT i1, PLINT n1, PLINT_VECTOR x1, PLINT_VECTOR y1,
                  PLINT n2, PLINT_VECTOR x2, PLINT_VECTOR y2 );
#endif

static int
notcrossed( PLINT *xintersect, PLINT *yintersect,
            PLINT xA1, PLINT yA1, PLINT xA2, PLINT yA2,
            PLINT xB1, PLINT yB1, PLINT xB2, PLINT yB2 );

//--------------------------------------------------------------------------
// void plfill()
//
// Pattern fills the polygon bounded by the input points.
// For a number of vertices greater than PL_MAXPOLY-1, memory is managed via
// malloc/free. Otherwise statically defined arrays of length PL_MAXPOLY
// are used.
// The final point is explicitly added if it doesn't match up to the first,
// to prevent clipping problems.
//--------------------------------------------------------------------------

void
c_plfill( PLINT n, PLFLT_VECTOR x, PLFLT_VECTOR y )
{
    PLINT _xpoly[PL_MAXPOLY], _ypoly[PL_MAXPOLY];
    PLINT *xpoly, *ypoly;
    PLINT i, npts;
    PLFLT xt, yt;

    if ( plsc->level < 3 )
    {
        plabort( "plfill: Please set up window first" );
        return;
    }
    if ( n < 3 )
    {
        plabort( "plfill: Not enough points in object" );
        return;
    }
    npts = n;
    if ( n > PL_MAXPOLY - 1 )
    {
        xpoly = (PLINT *) malloc( (size_t) ( n + 1 ) * sizeof ( PLINT ) );
        ypoly = (PLINT *) malloc( (size_t) ( n + 1 ) * sizeof ( PLINT ) );

        if ( ( xpoly == NULL ) || ( ypoly == NULL ) )
        {
            plexit( "plfill: Insufficient memory for large polygon" );
        }
    }
    else
    {
        xpoly = _xpoly;
        ypoly = _ypoly;
    }

    for ( i = 0; i < n; i++ )
    {
        TRANSFORM( x[i], y[i], &xt, &yt );
        xpoly[i] = plP_wcpcx( xt );
        ypoly[i] = plP_wcpcy( yt );
    }

    if ( xpoly[0] != xpoly[n - 1] || ypoly[0] != ypoly[n - 1] )
    {
        n++;
        xpoly[n - 1] = xpoly[0];
        ypoly[n - 1] = ypoly[0];
    }

    plP_plfclp( xpoly, ypoly, n, plsc->clpxmi, plsc->clpxma,
        plsc->clpymi, plsc->clpyma, plP_fill );

    if ( npts > PL_MAXPOLY - 1 )
    {
        free( xpoly );
        free( ypoly );
    }
}

//--------------------------------------------------------------------------
// void plfill3()
//
// Pattern fills the polygon in 3d bounded by the input points.
// For a number of vertices greater than PL_MAXPOLY-1, memory is managed via
// malloc/free. Otherwise statically defined arrays of length PL_MAXPOLY
// are used.
// The final point is explicitly added if it doesn't match up to the first,
// to prevent clipping problems.
//--------------------------------------------------------------------------

void
c_plfill3( PLINT n, PLFLT_VECTOR x, PLFLT_VECTOR y, PLFLT_VECTOR z )
{
    PLFLT _tx[PL_MAXPOLY], _ty[PL_MAXPOLY], _tz[PL_MAXPOLY];
    PLFLT *tx, *ty, *tz;
    PLFLT *V[3];
    PLINT _xpoly[PL_MAXPOLY], _ypoly[PL_MAXPOLY];
    PLINT *xpoly, *ypoly;
    PLINT i;
    PLINT npts;
    PLFLT xmin, xmax, ymin, ymax, zmin, zmax, zscale;

    if ( plsc->level < 3 )
    {
        plabort( "plfill3: Please set up window first" );
        return;
    }
    if ( n < 3 )
    {
        plabort( "plfill3: Not enough points in object" );
        return;
    }

    npts = n;
    if ( n > PL_MAXPOLY - 1 )
    {
        tx    = (PLFLT *) malloc( (size_t) ( n + 1 ) * sizeof ( PLFLT ) );
        ty    = (PLFLT *) malloc( (size_t) ( n + 1 ) * sizeof ( PLFLT ) );
        tz    = (PLFLT *) malloc( (size_t) ( n + 1 ) * sizeof ( PLFLT ) );
        xpoly = (PLINT *) malloc( (size_t) ( n + 1 ) * sizeof ( PLINT ) );
        ypoly = (PLINT *) malloc( (size_t) ( n + 1 ) * sizeof ( PLINT ) );

        if ( ( tx == NULL ) || ( ty == NULL ) || ( tz == NULL ) ||
             ( xpoly == NULL ) || ( ypoly == NULL ) )
        {
            plexit( "plfill3: Insufficient memory for large polygon" );
        }
    }
    else
    {
        tx    = _tx;
        ty    = _ty;
        tz    = _tz;
        xpoly = _xpoly;
        ypoly = _ypoly;
    }

    plP_gdom( &xmin, &xmax, &ymin, &ymax );
    plP_grange( &zscale, &zmin, &zmax );

    // copy the vertices so we can clip without corrupting the input
    for ( i = 0; i < n; i++ )
    {
        tx[i] = x[i]; ty[i] = y[i]; tz[i] = z[i];
    }
    if ( tx[0] != tx[n - 1] || ty[0] != ty[n - 1] || tz[0] != tz[n - 1] )
    {
        n++;
        tx[n - 1] = tx[0]; ty[n - 1] = ty[0]; tz[n - 1] = tz[0];
    }
    V[0] = tx; V[1] = ty; V[2] = tz;
    n    = plP_clip_poly( n, V, 0, 1, -xmin );
    n    = plP_clip_poly( n, V, 0, -1, xmax );
    n    = plP_clip_poly( n, V, 1, 1, -ymin );
    n    = plP_clip_poly( n, V, 1, -1, ymax );
    n    = plP_clip_poly( n, V, 2, 1, -zmin );
    n    = plP_clip_poly( n, V, 2, -1, zmax );
    for ( i = 0; i < n; i++ )
    {
        xpoly[i] = plP_wcpcx( plP_w3wcx( tx[i], ty[i], tz[i] ) );
        ypoly[i] = plP_wcpcy( plP_w3wcy( tx[i], ty[i], tz[i] ) );
    }

// AWI: in the past we have used
//  plP_fill(xpoly, ypoly, n);
// here, but our educated guess is this fill should be done via the clipping
// interface instead as below.
// No example tests this code so one of our users will end up inadvertently
// testing this for us.
//
// jc: I have checked, and both versions does give the same result, i.e., clipping
// to the window boundaries. The reason is that the above plP_clip_poly() does
// the clipping. To check this, is enough to diminish the x/y/z min/max arguments in
// plw3d() in x08c. But let's keep it, although 10% slower...
//
    plP_plfclp( xpoly, ypoly, n, plsc->clpxmi, plsc->clpxma,
        plsc->clpymi, plsc->clpyma, plP_fill );

// If the original number of points is large, then free the arrays
    if ( npts > PL_MAXPOLY - 1 )
    {
        free( tx );
        free( ty );
        free( tz );
        free( xpoly );
        free( ypoly );
    }
}

//--------------------------------------------------------------------------
// void plfill_soft()
//
// Pattern fills in software the polygon bounded by the input points.
//--------------------------------------------------------------------------

void
plfill_soft( short *x, short *y, PLINT n )
{
    PLINT  i, j;
    PLINT  xp1, yp1, xp2, yp2, xp3, yp3;
    PLINT  k, dinc;
    PLFLT  ci, si;
    PLINT  plbuf_write;
    double temp;

    buffersize = 2 * BINC;
    buffer     = (PLINT *) malloc( (size_t) buffersize * sizeof ( PLINT ) );
    if ( !buffer )
    {
        plabort( "plfill: Out of memory" );
        return;
    }

    //do not write the hatching lines to the buffer as we have already
    //written the fill to the buffer
    plbuf_write       = plsc->plbuf_write;
    plsc->plbuf_write = FALSE;
// Loop over sets of lines in pattern

    for ( k = 0; k < plsc->nps; k++ )
    {
        bufferleng = 0;

        temp = DTOR * plsc->inclin[k] * 0.1;
        si   = sin( temp ) * plsc->ypmm;
        ci   = cos( temp ) * plsc->xpmm;

        // normalize: 1 = si*si + ci*ci

        temp = sqrt( (double) ( si * si + ci * ci ) );
        si  /= temp;
        ci  /= temp;

        dinc = (PLINT) ( plsc->delta[k] * SSQR( plsc->ypmm * ABS( ci ),
                             plsc->xpmm * ABS( si ) ) / 1000. );

        if ( dinc < 0 )
            dinc = -dinc;
        if ( dinc == 0 )
            dinc = 1;

        xp1 = x[n - 2];
        yp1 = y[n - 2];
        tran( &xp1, &yp1, (PLFLT) ci, (PLFLT) si );

        xp2 = x[n - 1];
        yp2 = y[n - 1];
        tran( &xp2, &yp2, (PLFLT) ci, (PLFLT) si );

