/****************************************************************************
** $Id: qpointarray.cpp,v 2.27.2.1 1999/09/01 10:49:34 aavit Exp $
**
** Implementation of QPointArray class
**
** Created : 940213
**
** Copyright (C) 1992-1999 Troll Tech AS.  All rights reserved.
**
** This file is part of the Qt GUI Toolkit.
**
** This file may be distributed under the terms of the Q Public License
** as defined by Troll Tech AS of Norway and appearing in the file
** LICENSE.QPL included in the packaging of this file.
**
** Licensees holding valid Qt Professional Edition licenses may use this
** file in accordance with the Qt Professional Edition License Agreement
** provided with the Qt Professional Edition.
**
** See http://www.troll.no/pricing.html or email sales@troll.no for
** information about the Professional Edition licensing, or see
** http://www.troll.no/qpl/ for QPL licensing information.
**
*****************************************************************************/

#include "qpointarray.h"
#include "qrect.h"
#include "qbitarray.h"
#include "qdatastream.h"
#include "qwmatrix.h"
#include <stdarg.h>

const double Q_PI   = 3.14159265358979323846;   // pi


/*!
  \class QPointArray qpointarray.h
  \brief The QPointArray class provides an array of points.

  \ingroup drawing

  \inherit QArray

  The QPointArray is an array of QPoint objects. In addition to the functions 
  provided by QArray, QPointArray provides some handy methods:

  For convenient reading and writing of the point data: setPoints(), 
  putPoints(), point(), and setPoint().

  For geometry operations: boundingRect() and translate(). As for the latter,
  note that QWMatrix provides a map() function for more general transformation
  of QPointArrays.

  QPointArray is used by the QPainter to draw
  \link QPainter::drawLineSegments() line segments\endlink,
  \link QPainter::drawPolyline() polylines\endlink,
  \link QPainter::drawPolygon() polygons\endlink and
  \link QPainter::drawQuadBezier() Bezier curves\endlink.


  Note that since this class is a QArray, it is
  \link shclass.html explicitly shared\endlink
  and works with shallow copies by default.
*/


/*****************************************************************************
  QPointArray member functions
 *****************************************************************************/

/*!
  \fn QPointArray::QPointArray()
  Constructs a null point array.
  \sa isNull()
*/

/*!
  \fn QPointArray::QPointArray( int size )
  Constructs a point array with room for \e size points.
  Makes a null array if \e size == 0.

  \sa resize(), isNull()
*/

/*!
  \fn QPointArray::QPointArray( const QPointArray &a )
  Constructs a
  \link shclass.html shallow copy\endlink of the point array \e a.

  \sa copy()
*/

/*!
  Constructs a point array from the rectangle \e r.

  If \e closed is FALSE, then the point array will contain the
  following four points (in the listed order):
  <ol>
  <li> r.topLeft()
  <li> r.topRight()
  <li> r.bottomRight()
  <li> r.bottomLeft()
  </ol>

  If \e closed is TRUE, then a fifth point is set to r.topLeft() to
  close the point array.
*/

QPointArray::QPointArray( const QRect &r, bool closed )
{
    setPoints( 4, r.left(),  r.top(),
		  r.right(), r.top(),
		  r.right(), r.bottom(),
		  r.left(),  r.bottom() );
    if ( closed ) {
	resize( 5 );
	setPoint( 4, r.left(), r.top() );
    }
}

/*!
  Constructs a point array with \e nPoints points, taken from the
  \e points array.

  Equivalent to setPoints(nPoints,points).
*/

QPointArray::QPointArray( int nPoints, const QCOORD *points )
{
    setPoints( nPoints, points );
}


/*!
  \fn QPointArray &QPointArray::operator=( const QPointArray &a )
  Assigns a
  \link shclass.html shallow copy\endlink of \e a to this point array
  and returns a reference to this point array.

  Equivalent to assign( a ).

