/*M///////////////////////////////////////////////////////////////////////////////////////
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//
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//                For Open Source Computer Vision Library
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#ifndef __OPENCV_CORE_OPERATIONS_HPP__
#define __OPENCV_CORE_OPERATIONS_HPP__

#ifndef SKIP_INCLUDES
  #include <string.h>
  #include <limits.h>
#endif // SKIP_INCLUDES

#ifdef __cplusplus

/////// exchange-add operation for atomic operations on reference counters ///////
#ifdef __GNUC__
    
  #if __GNUC__*10 + __GNUC_MINOR__ >= 42

    #if !defined WIN32 && (defined __i486__ || defined __i586__ || \
        defined __i686__ || defined __MMX__ || defined __SSE__  || defined __ppc__)
      #define CV_XADD __sync_fetch_and_add
    #else
      #include <ext/atomicity.h>
      #define CV_XADD __gnu_cxx::__exchange_and_add
    #endif

  #else
    #include <bits/atomicity.h>
    #if __GNUC__*10 + __GNUC_MINOR__ >= 34
      #define CV_XADD __gnu_cxx::__exchange_and_add
    #else
      #define CV_XADD __exchange_and_add
    #endif
  #endif
    
#elif defined WIN32 || defined _WIN32
  #include <intrin.h>
  #define CV_XADD(addr,delta) _InterlockedExchangeAdd((long volatile*)(addr), (delta))
#else

  template<typename _Tp> static inline _Tp CV_XADD(_Tp* addr, _Tp delta)
  { int tmp = *addr; *addr += delta; return tmp; }
    
#endif

#include <limits>

namespace cv
{
    
using std::cos;
using std::sin;
using std::max;
using std::min;
using std::exp;
using std::log;
using std::pow;
using std::sqrt;

    
/////////////// saturate_cast (used in image & signal processing) ///////////////////

template<typename _Tp> static inline _Tp saturate_cast(uchar v) { return _Tp(v); }
template<typename _Tp> static inline _Tp saturate_cast(schar v) { return _Tp(v); }
template<typename _Tp> static inline _Tp saturate_cast(ushort v) { return _Tp(v); }
template<typename _Tp> static inline _Tp saturate_cast(short v) { return _Tp(v); }
template<typename _Tp> static inline _Tp saturate_cast(unsigned v) { return _Tp(v); }
template<typename _Tp> static inline _Tp saturate_cast(int v) { return _Tp(v); }
template<typename _Tp> static inline _Tp saturate_cast(float v) { return _Tp(v); }
template<typename _Tp> static inline _Tp saturate_cast(double v) { return _Tp(v); }

template<> inline uchar saturate_cast<uchar>(schar v)
{ return (uchar)std::max((int)v, 0); }
template<> inline uchar saturate_cast<uchar>(ushort v)
{ return (uchar)std::min((unsigned)v, (unsigned)UCHAR_MAX); }
template<> inline uchar saturate_cast<uchar>(int v)
{ return (uchar)((unsigned)v <= UCHAR_MAX ? v : v > 0 ? UCHAR_MAX : 0); }
template<> inline uchar saturate_cast<uchar>(short v)
{ return saturate_cast<uchar>((int)v); }
template<> inline uchar saturate_cast<uchar>(unsigned v)
{ return (uchar)std::min(v, (unsigned)UCHAR_MAX); }
template<> inline uchar saturate_cast<uchar>(float v)
{ int iv = cvRound(v); return saturate_cast<uchar>(iv); }
template<> inline uchar saturate_cast<uchar>(double v)
{ int iv = cvRound(v); return saturate_cast<uchar>(iv); }

template<> inline schar saturate_cast<schar>(uchar v)
{ return (schar)std::min((int)v, SCHAR_MAX); }
template<> inline schar saturate_cast<schar>(ushort v)
{ return (schar)std::min((unsigned)v, (unsigned)SCHAR_MAX); }
template<> inline schar saturate_cast<schar>(int v)
{
    return (schar)((unsigned)(v-SCHAR_MIN) <= (unsigned)UCHAR_MAX ?
                v : v > 0 ? SCHAR_MAX : SCHAR_MIN);
}
template<> inline schar saturate_cast<schar>(short v)
{ return saturate_cast<schar>((int)v); }
template<> inline schar saturate_cast<schar>(unsigned v)
{ return (schar)std::min(v, (unsigned)SCHAR_MAX); }

template<> inline schar saturate_cast<schar>(float v)
{ int iv = cvRound(v); return saturate_cast<schar>(iv); }
template<> inline schar saturate_cast<schar>(double v)
{ int iv = cvRound(v); return saturate_cast<schar>(iv); }

template<> inline ushort saturate_cast<ushort>(schar v)
{ return (ushort)std::max((int)v, 0); }
template<> inline ushort saturate_cast<ushort>(short v)
{ return (ushort)std::max((int)v, 0); }
template<> inline ushort saturate_cast<ushort>(int v)
{ return (ushort)((unsigned)v <= (unsigned)USHRT_MAX ? v : v > 0 ? USHRT_MAX : 0); }
template<> inline ushort saturate_cast<ushort>(unsigned v)
{ return (ushort)std::min(v, (unsigned)USHRT_MAX); }
template<> inline ushort saturate_cast<ushort>(float v)
{ int iv = cvRound(v); return saturate_cast<ushort>(iv); }
template<> inline ushort saturate_cast<ushort>(double v)
{ int iv = cvRound(v); return saturate_cast<ushort>(iv); }

template<> inline short saturate_cast<short>(ushort v)
{ return (short)std::min((int)v, SHRT_MAX); }
template<> inline short saturate_cast<short>(int v)
{
    return (short)((unsigned)(v - SHRT_MIN) <= (unsigned)USHRT_MAX ?
            v : v > 0 ? SHRT_MAX : SHRT_MIN);
}
template<> inline short saturate_cast<short>(unsigned v)
{ return (short)std::min(v, (unsigned)SHRT_MAX); }
template<> inline short saturate_cast<short>(float v)
{ int iv = cvRound(v); return saturate_cast<short>(iv); }
template<> inline short saturate_cast<short>(double v)
{ int iv = cvRound(v); return saturate_cast<short>(iv); }

template<> inline int saturate_cast<int>(float v) { return cvRound(v); }
template<> inline int saturate_cast<int>(double v) { return cvRound(v); }

// we intentionally do not clip negative numbers, to make -1 become 0xffffffff etc.
template<> inline unsigned saturate_cast<unsigned>(float v){ return cvRound(v); }
template<> inline unsigned saturate_cast<unsigned>(double v) { return cvRound(v); }