// Loop over points in polygon

        for ( i = 0; i < n; i++ )
        {
            xp3 = x[i];
            yp3 = y[i];
            tran( &xp3, &yp3, (PLFLT) ci, (PLFLT) si );
            buildlist( xp1, yp1, xp2, yp2, xp3, yp3, dinc );
            xp1 = xp2;
            yp1 = yp2;
            xp2 = xp3;
            yp2 = yp3;
        }

// Sort list by y then x

        qsort( (void *) buffer, (size_t) bufferleng / 2,
            (size_t) sizeof ( struct point ), compar );

// OK, now do the hatching

        i = 0;

        while ( i < bufferleng )
        {
            xp1 = buffer[i];
            yp1 = buffer[i + 1];
            i  += 2;
            xp2 = xp1;
            yp2 = yp1;
            tran( &xp1, &yp1, (PLFLT) ci, (PLFLT) ( -si ) );
            plP_movphy( xp1, yp1 );
            xp1 = buffer[i];
            yp1 = buffer[i + 1];
            i  += 2;
            if ( yp2 != yp1 )
            {
                fprintf( stderr, "plfill: oh oh we are lost\n" );
                for ( j = 0; j < bufferleng; j += 2 )
                {
                    fprintf( stderr, "plfill: %d %d\n",
                        (int) buffer[j], (int) buffer[j + 1] );
                }
                continue;       // Uh oh we're lost
            }
            tran( &xp1, &yp1, (PLFLT) ci, (PLFLT) ( -si ) );
            plP_draphy( xp1, yp1 );
        }
    }
    //reinstate the buffer writing parameter and free memory
    plsc->plbuf_write = plbuf_write;
    free( (void *) buffer );
}

//--------------------------------------------------------------------------
// Utility functions
//--------------------------------------------------------------------------

void
tran( PLINT *a, PLINT *b, PLFLT c, PLFLT d )
{
    PLINT ta, tb;

    ta = *a;
    tb = *b;

    *a = (PLINT) floor( (double) ( ta * c + tb * d + 0.5 ) );
    *b = (PLINT) floor( (double) ( tb * c - ta * d + 0.5 ) );
}

void
buildlist( PLINT xp1, PLINT yp1, PLINT xp2, PLINT yp2, PLINT PL_UNUSED( xp3 ), PLINT yp3,
           PLINT dinc )
{
    PLINT min_y, max_y;
    PLINT dx, dy, cstep, nstep, ploty, plotx;

    dx = xp2 - xp1;
    dy = yp2 - yp1;

    if ( dy == 0 )
    {
        if ( yp2 > yp3 && ( ( yp2 % dinc ) == 0 ) )
            addcoord( xp2, yp2 );
        return;
    }

    if ( dy > 0 )
    {
        cstep = 1;
        min_y = yp1;
        max_y = yp2;
    }
    else
    {
        cstep = -1;
        min_y = yp2;
        max_y = yp1;
    }

    nstep = ( yp3 > yp2 ? 1 : -1 );
    if ( yp3 == yp2 )
        nstep = 0;

    // Build coordinate list

    ploty = ( min_y / dinc ) * dinc;
    if ( ploty < min_y )
        ploty += dinc;

    for (; ploty <= max_y; ploty += dinc )
    {
        if ( ploty == yp1 )
            continue;
        if ( ploty == yp2 )
        {
            if ( cstep == -nstep )
                continue;
            if ( yp2 == yp3 && yp1 > yp2 )
                continue;
        }
        plotx = xp1 + (PLINT) floor( ( (double) ( ploty - yp1 ) * dx ) / dy + 0.5 );
        addcoord( plotx, ploty );
    }
}

void
addcoord( PLINT xp1, PLINT yp1 )
{
    PLINT *temp;

    if ( bufferleng + 2 > buffersize )
    {
        buffersize += 2 * BINC;
        temp        = (PLINT *) realloc( (void *) buffer,
            (size_t) buffersize * sizeof ( PLINT ) );
        if ( !temp )
        {
            free( (void *) buffer );
            plexit( "plfill: Out of memory!" );
        }
        buffer = temp;
    }

    buffer[bufferleng++] = xp1;
    buffer[bufferleng++] = yp1;
}

int
compar( const void *pnum1, const void *pnum2 )
{
    const struct point *pnt1, *pnt2;

    pnt1 = (const struct point *) pnum1;
    pnt2 = (const struct point *) pnum2;

    if ( pnt1->y < pnt2->y )
        return -1;
    else if ( pnt1->y > pnt2->y )
        return 1;

    // Only reach here if y coords are equal, so sort by x

    if ( pnt1->x < pnt2->x )
        return -1;
    else if ( pnt1->x > pnt2->x )
        return 1;

    return 0;
}

//--------------------------------------------------------------------------
// void plP_plfclp()
//
// Fills a polygon within the clip limits.
//--------------------------------------------------------------------------

void
plP_plfclp( PLINT *x, PLINT *y, PLINT npts,
            PLINT xmin, PLINT xmax, PLINT ymin, PLINT ymax,
            void ( *draw )( short *, short *, PLINT ) )
{
#ifdef USE_FILL_INTERSECTION_POLYGON
    PLINT *x10, *y10, *x1, *y1, *if1, i1start = 0, i, im1, n1, n1m1,
           ifnotpointinpolygon;
    PLINT x2[4]  = { xmin, xmax, xmax, xmin };
    PLINT y2[4]  = { ymin, ymin, ymax, ymax };
    PLINT if2[4] = { 0, 0, 0, 0 };
    PLINT n2     = 4;

    // Must have at least 3 points and draw() specified
    if ( npts < 3 || !draw )
        return;

    if ( ( x10 = (PLINT *) malloc( (size_t) npts * sizeof ( PLINT ) ) ) == NULL )
    {
        plexit( "plP_plfclp: Insufficient memory" );
    }
    if ( ( y10 = (PLINT *) malloc( (size_t) npts * sizeof ( PLINT ) ) ) == NULL )
    {
        plexit( "plP_plfclp: Insufficient memory" );
    }
    // Polygon 2 obviously has no dups nor two consective segments that
    // are parallel, but get rid of those type of segments in polygon 1
    // if they exist.

    im1 = npts - 1;
    n1  = 0;
    for ( i = 0; i < npts; i++ )
    {
        if ( !( x[i] == x[im1] && y[i] == y[im1] ) )
        {
            x10[n1]   = x[i];
            y10[n1++] = y[i];
        }
        im1 = i;
    }

    // Must have at least three points that satisfy the above criteria.
    if ( n1 < 3 )
    {
        free( x10 );
        free( y10 );
        return;
    }

    // Polygon 2 obviously has a positive orientation (i.e., as you
    // ascend in index along the boundary, the points just adjacent to
    // the boundary and on the left are interior points for the
    // polygon), but enforce this condition demanded by
    // fill_intersection_polygon for polygon 1 as well.
    if ( positive_orientation( n1, x10, y10 ) )
    {
        x1 = x10;
        y1 = y10;
    }
    else
    {
        if ( ( x1 = (PLINT *) malloc( (size_t) n1 * sizeof ( PLINT ) ) ) == NULL )
        {
            plexit( "plP_plfclp: Insufficient memory" );
        }
        if ( ( y1 = (PLINT *) malloc( (size_t) n1 * sizeof ( PLINT ) ) ) == NULL )
        {
            plexit( "plP_plfclp: Insufficient memory" );
        }
        n1m1 = n1 - 1;
        for ( i = 0; i < n1; i++ )
        {
            x1[n1m1 - i] = x10[i];
            y1[n1m1 - i] = y10[i];
        }
        free( x10 );
        free( y10 );
    }

    // Insure that the first vertex of polygon 1 (starting with n1 -
    // 1) that is not on the border of polygon 2 is definitely outside
    // polygon 2.
    im1 = n1 - 1;
    for ( i = 0; i < n1; i++ )
    {
        if ( ( ifnotpointinpolygon =
                   notpointinpolygon( n2, x2, y2, x1[im1], y1[im1] ) ) != 1 )
            break;
        im1 = i;
    }

    if ( ifnotpointinpolygon )
        fill_intersection_polygon( 0, 0, 0, draw, x1, y1, i1start, n1, x2, y2, if2, n2 );
    else
    {
        if ( ( if1 = (PLINT *) calloc( n1, sizeof ( PLINT ) ) ) == NULL )
        {
            plexit( "plP_plfclp: Insufficient memory" );
        }
        fill_intersection_polygon( 0, 0, 0, draw, x2, y2, i1start, n2, x1, y1, if1, n1 );
        free( if1 );
    }
    free( x1 );
    free( y1 );
    return;
}
#else // USE_FILL_INTERSECTION_POLYGON

