/*M///////////////////////////////////////////////////////////////////////////////////////
//
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//  If you do not agree to this license, do not download, install,
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//
//                        Intel License Agreement
//                For Open Source Computer Vision Library
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//M*/
#include "_cv.h"

/* calculates length of a curve (e.g. contour perimeter) */
CV_IMPL  double
cvArcLength( const void *array, CvSlice slice, int is_closed )
{
    double perimeter = 0;

    CV_FUNCNAME( "cvArcLength" );

    __BEGIN__;

    int i, j = 0, count;
    const int N = 16;
    float buf[N];
    CvMat buffer = cvMat( 1, N, CV_32F, buf ); 
    CvSeqReader reader;
    CvContour contour_header;
    CvSeq* contour = 0;
    CvSeqBlock block;

    if( CV_IS_SEQ( array ))
    {
        contour = (CvSeq*)array;
        if( !CV_IS_SEQ_POLYLINE( contour ))
            CV_ERROR( CV_StsBadArg, "Unsupported sequence type" );
        if( is_closed < 0 )
            is_closed = CV_IS_SEQ_CLOSED( contour );
    }
    else
    {
        is_closed = is_closed > 0;
        CV_CALL( contour = cvPointSeqFromMat(
            CV_SEQ_KIND_CURVE | (is_closed ? CV_SEQ_FLAG_CLOSED : 0),
            array, &contour_header, &block ));
    }

    if( contour->total > 1 )
    {
        int is_float = CV_SEQ_ELTYPE( contour ) == CV_32FC2;
        
        cvStartReadSeq( contour, &reader, 0 );
        cvSetSeqReaderPos( &reader, slice.start_index );
        count = cvSliceLength( slice, contour );

        count -= !is_closed && count == contour->total;

        /* scroll the reader by 1 point */
        reader.prev_elem = reader.ptr;
        CV_NEXT_SEQ_ELEM( sizeof(CvPoint), reader );

        for( i = 0; i < count; i++ )
        {
            float dx, dy;

            if( !is_float )
            {
                CvPoint* pt = (CvPoint*)reader.ptr;
                CvPoint* prev_pt = (CvPoint*)reader.prev_elem;

                dx = (float)pt->x - (float)prev_pt->x;
                dy = (float)pt->y - (float)prev_pt->y;
            }
            else
            {
                CvPoint2D32f* pt = (CvPoint2D32f*)reader.ptr;
                CvPoint2D32f* prev_pt = (CvPoint2D32f*)reader.prev_elem;

                dx = pt->x - prev_pt->x;
                dy = pt->y - prev_pt->y;
            }

            reader.prev_elem = reader.ptr;
            CV_NEXT_SEQ_ELEM( contour->elem_size, reader );

            buffer.data.fl[j] = dx * dx + dy * dy;
            if( ++j == N || i == count - 1 )
            {
                buffer.cols = j;
                cvPow( &buffer, &buffer, 0.5 );
                for( ; j > 0; j-- )
                    perimeter += buffer.data.fl[j-1];
            }
        }
    }

    __END__;

    return perimeter;
}


static CvStatus
icvFindCircle( CvPoint2D32f pt0, CvPoint2D32f pt1,
               CvPoint2D32f pt2, CvPoint2D32f * center, float *radius )
{
    double x1 = (pt0.x + pt1.x) * 0.5;
    double dy1 = pt0.x - pt1.x;
    double x2 = (pt1.x + pt2.x) * 0.5;
    double dy2 = pt1.x - pt2.x;
    double y1 = (pt0.y + pt1.y) * 0.5;
    double dx1 = pt1.y - pt0.y;
    double y2 = (pt1.y + pt2.y) * 0.5;
    double dx2 = pt2.y - pt1.y;
    double t = 0;

    CvStatus result = CV_OK;

    if( icvIntersectLines( x1, dx1, y1, dy1, x2, dx2, y2, dy2, &t ) >= 0 )
    {
        center->x = (float) (x2 + dx2 * t);
        center->y = (float) (y2 + dy2 * t);
        *radius = (float) icvDistanceL2_32f( *center, pt0 );
    }
    else
    {
        center->x = center->y = 0.f;
        radius = 0;
        result = CV_NOTDEFINED_ERR;
    }

    return result;
}


CV_INLINE double icvIsPtInCircle( CvPoint2D32f pt, CvPoint2D32f center, float radius )
{
    double dx = pt.x - center.x;
    double dy = pt.y - center.y;
    return (double)radius*radius - dx*dx - dy*dy;
}