  \sa copy()
*/

/*!
  \fn QPointArray QPointArray::copy() const

  Creates a
  \link shclass.html deep copy\endlink of the array.
*/



/*!
  Translates all points in the array \e (dx,dy).
*/

void QPointArray::translate( int dx, int dy )
{
    register QPoint *p = data();
    register int i = size();
    QPoint pt( dx, dy );
    while ( i-- ) {
	*p += pt;
	p++;
    }
}


/*!
  Returns the point at position \e index in the array in \e *x and \e *y.
*/

void QPointArray::point( uint index, int *x, int *y ) const
{
    QPoint p = QArray<QPoint>::at( index );
    *x = (int)p.x();
    *y = (int)p.y();
}

/*!
  Returns the point at position \e index in the array.
*/

QPoint QPointArray::point( uint index ) const
{
    return QArray<QPoint>::at( index );
}

/*!
  Sets the point at position \e index in the array to \e (x,y).
*/

void QPointArray::setPoint( uint index, int x, int y )
{
    QArray<QPoint>::at( index ) = QPoint( x, y );
}

/*!
  Resizes the array to \e nPoints and sets the points in the array to
  the values taken from \e points.

  Returns TRUE if successful, or FALSE if the array could not be resized.

  Example:
  \code
    static QCOORD points[] = { 1,2, 3,4 };
    QPointArray a;
    a.setPoints( 2, points );
  \endcode

  The example code creates an array with two points (1,2) and (3,4).

  \sa resize(), putPoints()
*/

bool QPointArray::setPoints( int nPoints, const QCOORD *points )
{
    if ( !resize(nPoints) )
	return FALSE;
    int i = 0;
    while ( nPoints-- ) {			// make array of points
	setPoint( i++, *points, *(points+1) );
	points++;
	points++;
    }
    return TRUE;
}

/*!
  \fn void QPointArray::setPoint( uint i, const QPoint &p )

  Equivalent to setPoint( i, p.x(), p.y() ).
*/

/*!
  Resizes the array to \e nPoints and sets the points in the array to
  the values taken from the variable argument list.

  Returns TRUE if successful, or FALSE if the array could not be resized.

  Example:
  \code
    QPointArray a;
    a.setPoints( 2, 1,2, 3,4 );
  \endcode

  The example code creates an array with two points (1,2) and (3,4).

  \sa resize(), putPoints()
*/

bool QPointArray::setPoints( int nPoints, int firstx, int firsty,
			     ... )
{
    va_list ap;
    if ( !resize(nPoints) )
	return FALSE;
    setPoint( 0, firstx, firsty );		// set first point
    int i = 1, x, y;
    nPoints--;
    va_start( ap, firsty );
    while ( nPoints-- ) {
	x = va_arg( ap, int );
	y = va_arg( ap, int );
	setPoint( i++, x, y );
    }
    va_end( ap );
    return TRUE;
}

/*!
  Copies \e nPoints points from the \e points array into this point array.
  Will resize this point array if <code>index+nPoints</code> exceeds
  the size of the array.

  Returns TRUE if successful, or FALSE if the array could not be resized.

  Example:
  \code
    QPointArray a( 1 );
    a[0] = QPoint( 1, 2 );
    static QCOORD points[] = { 3,4, 5,6 };
    a.putPoints( 1, 2, points );
  \endcode

  The example code creates an array with three points: (1,2), (3,4)
  and (5,6).

  This function differs from setPoints() in that it does not resize the
  array unless the array size is exceeded.

  \sa resize(), setPoints()
*/

bool QPointArray::putPoints( int index, int nPoints, const QCOORD *points )
{
    if ( index + nPoints > (int)size() ) {	// extend array
	if ( !resize( index + nPoints ) )
	    return FALSE;
    }
    int i = index;
    while ( nPoints-- ) {			// make array of points
	setPoint( i++, *points, *(points+1) );
	points++;
	points++;
    }
    return TRUE;
}

/*!
  Copies \e nPoints points from the variable argument list into this point
  array. Will resize this point array if <code>index+nPoints</code> exceeds
  the size of the array.

  Returns TRUE if successful, or FALSE if the array could not be resized.

  Example:
  \code
    QPointArray a( 1 );
    a[0] = QPoint( 1, 2 );
    a.putPoints( 1, 2, 3,4, 5,6 );
  \endcode

  The example code creates an array with two points (1,2), (3,4) and (5,6).

  This function differs from setPoints() because it does not resize the
  array unless the array size is exceeded.