//////////////////////////////// Matx /////////////////////////////////


template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx()
{
    for(int i = 0; i < channels; i++) val[i] = _Tp(0);
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(_Tp v0)
{
    val[0] = v0;
    for(int i = 1; i < channels; i++) val[i] = _Tp(0);
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1)
{
    assert(channels >= 2);
    val[0] = v0; val[1] = v1;
    for(int i = 2; i < channels; i++) val[i] = _Tp(0);
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2)
{
    assert(channels >= 3);
    val[0] = v0; val[1] = v1; val[2] = v2;
    for(int i = 3; i < channels; i++) val[i] = _Tp(0);
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3)
{
    assert(channels >= 4);
    val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    for(int i = 4; i < channels; i++) val[i] = _Tp(0);
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4)
{
    assert(channels >= 5);
    val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3; val[4] = v4;
    for(int i = 5; i < channels; i++) val[i] = _Tp(0);
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                                                        _Tp v4, _Tp v5)
{
    assert(channels >= 6);
    val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    val[4] = v4; val[5] = v5;
    for(int i = 6; i < channels; i++) val[i] = _Tp(0);
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                                                        _Tp v4, _Tp v5, _Tp v6)
{
    assert(channels >= 7);
    val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    val[4] = v4; val[5] = v5; val[6] = v6;
    for(int i = 7; i < channels; i++) val[i] = _Tp(0);
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                                                        _Tp v4, _Tp v5, _Tp v6, _Tp v7)
{
    assert(channels >= 8);
    val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
    for(int i = 8; i < channels; i++) val[i] = _Tp(0);
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                                                        _Tp v4, _Tp v5, _Tp v6, _Tp v7,
                                                        _Tp v8)
{
    assert(channels >= 9);
    val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
    val[8] = v8;
    for(int i = 9; i < channels; i++) val[i] = _Tp(0);
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                                                        _Tp v4, _Tp v5, _Tp v6, _Tp v7,
                                                        _Tp v8, _Tp v9)
{
    assert(channels >= 10);
    val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
    val[8] = v8; val[9] = v9;
    for(int i = 10; i < channels; i++) val[i] = _Tp(0);
}

    
template<typename _Tp, int m, int n>
inline Matx<_Tp,m,n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                            _Tp v4, _Tp v5, _Tp v6, _Tp v7,
                            _Tp v8, _Tp v9, _Tp v10, _Tp v11)
{
    assert(channels == 12);
    val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
    val[8] = v8; val[9] = v9; val[10] = v10; val[11] = v11;
}

template<typename _Tp, int m, int n>
inline Matx<_Tp,m,n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                           _Tp v4, _Tp v5, _Tp v6, _Tp v7,
                           _Tp v8, _Tp v9, _Tp v10, _Tp v11,
                           _Tp v12, _Tp v13, _Tp v14, _Tp v15)
{
    assert(channels == 16);
    val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
    val[8] = v8; val[9] = v9; val[10] = v10; val[11] = v11;
    val[12] = v12; val[13] = v13; val[14] = v14; val[15] = v15;
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n>::Matx(const _Tp* values)
{
    for( int i = 0; i < channels; i++ ) val[i] = values[i];
}

template<typename _Tp, int m, int n> inline Matx<_Tp, m, n> Matx<_Tp, m, n>::all(_Tp alpha)
{
    Matx<_Tp, m, n> M;
    for( int i = 0; i < m*n; i++ ) M.val[i] = alpha;
    return M;
}

template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n> Matx<_Tp,m,n>::zeros()
{
    return all(0);
}

template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n> Matx<_Tp,m,n>::ones()
{
    return all(1);
}

template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n> Matx<_Tp,m,n>::eye()
{
    Matx<_Tp,m,n> M;
    for(int i = 0; i < MIN(m,n); i++)
        M(i,i) = 1;
    return M;
}

template<typename _Tp, int m, int n> inline _Tp Matx<_Tp, m, n>::dot(const Matx<_Tp, m, n>& M) const
{
    _Tp s = 0;
    for( int i = 0; i < m*n; i++ ) s += val[i]*M.val[i];
    return s;
}

    
template<typename _Tp, int m, int n> inline double Matx<_Tp, m, n>::ddot(const Matx<_Tp, m, n>& M) const
{
    double s = 0;
    for( int i = 0; i < m*n; i++ ) s += (double)val[i]*M.val[i];
    return s;
}



template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n> Matx<_Tp,m,n>::diag(const Matx<_Tp,MIN(m,n),1>& d)
{
    Matx<_Tp,m,n> M;
    for(int i = 0; i < MIN(m,n); i++)
        M(i,i) = d(i, 0);
    return M;
}

template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n> Matx<_Tp,m,n>::randu(_Tp a, _Tp b)
{
    Matx<_Tp,m,n> M;
    Mat matM(M, false);
    cv::randu(matM, Scalar(a), Scalar(b));
    return M;
}
    
template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n> Matx<_Tp,m,n>::randn(_Tp a, _Tp b)
{
    Matx<_Tp,m,n> M;
    Mat matM(M, false);
    cv::randn(matM, Scalar(a), Scalar(b));
    return M;
}
    
template<typename _Tp, int m, int n> template<typename T2>
inline Matx<_Tp, m, n>::operator Matx<T2, m, n>() const
{
    Matx<T2, m, n> M;
    for( int i = 0; i < m*n; i++ ) M.val[i] = saturate_cast<T2>(val[i]);
    return M;
}
    

template<typename _Tp, int m, int n> template<int m1, int n1> inline
Matx<_Tp, m1, n1> Matx<_Tp, m, n>::reshape() const
{
    CV_DbgAssert(m1*n1 == m*n);
    return (const Matx<_Tp, m1, n1>&)*this;
}


template<typename _Tp, int m, int n>
template<int m1, int n1> inline
Matx<_Tp, m1, n1> Matx<_Tp, m, n>::get_minor(int i, int j) const
{
    CV_DbgAssert(0 <= i && i+m1 <= m && 0 <= j && j+n1 <= n);
    Matx<_Tp, m1, n1> s;
    for( int di = 0; di < m1; di++ )
        for( int dj = 0; dj < n1; dj++ )
            s(di, dj) = (*this)(i+di, j+dj);
    return s;
}


template<typename _Tp, int m, int n> inline
Matx<_Tp, 1, n> Matx<_Tp, m, n>::row(int i) const
{
    CV_DbgAssert((unsigned)i < (unsigned)m);
    return Matx<_Tp, 1, n>(&val[i*n]);
}

    
template<typename _Tp, int m, int n> inline
Matx<_Tp, m, 1> Matx<_Tp, m, n>::col(int j) const
{
    CV_DbgAssert((unsigned)j < (unsigned)n);
    Matx<_Tp, m, 1> v;
    for( int i = 0; i < m; i++ )
        v[i] = val[i*n + j];
    return v;
}

    
template<typename _Tp, int m, int n> inline
Matx<_Tp, MIN(m,n), 1> Matx<_Tp, m, n>::diag() const
{
    diag_type d;
    for( int i = 0; i < MIN(m, n); i++ )
        d.val[i] = val[i*n + i];
    return d;
}

    
template<typename _Tp, int m, int n> inline
const _Tp& Matx<_Tp, m, n>::operator ()(int i, int j) const
{
    CV_DbgAssert( (unsigned)i < (unsigned)m && (unsigned)j < (unsigned)n );
    return this->val[i*n + j];
}

    
template<typename _Tp, int m, int n> inline
_Tp& Matx<_Tp, m, n>::operator ()(int i, int j)
{
    CV_DbgAssert( (unsigned)i < (unsigned)m && (unsigned)j < (unsigned)n );
    return val[i*n + j];
}


template<typename _Tp, int m, int n> inline
const _Tp& Matx<_Tp, m, n>::operator ()(int i) const
{
    CV_DbgAssert( (m == 1 || n == 1) && (unsigned)i < (unsigned)(m+n-1) );
    return val[i];
}


template<typename _Tp, int m, int n> inline
_Tp& Matx<_Tp, m, n>::operator ()(int i)
{
    CV_DbgAssert( (m == 1 || n == 1) && (unsigned)i < (unsigned)(m+n-1) );
    return val[i];
}