static int
icvFindEnslosingCicle4pts_32f( CvPoint2D32f * pts, CvPoint2D32f * _center, float *_radius )
{
    int shuffles[4][4] = { {0, 1, 2, 3}, {0, 1, 3, 2}, {2, 3, 0, 1}, {2, 3, 1, 0} };

    int idxs[4] = { 0, 1, 2, 3 };
    int i, j, k = 1, mi = 0;
    float max_dist = 0;
    CvPoint2D32f center;
    CvPoint2D32f min_center;
    float radius, min_radius = FLT_MAX;
    CvPoint2D32f res_pts[4];

    center = min_center = pts[0];
    radius = 1.f;

    for( i = 0; i < 4; i++ )
        for( j = i + 1; j < 4; j++ )
        {
            float dist = icvDistanceL2_32f( pts[i], pts[j] );

            if( max_dist < dist )
            {
                max_dist = dist;
                idxs[0] = i;
                idxs[1] = j;
            }
        }

    if( max_dist == 0 )
        goto function_exit;

    k = 2;
    for( i = 0; i < 4; i++ )
    {
        for( j = 0; j < k; j++ )
            if( i == idxs[j] )
                break;
        if( j == k )
            idxs[k++] = i;
    }

    center = cvPoint2D32f( (pts[idxs[0]].x + pts[idxs[1]].x)*0.5f,
                           (pts[idxs[0]].y + pts[idxs[1]].y)*0.5f );
    radius = (float)(icvDistanceL2_32f( pts[idxs[0]], center )*1.03);
    if( radius < 1.f )
        radius = 1.f;

    if( icvIsPtInCircle( pts[idxs[2]], center, radius ) >= 0 &&
        icvIsPtInCircle( pts[idxs[3]], center, radius ) >= 0 )
    {
        k = 2; //rand()%2+2;
    }
    else
    {
        mi = -1;
        for( i = 0; i < 4; i++ )
        {
            if( icvFindCircle( pts[shuffles[i][0]], pts[shuffles[i][1]],
                               pts[shuffles[i][2]], &center, &radius ) >= 0 )
            {
                radius *= 1.03f;
                if( radius < 2.f )
                    radius = 2.f;

                if( icvIsPtInCircle( pts[shuffles[i][3]], center, radius ) >= 0 &&
                    min_radius > radius )
                {
                    min_radius = radius;
                    min_center = center;
                    mi = i;
                }
            }
        }
        assert( mi >= 0 );
        if( mi < 0 )
            mi = 0;
        k = 3;
        center = min_center;
        radius = min_radius;
        for( i = 0; i < 4; i++ )
            idxs[i] = shuffles[mi][i];
    }

  function_exit:

    *_center = center;
    *_radius = radius;

    /* reorder output points */
    for( i = 0; i < 4; i++ )
        res_pts[i] = pts[idxs[i]];

    for( i = 0; i < 4; i++ )
    {
        pts[i] = res_pts[i];
        assert( icvIsPtInCircle( pts[i], center, radius ) >= 0 );
    }

    return k;
}


CV_IMPL int
cvMinEnclosingCircle( const void* array, CvPoint2D32f * _center, float *_radius )
{
    const int max_iters = 100;
    CvPoint2D32f center = { 0, 0 };
    float radius = 0;
    int result = 0;

    if( _center )
        _center->x = _center->y = 0.f;
    if( _radius )
        *_radius = 0;

    CV_FUNCNAME( "cvMinEnclosingCircle" );

    __BEGIN__;

    CvSeqReader reader;
    int i, k, count;
    CvPoint2D32f pts[8];
    CvContour contour_header;
    CvSeqBlock block;
    CvSeq* sequence = 0;
    int is_float;

    if( !_center || !_radius )
        CV_ERROR( CV_StsNullPtr, "Null center or radius pointers" );

    if( CV_IS_SEQ(array) )
    {
        sequence = (CvSeq*)array;
        if( !CV_IS_SEQ_POINT_SET( sequence ))
            CV_ERROR( CV_StsBadArg, "The passed sequence is not a valid contour" );
    }
    else
    {
        CV_CALL( sequence = cvPointSeqFromMat(
            CV_SEQ_KIND_GENERIC, array, &contour_header, &block ));
    }

    if( sequence->total <= 0 )
        CV_ERROR_FROM_STATUS( CV_BADSIZE_ERR );