    PLINT i, x1, x2, y1, y2;
    int   iclp = 0, iout = 2;
    short _xclp[2 * PL_MAXPOLY + 2], _yclp[2 * PL_MAXPOLY + 2];
    short *xclp = NULL, *yclp = NULL;
    int   drawable;
    int   crossed_xmin1 = 0, crossed_xmax1 = 0;
    int   crossed_ymin1 = 0, crossed_ymax1 = 0;
    int   crossed_xmin2 = 0, crossed_xmax2 = 0;
    int   crossed_ymin2 = 0, crossed_ymax2 = 0;
    int   crossed_up    = 0, crossed_down = 0;
    int   crossed_left  = 0, crossed_right = 0;
    int   inside_lb;
    int   inside_lu;
    int   inside_rb;
    int   inside_ru;

    // Must have at least 3 points and draw() specified
    if ( npts < 3 || !draw )
        return;

    if ( npts < PL_MAXPOLY )
    {
        xclp = _xclp;
        yclp = _yclp;
    }
    else
    {
        if ( ( ( xclp = (short *) malloc( (size_t) ( 2 * npts + 2 ) * sizeof ( short ) ) ) == NULL ) ||
             ( ( yclp = (short *) malloc( (size_t) ( 2 * npts + 2 ) * sizeof ( short ) ) ) == NULL ) )
        {
            plexit( "plP_plfclp: Insufficient memory" );
        }
    }
    inside_lb = !notpointinpolygon( npts, x, y, xmin, ymin );
    inside_lu = !notpointinpolygon( npts, x, y, xmin, ymax );
    inside_rb = !notpointinpolygon( npts, x, y, xmax, ymin );
    inside_ru = !notpointinpolygon( npts, x, y, xmax, ymax );

    for ( i = 0; i < npts - 1; i++ )
    {
        x1 = x[i]; x2 = x[i + 1];
        y1 = y[i]; y2 = y[i + 1];

        drawable = ( INSIDE( x1, y1 ) && INSIDE( x2, y2 ) );
        if ( !drawable )
            drawable = !plP_clipline( &x1, &y1, &x2, &y2,
                xmin, xmax, ymin, ymax );

        if ( drawable )
        {
            // Boundary crossing condition -- coming in.
            crossed_xmin2 = ( x1 == xmin ); crossed_xmax2 = ( x1 == xmax );
            crossed_ymin2 = ( y1 == ymin ); crossed_ymax2 = ( y1 == ymax );

            crossed_left  = ( crossed_left || crossed_xmin2 );
            crossed_right = ( crossed_right || crossed_xmax2 );
            crossed_down  = ( crossed_down || crossed_ymin2 );
            crossed_up    = ( crossed_up || crossed_ymax2 );
            iout          = iclp + 2;
            // If the first segment, just add it.

            if ( iclp == 0 )
            {
                xclp[iclp] = (short) x1; yclp[iclp] = (short) y1; iclp++;
                xclp[iclp] = (short) x2; yclp[iclp] = (short) y2; iclp++;
            }

            // Not first point.  If first point of this segment matches up to the
            // previous point, just add it.

            else if ( x1 == (int) xclp[iclp - 1] && y1 == (int) yclp[iclp - 1] )
            {
                xclp[iclp] = (short) x2; yclp[iclp] = (short) y2; iclp++;
            }

            // Otherwise, we need to add both points, to connect the points in the
            // polygon along the clip boundary.  If we encircled a corner, we have
            // to add that first.
            //

            else
            {
                // Treat the case where we encircled two corners:
                // Construct a polygon out of the subset of vertices
                // Note that the direction is important too when adding
                // the extra points
                xclp[iclp + 1] = (short) x2; yclp[iclp + 1] = (short) y2;
                xclp[iclp + 2] = (short) x1; yclp[iclp + 2] = (short) y1;
                iout           = iout - iclp + 1;
                // Upper two
                if ( ( ( crossed_xmin1 && crossed_xmax2 ) ||
                       ( crossed_xmin2 && crossed_xmax1 ) ) &&
                     inside_lu )
                {
                    if ( crossed_xmin1 )
                    {
                        xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
                        xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
                    }
                    else
                    {
                        xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
                        xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
                    }
                }
                // Lower two
                else if ( ( ( crossed_xmin1 && crossed_xmax2 ) ||
                            ( crossed_xmin2 && crossed_xmax1 ) ) &&
                          inside_lb )
                {
                    if ( crossed_xmin1 )
                    {
                        xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
                        xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
                    }
                    else
                    {
                        xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
                        xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
                    }
                }
                // Left two
                else if ( ( ( crossed_ymin1 && crossed_ymax2 ) ||
                            ( crossed_ymin2 && crossed_ymax1 ) ) &&
                          inside_lb )
                {
                    if ( crossed_ymin1 )
                    {
                        xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
                        xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
                    }
                    else
                    {
                        xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
                        xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
                    }
                }
                // Right two
                else if ( ( ( crossed_ymin1 && crossed_ymax2 ) ||
                            ( crossed_ymin2 && crossed_ymax1 ) ) &&
                          inside_rb )
                {
                    if ( crossed_ymin1 )
                    {
                        xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
                        xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
                    }
                    else
                    {
                        xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
                        xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
                    }
                }
                // Now the case where we encircled one corner
                // Lower left
                else if ( ( crossed_xmin1 && crossed_ymin2 ) ||
                          ( crossed_ymin1 && crossed_xmin2 ) )
                {
                    xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
                }
                // Lower right
                else if ( ( crossed_xmax1 && crossed_ymin2 ) ||
                          ( crossed_ymin1 && crossed_xmax2 ) )
                {
                    xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
                }
                // Upper left
                else if ( ( crossed_xmin1 && crossed_ymax2 ) ||
                          ( crossed_ymax1 && crossed_xmin2 ) )
                {
                    xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
                }
                // Upper right
                else if ( ( crossed_xmax1 && crossed_ymax2 ) ||
                          ( crossed_ymax1 && crossed_xmax2 ) )
                {
                    xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
                }

                // Now add current segment.
                xclp[iclp] = (short) x1; yclp[iclp] = (short) y1; iclp++;
                xclp[iclp] = (short) x2; yclp[iclp] = (short) y2; iclp++;
            }

            // Boundary crossing condition -- going out.
            crossed_xmin1 = ( x2 == xmin ); crossed_xmax1 = ( x2 == xmax );
            crossed_ymin1 = ( y2 == ymin ); crossed_ymax1 = ( y2 == ymax );
        }
    }

    // Limit case - all vertices are outside of bounding box.  So just fill entire
    // box, *if* the bounding box is completely encircled.
    //
    if ( iclp == 0 )
    {
        if ( inside_lb )
        {
            xclp[0] = (short) xmin; yclp[0] = (short) ymin;
            xclp[1] = (short) xmax; yclp[1] = (short) ymin;
            xclp[2] = (short) xmax; yclp[2] = (short) ymax;
            xclp[3] = (short) xmin; yclp[3] = (short) ymax;
            xclp[4] = (short) xmin; yclp[4] = (short) ymin;
            ( *draw )( xclp, yclp, 5 );

            if ( xclp != _xclp )
            {
                free( xclp );
                free( yclp );
            }

            return;
        }
    }

    // Now handle cases where fill polygon intersects two sides of the box

    if ( iclp >= 2 )
    {
        int debug = 0;
        int dir   = circulation( x, y, npts );
        if ( debug )
        {
            if ( ( xclp[0] == (short) xmin && xclp[iclp - 1] == (short) xmax ) ||
                 ( xclp[0] == (short) xmax && xclp[iclp - 1] == (short) xmin ) ||
                 ( yclp[0] == (short) ymin && yclp[iclp - 1] == (short) ymax ) ||
                 ( yclp[0] == (short) ymax && yclp[iclp - 1] == (short) ymin ) ||
                 ( xclp[0] == (short) xmin && yclp[iclp - 1] == (short) ymin ) ||
                 ( yclp[0] == (short) ymin && xclp[iclp - 1] == (short) xmin ) ||
                 ( xclp[0] == (short) xmax && yclp[iclp - 1] == (short) ymin ) ||
                 ( yclp[0] == (short) ymin && xclp[iclp - 1] == (short) xmax ) ||
                 ( xclp[0] == (short) xmax && yclp[iclp - 1] == (short) ymax ) ||
                 ( yclp[0] == (short) ymax && xclp[iclp - 1] == (short) xmax ) ||
                 ( xclp[0] == (short) xmin && yclp[iclp - 1] == (short) ymax ) ||
                 ( yclp[0] == (short) ymax && xclp[iclp - 1] == (short) xmin ) )
            {
                printf( "dir=%d, clipped points:\n", dir );
                for ( i = 0; i < iclp; i++ )
                    printf( " x[%d]=%hd y[%d]=%hd", i, xclp[i], i, yclp[i] );
                printf( "\n" );
                printf( "pre-clipped points:\n" );
                for ( i = 0; i < npts; i++ )
                    printf( " x[%d]=%d y[%d]=%d", i, x[i], i, y[i] );
                printf( "\n" );
            }
        }