    
template<typename _Tp1, typename _Tp2, int m, int n> static inline
Matx<_Tp1, m, n>& operator += (Matx<_Tp1, m, n>& a, const Matx<_Tp2, m, n>& b)
{
    for( int i = 0; i < m*n; i++ )
        a.val[i] = saturate_cast<_Tp1>(a.val[i] + b.val[i]);
    return a;
}    

    
template<typename _Tp1, typename _Tp2, int m, int n> static inline
Matx<_Tp1, m, n>& operator -= (Matx<_Tp1, m, n>& a, const Matx<_Tp2, m, n>& b)
{
    for( int i = 0; i < m*n; i++ )
        a.val[i] = saturate_cast<_Tp1>(a.val[i] - b.val[i]);
    return a;
}    


template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_AddOp)
{
    for( int i = 0; i < m*n; i++ )
        val[i] = saturate_cast<_Tp>(a.val[i] + b.val[i]);
}

    
template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_SubOp)
{
    for( int i = 0; i < m*n; i++ )
        val[i] = saturate_cast<_Tp>(a.val[i] - b.val[i]);
}
    
    
template<typename _Tp, int m, int n> template<typename _T2> inline
Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, _T2 alpha, Matx_ScaleOp)
{
    for( int i = 0; i < m*n; i++ )
        val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
}
    
    
template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_MulOp)
{
    for( int i = 0; i < m*n; i++ )
        val[i] = saturate_cast<_Tp>(a.val[i] * b.val[i]);
}
    
    
template<typename _Tp, int m, int n> template<int l> inline
Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, l>& a, const Matx<_Tp, l, n>& b, Matx_MatMulOp)
{
    for( int i = 0; i < m; i++ )
        for( int j = 0; j < n; j++ )
        {
            _Tp s = 0;
            for( int k = 0; k < l; k++ )
                s += a(i, k) * b(k, j);
            val[i*n + j] = s;
        }
}
    
    
template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n>::Matx(const Matx<_Tp, n, m>& a, Matx_TOp)
{
    for( int i = 0; i < m; i++ )
        for( int j = 0; j < n; j++ )
            val[i*n + j] = a(j, i);
}

    
template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n> operator + (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
{
    return Matx<_Tp, m, n>(a, b, Matx_AddOp());
}
    
    
template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n> operator - (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
{
    return Matx<_Tp, m, n>(a, b, Matx_SubOp());
}    
    

template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n>& operator *= (Matx<_Tp, m, n>& a, int alpha)
{
    for( int i = 0; i < m*n; i++ )
        a.val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
    return a;
}        
    
template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n>& operator *= (Matx<_Tp, m, n>& a, float alpha)
{
    for( int i = 0; i < m*n; i++ )
        a.val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
    return a;
}    

template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n>& operator *= (Matx<_Tp, m, n>& a, double alpha)
{
    for( int i = 0; i < m*n; i++ )
        a.val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
    return a;
}        

template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n> operator * (const Matx<_Tp, m, n>& a, int alpha)
{
    return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
}        

template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n> operator * (const Matx<_Tp, m, n>& a, float alpha)
{
    return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
}        

template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n> operator * (const Matx<_Tp, m, n>& a, double alpha)
{
    return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
}            
    
template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n> operator * (int alpha, const Matx<_Tp, m, n>& a)
{
    return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
}        

template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n> operator * (float alpha, const Matx<_Tp, m, n>& a)
{
    return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
}        

template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n> operator * (double alpha, const Matx<_Tp, m, n>& a)
{
    return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
}            
    
template<typename _Tp, int m, int n> static inline
Matx<_Tp, m, n> operator - (const Matx<_Tp, m, n>& a)
{
    return Matx<_Tp, m, n>(a, -1, Matx_ScaleOp());
}


template<typename _Tp, int m, int n, int l> static inline
Matx<_Tp, m, n> operator * (const Matx<_Tp, m, l>& a, const Matx<_Tp, l, n>& b)
{
    return Matx<_Tp, m, n>(a, b, Matx_MatMulOp());
}

    
template<typename _Tp> static inline
Point_<_Tp> operator * (const Matx<_Tp, 2, 2>& a, const Point_<_Tp>& b)
{
    Matx<_Tp, 2, 1> tmp = a*Vec<_Tp,2>(b.x, b.y);
    return Point_<_Tp>(tmp.val[0], tmp.val[1]);
}

    
template<typename _Tp> static inline
Point3_<_Tp> operator * (const Matx<_Tp, 3, 3>& a, const Point3_<_Tp>& b)
{
    Matx<_Tp, 3, 1> tmp = a*Vec<_Tp,3>(b.x, b.y, b.z);
    return Point3_<_Tp>(tmp.val[0], tmp.val[1], tmp.val[2]);
}    


template<typename _Tp> static inline
Point3_<_Tp> operator * (const Matx<_Tp, 3, 3>& a, const Point_<_Tp>& b)
{
    Matx<_Tp, 3, 1> tmp = a*Vec<_Tp,3>(b.x, b.y, 1);
    return Point3_<_Tp>(tmp.val[0], tmp.val[1], tmp.val[2]);
}    

    
template<typename _Tp> static inline
Matx<_Tp, 4, 1> operator * (const Matx<_Tp, 4, 4>& a, const Point3_<_Tp>& b)
{
    return a*Matx<_Tp, 4, 1>(b.x, b.y, b.z, 1);
}    

    
template<typename _Tp> static inline
Scalar operator * (const Matx<_Tp, 4, 4>& a, const Scalar& b)
{
    return Scalar(a*Matx<_Tp, 4, 1>(b[0],b[1],b[2],b[3]));
}    
    

template<typename _Tp, int m, int n> inline
Matx<_Tp, m, n> Matx<_Tp, m, n>::mul(const Matx<_Tp, m, n>& a) const
{
    return Matx<_Tp, m, n>(*this, a, Matx_MulOp());
}

    
CV_EXPORTS int LU(float* A, size_t astep, int m, float* b, size_t bstep, int n);
CV_EXPORTS int LU(double* A, size_t astep, int m, double* b, size_t bstep, int n);
CV_EXPORTS bool Cholesky(float* A, size_t astep, int m, float* b, size_t bstep, int n);
CV_EXPORTS bool Cholesky(double* A, size_t astep, int m, double* b, size_t bstep, int n);    


template<typename _Tp, int m> struct CV_EXPORTS Matx_DetOp
{
    double operator ()(const Matx<_Tp, m, m>& a) const
    {
        Matx<_Tp, m, m> temp = a;
        double p = LU(temp.val, m, m, 0, 0, 0);
        if( p == 0 )
            return p;
        for( int i = 0; i < m; i++ )
            p *= temp(i, i);
        return p;
    }
};
    

template<typename _Tp> struct CV_EXPORTS Matx_DetOp<_Tp, 1>
{
    double operator ()(const Matx<_Tp, 1, 1>& a) const
    {
        return a(0,0);
    }
};


template<typename _Tp> struct CV_EXPORTS Matx_DetOp<_Tp, 2>
{
    double operator ()(const Matx<_Tp, 2, 2>& a) const
    {
        return a(0,0)*a(1,1) - a(0,1)*a(1,0);
    }
};