    CV_CALL( cvStartReadSeq( sequence, &reader, 0 ));

    count = sequence->total;
    is_float = CV_SEQ_ELTYPE(sequence) == CV_32FC2;

    if( !is_float )
    {
        CvPoint *pt_left, *pt_right, *pt_top, *pt_bottom;
        CvPoint pt;
        pt_left = pt_right = pt_top = pt_bottom = (CvPoint *)(reader.ptr);
        CV_READ_SEQ_ELEM( pt, reader );

        for( i = 1; i < count; i++ )
        {
            CvPoint* pt_ptr = (CvPoint*)reader.ptr;
            CV_READ_SEQ_ELEM( pt, reader );

            if( pt.x < pt_left->x )
                pt_left = pt_ptr;
            if( pt.x > pt_right->x )
                pt_right = pt_ptr;
            if( pt.y < pt_top->y )
                pt_top = pt_ptr;
            if( pt.y > pt_bottom->y )
                pt_bottom = pt_ptr;
        }

        pts[0] = cvPointTo32f( *pt_left );
        pts[1] = cvPointTo32f( *pt_right );
        pts[2] = cvPointTo32f( *pt_top );
        pts[3] = cvPointTo32f( *pt_bottom );
    }
    else
    {
        CvPoint2D32f *pt_left, *pt_right, *pt_top, *pt_bottom;
        CvPoint2D32f pt;
        pt_left = pt_right = pt_top = pt_bottom = (CvPoint2D32f *) (reader.ptr);
        CV_READ_SEQ_ELEM( pt, reader );

        for( i = 1; i < count; i++ )
        {
            CvPoint2D32f* pt_ptr = (CvPoint2D32f*)reader.ptr;
            CV_READ_SEQ_ELEM( pt, reader );

            if( pt.x < pt_left->x )
                pt_left = pt_ptr;
            if( pt.x > pt_right->x )
                pt_right = pt_ptr;
            if( pt.y < pt_top->y )
                pt_top = pt_ptr;
            if( pt.y > pt_bottom->y )
                pt_bottom = pt_ptr;
        }

        pts[0] = *pt_left;
        pts[1] = *pt_right;
        pts[2] = *pt_top;
        pts[3] = *pt_bottom;
    }

    for( k = 0; k < max_iters; k++ )
    {
        double min_delta = 0, delta;
        CvPoint2D32f ptfl;
        
        icvFindEnslosingCicle4pts_32f( pts, &center, &radius );
        cvStartReadSeq( sequence, &reader, 0 );

        for( i = 0; i < count; i++ )
        {
            if( !is_float )
            {
                ptfl.x = (float)((CvPoint*)reader.ptr)->x;
                ptfl.y = (float)((CvPoint*)reader.ptr)->y;
            }
            else
            {
                ptfl = *(CvPoint2D32f*)reader.ptr;
            }
            CV_NEXT_SEQ_ELEM( sequence->elem_size, reader );

            delta = icvIsPtInCircle( ptfl, center, radius );
            if( delta < min_delta )
            {
                min_delta = delta;
                pts[3] = ptfl;
            }
        }
        result = min_delta >= 0;
        if( result )
            break;
    }

    if( !result )
    {
        cvStartReadSeq( sequence, &reader, 0 );
        radius = 0.f;

        for( i = 0; i < count; i++ )
        {
            CvPoint2D32f ptfl;
            float t, dx, dy;

            if( !is_float )
            {
                ptfl.x = (float)((CvPoint*)reader.ptr)->x;
                ptfl.y = (float)((CvPoint*)reader.ptr)->y;
            }
            else
            {
                ptfl = *(CvPoint2D32f*)reader.ptr;
            }

            CV_NEXT_SEQ_ELEM( sequence->elem_size, reader );
            dx = center.x - ptfl.x;
            dy = center.y - ptfl.y;
            t = dx*dx + dy*dy;
            radius = MAX(radius,t);
        }

        radius = (float)sqrt(radius);
        result = 1;
    }

    __END__;

    *_center = center;
    *_radius = radius;

    return result;
}


/* area of a whole sequence */
static CvStatus
icvContourArea( const CvSeq* contour, double *area )
{
    if( contour->total )
    {
        CvSeqReader reader;
        int lpt = contour->total;
        double a00 = 0, xi_1, yi_1;
        int is_float = CV_SEQ_ELTYPE(contour) == CV_32FC2;