        // The cases where the fill region is divided 2/2
        // Divided horizontally
        if ( xclp[0] == (short) xmin && xclp[iclp - 1] == (short) xmax )
        {
            if ( dir > 0 )
            {
                xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
                xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
            }
            else
            {
                xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
                xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
            }
        }
        else if ( xclp[0] == (short) xmax && xclp[iclp - 1] == (short) xmin )
        {
            if ( dir > 0 )
            {
                xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
                xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
            }
            else
            {
                xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
                xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
            }
        }

        // Divided vertically
        else if ( yclp[0] == (short) ymin && yclp[iclp - 1] == (short) ymax )
        {
            if ( dir > 0 )
            {
                xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
                xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
            }
            else
            {
                xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
                xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
            }
        }
        else if ( yclp[0] == (short) ymax && yclp[iclp - 1] == (short) ymin )
        {
            if ( dir > 0 )
            {
                xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
                xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
            }
            else
            {
                xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
                xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
            }
        }

        // The cases where the fill region is divided 3/1 --
        //    LL           LR           UR           UL
        // +-----+      +-----+      +-----+      +-----+
        // |     |      |     |      |    \|      |/    |
        // |     |      |     |      |     |      |     |
        // |\    |      |    /|      |     |      |     |
        // +-----+      +-----+      +-----+      +-----+
        //
        // Note when we go the long way around, if the direction is reversed the
        // three vertices must be visited in the opposite order.
        //
        // LL, short way around
        else if ( ( xclp[0] == (short) xmin && yclp[iclp - 1] == (short) ymin && dir < 0 ) ||
                  ( yclp[0] == (short) ymin && xclp[iclp - 1] == (short) xmin && dir > 0 ) )
        {
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
        }
        // LL, long way around, counterclockwise
        else if ( ( xclp[0] == (short) xmin && yclp[iclp - 1] == (short) ymin && dir > 0 ) )
        {
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
        }
        // LL, long way around, clockwise
        else if ( ( yclp[0] == ymin && xclp[iclp - 1] == xmin && dir < 0 ) )
        {
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
        }
        // LR, short way around
        else if ( ( xclp[0] == (short) xmax && yclp[iclp - 1] == (short) ymin && dir > 0 ) ||
                  ( yclp[0] == (short) ymin && xclp[iclp - 1] == (short) xmax && dir < 0 ) )
        {
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
        }
        // LR, long way around, counterclockwise
        else if ( yclp[0] == (short) ymin && xclp[iclp - 1] == (short) xmax && dir > 0 )
        {
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
        }
        // LR, long way around, clockwise
        else if ( xclp[0] == (short) xmax && yclp[iclp - 1] == (short) ymin && dir < 0 )
        {
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
        }
        // UR, short way around
        else if ( ( xclp[0] == (short) xmax && yclp[iclp - 1] == (short) ymax && dir < 0 ) ||
                  ( yclp[0] == (short) ymax && xclp[iclp - 1] == (short) xmax && dir > 0 ) )
        {
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
        }
        // UR, long way around, counterclockwise
        else if ( xclp[0] == (short) xmax && yclp[iclp - 1] == (short) ymax && dir > 0 )
        {
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
        }
        // UR, long way around, clockwise
        else if ( yclp[0] == (short) ymax && xclp[iclp - 1] == (short) xmax && dir < 0 )
        {
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
        }
        // UL, short way around
        else if ( ( xclp[0] == (short) xmin && yclp[iclp - 1] == (short) ymax && dir > 0 ) ||
                  ( yclp[0] == (short) ymax && xclp[iclp - 1] == (short) xmin && dir < 0 ) )
        {
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymax; iclp++;
        }
        // UL, long way around, counterclockwise
        else if ( yclp[0] == (short) ymax && xclp[iclp - 1] == (short) xmin && dir > 0 )
        {
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
        }
        // UL, long way around, clockwise
        else if ( xclp[0] == (short) xmin && yclp[iclp - 1] == (short) ymax && dir < 0 )
        {
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymax; iclp++;
            xclp[iclp] = (short) xmax; yclp[iclp] = (short) ymin; iclp++;
            xclp[iclp] = (short) xmin; yclp[iclp] = (short) ymin; iclp++;
        }
    }

    // Check for the case that only one side has been crossed
    // (AM) Just checking a single point turns out not to be
    // enough, apparently the crossed_*1 and crossed_*2 variables
    // are not quite what I expected.
    //
    if ( inside_lb + inside_rb + inside_lu + inside_ru == 4 )
    {
        int   dir = circulation( x, y, npts );
        PLINT xlim[4], ylim[4];
        int   insert = -99;
        int   incr   = -99;

        xlim[0] = xmin; ylim[0] = ymin;
        xlim[1] = xmax; ylim[1] = ymin;
        xlim[2] = xmax; ylim[2] = ymax;
        xlim[3] = xmin; ylim[3] = ymax;

        if ( crossed_left + crossed_right + crossed_down + crossed_up == 1 )
        {
            if ( dir > 0 )
            {
                incr   = 1;
                insert = 0 * crossed_left + 1 * crossed_down + 2 * crossed_right +
                         3 * crossed_up;
            }
            else
            {
                incr   = -1;
                insert = 3 * crossed_left + 2 * crossed_up + 1 * crossed_right +
                         0 * crossed_down;
            }
        }

        if ( crossed_left + crossed_right == 2 && crossed_down + crossed_up == 0 )
        {
            if ( xclp[iclp - 1] == xmin )
            {
                if ( dir == 1 )
                {
                    incr   = 1;
                    insert = 0;
                }
                else
                {
                    incr   = -1;
                    insert = 3;
                }
            }
            else
            {
                if ( dir == 1 )
                {
                    incr   = 1;
                    insert = 1;
                }
                else
                {
                    incr   = -1;
                    insert = 2;
                }
            }
        }

        if ( crossed_left + crossed_right == 0 && crossed_down + crossed_up == 2 )
        {
            if ( yclp[iclp - 1] == ymin )
            {
                if ( dir == 1 )
                {
                    incr   = 1;
                    insert = 1;
                }
                else
                {
                    incr   = -1;
                    insert = 0;
                }
            }
            else
            {
                if ( dir == 1 )
                {
                    incr   = 1;
                    insert = 3;
                }
                else
                {
                    incr   = -1;
                    insert = 2;
                }
            }
        }

        for ( i = 0; i < 4; i++ )
        {
            xclp[iclp] = (short) xlim[insert];
            yclp[iclp] = (short) ylim[insert];
            iclp++;
            insert += incr;
            if ( insert > 3 )
                insert = 0;
            if ( insert < 0 )
                insert = 3;
        }
    }

    // Draw the sucker
    if ( iclp >= 3 )
        ( *draw )( xclp, yclp, iclp );

    if ( xclp != _xclp )
    {
        free( xclp );
        free( yclp );
    }
}
#endif // USE_FILL_INTERSECTION_POLYGON

//--------------------------------------------------------------------------
// int circulation()
//
// Returns the circulation direction for a given polyline: positive is
// counterclockwise, negative is clockwise (right hand rule).
//
// Used to get the circulation of the fill polygon around the bounding box,
// when the fill polygon is larger than the bounding box.  Counts left
// (positive) vs right (negative) hand turns using a cross product, instead of
// performing all the expensive trig calculations needed to get this 100%
// correct.  For the fill cases encountered in plplot, this treatment should
// give the correct answer most of the time, by far.  When used with plshades,
// the typical return value is 3 or -3, since 3 turns are necessary in order
// to complete the fill region.  Only for really oddly shaped fill regions
// will it give the wrong answer.
//
// AM:
// Changed the computation: use the outer product to compute the surface
// area, the sign determines if the polygon is followed clockwise or
// counterclockwise. This is more reliable. Floating-point numbers
// are used to avoid overflow.
//--------------------------------------------------------------------------

int
circulation( PLINT *x, PLINT *y, PLINT npts )
{
    PLFLT xproduct;
    int direction = 0;
    PLFLT x1, y1, x2, y2, x3, y3;
    int i;

    xproduct = 0.0;
    x1       = x[0];
    y1       = y[0];
    for ( i = 1; i < npts - 2; i++ )
    {
        x2       = x[i + 1];
        y2       = y[i + 1];
        x3       = x[i + 2];
        y3       = y[i + 2];
        xproduct = xproduct + ( x2 - x1 ) * ( y3 - y2 ) - ( y2 - y1 ) * ( x3 - x2 );
    }

    if ( xproduct > 0.0 )
        direction = 1;
    if ( xproduct < 0.0 )
        direction = -1;
    return direction;
}