template<typename _Tp> struct CV_EXPORTS Matx_DetOp<_Tp, 3>
{
    double operator ()(const Matx<_Tp, 3, 3>& a) const
    {
        return a(0,0)*(a(1,1)*a(2,2) - a(2,1)*a(1,2)) -
            a(0,1)*(a(1,0)*a(2,2) - a(2,0)*a(1,2)) +
            a(0,2)*(a(1,0)*a(2,1) - a(2,0)*a(1,1));
    }
};
    
template<typename _Tp, int m> static inline
double determinant(const Matx<_Tp, m, m>& a)
{
    return Matx_DetOp<_Tp, m>()(a);   
}
        

template<typename _Tp, int m, int n> static inline
double trace(const Matx<_Tp, m, n>& a)
{
    _Tp s = 0;
    for( int i = 0; i < std::min(m, n); i++ )
        s += a(i,i);
    return s;
}       

    
template<typename _Tp, int m, int n> inline
Matx<_Tp, n, m> Matx<_Tp, m, n>::t() const
{
    return Matx<_Tp, n, m>(*this, Matx_TOp());
}


template<typename _Tp, int m> struct CV_EXPORTS Matx_FastInvOp
{
    bool operator()(const Matx<_Tp, m, m>& a, Matx<_Tp, m, m>& b, int method) const
    {
        Matx<_Tp, m, m> temp = a;
        
        // assume that b is all 0's on input => make it a unity matrix
        for( int i = 0; i < m; i++ )
            b(i, i) = (_Tp)1;
        
        if( method == DECOMP_CHOLESKY )
            return Cholesky(temp.val, m*sizeof(_Tp), m, b.val, m*sizeof(_Tp), m);
        
        return LU(temp.val, m*sizeof(_Tp), m, b.val, m*sizeof(_Tp), m) != 0;
    }
};

    
template<typename _Tp> struct CV_EXPORTS Matx_FastInvOp<_Tp, 2>
{
    bool operator()(const Matx<_Tp, 2, 2>& a, Matx<_Tp, 2, 2>& b, int) const
    {
        _Tp d = determinant(a);
        if( d == 0 )
            return false;
        d = 1/d;
        b(1,1) = a(0,0)*d;
        b(0,0) = a(1,1)*d;
        b(0,1) = -a(0,1)*d;
        b(1,0) = -a(1,0)*d;
        return true;
    }
};

    
template<typename _Tp> struct CV_EXPORTS Matx_FastInvOp<_Tp, 3>
{
    bool operator()(const Matx<_Tp, 3, 3>& a, Matx<_Tp, 3, 3>& b, int) const
    {
        _Tp d = determinant(a);
        if( d == 0 )
            return false;
        d = 1/d;
        b(0,0) = (a(1,1) * a(2,2) - a(1,2) * a(2,1)) * d;
        b(0,1) = (a(0,2) * a(2,1) - a(0,1) * a(2,2)) * d;
        b(0,2) = (a(0,1) * a(1,2) - a(0,2) * a(1,1)) * d;
                                      
        b(1,0) = (a(1,2) * a(2,0) - a(1,0) * a(2,2)) * d;
        b(1,1) = (a(0,0) * a(2,2) - a(0,2) * a(2,0)) * d;
        b(1,2) = (a(0,2) * a(1,0) - a(0,0) * a(1,2)) * d;
                                                                    
        b(2,0) = (a(1,0) * a(2,1) - a(1,1) * a(2,0)) * d;
        b(2,1) = (a(0,1) * a(2,0) - a(0,0) * a(2,1)) * d;
        b(2,2) = (a(0,0) * a(1,1) - a(0,1) * a(1,0)) * d;
        return true;
    }
};

    
template<typename _Tp, int m, int n> inline
Matx<_Tp, n, m> Matx<_Tp, m, n>::inv(int method) const
{
    Matx<_Tp, n, m> b;
    bool ok;
    if( method == DECOMP_LU || method == DECOMP_CHOLESKY )
        ok = Matx_FastInvOp<_Tp, m>()(*this, b, method);
    else
    {
        Mat A(*this, false), B(b, false);
        ok = invert(A, B, method);
    }
    return ok ? b : Matx<_Tp, n, m>::zeros();
}


template<typename _Tp, int m, int n> struct CV_EXPORTS Matx_FastSolveOp
{
    bool operator()(const Matx<_Tp, m, m>& a, const Matx<_Tp, m, n>& b,
                    Matx<_Tp, m, n>& x, int method) const
    {
        Matx<_Tp, m, m> temp = a;
        x = b;
        if( method == DECOMP_CHOLESKY )
            return Cholesky(temp.val, m*sizeof(_Tp), m, x.val, n*sizeof(_Tp), n);
        
        return LU(temp.val, m*sizeof(_Tp), m, x.val, n*sizeof(_Tp), n) != 0;
    }
};


template<typename _Tp> struct CV_EXPORTS Matx_FastSolveOp<_Tp, 2, 1>
{
    bool operator()(const Matx<_Tp, 2, 2>& a, const Matx<_Tp, 2, 1>& b,
                    Matx<_Tp, 2, 1>& x, int method) const
    {
        _Tp d = determinant(a);
        if( d == 0 )
            return false;
        d = 1/d;
        x(0) = (b(0)*a(1,1) - b(1)*a(0,1))*d;
        x(1) = (b(1)*a(0,0) - b(0)*a(1,0))*d;
        return true;
    }
};

    
template<typename _Tp> struct CV_EXPORTS Matx_FastSolveOp<_Tp, 3, 1>
{
    bool operator()(const Matx<_Tp, 3, 3>& a, const Matx<_Tp, 3, 1>& b,
                    Matx<_Tp, 3, 1>& x, int method) const
    {
        _Tp d = determinant(a);
        if( d == 0 )
            return false;
        d = 1/d;
        x(0) = d*(b(0)*(a(1,1)*a(2,2) - a(1,2)*a(2,1)) -
                a(0,1)*(b(1)*a(2,2) - a(1,2)*b(2)) +
                a(0,2)*(b(1)*a(2,1) - a(1,1)*b(2)));
        
        x(1) = d*(a(0,0)*(b(1)*a(2,2) - a(1,2)*b(2)) -
                b(0)*(a(1,0)*a(2,2) - a(1,2)*a(2,0)) +
                a(0,2)*(a(1,0)*b(2) - b(1)*a(2,0)));
        
        x(2) = d*(a(0,0)*(a(1,1)*b(2) - b(1)*a(2,1)) -
                a(0,1)*(a(1,0)*b(2) - b(1)*a(2,0)) +
                b(0)*(a(1,0)*a(2,1) - a(1,1)*a(2,0)));
        return true;
    }
};
                      
    
template<typename _Tp, int m, int n> template<int l> inline
Matx<_Tp, n, l> Matx<_Tp, m, n>::solve(const Matx<_Tp, m, l>& rhs, int method) const
{
    Matx<_Tp, n, l> x;
    bool ok;
    if( method == DECOMP_LU || method == DECOMP_CHOLESKY )
        ok = Matx_FastSolveOp<_Tp, m, l>()(*this, rhs, x, method);
    else
    {
        Mat A(*this, false), B(rhs, false), X(x, false);
        ok = cv::solve(A, B, X, method);
    }

    return ok ? x : Matx<_Tp, n, l>::zeros();
}


template<typename _Tp, int m, int n> static inline
double norm(const Matx<_Tp, m, n>& M)
{
    double s = 0;
    for( int i = 0; i < m*n; i++ )
        s += (double)M.val[i]*M.val[i];
    return std::sqrt(s);
}

    
template<typename _Tp, int m, int n> static inline
double norm(const Matx<_Tp, m, n>& M, int normType)
{
    if( normType == NORM_INF )
    {
        _Tp s = 0;
        for( int i = 0; i < m*n; i++ )
            s = std::max(s, std::abs(M.val[i]));
        return s;
    }
    
    if( normType == NORM_L1 )
    {
        _Tp s = 0;
        for( int i = 0; i < m*n; i++ )
            s += std::abs(M.val[i]);
        return s;
    }
    