  \sa resize(), setPoints()
*/

bool QPointArray::putPoints( int index, int nPoints, int firstx, int firsty,
			     ... )
{
    va_list ap;
    if ( index + nPoints > (int)size() ) {	// extend array
	if ( !resize(index + nPoints) )
	    return FALSE;
    }
    if ( nPoints <= 0 )
	return TRUE;
    setPoint( index, firstx, firsty );		// set first point
    int i = index + 1, x, y;
    nPoints--;
    va_start( ap, firsty );
    while ( nPoints-- ) {
	x = va_arg( ap, int );
	y = va_arg( ap, int );
	setPoint( i++, x, y );
    }
    va_end( ap );
    return TRUE;
}


/*!
  Returns the bounding rectangle of the points in the array, or
  QRect(0,0,0,0) if the array is empty.
*/

QRect QPointArray::boundingRect() const
{
    if ( isEmpty() )
	return QRect( 0, 0, 0, 0 );		// null rectangle
    register QPoint *pd = data();
    int minx, maxx, miny, maxy;
    minx = maxx = pd->x();
    miny = maxy = pd->y();
    pd++;
    for ( int i=1; i<(int)size(); i++ ) {	// find min+max x and y
	if ( pd->x() < minx )
	    minx = pd->x();
	else if ( pd->x() > maxx )
	    maxx = pd->x();
	if ( pd->y() < miny )
	    miny = pd->y();
	else if ( pd->y() > maxy )
	    maxy = pd->y();
	pd++;
    }
    return QRect( QPoint(minx,miny), QPoint(maxx,maxy) );
}


static inline int fix_angle( int a )
{
    if ( a > 16*360 )
	a %= 16*360;
    else if ( a < -16*360 )
	a = -((-a) % 16*360);
    return a;
}

/*!
  Sets the points of the array to those describing an arc of an
  ellipse with size \a w by \a h and position (\a x, \a y ), starting
  from angle \a1, spanning \a a2.  The resulting array has sufficient
  resolution for pixel accuracy (see the overloaded function which
  takes an additional QWMatrix parameter).

  Angles are specified in 16ths of a degree,
  i.e. a full circle equals 5760 (16*360). Positive values mean
  counter-clockwise while negative values mean clockwise direction.
  Zero degrees is at the 3'o clock position.
*/

void QPointArray::makeArc( int x, int y, int w, int h, int a1, int a2 )
{
    QWMatrix unit;
    makeArc(x,y,w,h,a1,a2,unit);
#if QT_OLD_MAKEELLIPSE // ### WWA says discard this.
    a1 = fix_angle( a1 );
    if ( a1 < 0 )
	a1 += 16*360;
    a2 = fix_angle( a2 );
    int a3 = a2 > 0 ? a2 : -a2;			// abs angle
    makeEllipse( x, y, w, h );
    int npts = a3*size()/(16*360);		// # points in arc array
    QPointArray a(npts);
    int i = a1*size()/(16*360);
    int j = 0;
    if ( a2 > 0 ) {
	while ( npts-- ) {
	    if ( i >= (int)size() )			// wrap index
		i = 0;
	    a.QArray<QPoint>::at( j++ ) = QArray<QPoint>::at( i++ );
	}
    } else {
	while ( npts-- ) {
	    if ( i < 0 )				// wrap index
		i = (int)size()-1;
	    a.QArray<QPoint>::at( j++ ) = QArray<QPoint>::at( i-- );
	}
    }
    *this = a;
    return;
#endif
}


// Based upon:
//   parelarc.c from Graphics Gems III
//   VanAken / Simar, "A Parametric Elliptical Arc Algorithm"
//
static void
qtr_elips(QPointArray& a, int& offset, double dxP, double dyP, double dxQ, double dyQ, double dxK, double dyK, int m)
{
#define PIV2  102944     /* fixed point PI/2 */
#define TWOPI 411775     /* fixed point 2*PI */
#define HALF  32768      /* fixed point 1/2 */

    int xP, yP, xQ, yQ, xK, yK;
    xP = int(dxP * 65536.0); yP = int(dyP * 65536.0);
    xQ = int(dxQ * 65536.0); yQ = int(dyQ * 65536.0);
    xK = int(dxK * 65536.0); yK = int(dyK * 65536.0);

    int i;
    int vx, ux, vy, uy, xJ, yJ;

    vx = xK - xQ;                 /* displacements from center */
    ux = xK - xP;
    vy = yK - yQ;
    uy = yK - yP;
    xJ = xP - vx + HALF;          /* center of ellipse J */
    yJ = yP - vy + HALF;