// PLFLT wrapper for !notpointinpolygon.
int
plP_pointinpolygon( PLINT n, PLFLT_VECTOR x, PLFLT_VECTOR y, PLFLT xp, PLFLT yp )
{
    int i, return_value;
    PLINT *xint, *yint;
    PLFLT xmaximum = fabs( xp ), ymaximum = fabs( yp ), xscale, yscale;
    if ( ( xint = (PLINT *) malloc( (size_t) n * sizeof ( PLINT ) ) ) == NULL )
    {
        plexit( "PlP_pointinpolygon: Insufficient memory" );
    }
    if ( ( yint = (PLINT *) malloc( (size_t) n * sizeof ( PLINT ) ) ) == NULL )
    {
        plexit( "PlP_pointinpolygon: Insufficient memory" );
    }
    for ( i = 0; i < n; i++ )
    {
        xmaximum = MAX( xmaximum, fabs( x[i] ) );
        ymaximum = MAX( ymaximum, fabs( y[i] ) );
    }
    xscale = 1.e8 / xmaximum;
    yscale = 1.e8 / ymaximum;
    for ( i = 0; i < n; i++ )
    {
        xint[i] = (PLINT) ( xscale * x[i] );
        yint[i] = (PLINT) ( yscale * y[i] );
    }
    return_value = !notpointinpolygon( n, xint, yint,
        (PLINT) ( xscale * xp ), (PLINT) ( yscale * yp ) );
    free( xint );
    free( yint );
    return return_value;
}
//--------------------------------------------------------------------------
// int notpointinpolygon()
//
// Returns 0, 1, or 2 depending on whether the test point is definitely
// inside, near the border, or definitely outside the polygon.
// Notes:
// This "Ray casting algorithm" has been described in
// http://en.wikipedia.org/wiki/Point_in_polygon.
// Logic still needs to be inserted to take care of the "ray passes
// through vertex" problem in a numerically robust way.
//--------------------------------------------------------------------------

// Temporary until get rid of old code altogether.
#define NEW_NOTPOINTINPOLYGON_CODE
static int
notpointinpolygon( PLINT n, PLINT_VECTOR x, PLINT_VECTOR y, PLINT xp, PLINT yp )
{
#ifdef NEW_NOTPOINTINPOLYGON_CODE
    int i, im1, ifnotcrossed;
    int count_crossings = 0;
    PLINT xmin, xout, yout, xintersect, yintersect;


    // Determine a point outside the polygon

    xmin = x[0];
    xout = x[0];
    yout = y[0];
    for ( i = 1; i < n; i++ )
    {
        xout = MAX( xout, x[i] );
        xmin = MIN( xmin, x[i] );
    }
    // + 10 to make sure completely outside.
    xout = xout + ( xout - xmin ) + 10;

    // Determine whether the line between (xout, yout) and (xp, yp) intersects
    // one of the polygon segments.

    im1 = n - 1;
    for ( i = 0; i < n; i++ )
    {
        if ( !( x[im1] == x[i] && y[im1] == y[i] ) )
        {
            ifnotcrossed = notcrossed( &xintersect, &yintersect,
                x[im1], y[im1], x[i], y[i],
                xp, yp, xout, yout );

            if ( !ifnotcrossed )
                count_crossings++;
            else if ( ifnotcrossed & ( PL_NEAR_A1 | PL_NEAR_A2 | PL_NEAR_B1 | PL_NEAR_B2 ) )
                return 1;
        }
        im1 = i;
    }

    // return 0 if the test point is definitely inside
    // (count_crossings odd), return 1 if the test point is near (see
    // above logic), and return 2 if the test point is definitely
    // outside the border (count_crossings even).
    if ( ( count_crossings % 2 ) == 1 )
        return 0;
    else
        return 2;
}
#else // NEW_NOTPOINTINPOLYGON_CODE
    int i;
    int count_crossings;
    PLFLT x1, y1, x2, y2, xpp, ypp, xout, yout, xmax;
    PLFLT xvp, yvp, xvv, yvv, xv1, yv1, xv2, yv2;
    PLFLT inprod1, inprod2;

    xpp = (PLFLT) xp;
    ypp = (PLFLT) yp;

    count_crossings = 0;


    // Determine a point outside the polygon

    xmax = x[0];
    xout = x[0];
    yout = y[0];
    for ( i = 0; i < n; i++ )
    {
        if ( xout > x[i] )
        {
            xout = x[i];
        }
        if ( xmax < x[i] )
        {
            xmax = x[i];
        }
    }
    xout = xout - ( xmax - xout );

    // Determine for each side whether the line segment between
    // our two points crosses the vertex

    xpp = (PLFLT) xp;
    ypp = (PLFLT) yp;

    xvp = xpp - xout;
    yvp = ypp - yout;

    for ( i = 0; i < n; i++ )
    {
        x1 = (PLFLT) x[i];
        y1 = (PLFLT) y[i];
        if ( i < n - 1 )
        {
            x2 = (PLFLT) x[i + 1];
            y2 = (PLFLT) y[i + 1];
        }
        else
        {
            x2 = (PLFLT) x[0];
            y2 = (PLFLT) y[0];
        }

        // Skip zero-length segments
        if ( x1 == x2 && y1 == y2 )
        {
            continue;
        }

        // Line through the two fixed points:
        // Are x1 and x2 on either side?
        xv1     = x1 - xout;
        yv1     = y1 - yout;
        xv2     = x2 - xout;
        yv2     = y2 - yout;
        inprod1 = xv1 * yvp - yv1 * xvp; // Well, with the normal vector
        inprod2 = xv2 * yvp - yv2 * xvp;
        if ( inprod1 * inprod2 >= 0.0 )
        {
            // No crossing possible!
            continue;
        }

        // Line through the two vertices:
        // Are xout and xpp on either side?
        xvv     = x2 - x1;
        yvv     = y2 - y1;
        xv1     = xpp - x1;
        yv1     = ypp - y1;
        xv2     = xout - x1;
        yv2     = yout - y1;
        inprod1 = xv1 * yvv - yv1 * xvv;
        inprod2 = xv2 * yvv - yv2 * xvv;
        if ( inprod1 * inprod2 >= 0.0 )
        {
            // No crossing possible!
            continue;
        }

        // We do have a crossing
        count_crossings++;
    }

    // Return the result: an even number of crossings means the
    // point is outside the polygon

    return !( count_crossings % 2 );
}
#endif // NEW_NOTPOINTINPOLYGON_CODE

#define MAX_RECURSION_DEPTH    10

// Fill intersection of two simple polygons that do no self-intersect,
// and which have no duplicate vertices or two consecutive edges that
// are parallel.  A further requirement is that both polygons have a
// positive orientation (see
// http://en.wikipedia.org/wiki/Curve_orientation).  That is, as you
// traverse the boundary in index order, the inside area of the
// polygon is always on the left.  Finally, the first vertex of
// polygon 1 (starting with n1 -1) that is not near the border of
// polygon 2 must be outside polygon 2.  N.B. it is the calling
// routine's responsibility to insure all those requirements are
// satisfied.
//
// Two polygons that do not self intersect must have an even number of
// edge crossings between them.  (ignoring vertex intersections which
// touch, but do not cross).  fill_intersection_polygon eliminates
// those intersection crossings by recursion (calling the same routine
// twice again with the second polygon split at a boundary defined by
// the first intersection point, all polygon 1 vertices between the
// intersections, and the second intersection point).  Once the
// recursion has eliminated all crossing edges, fill or not using the
// appropriate polygon depending on whether the first and second
// polygons are identical or whether one of them is entirely inside
// the other of them.  If ifextrapolygon is true, the fill step will
// consist of another recursive call to the routine with
// ifextrapolygon false, and the second polygon set to an additional
// polygon defined by the stream (not yet implemented).

// arguments to intersection_polygon:
// recursion_depth is just what it says.
// ifextrapolygon used to decide whether to use extra polygon from the stream.
//fill is the fill routine.
//x1, *y1, n1 define the polygon 1 vertices.
// i1start is the first polygon 1 index to look at (because all the previous
//     ones have been completely processed).
//x2, *y2, *if2, n2 define the polygon 2 vertices plus a status indicator
//     for each vertex which is 1 for a previous crossing and 2 for a polygon
//     1 vertex.
// fill_status is 1 when polygons 1 and 2 _must_ include some joint
//     filled area and is -1 when polygons 1 and 2 _must_ include some
//     unfilled area.  fill_status of +/- 1 is determined from the
//     orientations of polygon 1 and 2 from the next higher recursion
//     level and how those two are combined to form the polygon 2
//     split at this recursion level.  fill_status = 0 occurs (at
//     recursion level 0) for polygons 1 and 2 that are independent of
//     each other.