        cvStartReadSeq( contour, &reader, 0 );

        if( !is_float )
        {
            xi_1 = ((CvPoint*)(reader.ptr))->x;
            yi_1 = ((CvPoint*)(reader.ptr))->y;
        }
        else
        {
            xi_1 = ((CvPoint2D32f*)(reader.ptr))->x;
            yi_1 = ((CvPoint2D32f*)(reader.ptr))->y;
        }
        CV_NEXT_SEQ_ELEM( contour->elem_size, reader );
        
        while( lpt-- > 0 )
        {
            double dxy, xi, yi;

            if( !is_float )
            {
                xi = ((CvPoint*)(reader.ptr))->x;
                yi = ((CvPoint*)(reader.ptr))->y;
            }
            else
            {
                xi = ((CvPoint2D32f*)(reader.ptr))->x;
                yi = ((CvPoint2D32f*)(reader.ptr))->y;
            }
            CV_NEXT_SEQ_ELEM( contour->elem_size, reader );

            dxy = xi_1 * yi - xi * yi_1;
            a00 += dxy;
            xi_1 = xi;
            yi_1 = yi;
        }

        *area = a00 * 0.5;
    }
    else
        *area = 0;

    return CV_OK;
}


/****************************************************************************************\

 copy data from one buffer to other buffer 

\****************************************************************************************/

static CvStatus
icvMemCopy( double **buf1, double **buf2, double **buf3, int *b_max )
{
    int bb;

    if( *buf1 == NULL && *buf2 == NULL || *buf3 == NULL )
        return CV_NULLPTR_ERR;

    bb = *b_max;
    if( *buf2 == NULL )
    {
        *b_max = 2 * (*b_max);
        *buf2 = (double *)cvAlloc( (*b_max) * sizeof( double ));

        if( *buf2 == NULL )
            return CV_OUTOFMEM_ERR;

        memcpy( *buf2, *buf3, bb * sizeof( double ));

        *buf3 = *buf2;
        cvFree( (void**)buf1 );
        *buf1 = NULL;
    }
    else
    {
        *b_max = 2 * (*b_max);
        *buf1 = (double *) cvAlloc( (*b_max) * sizeof( double ));

        if( *buf1 == NULL )
            return CV_OUTOFMEM_ERR;

        memcpy( *buf1, *buf3, bb * sizeof( double ));

        *buf3 = *buf1;
        cvFree( (void**)buf2 );
        *buf2 = NULL;
    }
    return CV_OK;
}


/* area of a contour sector */
static CvStatus icvContourSecArea( CvSeq * contour, CvSlice slice, double *area )
{
    CvPoint pt;                 /*  pointer to points   */
    CvPoint pt_s, pt_e;         /*  first and last points  */
    CvSeqReader reader;         /*  points reader of contour   */

    int p_max = 2, p_ind;
    int lpt, flag, i;
    double a00;                 /* unnormalized moments m00    */
    double xi, yi, xi_1, yi_1, x0, y0, dxy, sk, sk1, t;
    double x_s, y_s, nx, ny, dx, dy, du, dv;
    double eps = 1.e-5;
    double *p_are1, *p_are2, *p_are;

    assert( contour != NULL );

    if( contour == NULL )
        return CV_NULLPTR_ERR;

    if( !CV_IS_SEQ_POLYGON( contour ))
        return CV_BADFLAG_ERR;

    lpt = cvSliceLength( slice, contour );
    /*if( n2 >= n1 )
        lpt = n2 - n1 + 1;
    else
        lpt = contour->total - n1 + n2 + 1;*/

    if( contour->total && lpt > 2 )
    {
        a00 = x0 = y0 = xi_1 = yi_1 = 0;
        sk1 = 0;
        flag = 0;
        dxy = 0;
        p_are1 = (double *) cvAlloc( p_max * sizeof( double ));

        if( p_are1 == NULL )
            return CV_OUTOFMEM_ERR;

        p_are = p_are1;
        p_are2 = NULL;

        cvStartReadSeq( contour, &reader, 0 );
        cvSetSeqReaderPos( &reader, slice.start_index );
        CV_READ_SEQ_ELEM( pt_s, reader );
        p_ind = 0;
        cvSetSeqReaderPos( &reader, slice.end_index );
        CV_READ_SEQ_ELEM( pt_e, reader );