    int r;
    ux -= (r = ux >> (2*m + 3));  /* cancel 2nd-order error */
    ux -= (r >>= (2*m + 4));      /* cancel 4th-order error */
    ux -= r >> (2*m + 3);         /* cancel 6th-order error */
    ux += vx >> (m + 1);          /* cancel 1st-order error */
    uy -= (r = uy >> (2*m + 3));  /* cancel 2nd-order error */
    uy -= (r >>= (2*m + 4));      /* cancel 4th-order error */
    uy -= r >> (2*m + 3);         /* cancel 6th-order error */
    uy += vy >> (m + 1);          /* cancel 1st-order error */

    int n = offset;
    for (i = (PIV2 << m) >> 16; i >= 0; --i) {
        a[n++] = QPoint((xJ + vx) >> 16, (yJ + vy) >> 16);
        ux -= vx >> m;
        vx += ux >> m;
        uy -= vy >> m;
        vy += uy >> m;
    }
    offset = n;

#undef PIV2
#undef TWOPI
#undef HALF
}


/*!
  Sets the points of the array to those describing an arc of an
  ellipse with size \a w by \a h and position (\a x, \a y ), starting
  from angle \a1, spanning \a a2, transformed by the matrix \a xf.
  The resulting array has sufficient resolution for pixel accuracy.

  Angles are specified in 16ths of a degree,
  i.e. a full circle equals 5760 (16*360). Positive values mean
  counter-clockwise while negative values mean clockwise direction.
  Zero degrees is at the 3'o clock position.
*/
void QPointArray::makeArc( int x, int y, int w, int h,
			       int a1, int a2,
			       const QWMatrix& xf )
{
    bool rev = a2 < 0;
    if ( rev ) {
	a1 += a2;
	a2 = -a2;
    }
    a1 = fix_angle( a1 );
    if ( a1 < 0 )
	a1 += 16*360;
    a2 = fix_angle( a2 );

    bool arc = a1 != 0 || a2 != 360*16 || rev;


    double xP, yP, xQ, yQ, xK, yK;

    xf.map(x+w, y+h/2.0, &xP, &yP);
    xf.map(x+w/2.0, y, &xQ, &yQ);
    xf.map(x+w, y, &xK, &yK);

    int m = 2;
    int max;
    int q = int(QMAX(QABS(xP-xQ),QABS(yP-yQ)));
    if ( arc )
	q *= 2;
    do {
	m++;
	max = 4*(1 + int((Q_PI/2)*(1<<m)));
    } while (max < q && m < 16); // 16 limits memory usage on HUGE arcs
    resize(max);

    int n = 0;

    double inc = 1.0/(1<<m);

    int nquad[4];
    nquad[0]=0;

    qtr_elips(*this, n, xP, yP, xQ, yQ, xK, yK, m);
    nquad[1] = n;

    xP = xQ; yP = yQ;
    xf.map(x, y+h/2.0, &xQ, &yQ);
    xf.map(x, y, &xK, &yK);
    qtr_elips(*this, n, xP, yP, xQ, yQ, xK, yK, m);
    nquad[2] = n;

    xP = xQ; yP = yQ;
    xf.map(x+w/2.0, y+h, &xQ, &yQ);
    xf.map(x, y+h, &xK, &yK);
    qtr_elips(*this, n, xP, yP, xQ, yQ, xK, yK, m);
    nquad[3] = n;

    xP = xQ; yP = yQ;
    xf.map(x+w, y+h/2.0, &xQ, &yQ);
    xf.map(x+w, y+h, &xK, &yK);
    qtr_elips(*this, n, xP, yP, xQ, yQ, xK, yK, m);

    if ( arc ) {
	// We could merge the sub-ellipse extraction into the above so
	// that we didn't generate points we don't need, but this is
	// clearer, and optimizes for the common case.
	double da1 = double(a1)*Q_PI / (360*8);
	double da2 = double(a2)*Q_PI / (360*8);
	int t = 0;
	while ( da1 > Q_PI/2 ) {
	    da1 -= Q_PI/2;
	    t++;
	}
	int i = nquad[t]+int(da1/inc+0.5);
	int k = int(da2/inc+0.5);
	if ( rev ) {
	    QPointArray r(k);
	    int j = 0;
	    while (k--)
		r[j++] = at((i+k)%n);
	    *this = r;
	} else {
	    int j = 0;
	    while (j < k) {
		setPoint(j,at((k+j)%n));
		j++;
	    }
	    resize(j);
	}
    } else {
	resize(n);
    }
}

/*!
  Sets the points of the array to those describing an ellipse with
  size \a w by \a h and position (\a x, \a y ).