#ifdef USE_FILL_INTERSECTION_POLYGON
void
fill_intersection_polygon( PLINT recursion_depth, PLINT ifextrapolygon,
                           PLINT fill_status,
                           void ( *fill )( short *, short *, PLINT ),
                           PLINT_VECTOR x1, PLINT_VECTOR y1,
                           PLINT i1start, PLINT n1,
                           PLINT_VECTOR x2, PLINT_VECTOR y2,
                           PLINT_VECTOR if2, PLINT n2 )
{
    PLINT i1, i1m1, i1start_new,
          i2, i2m1,
          kk, kkstart1, kkstart21, kkstart22,
          k, kstart, range1,
          range21, range22, ncrossed, ncrossed_change,
          nsplit1, nsplit2, nsplit2m1;
    PLINT xintersect[2], yintersect[2], i1intersect[2],
          i2intersect[2];
    PLINT *xsplit1, *ysplit1, *ifsplit1,
    *xsplit2, *ysplit2, *ifsplit2;
    PLINT ifill, nfill = 0,
          ifnotpolygon1inpolygon2, ifnotpolygon2inpolygon1;
    PLINT_VECTOR xfiller, *yfiller;
    short *xfill, *yfill;

    if ( recursion_depth > MAX_RECURSION_DEPTH )
    {
        plwarn( "fill_intersection_polygon: Recursion_depth too large.  "
            "Probably an internal error figuring out intersections. " );
        return;
    }

    if ( n1 < 3 )
    {
        plwarn( "fill_intersection_polygon: Internal error; n1 < 3." );
        return;
    }

    if ( n2 < 3 )
    {
        plwarn( "fill_intersection_polygon: Internal error; n2 < 3." );
        return;
    }

    if ( i1start < 0 || i1start >= n1 )
    {
        plwarn( "fill_intersection_polygon: invalid i1start." );
        return;
    }

    // Check that there are no duplicate vertices.
    i1m1 = i1start - 1;
    if ( i1m1 < 0 )
        i1m1 = n1 - 1;

    for ( i1 = i1start; i1 < n1; i1++ )
    {
        if ( x1[i1] == x1[i1m1] && y1[i1] == y1[i1m1] )
            break;
        i1m1 = i1;
    }

    if ( i1 < n1 )
    {
        plwarn( "fill_intersection_polygon: Internal error; i1 < n1." );
        return;
    }

    i2m1 = n2 - 1;
    for ( i2 = 0; i2 < n2; i2++ )
    {
        if ( x2[i2] == x2[i2m1] && y2[i2] == y2[i2m1] )
            break;
        i2m1 = i2;
    }

    if ( i2 < n2 )
    {
        plwarn( "fill_intersection_polygon: Internal error; i2 < n2." );
        return;
    }

    //
    //
    // Follow polygon 1 (checking intersections with polygon 2 for each
    // segment of polygon 1) until you have accumulated two
    // intersections with polygon 2.  Here is an ascii-art illustration
    // of the situation.
    //
    //
    //                  2???2
    //
    //                2       2
    //
    // --- 1    1
    //            1            2         1      1 ...
    //             X
    //                               1
    //                             X
    //           2
    //                1         1
    //                   1
    //                                 2
    //            2
    //                     2???2
    //
    //
    // "1" marks polygon 1 vertices, "2" marks polygon 2 vertices, "X"
    // marks the intersections, "---" stands for part of polygon 1
    // that has been previously searched for all possible intersections
    // from index 0, and "..." means polygon 1 continues
    // with more potential intersections above and/or below this diagram
    // before it finally hooks back to connect with the index 0 vertex.
    // "2???2" stands for parts of polygon 2 that must connect with each other
    // (since the polygon 1 path between the two intersections is
    // known to be free of intersections.)
    //
    // Polygon 2 is split at the boundary defined by the two
    // intersections and all (in this case three) polygon 1 vertices
    // between the two intersections for the next recursion level.  We
    // absolutely know for that boundary that no more intersections can
    // occur (both polygon 1 and polygon 2 are guaranteed not to
    // self-intersect) so we mark the status of those vertices with that
    // information so those polygon 2 split vertices will not be used to
    // search for further intersections at deeper recursion levels.
    // Note, we know nothing about whether the remaining "2???2" parts of the
    // split polygon 2 intersect with polygon 1 or not so those will
    // continued to be searched at deeper recursion levels. At the same
    // time, we absolutely know that the part of polygon 1 to the left of
    // rightmost x down to and including index 0 cannot yield more
    // intersections with any split of polygon 2 so we adjust the lower
    // limit of polygon 1 to be used for intersection searches at deeper
    // recursion levels.  The result should be that at sufficiently deep
    // recursion depth we always end up with the case that there are no
    // intersections to be found between polygon 1 and some polygon 2
    // split, and in that case we move on to the end phase below.
    //
    ncrossed = 0;
    i1m1     = i1start - 1;
    if ( i1m1 < 0 )
        i1m1 += n1;
    for ( i1 = i1start; i1 < n1; i1++ )
    {
        ncrossed_change = number_crossings(
            &xintersect[ncrossed], &yintersect[ncrossed],
            &i2intersect[ncrossed], 2 - ncrossed,
            i1, n1, x1, y1, n2, x2, y2 );
        if ( ncrossed_change > 0 )
        {
            i1intersect[ncrossed] = i1;
            if ( ncrossed_change == 2 )
            {
                ;
            }
            i1intersect[1] = i1;

            ncrossed += ncrossed_change;
            if ( ncrossed == 2 )
            {
                // Have discovered the first two crossings for
                // polygon 1 at i1 = i1start or above.

                // New i1start is the same as the current i1 (just
                // in case there are more crossings to find between
                // i1m1 and i1.)
                i1start_new = i1;

                // Split polygon 2 at the boundary consisting of
                // first intersection, intervening (if any) range1
                // polygon 1 points and second intersection.
                // range1 must always be non-negative because i1
                // range only traversed once.
                range1 = i1intersect[1] - i1intersect[0];
                // Polygon 2 intersects could be anywhere (since
                // i2 range repeated until get an intersect).
                // Divide polygon 2 into two polygons with a
                // common boundary consisting of the first intersect,
                // range1 points from polygon 1 starting at index
                // kkstart1 of polygon 1, and the second intersect.
                kkstart1 = i1intersect[0];

                // Calculate polygon 2 index range in split 1 (the
                // split that proceeds beyond the second intersect with
                // ascending i2 values).
                range21 = i2intersect[0] - i2intersect[1];
                if ( range21 < 0 )
                    range21 += n2;
                // i2 intersect values range between 0 and n2 - 1 so
                // the smallest untransformed range21 value is -n2 + 1,
                // and the largest untransformed range21 value is n2 - 1.
                // This means the smallest transformed range21 value is 0
                // (which occurs only ifi2intersect[0] = i2intersect[1],
                // see more commentary for that special case below) while
                // the largest transformed range21 value is n2 - 1.

                if ( range21 == 0 )
                {
                    int ifxsort, ifascend;
                    // For this case, the two crossings occur within the same
                    // polygon 2 boundary segment and if those two crossings
                    // are in ascending/descending order in i2, then split 1
                    // (the split with the positive fill_status) must include
                    // all/none of the points in polygon 2.
                    i2   = i2intersect[1];
                    i2m1 = i2 - 1;
                    if ( i2m1 < 0 )
                        i2m1 += n2;

                    ifxsort  = abs( x2[i2] - x2[i2m1] ) > abs( y2[i2] - y2[i2m1] );
                    ifascend = ( ifxsort && x2[i2] > x2[i2m1] ) ||
                               ( !ifxsort && y2[i2] > y2[i2m1] );
                    if ( ( ifxsort && ifascend && xintersect[0] < xintersect[1] ) ||
                         ( !ifxsort && ifascend && yintersect[0] < yintersect[1] ) ||
                         ( ifxsort && !ifascend && xintersect[0] >= xintersect[1] ) ||
                         ( !ifxsort && !ifascend && yintersect[0] >= yintersect[1] ) )
                    {
                        range21 = n2;
                    }
                }

                kkstart21 = i2intersect[1];
                nsplit1   = 2 + range1 + range21;

                // Split 2 of polygon 2 consists of the
                // boundary + range22 (= n2 - range21) points
                // between kkstart22 (= i2intersect[1]-1) and i2intersect[0] in
                // descending order of polygon 2 indices.
                range22 = n2 - range21;
                // Starting i2 index of split 2.
                kkstart22 = i2intersect[1] - 1;
                if ( kkstart22 < 0 )
                    kkstart22 += n2;
                nsplit2 = 2 + range1 + range22;

                if ( ( xsplit1 = (PLINT *) malloc( (size_t) nsplit1 * sizeof ( PLINT ) ) ) == NULL )
                {
                    plexit( "fill_intersection_polygon: Insufficient memory" );
                }
                if ( ( ysplit1 = (PLINT *) malloc( (size_t) nsplit1 * sizeof ( PLINT ) ) ) == NULL )
                {
                    plexit( "fill_intersection_polygon: Insufficient memory" );
                }
                if ( ( ifsplit1 = (PLINT *) malloc( (size_t) nsplit1 * sizeof ( PLINT ) ) ) == NULL )
                {
                    plexit( "fill_intersection_polygon: Insufficient memory" );
                }