/*    normal coefficients    */
        nx = pt_s.y - pt_e.y;
        ny = pt_e.x - pt_s.x;
        cvSetSeqReaderPos( &reader, slice.start_index );

        while( lpt-- > 0 )
        {
            CV_READ_SEQ_ELEM( pt, reader );

            if( flag == 0 )
            {
                xi_1 = (double) pt.x;
                yi_1 = (double) pt.y;
                x0 = xi_1;
                y0 = yi_1;
                sk1 = 0;
                flag = 1;
            }
            else
            {
                xi = (double) pt.x;
                yi = (double) pt.y;

/****************   edges intersection examination   **************************/
                sk = nx * (xi - pt_s.x) + ny * (yi - pt_s.y);
                if( fabs( sk ) < eps && lpt > 0 || sk * sk1 < -eps )
                {
                    if( fabs( sk ) < eps )
                    {
                        dxy = xi_1 * yi - xi * yi_1;
                        a00 = a00 + dxy;
                        dxy = xi * y0 - x0 * yi;
                        a00 = a00 + dxy;

                        if( p_ind >= p_max )
                            icvMemCopy( &p_are1, &p_are2, &p_are, &p_max );

                        p_are[p_ind] = a00 / 2.;
                        p_ind++;
                        a00 = 0;
                        sk1 = 0;
                        x0 = xi;
                        y0 = yi;
                        dxy = 0;
                    }
                    else
                    {
/*  define intersection point    */
                        dv = yi - yi_1;
                        du = xi - xi_1;
                        dx = ny;
                        dy = -nx;
                        if( fabs( du ) > eps )
                            t = ((yi_1 - pt_s.y) * du + dv * (pt_s.x - xi_1)) /
                                (du * dy - dx * dv);
                        else
                            t = (xi_1 - pt_s.x) / dx;
                        if( t > eps && t < 1 - eps )
                        {
                            x_s = pt_s.x + t * dx;
                            y_s = pt_s.y + t * dy;
                            dxy = xi_1 * y_s - x_s * yi_1;
                            a00 += dxy;
                            dxy = x_s * y0 - x0 * y_s;
                            a00 += dxy;
                            if( p_ind >= p_max )
                                icvMemCopy( &p_are1, &p_are2, &p_are, &p_max );

                            p_are[p_ind] = a00 / 2.;
                            p_ind++;

                            a00 = 0;
                            sk1 = 0;
                            x0 = x_s;
                            y0 = y_s;
                            dxy = x_s * yi - xi * y_s;
                        }
                    }
                }
                else
                    dxy = xi_1 * yi - xi * yi_1;

                a00 += dxy;
                xi_1 = xi;
                yi_1 = yi;
                sk1 = sk;

            }
        }

        xi = x0;
        yi = y0;
        dxy = xi_1 * yi - xi * yi_1;

        a00 += dxy;

        if( p_ind >= p_max )
            icvMemCopy( &p_are1, &p_are2, &p_are, &p_max );

        p_are[p_ind] = a00 / 2.;
        p_ind++;

/*     common area calculation    */
        *area = 0;
        for( i = 0; i < p_ind; i++ )
            (*area) += fabs( p_are[i] );

        if( p_are1 != NULL )
            cvFree( (void**)&p_are1 );
        else if( p_are2 != NULL )
            cvFree( (void**)&p_are2 );

        return CV_OK;
    }
    else
        return CV_BADSIZE_ERR;
}


/* external contour area function */
CV_IMPL double
cvContourArea( const void *array, CvSlice slice )
{
    double area = 0;

    CV_FUNCNAME( "cvContourArea" );

    __BEGIN__;

    CvContour contour_header;
    CvSeq* contour = 0;
    CvSeqBlock block;

    if( CV_IS_SEQ( array ))
    {
        contour = (CvSeq*)array;
        if( !CV_IS_SEQ_POLYLINE( contour ))
            CV_ERROR( CV_StsBadArg, "Unsupported sequence type" );
    }
    else
    {
        CV_CALL( contour = cvPointSeqFromMat(
            CV_SEQ_KIND_CURVE, array, &contour_header, &block ));
    }

    if( cvSliceLength( slice, contour ) == contour->total )
    {
        IPPI_CALL( icvContourArea( contour, &area ));
    }
    else
    {
        if( CV_SEQ_ELTYPE( contour ) != CV_32SC2 )
            CV_ERROR( CV_StsUnsupportedFormat,
            "Only curves with integer coordinates are supported in case of contour slice" );
        IPPI_CALL( icvContourSecArea( contour, slice, &area ));
    }