    CV_DbgAssert( normType == NORM_L2 );
    return norm(M);
}
    
    
template<typename _Tp, int m, int n> static inline
bool operator == (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
{
    for( int i = 0; i < m*n; i++ )
        if( a.val[i] != b.val[i] ) return false;
    return true;
}
    
template<typename _Tp, int m, int n> static inline
bool operator != (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
{
    return !(a == b);
}


template<typename _Tp, typename _T2, int m, int n> static inline
MatxCommaInitializer<_Tp, m, n> operator << (const Matx<_Tp, m, n>& mtx, _T2 val)
{
    MatxCommaInitializer<_Tp, m, n> commaInitializer((Matx<_Tp, m, n>*)&mtx);
    return (commaInitializer, val);
}

template<typename _Tp, int m, int n> inline
MatxCommaInitializer<_Tp, m, n>::MatxCommaInitializer(Matx<_Tp, m, n>* _mtx)
    : dst(_mtx), idx(0)
{}

template<typename _Tp, int m, int n> template<typename _T2> inline
MatxCommaInitializer<_Tp, m, n>& MatxCommaInitializer<_Tp, m, n>::operator , (_T2 value)
{
    CV_DbgAssert( idx < m*n );
    dst->val[idx++] = saturate_cast<_Tp>(value);
    return *this;
}

template<typename _Tp, int m, int n> inline
Matx<_Tp, m, n> MatxCommaInitializer<_Tp, m, n>::operator *() const
{
    CV_DbgAssert( idx == n*m );
    return *dst;
}    

/////////////////////////// short vector (Vec) /////////////////////////////

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec()
{}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(_Tp v0)
    : Matx<_Tp, cn, 1>(v0)
{}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1)
    : Matx<_Tp, cn, 1>(v0, v1)
{}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2)
    : Matx<_Tp, cn, 1>(v0, v1, v2)
{}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3)
    : Matx<_Tp, cn, 1>(v0, v1, v2, v3)
{}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4)
    : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4)
{}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5)
    : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5)
{}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                                                        _Tp v4, _Tp v5, _Tp v6)
    : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6)
{}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                                                        _Tp v4, _Tp v5, _Tp v6, _Tp v7)
    : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7)
{}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                                                        _Tp v4, _Tp v5, _Tp v6, _Tp v7,
                                                        _Tp v8)
    : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7, v8)
{}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
                                                        _Tp v4, _Tp v5, _Tp v6, _Tp v7,
                                                        _Tp v8, _Tp v9)
    : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9)
{}
    
template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(const _Tp* values)
    : Matx<_Tp, cn, 1>(values)
{}
        

template<typename _Tp, int cn> inline Vec<_Tp, cn>::Vec(const Vec<_Tp, cn>& m)
    : Matx<_Tp, cn, 1>(m.val)
{}

template<typename _Tp, int cn> inline
Vec<_Tp, cn>::Vec(const Matx<_Tp, cn, 1>& a, const Matx<_Tp, cn, 1>& b, Matx_AddOp op)
: Matx<_Tp, cn, 1>(a, b, op)
{}

template<typename _Tp, int cn> inline
Vec<_Tp, cn>::Vec(const Matx<_Tp, cn, 1>& a, const Matx<_Tp, cn, 1>& b, Matx_SubOp op)
: Matx<_Tp, cn, 1>(a, b, op)
{}

template<typename _Tp, int cn> template<typename _T2> inline
Vec<_Tp, cn>::Vec(const Matx<_Tp, cn, 1>& a, _T2 alpha, Matx_ScaleOp op)
: Matx<_Tp, cn, 1>(a, alpha, op)
{}    
        
template<typename _Tp, int cn> inline Vec<_Tp, cn> Vec<_Tp, cn>::all(_Tp alpha)
{
    Vec v;
    for( int i = 0; i < cn; i++ ) v.val[i] = alpha;
    return v;
}

template<typename _Tp, int cn> inline Vec<_Tp, cn> Vec<_Tp, cn>::mul(const Vec<_Tp, cn>& v) const
{
    Vec<_Tp, cn> w;
    for( int i = 0; i < cn; i++ ) w.val[i] = saturate_cast<_Tp>(this->val[i]*v.val[i]);
    return w;
}
    
template<typename _Tp, int cn> inline Vec<_Tp, cn> Vec<_Tp, cn>::cross(const Vec<_Tp, cn>& v) const
{
    CV_Error(CV_StsError, "for arbitrary-size vector there is no cross-product defined");
    return Vec<_Tp, cn>();
}
    
template<typename _Tp, int cn> template<typename T2>
inline Vec<_Tp, cn>::operator Vec<T2, cn>() const
{
    Vec<T2, cn> v;
    for( int i = 0; i < cn; i++ ) v.val[i] = saturate_cast<T2>(this->val[i]);
    return v;
}

template<typename _Tp, int cn> inline Vec<_Tp, cn>::operator CvScalar() const
{
    CvScalar s = {{0,0,0,0}};
    int i;
    for( i = 0; i < std::min(cn, 4); i++ ) s.val[i] = this->val[i];
    for( ; i < 4; i++ ) s.val[i] = 0;
    return s;
}

template<typename _Tp, int cn> inline const _Tp& Vec<_Tp, cn>::operator [](int i) const
{
    CV_DbgAssert( (unsigned)i < (unsigned)cn );
    return this->val[i];
}
    
template<typename _Tp, int cn> inline _Tp& Vec<_Tp, cn>::operator [](int i)
{
    CV_DbgAssert( (unsigned)i < (unsigned)cn );
    return this->val[i];
}

template<typename _Tp, int cn> inline const _Tp& Vec<_Tp, cn>::operator ()(int i) const
{
    CV_DbgAssert( (unsigned)i < (unsigned)cn );
    return this->val[i];
}

template<typename _Tp, int cn> inline _Tp& Vec<_Tp, cn>::operator ()(int i)
{
    CV_DbgAssert( (unsigned)i < (unsigned)cn );
    return this->val[i];
}    
    
template<typename _Tp1, typename _Tp2, int cn> static inline Vec<_Tp1, cn>&
operator += (Vec<_Tp1, cn>& a, const Vec<_Tp2, cn>& b)
{
    for( int i = 0; i < cn; i++ )
        a.val[i] = saturate_cast<_Tp1>(a.val[i] + b.val[i]);
    return a;
}    

template<typename _Tp1, typename _Tp2, int cn> static inline Vec<_Tp1, cn>&
operator -= (Vec<_Tp1, cn>& a, const Vec<_Tp2, cn>& b)
{
    for( int i = 0; i < cn; i++ )
        a.val[i] = saturate_cast<_Tp1>(a.val[i] - b.val[i]);
    return a;
}        
    
template<typename _Tp, int cn> static inline Vec<_Tp, cn>
operator + (const Vec<_Tp, cn>& a, const Vec<_Tp, cn>& b)
{
    return Vec<_Tp, cn>(a, b, Matx_AddOp());
}