  The returned array has sufficient
  resolution for use as pixels (see the overloaded function which
  takes an additional QWMatrix parameter).
*/
void QPointArray::makeEllipse( int xx, int yy, int w, int h )
{						// midpoint, 1/4 ellipse
    QWMatrix unit;
    makeArc(xx,yy,w,h,0,360*16,unit);
    return;

#if QT_OLD_MAKEELLIPSE // ### WWA says discard this.
    if ( w <= 0 || h <= 0 ) {
	if ( w == 0 || h == 0 ) {
	    resize( 0 );
	    return;
	}
	if ( w < 0 ) {				// negative width
	    w = -w;
	    xx -= w;
	}
	if ( h < 0 ) {				// negative height
	    h = -h;
	    yy -= h;
	}
    }
    int s = (w+h+2)/2;				// max size of x,y array
    int *px = new int[s];			// 1/4th of ellipse
    int *py = new int[s];
    int x, y, i=0;
    double d1, d2;
    double a2=(w/2)*(w/2),  b2=(h/2)*(h/2);
    x = 0;
    y = int(h/2);
    d1 = b2 - a2*(h/2) + 0.25*a2;
    px[i] = x;
    py[i] = y;
    i++;
    while ( a2*(y-0.5) > b2*(x+0.5) ) {		// region 1
	if ( d1 < 0 ) {
	    d1 = d1 + b2*(3.0+2*x);
	    x++;
	} else {
	    d1 = d1 + b2*(3.0+2*x) + 2.0*a2*(1-y);
	    x++;
	    y--;
	}
	px[i] = x;
	py[i] = y;
	i++;
    }
    d2 = b2*(x+0.5)*(x+0.5) + a2*(y-1)*(y-1) - a2*b2;
    while ( y > 0 ) {				// region 2
	if ( d2 < 0 ) {
	    d2 = d2 + 2.0*b2*(x+1) + a2*(3-2*y);
	    x++;
	    y--;
	} else {
	    d2 = d2 + a2*(3-2*y);
	    y--;
	}
	px[i] = x;
	py[i] = y;
	i++;
    }
    s = i;
    resize( 4*s );				// make full point array
    xx += w/2;
    yy += h/2;
    for ( i=0; i<s; i++ ) {			// mirror
	x = px[i];
	y = py[i];
	setPoint( s-i-1, xx+x, yy-y );
	setPoint( s+i, xx-x, yy-y );
	setPoint( 3*s-i-1, xx-x, yy+y );
	setPoint( 3*s+i, xx+x, yy+y );
    }
    delete[] px;
    delete[] py;
#endif
}


// Work functions for QPointArray::quadBezier()
static
void split(const double *p, double *l, double *r)
{
    double tmpx;
    double tmpy;

    l[0] =  p[0];
    l[1] =  p[1];
    r[6] =  p[6];
    r[7] =  p[7];

    l[2] = (p[0]+ p[2])/2;
    l[3] = (p[1]+ p[3])/2;
    tmpx = (p[2]+ p[4])/2;
    tmpy = (p[3]+ p[5])/2;
    r[4] = (p[4]+ p[6])/2;
    r[5] = (p[5]+ p[7])/2;

    l[4] = (l[2]+ tmpx)/2;
    l[5] = (l[3]+ tmpy)/2;
    r[2] = (tmpx + r[4])/2;
    r[3] = (tmpy + r[5])/2;