    __END__;

    return area;
}


/* for now this function works bad with singular cases
   You can see in the code, that when some troubles with
   matrices or some variables occur -
   box filled with zero values is returned.
   However in general function works fine.
*/
static CvStatus icvFitEllipse_32f( CvSeq* points, CvBox2D* box )
{
    CvStatus status = CV_OK;
    float u[6];

    CvMatr32f D = 0;
    float S[36];            /*  S = D' * D  */
    float C[36];

    float INVQ[36];

    /* transposed eigenvectors */
    float INVEIGV[36];

    /* auxulary matrices */
    float TMP1[36];
    float TMP2[36];

    int i, index = -1;
    float eigenvalues[6];
    float a, b, c, d, e, f;
    float offx, offy;
    float *matr;

    int n = points->total;
    CvSeqReader reader;
    int is_float = CV_SEQ_ELTYPE(points) == CV_32FC2;

    CvMat _S, _EIGVECS, _EIGVALS;

    /* create matrix D of  input points */
    D = icvCreateMatrix_32f( 6, n );

    offx = offy = 0;
    cvStartReadSeq( points, &reader );

    /* shift all points to zero */
    for( i = 0; i < n; i++ )
    {
        if( !is_float )
        {
            offx += (float)((CvPoint*)reader.ptr)->x;
            offy += (float)((CvPoint*)reader.ptr)->y;
        }
        else
        {
            offx += ((CvPoint2D32f*)reader.ptr)->x;
            offy += ((CvPoint2D32f*)reader.ptr)->y;
        }
        CV_NEXT_SEQ_ELEM( points->elem_size, reader );
    }

    c = 1.f / n;
    offx *= c;
    offy *= c;

    /* fill matrix rows as (x*x, x*y, y*y, x, y, 1 ) */
    matr = D;
    for( i = 0; i < n; i++ )
    {
        float x, y;
        
        if( !is_float )
        {
            x = (float)((CvPoint*)reader.ptr)->x - offx;
            y = (float)((CvPoint*)reader.ptr)->y - offy;
        }
        else
        {
            x = ((CvPoint2D32f*)reader.ptr)->x - offx;
            y = ((CvPoint2D32f*)reader.ptr)->y - offy;
        }
        CV_NEXT_SEQ_ELEM( points->elem_size, reader );
        
        matr[0] = x * x;
        matr[1] = x * y;
        matr[2] = y * y;
        matr[3] = x;
        matr[4] = y;
        matr[5] = 1.f;
        matr += 6;
    }

    /* compute S */
    icvMulTransMatrixR_32f( D, 6, n, S );

    /* fill matrix C */
    icvSetZero_32f( C, 6, 6 );
    C[2] = 2.f;  //icvSetElement_32f( C, 6, 6, 0, 2, 2.f );
    C[7] = -1.f; //icvSetElement_32f( C, 6, 6, 1, 1, -1.f );
    C[12] = 2.f; //icvSetElement_32f( C, 6, 6, 2, 0, 2.f );
    
    /* find eigenvalues */
    //status1 = icvJacobiEigens_32f( S, INVEIGV, eigenvalues, 6, 0.f );
    //assert( status1 == CV_OK );
    _S = cvMat( 6, 6, CV_32F, S );
    _EIGVECS = cvMat( 6, 6, CV_32F, INVEIGV );
    _EIGVALS = cvMat( 6, 1, CV_32F, eigenvalues );
    cvEigenVV( &_S, &_EIGVECS, &_EIGVALS, 0 );

    //avoid troubles with small negative values
    for( i = 0; i < 6; i++ )
        eigenvalues[i] = (float)fabs(eigenvalues[i]);

    cvbSqrt( eigenvalues, eigenvalues, 6 );
    cvbInvSqrt( eigenvalues, eigenvalues, 6 );

    for( i = 0; i < 6; i++ )
        icvScaleVector_32f( &INVEIGV[i * 6], &INVEIGV[i * 6], 6, eigenvalues[i] );

    // INVQ = transp(INVEIGV) * INVEIGV
    icvMulTransMatrixR_32f( INVEIGV, 6, 6, INVQ );
    
    /* create matrix INVQ*C*INVQ */
    icvMulMatrix_32f( INVQ, 6, 6, C, 6, 6, TMP1 );
    icvMulMatrix_32f( TMP1, 6, 6, INVQ, 6, 6, TMP2 );