template<typename _Tp, int cn> static inline Vec<_Tp, cn>
operator - (const Vec<_Tp, cn>& a, const Vec<_Tp, cn>& b)
{
    return Vec<_Tp, cn>(a, b, Matx_SubOp());
}

template<typename _Tp, int cn> static inline
Vec<_Tp, cn>& operator *= (Vec<_Tp, cn>& a, int alpha)
{
    for( int i = 0; i < cn; i++ )
        a[i] = saturate_cast<_Tp>(a[i]*alpha);
    return a;
}

template<typename _Tp, int cn> static inline
Vec<_Tp, cn>& operator *= (Vec<_Tp, cn>& a, float alpha)
{
    for( int i = 0; i < cn; i++ )
        a[i] = saturate_cast<_Tp>(a[i]*alpha);
    return a;
}
    
template<typename _Tp, int cn> static inline
Vec<_Tp, cn>& operator *= (Vec<_Tp, cn>& a, double alpha)
{
    for( int i = 0; i < cn; i++ )
        a[i] = saturate_cast<_Tp>(a[i]*alpha);
    return a;
}
    
    
template<typename _Tp, int cn> static inline Vec<_Tp, cn>
operator * (const Vec<_Tp, cn>& a, int alpha)
{
    return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
}

template<typename _Tp, int cn> static inline Vec<_Tp, cn>
operator * (int alpha, const Vec<_Tp, cn>& a)
{
    return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
}

template<typename _Tp, int cn> static inline Vec<_Tp, cn>
operator * (const Vec<_Tp, cn>& a, float alpha)
{
    return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
}

template<typename _Tp, int cn> static inline Vec<_Tp, cn>
operator * (float alpha, const Vec<_Tp, cn>& a)
{
    return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
}

template<typename _Tp, int cn> static inline Vec<_Tp, cn>
operator * (const Vec<_Tp, cn>& a, double alpha)
{
    return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
}

template<typename _Tp, int cn> static inline Vec<_Tp, cn>
operator * (double alpha, const Vec<_Tp, cn>& a)
{
    return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
}    

template<typename _Tp, int cn> static inline Vec<_Tp, cn>
operator - (const Vec<_Tp, cn>& a)
{
    Vec<_Tp,cn> t;
    for( int i = 0; i < cn; i++ ) t.val[i] = saturate_cast<_Tp>(-a.val[i]);
    return t;
}
    
template<> inline Vec<float, 3> Vec<float, 3>::cross(const Vec<float, 3>& v) const
{
    return Vec<float,3>(val[1]*v.val[2] - val[2]*v.val[1],
                     val[2]*v.val[0] - val[0]*v.val[2],
                     val[0]*v.val[1] - val[1]*v.val[0]);
}

template<> inline Vec<double, 3> Vec<double, 3>::cross(const Vec<double, 3>& v) const
{
    return Vec<double,3>(val[1]*v.val[2] - val[2]*v.val[1],
                     val[2]*v.val[0] - val[0]*v.val[2],
                     val[0]*v.val[1] - val[1]*v.val[0]);
}

template<typename T1, typename T2> static inline
Vec<T1, 2>& operator += (Vec<T1, 2>& a, const Vec<T2, 2>& b)
{
    a[0] = saturate_cast<T1>(a[0] + b[0]);
    a[1] = saturate_cast<T1>(a[1] + b[1]);
    return a;
}

template<typename T1, typename T2> static inline
Vec<T1, 3>& operator += (Vec<T1, 3>& a, const Vec<T2, 3>& b)
{
    a[0] = saturate_cast<T1>(a[0] + b[0]);
    a[1] = saturate_cast<T1>(a[1] + b[1]);
    a[2] = saturate_cast<T1>(a[2] + b[2]);
    return a;
}

    
template<typename T1, typename T2> static inline
Vec<T1, 4>& operator += (Vec<T1, 4>& a, const Vec<T2, 4>& b)
{
    a[0] = saturate_cast<T1>(a[0] + b[0]);
    a[1] = saturate_cast<T1>(a[1] + b[1]);
    a[2] = saturate_cast<T1>(a[2] + b[2]);
    a[3] = saturate_cast<T1>(a[3] + b[3]);
    return a;
}

        
template<typename _Tp, typename _T2, int cn> static inline
VecCommaInitializer<_Tp, cn> operator << (const Vec<_Tp, cn>& vec, _T2 val)
{
    VecCommaInitializer<_Tp, cn> commaInitializer((Vec<_Tp, cn>*)&vec);
    return (commaInitializer, val);
}
    
template<typename _Tp, int cn> inline
VecCommaInitializer<_Tp, cn>::VecCommaInitializer(Vec<_Tp, cn>* _vec)
    : MatxCommaInitializer<_Tp, cn, 1>(_vec)
{}

template<typename _Tp, int cn> template<typename _T2> inline
VecCommaInitializer<_Tp, cn>& VecCommaInitializer<_Tp, cn>::operator , (_T2 value)
{
    CV_DbgAssert( this->idx < cn );
    this->dst->val[this->idx++] = saturate_cast<_Tp>(value);
    return *this;
}

template<typename _Tp, int cn> inline
Vec<_Tp, cn> VecCommaInitializer<_Tp, cn>::operator *() const
{
    CV_DbgAssert( this->idx == cn );
    return *this->dst;
}    

//////////////////////////////// Complex //////////////////////////////

template<typename _Tp> inline Complex<_Tp>::Complex() : re(0), im(0) {}
template<typename _Tp> inline Complex<_Tp>::Complex( _Tp _re, _Tp _im ) : re(_re), im(_im) {}
template<typename _Tp> template<typename T2> inline Complex<_Tp>::operator Complex<T2>() const
{ return Complex<T2>(saturate_cast<T2>(re), saturate_cast<T2>(im)); }
template<typename _Tp> inline Complex<_Tp> Complex<_Tp>::conj() const
{ return Complex<_Tp>(re, -im); }

template<typename _Tp> static inline
bool operator == (const Complex<_Tp>& a, const Complex<_Tp>& b)
{ return a.re == b.re && a.im == b.im; }

template<typename _Tp> static inline
bool operator != (const Complex<_Tp>& a, const Complex<_Tp>& b)
{ return a.re != b.re || a.im != b.im; }    
    
template<typename _Tp> static inline
Complex<_Tp> operator + (const Complex<_Tp>& a, const Complex<_Tp>& b)
{ return Complex<_Tp>( a.re + b.re, a.im + b.im ); }

template<typename _Tp> static inline
Complex<_Tp>& operator += (Complex<_Tp>& a, const Complex<_Tp>& b)
{ a.re += b.re; a.im += b.im; return a; }

template<typename _Tp> static inline
Complex<_Tp> operator - (const Complex<_Tp>& a, const Complex<_Tp>& b)
{ return Complex<_Tp>( a.re - b.re, a.im - b.im ); }

template<typename _Tp> static inline
Complex<_Tp>& operator -= (Complex<_Tp>& a, const Complex<_Tp>& b)
{ a.re -= b.re; a.im -= b.im; return a; }

template<typename _Tp> static inline
Complex<_Tp> operator - (const Complex<_Tp>& a)
{ return Complex<_Tp>(-a.re, -a.im); }

template<typename _Tp> static inline
Complex<_Tp> operator * (const Complex<_Tp>& a, const Complex<_Tp>& b)
{ return Complex<_Tp>( a.re*b.re - a.im*b.im, a.re*b.im + a.im*b.re ); }