    l[6] = (l[4]+ r[2])/2;
    l[7] = (l[5]+ r[3])/2;
    r[0] = l[6];
    r[1] = l[7];
}
// Based on:
//
//   A Fast 2D Point-On-Line Test
//   by Alan Paeth
//   from "Graphics Gems", Academic Press, 1990
static
int pnt_on_line( const double* p, const double* q, const double* t )
{
/*
 * given a line through P:(px,py) Q:(qx,qy) and T:(tx,ty)
 * return 0 if T is not on the line through      <--P--Q-->
 *        1 if T is on the open ray ending at P: <--P
 *        2 if T is on the closed interior along:   P--Q
 *        3 if T is on the open ray beginning at Q:    Q-->
 *
 * Example: consider the line P = (3,2), Q = (17,7). A plot
 * of the test points T(x,y) (with 0 mapped onto '.') yields:
 *
 *     8| . . . . . . . . . . . . . . . . . 3 3
 *  Y  7| . . . . . . . . . . . . . . 2 2 Q 3 3    Q = 2
 *     6| . . . . . . . . . . . 2 2 2 2 2 . . .
 *  a  5| . . . . . . . . 2 2 2 2 2 2 . . . . .
 *  x  4| . . . . . 2 2 2 2 2 2 . . . . . . . .
 *  i  3| . . . 2 2 2 2 2 . . . . . . . . . . .
 *  s  2| 1 1 P 2 2 . . . . . . . . . . . . . .    P = 2
 *     1| 1 1 . . . . . . . . . . . . . . . . .
 *      +--------------------------------------
 *        1 2 3 4 5 X-axis 10        15      19
 *
 * Point-Line distance is normalized with the Infinity Norm
 * avoiding square-root code and tightening the test vs the
 * Manhattan Norm. All math is done on the field of integers.
 * The latter replaces the initial ">= MAX(...)" test with
 * "> (ABS(qx-px) + ABS(qy-py))" loosening both inequality
 * and norm, yielding a broader target line for selection.
 * The tightest test is employed here for best discrimination
 * in merging collinear (to grid coordinates) vertex chains
 * into a larger, spanning vectors within the Lemming editor.
 */

    if ( QABS((q[1]-p[1])*(t[0]-p[0])-(t[1]-p[1])*(q[0]-p[0])) >=
        (QMAX(QABS(q[0]-p[0]), QABS(q[1]-p[1])))) return 0;

    if (((q[0]<p[0])&&(p[0]<t[0])) || ((q[1]<p[1])&&(p[1]<t[1])))
	return 1 ;
    if (((t[0]<p[0])&&(p[0]<q[0])) || ((t[1]<p[1])&&(p[1]<q[1])))
	return 1 ;
    if (((p[0]<q[0])&&(q[0]<t[0])) || ((p[1]<q[1])&&(q[1]<t[1])))
	return 3 ;
    if (((t[0]<q[0])&&(q[0]<p[0])) || ((t[1]<q[1])&&(q[1]<p[1])))
	return 3 ;

    return 2 ;
}
static
void polygonizeQBezier( double* acc, int& accsize, const double ctrl[],
			int maxsize )
{
    if ( accsize > maxsize / 2 )
    {
	// This never happens in practice.

	if ( accsize >= maxsize-4 )
	    return;
	// Running out of space - approximate by a line.
        acc[accsize++] = ctrl[0];
	acc[accsize++] = ctrl[1];
	acc[accsize++] = ctrl[6];
	acc[accsize++] = ctrl[7];
	return;
    }

    //intersects:
    double l[8];
    double r[8];
    split( ctrl, l, r);

    if ( pnt_on_line( &ctrl[0], &ctrl[6], &ctrl[2] ) == 2
      && pnt_on_line( &ctrl[0], &ctrl[6], &ctrl[4] ) == 2 )
    {
	// Approximate by 2 lines.
	acc[accsize++] = l[0];
	acc[accsize++] = l[1];
	acc[accsize++] = l[6];
	acc[accsize++] = l[7];
	acc[accsize++] = r[6];
	acc[accsize++] = r[7];
	return;
    }

    // Too big and too curved - recusively subdivide.
    polygonizeQBezier( acc, accsize, l, maxsize );
    polygonizeQBezier( acc, accsize, r, maxsize );
}

/*!
  Returns the Bezier points for the four control points in this array.
*/

QPointArray QPointArray::quadBezier() const
{
#ifdef USE_SIMPLE_QBEZIER_CODE
    if ( size() != 4 ) {
#if defined(CHECK_RANGE)
	qWarning( "QPointArray::bezier: The array must have 4 control points" );
#endif
	QPointArray p;
	return p;
    }

    int v;
    const int n = 3;				// n + 1 control points
    float xvec[4];
    float yvec[4];
    for ( v=0; v<=n; v++ ) {			// store all x,y in xvec,yvec
	int x, y;
	point( v, &x, &y );
	xvec[v] = (float)x;
	yvec[v] = (float)y;
    }