    /* find its eigenvalues and vectors */
    //status1 = icvJacobiEigens_32f( TMP2, INVEIGV, eigenvalues, 6, 0.f );
    //assert( status1 == CV_OK );
    _S = cvMat( 6, 6, CV_32F, TMP2 );
    cvEigenVV( &_S, &_EIGVECS, &_EIGVALS, 0 );

    /* search for positive eigenvalue */
    for( i = 0; i < 3; i++ )
    {
        if( eigenvalues[i] > 0 )
        {
            index = i;
            break;
        }
    }

    /* only 3 eigenvalues must be not zero 
       and only one of them must be positive 
       if it is not true - return zero result
    */
    if( index == -1 )
    {
        box->center.x = box->center.y = 
        box->size.width = box->size.height = 
        box->angle = 0.f;
        goto error;
    }

    /* now find truthful eigenvector */
    icvTransformVector_32f( INVQ, &INVEIGV[index * 6], u, 6, 6 );
    /* extract vector components */
    a = u[0];
    b = u[1];
    c = u[2];
    d = u[3];
    e = u[4];
    f = u[5];
    {
        /* extract ellipse axes from above values */

        /* 
           1) find center of ellipse 
           it satisfy equation  
           | a     b/2 | *  | x0 | +  | d/2 | = |0 |
           | b/2    c  |    | y0 |    | e/2 |   |0 |

         */
        float x0, y0;
        float idet = 1.f / (a * c - b * b * 0.25f);

        /* we must normalize (a b c d e f ) to fit (4ac-b^2=1) */
        float scale = cvSqrt( 0.25f * idet );

        if (!scale) 
        {
            box->center.x = box->center.y = 
            box->size.width = box->size.height = 
            box->angle = 0.f;
            goto error;
        }
           
        a *= scale;
        b *= scale;
        c *= scale;
        d *= scale;
        e *= scale;
        f *= scale;

        //x0 = box->center.x = (-d * c * 0.5f + e * b * 0.25f) * 4.f;
        //y0 = box->center.y = (-a * e * 0.5f + d * b * 0.25f) * 4.f;
        x0 = box->center.x = (-d * c + e * b * 0.5f) * 2.f;
        y0 = box->center.y = (-a * e + d * b * 0.5f) * 2.f;

        /* offset ellipse to (x0,y0) */
        /* new f == F(x0,y0) */
        f += a * x0 * x0 + b * x0 * y0 + c * y0 * y0 + d * x0 + e * y0;

        if (!f) 
        {
            box->center.x = box->center.y = 
            box->size.width = box->size.height = 
            box->angle = 0.f;
            goto error;
        }

        scale = -1.f / f;
        /* normalize to f = 1 */
        a *= scale;
        b *= scale;
        c *= scale;
    }
    /* recover center */
    box->center.x += offx;
    box->center.y += offy;

    /* extract axis of ellipse */
    /* one more eigenvalue operation */
    TMP1[0] = a;
    TMP1[1] = TMP1[2] = b * 0.5f;
    TMP1[3] = c;

    //status1 = icvJacobiEigens_32f( TMP1, INVEIGV, eigenvalues, 2, 0.f );
    //assert( status1 == CV_OK );
    _S = cvMat( 2, 2, CV_32F, TMP1 );
    _EIGVECS = cvMat( 2, 2, CV_32F, INVEIGV );
    _EIGVALS = cvMat( 2, 1, CV_32F, eigenvalues );
    cvEigenVV( &_S, &_EIGVECS, &_EIGVALS, 0 );

    /* exteract axis length from eigenvectors */
    box->size.height = 2 * cvInvSqrt( eigenvalues[0] );
    box->size.width = 2 * cvInvSqrt( eigenvalues[1] );

    if ( !(box->size.height && box->size.width) )
    {
        assert(0);
    }

    /* calc angle */
    box->angle = cvFastArctan( INVEIGV[3], INVEIGV[2] );

error:

    if( D )
        icvDeleteMatrix( D );

    return status;
}


CV_IMPL CvBox2D
cvFitEllipse2( const CvArr* array )
{
    CvBox2D box;
    
    CV_FUNCNAME( "cvFitEllipse2" );

    memset( &box, 0, sizeof(box));