template<typename _Tp> static inline
Complex<_Tp> operator * (const Complex<_Tp>& a, _Tp b)
{ return Complex<_Tp>( a.re*b, a.im*b ); }

template<typename _Tp> static inline
Complex<_Tp> operator * (_Tp b, const Complex<_Tp>& a)
{ return Complex<_Tp>( a.re*b, a.im*b ); }

template<typename _Tp> static inline
Complex<_Tp> operator + (const Complex<_Tp>& a, _Tp b)
{ return Complex<_Tp>( a.re + b, a.im ); }

template<typename _Tp> static inline
Complex<_Tp> operator - (const Complex<_Tp>& a, _Tp b)
{ return Complex<_Tp>( a.re - b, a.im ); }

template<typename _Tp> static inline
Complex<_Tp> operator + (_Tp b, const Complex<_Tp>& a)
{ return Complex<_Tp>( a.re + b, a.im ); }

template<typename _Tp> static inline
Complex<_Tp> operator - (_Tp b, const Complex<_Tp>& a)
{ return Complex<_Tp>( b - a.re, -a.im ); }

template<typename _Tp> static inline
Complex<_Tp>& operator += (Complex<_Tp>& a, _Tp b)
{ a.re += b; return a; }

template<typename _Tp> static inline
Complex<_Tp>& operator -= (Complex<_Tp>& a, _Tp b)
{ a.re -= b; return a; }

template<typename _Tp> static inline
Complex<_Tp>& operator *= (Complex<_Tp>& a, _Tp b)
{ a.re *= b; a.im *= b; return a; }

template<typename _Tp> static inline
double abs(const Complex<_Tp>& a)
{ return std::sqrt( (double)a.re*a.re + (double)a.im*a.im); }

template<typename _Tp> static inline
Complex<_Tp> operator / (const Complex<_Tp>& a, const Complex<_Tp>& b)
{
    double t = 1./((double)b.re*b.re + (double)b.im*b.im);
    return Complex<_Tp>( (_Tp)((a.re*b.re + a.im*b.im)*t),
                        (_Tp)((-a.re*b.im + a.im*b.re)*t) );
}

template<typename _Tp> static inline
Complex<_Tp>& operator /= (Complex<_Tp>& a, const Complex<_Tp>& b)
{
    return (a = a / b);
}

template<typename _Tp> static inline
Complex<_Tp> operator / (const Complex<_Tp>& a, _Tp b)
{
    _Tp t = (_Tp)1/b;
    return Complex<_Tp>( a.re*t, a.im*t );
}

template<typename _Tp> static inline
Complex<_Tp> operator / (_Tp b, const Complex<_Tp>& a)
{
    return Complex<_Tp>(b)/a;
}

template<typename _Tp> static inline
Complex<_Tp> operator /= (const Complex<_Tp>& a, _Tp b)
{
    _Tp t = (_Tp)1/b;
    a.re *= t; a.im *= t; return a;
}

//////////////////////////////// 2D Point ////////////////////////////////

template<typename _Tp> inline Point_<_Tp>::Point_() : x(0), y(0) {}
template<typename _Tp> inline Point_<_Tp>::Point_(_Tp _x, _Tp _y) : x(_x), y(_y) {}
template<typename _Tp> inline Point_<_Tp>::Point_(const Point_& pt) : x(pt.x), y(pt.y) {}
template<typename _Tp> inline Point_<_Tp>::Point_(const CvPoint& pt) : x((_Tp)pt.x), y((_Tp)pt.y) {}
template<typename _Tp> inline Point_<_Tp>::Point_(const CvPoint2D32f& pt)
    : x(saturate_cast<_Tp>(pt.x)), y(saturate_cast<_Tp>(pt.y)) {}
template<typename _Tp> inline Point_<_Tp>::Point_(const Size_<_Tp>& sz) : x(sz.width), y(sz.height) {}
template<typename _Tp> inline Point_<_Tp>::Point_(const Vec<_Tp,2>& v) : x(v[0]), y(v[1]) {}
template<typename _Tp> inline Point_<_Tp>& Point_<_Tp>::operator = (const Point_& pt)
{ x = pt.x; y = pt.y; return *this; }

template<typename _Tp> template<typename _Tp2> inline Point_<_Tp>::operator Point_<_Tp2>() const
{ return Point_<_Tp2>(saturate_cast<_Tp2>(x), saturate_cast<_Tp2>(y)); }
template<typename _Tp> inline Point_<_Tp>::operator CvPoint() const
{ return cvPoint(saturate_cast<int>(x), saturate_cast<int>(y)); }
template<typename _Tp> inline Point_<_Tp>::operator CvPoint2D32f() const
{ return cvPoint2D32f((float)x, (float)y); }
template<typename _Tp> inline Point_<_Tp>::operator Vec<_Tp, 2>() const
{ return Vec<_Tp, 2>(x, y); }

template<typename _Tp> inline _Tp Point_<_Tp>::dot(const Point_& pt) const
{ return saturate_cast<_Tp>(x*pt.x + y*pt.y); }
template<typename _Tp> inline double Point_<_Tp>::ddot(const Point_& pt) const
{ return (double)x*pt.x + (double)y*pt.y; }

template<typename _Tp> static inline Point_<_Tp>&
operator += (Point_<_Tp>& a, const Point_<_Tp>& b)
{
    a.x = saturate_cast<_Tp>(a.x + b.x);
    a.y = saturate_cast<_Tp>(a.y + b.y);
    return a;
}

template<typename _Tp> static inline Point_<_Tp>&
operator -= (Point_<_Tp>& a, const Point_<_Tp>& b)
{
    a.x = saturate_cast<_Tp>(a.x - b.x);
    a.y = saturate_cast<_Tp>(a.y - b.y);
    return a;
}

template<typename _Tp> static inline Point_<_Tp>&
operator *= (Point_<_Tp>& a, int b)
{
    a.x = saturate_cast<_Tp>(a.x*b);
    a.y = saturate_cast<_Tp>(a.y*b);
    return a;
}

template<typename _Tp> static inline Point_<_Tp>&
operator *= (Point_<_Tp>& a, float b)
{
    a.x = saturate_cast<_Tp>(a.x*b);
    a.y = saturate_cast<_Tp>(a.y*b);
    return a;
}

template<typename _Tp> static inline Point_<_Tp>&
operator *= (Point_<_Tp>& a, double b)
{
    a.x = saturate_cast<_Tp>(a.x*b);
    a.y = saturate_cast<_Tp>(a.y*b);
    return a;
}    
    
template<typename _Tp> static inline double norm(const Point_<_Tp>& pt)
{ return std::sqrt((double)pt.x*pt.x + (double)pt.y*pt.y); }

template<typename _Tp> static inline bool operator == (const Point_<_Tp>& a, const Point_<_Tp>& b)
{ return a.x == b.x && a.y == b.y; }

template<typename _Tp> static inline bool operator != (const Point_<_Tp>& a, const Point_<_Tp>& b)
{ return a.x != b.x || a.y != b.y; }

template<typename _Tp> static inline Point_<_Tp> operator + (const Point_<_Tp>& a, const Point_<_Tp>& b)
{ return Point_<_Tp>( saturate_cast<_Tp>(a.x + b.x), saturate_cast<_Tp>(a.y + b.y) ); }