    QRect r = boundingRect();
    int m = QMAX(r.width(),r.height())/2;
    m = QMIN(m,30);				// m = number of result points
    if ( m < 2 )				// at least two points
	m = 2;
    QPointArray p( m );				// p = Bezier point array
    register QPointData *pd = p.data();

    float x0 = xvec[0],	 y0 = yvec[0];
    float dt = 1.0F/m;
    float cx = 3.0F * (xvec[1] - x0);
    float bx = 3.0F * (xvec[2] - xvec[1]) - cx;
    float ax = xvec[3] - (x0 + cx + bx);
    float cy = 3.0F * (yvec[1] - y0);
    float by = 3.0F * (yvec[2] - yvec[1]) - cy;
    float ay = yvec[3] - (y0 + cy + by);
    float t = dt;

    pd->rx() = (QCOORD)xvec[0];
    pd->ry() = (QCOORD)yvec[0];
    pd++;
    m -= 2;

    while ( m-- ) {
	pd->rx() = (QCOORD)qRound( ((ax * t + bx) * t + cx) * t + x0 );
	pd->ry() = (QCOORD)qRound( ((ay * t + by) * t + cy) * t + y0 );
	pd++;
	t += dt;
    }

    pd->rx() = (QCOORD)xvec[3];
    pd->ry() = (QCOORD)yvec[3];

    return p;
#else

    if ( size() != 4 ) {
#if defined(CHECK_RANGE)
	qWarning( "QPointArray::bezier: The array must have 4 control points" );
#endif
	QPointArray pa;
	return pa;
    } else {
	QRect r = boundingRect();
	int m = 4+2*QMAX(r.width(),r.height());
	double *p = new double[m];
	double *ctrl = new double[8];
	int i;
	for (i=0; i<4; i++) {
	    ctrl[i*2] = at(i).x();
	    ctrl[i*2+1] = at(i).y();
	}
	int len=0;
	polygonizeQBezier( p, len, ctrl, m );
	QPointArray pa(len/2);
	int j=0;
	for (i=0; j<len; i++) {
	    // Don't round - it looks terrible
	    int x = int(p[j++]);
	    int y = int(p[j++]);
	    pa[i] = QPoint(x,y);
	}
	delete[] p;
	delete[] ctrl;

	return pa;
    }

#endif
}


/*****************************************************************************
  QPointArray stream functions
 *****************************************************************************/

/*!
  \relates QPointArray
  Writes a point array to the stream and returns a reference to the stream.

  The serialization format is:
  <ol>
  <li> The array size (UINT32)
  <li> The array points (QPoint)
  </ol>
*/

QDataStream &operator<<( QDataStream &s, const QPointArray &a )
{
    register uint i;
    uint len = a.size();
    s << len;					// write size of array
    for ( i=0; i<len; i++ )			// write each point
	s << a.point( i );
    return s;
}

/*!
  \relates QPointArray
  Reads a point array from the stream and returns a reference to the stream.
*/

QDataStream &operator>>( QDataStream &s, QPointArray &a )
{
    register uint i;
    uint len;
    s >> len;					// read size of array
    if ( !a.resize( len ) )			// no memory
	return s;
    QPoint p;
    for ( i=0; i<len; i++ ) {			// read each point
	s >> p;
	a.setPoint( i, p );
    }
    return s;
}




struct QShortPoint {			// Binary compatible with XPoint
    short x, y;
};

uint QPointArray::splen = 0;
void* QPointArray::sp = 0;		// Really a QShortPoint*

/*!
  \internal

  Converts the point coords to short (16bit) size, compatible with
  X11's XPoint structure. The pointer returned points to a static
  array, so its contents will be overwritten the next time this
  function is called.
*/

void* QPointArray::shortPoints( int index, int nPoints ) const
{

    if ( isNull() || !nPoints )
	return 0;
    QPoint* p = data();
    p += index;
    uint i = nPoints < 0 ? size() : nPoints;
    if ( splen < i ) {
	if ( sp )
	    delete[] ((QShortPoint*)sp);
	sp = new QShortPoint[i];
	splen = i;
    }
    QShortPoint* ps = (QShortPoint*)sp;
    while ( i-- ) {
	ps->x = (short)p->x();
	ps->y = (short)p->y();
	p++;
	ps++;
    }
    return sp;
}


/*!
  \internal

  Deallocates the internal buffer used by shortPoints().
*/

void QPointArray::cleanBuffers()
{
    if ( sp )
	delete[] ((QShortPoint*)sp);
    sp = 0;
    splen = 0;
}