    __BEGIN__;

    CvContour contour_header;
    CvSeq* ptseq = 0;
    CvSeqBlock block;

    if( CV_IS_SEQ( array ))
    {
        ptseq = (CvSeq*)array;
        if( !CV_IS_SEQ_POINT_SET( ptseq ))
            CV_ERROR( CV_StsBadArg, "Unsupported sequence type" );
    }
    else
    {
        CV_CALL( ptseq = cvPointSeqFromMat(
            CV_SEQ_KIND_GENERIC, array, &contour_header, &block ));
    }

    if( ptseq->total < 6 )
        CV_ERROR( CV_StsBadSize, "Number of points should be >= 6" );

    IPPI_CALL( icvFitEllipse_32f( ptseq, &box ));

    __END__;

    return box;
}


/* Calculates bounding rectagnle of a point set or retrieves already calculated */
CV_IMPL  CvRect
cvBoundingRect( CvArr* array, int update )
{
    CvSeqReader reader;
    CvRect  rect = { 0, 0, 0, 0 };
    CvContour contour_header;
    CvSeq* ptseq = 0;
    CvSeqBlock block;

    CV_FUNCNAME( "cvBoundingRect" );

    __BEGIN__;

    int calculate = update;

    if( CV_IS_SEQ( array ))
    {
        ptseq = (CvSeq*)array;
        if( !CV_IS_SEQ_POINT_SET( ptseq ))
            CV_ERROR( CV_StsBadArg, "Unsupported sequence type" );

        if( ptseq->header_size < (int)sizeof(CvContour))
        {
            if( update == 1 )
                CV_ERROR( CV_StsBadArg, "The header is too small to fit the rectangle, "
                                        "so it could not be updated" );
            calculate = 1;
        }
    }
    else
    {
        CV_CALL( ptseq = cvPointSeqFromMat(
            CV_SEQ_KIND_GENERIC, array, &contour_header, &block ));
        calculate = 1;
    }

    if( calculate )
    {
        if( ptseq->total )
        {   
            int  is_float = CV_SEQ_ELTYPE(ptseq) == CV_32FC2;
            int  xmin, ymin, xmax, ymax, i;
            cvStartReadSeq( ptseq, &reader, 0 );

            if( !is_float )
            {
                CvPoint pt;
                /* init values */
                CV_READ_SEQ_ELEM( pt, reader );
                xmin = xmax = pt.x;
                ymin = ymax = pt.y;
    
                for( i = 1; i < ptseq->total; i++ )
                {            
                    CV_READ_SEQ_ELEM( pt, reader );
            
                    if( xmin > pt.x )
                        xmin = pt.x;
            
                    if( xmax < pt.x )
                        xmax = pt.x;

                    if( ymin > pt.y )
                        ymin = pt.y;

                    if( ymax < pt.y )
                        ymax = pt.y;
                }
            }
            else
            {
                CvPoint pt;
                /* init values */
                CV_READ_SEQ_ELEM( pt, reader );
                xmin = xmax = CV_TOGGLE_FLT(pt.x);
                ymin = ymax = CV_TOGGLE_FLT(pt.y);
    
                for( i = 1; i < ptseq->total; i++ )
                {            
                    CV_READ_SEQ_ELEM( pt, reader );
                    pt.x = CV_TOGGLE_FLT(pt.x);
                    pt.y = CV_TOGGLE_FLT(pt.y);
            
                    if( xmin > pt.x )
                        xmin = pt.x;
            
                    if( xmax < pt.x )
                        xmax = pt.x;

                    if( ymin > pt.y )
                        ymin = pt.y;

                    if( ymax < pt.y )
                        ymax = pt.y;
                }

                xmin = CV_TOGGLE_FLT(xmin);
                ymin = CV_TOGGLE_FLT(ymin);
                xmax = CV_TOGGLE_FLT(xmax);
                ymax = CV_TOGGLE_FLT(ymax);

                xmin = cvFloor( (float&)xmin );
                ymin = cvFloor( (float&)ymin );
                /* because right and bottom sides of
                   the bounding rectangle are not inclusive,
                   cvFloor is used here (instead of cvCeil) */
                xmax = cvFloor( (float&)xmax );
                ymax = cvFloor( (float&)ymax );
            }

            rect.x = xmin;
            rect.y = ymin;
            rect.width = xmax - xmin + 1;
            rect.height = ymax - ymin + 1;
        }

        if( update )
            ((CvContour*)ptseq)->rect = rect;
    }
    else
    {
        rect = ((CvContour*)ptseq)->rect;
    }

    __END__;

    return rect;
}


/* End of file. */