                if ( ( xsplit2 = (PLINT *) malloc( (size_t) nsplit2 * sizeof ( PLINT ) ) ) == NULL )
                {
                    plexit( "fill_intersection_polygon: Insufficient memory" );
                }
                if ( ( ysplit2 = (PLINT *) malloc( (size_t) nsplit2 * sizeof ( PLINT ) ) ) == NULL )
                {
                    plexit( "fill_intersection_polygon: Insufficient memory" );
                }
                if ( ( ifsplit2 = (PLINT *) malloc( (size_t) nsplit2 * sizeof ( PLINT ) ) ) == NULL )
                {
                    plexit( "fill_intersection_polygon: Insufficient memory" );
                }
                // Common boundary between split1 and split2.
                // N.B. Although basic index arithmetic for
                // split 2 is done in negative orientation
                // order because the index is decrementing
                // relative to the index of split 2, actually
                // store results in reverse order to preserve
                // the positive orientation that by assumption
                // both polygon 1 and 2 have.
                k                       = 0;
                xsplit1[k]              = xintersect[0];
                ysplit1[k]              = yintersect[0];
                ifsplit1[k]             = 1;
                nsplit2m1               = nsplit2 - 1;
                xsplit2[nsplit2m1 - k]  = xintersect[0];
                ysplit2[nsplit2m1 - k]  = yintersect[0];
                ifsplit2[nsplit2m1 - k] = 1;
                kstart                  = k + 1;
                kk                      = kkstart1;
                // No wrap checks on kk index below because
                // it must always be in valid range (since
                // polygon 1 traversed only once).
                for ( k = kstart; k < range1 + 1; k++ )
                {
                    xsplit1[k]              = x1[kk];
                    ysplit1[k]              = y1[kk];
                    ifsplit1[k]             = 2;
                    xsplit2[nsplit2m1 - k]  = x1[kk];
                    ysplit2[nsplit2m1 - k]  = y1[kk++];
                    ifsplit2[nsplit2m1 - k] = 2;
                }
                xsplit1[k]              = xintersect[1];
                ysplit1[k]              = yintersect[1];
                ifsplit1[k]             = 1;
                xsplit2[nsplit2m1 - k]  = xintersect[1];
                ysplit2[nsplit2m1 - k]  = yintersect[1];
                ifsplit2[nsplit2m1 - k] = 1;

                // Finish off collecting split1 using ascending kk
                // values.
                kstart = k + 1;
                kk     = kkstart21;
                for ( k = kstart; k < nsplit1; k++ )
                {
                    xsplit1[k]  = x2[kk];
                    ysplit1[k]  = y2[kk];
                    ifsplit1[k] = if2[kk++];
                    if ( kk >= n2 )
                        kk -= n2;
                }

                // N.B. the positive orientation of split1 is
                // preserved since the index order is the same
                // as that of polygon 2, and by assumption
                // that polygon and polygon 1 have identical
                // positive orientations.
                fill_intersection_polygon(
                    recursion_depth + 1, ifextrapolygon, 1, fill,
                    x1, y1, i1start_new, n1,
                    xsplit1, ysplit1, ifsplit1, nsplit1 );
                free( xsplit1 );
                free( ysplit1 );
                free( ifsplit1 );

                // Finish off collecting split2 using descending kk
                // values.
                kk = kkstart22;
                for ( k = kstart; k < nsplit2; k++ )
                {
                    xsplit2[nsplit2m1 - k]  = x2[kk];
                    ysplit2[nsplit2m1 - k]  = y2[kk];
                    ifsplit2[nsplit2m1 - k] = if2[kk--];
                    if ( kk < 0 )
                        kk += n2;
                }

                // N.B. the positive orientation of split2 is
                // preserved since the index order is the same
                // as that of polygon 2, and by assumption
                // that polygon and polygon 1 have identical
                // positive orientations.
                fill_intersection_polygon(
                    recursion_depth + 1, ifextrapolygon, -1, fill,
                    x1, y1, i1start_new, n1,
                    xsplit2, ysplit2, ifsplit2, nsplit2 );
                free( xsplit2 );
                free( ysplit2 );
                free( ifsplit2 );
                return;
            }
        }
        i1m1 = i1;
    }

    if ( ncrossed != 0 )
    {
        plwarn( "fill_intersection_polygon: Internal error; ncrossed != 0." );
        return;
    }

    // This end phase is reached only if no crossings are found.

    // If a fill_status of +/- 1 is known, use that to fill or not since
    // +1 corresponds to all of polygon 2 inside polygon 1 and -1
    // corresponds to none of polygon 2 inside polygon 1.
    if ( fill_status == -1 )
        return;
    else if ( fill_status == 1 )
    {
        nfill   = n2;
        xfiller = x2;
        yfiller = y2;
    }
    else if ( fill_status == 0 )
    //else if ( 1 )
    {
        if ( recursion_depth != 0 )
        {
            plwarn( "fill_intersection_polygon: Internal error; fill_status == 0 for recursion_depth > 0" );
            return;
        }
        // For this case (recursion level 0) the two polygons are
        // completely independent with no crossings between them or
        // edges constructed from one another.
        //
        // The intersection of polygon 2 and 1, must be either of them (in
        // which case fill with the inner one), or neither of them (in
        // which case don't fill at all).

        // Classify polygon 1 by looking for first vertex in polygon 1
        // that is definitely inside or outside polygon 2.
        for ( i1 = 0; i1 < n1; i1++ )
        {
            if ( ( ifnotpolygon1inpolygon2 =
                       notpointinpolygon( n2, x2, y2, x1[i1], y1[i1] ) ) != 1 )
                break;
        }

        // Classify polygon 2 by looking for first vertex in polygon 2
        // that is definitely inside or outside polygon 1.
        ifnotpolygon2inpolygon1 = 1;
        for ( i2 = 0; i2 < n2; i2++ )
        {
            // Do not bother checking vertices already known to be on the
            // boundary with polygon 1.
            if ( !if2[i2] && ( ifnotpolygon2inpolygon1 =
                                   notpointinpolygon( n1, x1, y1, x2[i2], y2[i2] ) ) != 1 )
                break;
        }

        if ( ifnotpolygon2inpolygon1 == 0 && ifnotpolygon1inpolygon2 == 0 )
            plwarn( "fill_intersection_polygon: Internal error; no intersections found but each polygon definitely inside the other!" );
        else if ( ifnotpolygon2inpolygon1 == 2 && ifnotpolygon1inpolygon2 == 2 )
            // The polygons do not intersect each other so do not fill in this
            // case.
            return;
        else if ( ifnotpolygon2inpolygon1 == 0 )
        {
            // Polygon 2 definitely inside polygon 1.
            nfill   = n2;
            xfiller = x2;
            yfiller = y2;
        }
        else if ( ifnotpolygon1inpolygon2 == 0 )
        {
            // Polygon 1 definitely inside polygon 2.
            nfill   = n1;
            xfiller = x1;
            yfiller = y1;
        }
        else if ( ifnotpolygon2inpolygon1 == 1 && ifnotpolygon1inpolygon2 == 1 )
        {
            // Polygon 2 vertices near polygon 1 border and vice versa which
            // implies the polygons are identical.
            nfill   = n2;
            xfiller = x2;
            yfiller = y2;
        }
        else
        {
            // Polygon 1 inscribed in polygon 2 or vice versa.  This is normally
            // unlikely for two independent polygons so the implementation is
            // ToDo.
            plwarn( "fill_intersection_polygon: inscribed polygons are still ToDo" );
        }
    }

    if ( nfill > 0 )
    {
        if ( ( xfill = (short *) malloc( (size_t) nfill * sizeof ( short ) ) ) == NULL )
        {
            plexit( "fill_intersection_polygon: Insufficient memory" );
        }
        if ( ( yfill = (short *) malloc( (size_t) nfill * sizeof ( short ) ) ) == NULL )
        {
            plexit( "fill_intersection_polygon: Insufficient memory" );
        }
        for ( ifill = 0; ifill < nfill; ifill++ )
        {
            xfill[ifill] = (short) xfiller[ifill];
            yfill[ifill] = (short) yfiller[ifill];
        }
        ( *fill )( xfill, yfill, nfill );
        free( xfill );
        free( yfill );
    }

    return;
}
#endif

// Returns a 0 status code
// if the two line segments A, and B defined
// by their end points (xA1, yA1, xA2, yA2, xB1, yB1, xB2, and yB2)
// definitely (i.e., intersection point is not near the ends of either
// of the line segments) cross each other.  Otherwise, return a status
// code specifying the type of non-crossing (i.e., completely
// separate, near one of the ends, parallel).
// Only if status = 0, return the actual
// intersection via the argument list pointers to
// xintersect and yintersect.

int
notcrossed( PLINT * xintersect, PLINT * yintersect,
            PLINT xA1, PLINT yA1, PLINT xA2, PLINT yA2,
            PLINT xB1, PLINT yB1, PLINT xB2, PLINT yB2 )
{
    PLFLT factor, factor_NBCC, fxintersect, fyintersect;
    // These variables are PLFLT not for precision, but to
    // avoid integer overflows if they were typed as PLINT.
    PLFLT xA2A1, yA2A1, xB2B1, yB2B1;
    PLFLT xB1A1, yB1A1, xB2A1, yB2A1;
    PLINT status = 0;
    //
    // Two linear equations to be solved for x and y.
    // y = ((x - xA1)*yA2 + (xA2 - x)*yA1)/(xA2 - xA1)
    // y = ((x - xB1)*yB2 + (xB2 - x)*yB1)/(xB2 - xB1)
    //
    // Transform those two equations to coordinate system with origin
    // at (xA1, yA1).
    // y' = x'*yA2A1/xA2A1
    // y' = ((x' - xB1A1)*yB2A1 + (xB2A1 - x')*yB1A1)/xB2B1
    // ==>
    // x' = -(
    // (-xB1A1*yB2A1 + xB2A1*yB1A1)/xB2B1)/
    // (yB2B1/xB2B1 - yA2A1/xA2A1)
    // = (xB1A1*yB2A1 - xB2A1*yB1A1)*xA2A1/
    // (xA2A1*yB2B1 - yA2A1*xB2B1)
    //
    //

    xA2A1 = xA2 - xA1;
    yA2A1 = yA2 - yA1;
    xB2B1 = xB2 - xB1;
    yB2B1 = yB2 - yB1;

    factor      = xA2A1 * yB2B1 - yA2A1 * xB2B1;
    factor_NBCC = PL_NBCC * ( fabs( xA2A1 ) + fabs( yB2B1 ) + fabs( yA2A1 ) + fabs( xB2B1 ) );
    if ( fabs( factor ) <= factor_NBCC )
    {
        if ( fabs( factor ) > 0. )
            status = status | PL_NEAR_PARALLEL;
        else
            status = status | PL_PARALLEL;
    }
    else
    {
        xB1A1 = xB1 - xA1;
        yB1A1 = yB1 - yA1;
        xB2A1 = xB2 - xA1;
        yB2A1 = yB2 - yA1;

        factor      = ( xB1A1 * yB2A1 - yB1A1 * xB2A1 ) / factor;
        fxintersect = factor * xA2A1 + xA1;
        fyintersect = factor * yA2A1 + yA1;
        // The "redundant" x and y segment range checks (which include near the
        // end points) are needed for the vertical and the horizontal cases.
        if ( ( BETW_NBCC( fxintersect, xA1, xA2 ) && BETW_NBCC( fyintersect, yA1, yA2 ) ) &&
             ( BETW_NBCC( fxintersect, xB1, xB2 ) && BETW_NBCC( fyintersect, yB1, yB2 ) ) )
        {
            // The intersect is close (within +/- PL_NBCC) to an end point or
            // corresponds to a definite crossing of the two line segments.
            // Find out which.
            if ( fabs( fxintersect - xA1 ) <= PL_NBCC && fabs( fyintersect - yA1 ) <= PL_NBCC )
                status = status | PL_NEAR_A1;
            else if ( fabs( fxintersect - xA2 ) <= PL_NBCC && fabs( fyintersect - yA2 ) <= PL_NBCC )
                status = status | PL_NEAR_A2;
            else if ( fabs( fxintersect - xB1 ) <= PL_NBCC && fabs( fyintersect - yB1 ) <= PL_NBCC )
                status = status | PL_NEAR_B1;
            else if ( fabs( fxintersect - xB2 ) <= PL_NBCC && fabs( fyintersect - yB2 ) <= PL_NBCC )
                status = status | PL_NEAR_B2;
            // N.B. if none of the above conditions hold then status remains at
            // zero to signal we have a definite crossing.
        }
        else
            status = status | PL_NOT_CROSSED;
    }
    if ( !status )
    {
        *xintersect = (PLINT) fxintersect;
        *yintersect = (PLINT) fyintersect;
    }

    return status;
}

#ifdef USE_FILL_INTERSECTION_POLYGON
// Decide if polygon has a positive orientation or not.
// Note the simple algorithm given in
// http://en.wikipedia.org/wiki/Curve_orientation is incorrect for
// non-convex polygons.  Instead, for the general nonintersecting case
// use the polygon area method given by
// http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/ where
// you project each edge of the polygon down to the X axis and take the
// area of the enclosed trapezoid.  The trapezoid areas outside the
// polygon are completely cancelled if you sum over all edges.  Furthermore,
// the sum of the trapezoid areas have terms which are zero when calculated
// with the telescoping rule so the final formula is quite simple.
int
positive_orientation( PLINT n, PLINT_VECTOR x, PLINT_VECTOR y )
{
    PLINT i, im1;
    // Use PLFLT for all calculations to avoid integer overflows.  Also,
    // the normal PLFLT has 64-bits which means you get exact integer
    // arithmetic well beyond the normal integer overflow limits.
    PLFLT twice_area = 0.;
    if ( n < 3 )
    {
        plwarn( "positive_orientation: internal logic error, n < 3" );
        return 0;
    }
    im1 = n - 1;
    for ( i = 0; i < n; i++ )
    {
        twice_area += (PLFLT) x[im1] * (PLFLT) y[i] - (PLFLT) x[i] * (PLFLT) y[im1];
        im1         = i;
    }
    if ( twice_area == 0. )
    {
        plwarn( "positive_orientation: internal logic error, twice_area == 0." );
        return 0;
    }
    else
        return twice_area > 0.;
}

// For the line with endpoints which are the (i1-1)th, and i1th
// vertices of polygon 1 with polygon 2 find all definite crossings
// with polygon 1.  (The full polygon 1 information is needed only to
// help sort out (NOT IMPLEMENTED YET) ambiguous crossings near a
// vertex of polygon 1.)  Sort those definite crossings in ascending
// order along the line between the (i1-1)th and i1th vertices of
// polygon 1, and return the first ncross (= 1 or = 2) crossings in the
// xcross, ycross, and i2cross arrays.  Return a zero or positive
// status code of the actual number of crossings retained up to the
// maximum allowed value of ncross.  If some error occurred, return a
// negative status code.

int
number_crossings( PLINT *xcross, PLINT *ycross, PLINT *i2cross, PLINT ncross,
                  PLINT i1, PLINT n1, PLINT_VECTOR x1, PLINT_VECTOR y1,
                  PLINT n2, PLINT_VECTOR x2, PLINT_VECTOR y2 )
{
    int i1m1, i2, i2m1, ifnotcrossed;
    int ifxsort, ifascend, count_crossings = 0, status = 0;
    PLINT xintersect, yintersect;

    i1m1 = i1 - 1;
    if ( i1m1 < 0 )
        i1m1 += n1;
    if ( !( ncross == 1 || ncross == 2 ) ||
         ( x1[i1m1] == x1[i1] && y1[i1m1] == y1[i1] ) || n1 < 2 || n2 < 2 )
    {
        plwarn( "findcrossings: invalid call" );
        return -1;
    }

    ifxsort  = abs( x1[i1] - x1[i1m1] ) > abs( y1[i1] - y1[i1m1] );
    ifascend = ( ifxsort && x1[i1] > x1[i1m1] ) ||
               ( !ifxsort && y1[i1] > y1[i1m1] );

    // Determine all crossings between the line between the (i1-1)th
    // and i1th vertices of polygon 1 and all edges of polygon 2.
    // Retain the lowest and (if ncross ==2) next lowest crossings in
    // order of x (or y if ifxsort is false) along the line from i1-1
    // to i1.

    i1m1 = i1 - 1;
    if ( i1m1 < 0 )
        i1m1 += n1;
    i2m1 = n2 - 1;
    for ( i2 = 0; i2 < n2; i2++ )
    {
        if ( !( x2[i2m1] == x2[i2] && y2[i2m1] == y2[i2] ) )
        {
            ifnotcrossed = notcrossed( &xintersect, &yintersect,
                x1[i1m1], y1[i1m1], x1[i1], y1[i1],
                x2[i2m1], y2[i2m1], x2[i2], y2[i2] );

            if ( !ifnotcrossed )
            {
                count_crossings++;
                if ( count_crossings == 1 )
                {
                    xcross[0]  = xintersect;
                    ycross[0]  = yintersect;
                    i2cross[0] = i2;
                    status     = 1;
                }
                else
                {
                    if ( ( ifxsort && ifascend && xintersect < xcross[0] ) ||
                         ( !ifxsort && ifascend && yintersect < ycross[0] ) ||
                         ( ifxsort && !ifascend && xintersect >= xcross[0] ) ||
                         ( !ifxsort && !ifascend && yintersect >= ycross[0] ) )
                    {
                        if ( ncross == 2 )
                        {
                            xcross[1]  = xcross[0];
                            ycross[1]  = ycross[0];
                            i2cross[1] = i2cross[0];
                            status     = 2;
                        }
                        xcross[0]  = xintersect;
                        ycross[0]  = yintersect;
                        i2cross[0] = i2;
                    }
                    else if ( ncross == 2 && ( count_crossings == 2 || (
                                                   ( ifxsort && ifascend && xintersect < xcross[1] ) ||
                                                   ( !ifxsort && ifascend && yintersect < ycross[1] ) ||
                                                   ( ifxsort && !ifascend && xintersect >= xcross[1] ) ||
                                                   ( !ifxsort && !ifascend && yintersect >= ycross[1] ) ) ) )
                    {
                        xcross[1]  = xintersect;
                        ycross[1]  = yintersect;
                        i2cross[1] = i2;
                        status     = 2;
                    }
                }
            }
        }
        i2m1 = i2;
    }
    return status;
}
#endif