template<typename _Tp> static inline Point_<_Tp> operator - (const Point_<_Tp>& a, const Point_<_Tp>& b)
{ return Point_<_Tp>( saturate_cast<_Tp>(a.x - b.x), saturate_cast<_Tp>(a.y - b.y) ); }

template<typename _Tp> static inline Point_<_Tp> operator - (const Point_<_Tp>& a)
{ return Point_<_Tp>( saturate_cast<_Tp>(-a.x), saturate_cast<_Tp>(-a.y) ); }

template<typename _Tp> static inline Point_<_Tp> operator * (const Point_<_Tp>& a, int b)
{ return Point_<_Tp>( saturate_cast<_Tp>(a.x*b), saturate_cast<_Tp>(a.y*b) ); }

template<typename _Tp> static inline Point_<_Tp> operator * (int a, const Point_<_Tp>& b)
{ return Point_<_Tp>( saturate_cast<_Tp>(b.x*a), saturate_cast<_Tp>(b.y*a) ); }
    
template<typename _Tp> static inline Point_<_Tp> operator * (const Point_<_Tp>& a, float b)
{ return Point_<_Tp>( saturate_cast<_Tp>(a.x*b), saturate_cast<_Tp>(a.y*b) ); }

template<typename _Tp> static inline Point_<_Tp> operator * (float a, const Point_<_Tp>& b)
{ return Point_<_Tp>( saturate_cast<_Tp>(b.x*a), saturate_cast<_Tp>(b.y*a) ); }

template<typename _Tp> static inline Point_<_Tp> operator * (const Point_<_Tp>& a, double b)
{ return Point_<_Tp>( saturate_cast<_Tp>(a.x*b), saturate_cast<_Tp>(a.y*b) ); }

template<typename _Tp> static inline Point_<_Tp> operator * (double a, const Point_<_Tp>& b)
{ return Point_<_Tp>( saturate_cast<_Tp>(b.x*a), saturate_cast<_Tp>(b.y*a) ); }    
    
//////////////////////////////// 3D Point ////////////////////////////////

template<typename _Tp> inline Point3_<_Tp>::Point3_() : x(0), y(0), z(0) {}
template<typename _Tp> inline Point3_<_Tp>::Point3_(_Tp _x, _Tp _y, _Tp _z) : x(_x), y(_y), z(_z) {}
template<typename _Tp> inline Point3_<_Tp>::Point3_(const Point3_& pt) : x(pt.x), y(pt.y), z(pt.z) {}
template<typename _Tp> inline Point3_<_Tp>::Point3_(const Point_<_Tp>& pt) : x(pt.x), y(pt.y), z(_Tp()) {}
template<typename _Tp> inline Point3_<_Tp>::Point3_(const CvPoint3D32f& pt) :
    x(saturate_cast<_Tp>(pt.x)), y(saturate_cast<_Tp>(pt.y)), z(saturate_cast<_Tp>(pt.z)) {}
template<typename _Tp> inline Point3_<_Tp>::Point3_(const Vec<_Tp, 3>& v) : x(v[0]), y(v[1]), z(v[2]) {}

template<typename _Tp> template<typename _Tp2> inline Point3_<_Tp>::operator Point3_<_Tp2>() const
{ return Point3_<_Tp2>(saturate_cast<_Tp2>(x), saturate_cast<_Tp2>(y), saturate_cast<_Tp2>(z)); }

template<typename _Tp> inline Point3_<_Tp>::operator CvPoint3D32f() const
{ return cvPoint3D32f((float)x, (float)y, (float)z); }

template<typename _Tp> inline Point3_<_Tp>::operator Vec<_Tp, 3>() const
{ return Vec<_Tp, 3>(x, y, z); }

template<typename _Tp> inline Point3_<_Tp>& Point3_<_Tp>::operator = (const Point3_& pt)
{ x = pt.x; y = pt.y; z = pt.z; return *this; }

template<typename _Tp> inline _Tp Point3_<_Tp>::dot(const Point3_& pt) const
{ return saturate_cast<_Tp>(x*pt.x + y*pt.y + z*pt.z); }
template<typename _Tp> inline double Point3_<_Tp>::ddot(const Point3_& pt) const
{ return (double)x*pt.x + (double)y*pt.y + (double)z*pt.z; }
    
template<typename _Tp> inline Point3_<_Tp> Point3_<_Tp>::cross(const Point3_<_Tp>& pt) const
{
    return Point3_<_Tp>(y*pt.z - z*pt.y, z*pt.x - x*pt.z, x*pt.y - y*pt.x);
}

template<typename _Tp> static inline Point3_<_Tp>&
operator += (Point3_<_Tp>& a, const Point3_<_Tp>& b)
{
    a.x = saturate_cast<_Tp>(a.x + b.x);
    a.y = saturate_cast<_Tp>(a.y + b.y);
    a.z = saturate_cast<_Tp>(a.z + b.z);
    return a;
}
    
template<typename _Tp> static inline Point3_<_Tp>&
operator -= (Point3_<_Tp>& a, const Point3_<_Tp>& b)
{
    a.x = saturate_cast<_Tp>(a.x - b.x);
    a.y = saturate_cast<_Tp>(a.y - b.y);
    a.z = saturate_cast<_Tp>(a.z - b.z);
    return a;
}    
    
template<typename _Tp> static inline Point3_<_Tp>&
operator *= (Point3_<_Tp>& a, int b)
{
    a.x = saturate_cast<_Tp>(a.x*b);
    a.y = saturate_cast<_Tp>(a.y*b);
    a.z = saturate_cast<_Tp>(a.z*b);
    return a;
}

template<typename _Tp> static inline Point3_<_Tp>&
operator *= (Point3_<_Tp>& a, float b)
{
    a.x = saturate_cast<_Tp>(a.x*b);
    a.y = saturate_cast<_Tp>(a.y*b);
    a.z = saturate_cast<_Tp>(a.z*b);
    return a;
}

template<typename _Tp> static inline Point3_<_Tp>&
operator *= (Point3_<_Tp>& a, double b)
{
    a.x = saturate_cast<_Tp>(a.x*b);
    a.y = saturate_cast<_Tp>(a.y*b);
    a.z = saturate_cast<_Tp>(a.z*b);
    return a;
}    
    
template<typename _Tp> static inline double norm(const Point3_<_Tp>& pt)
{ return std::sqrt((double)pt.x*pt.x + (double)pt.y*pt.y + (double)pt.z*pt.z); }

template<typename _Tp> static inline bool operator == (const Point3_<_Tp>& a, const Point3_<_Tp>& b)
{ return a.x == b.x && a.y == b.y && a.z == b.z; }

template<typename _Tp> static inline bool operator != (const Point3_<_Tp>& a, const Point3_<_Tp>& b)
{ return a.x != b.x || a.y != b.y || a.z != b.z; }
    
template<typename _Tp> static inline Point3_<_Tp> operator + (const Point3_<_Tp>& a, const Point3_<_Tp>& b)
{ return Point3_<_Tp>( saturate_cast<_Tp>(a.x + b.x),
                      saturate_cast<_Tp>(a.y + b.y),
                      saturate_cast<_Tp>(a.z + b.z)); }

template<typename _Tp> static inline Point3_<_Tp> operator - (const Point3_<_Tp>& a, const Point3_<_Tp>& b)
{ return Point3_<_Tp>( saturate_cast<_Tp>(a.x - b.x),
                        saturate_cast<_Tp>(a.y - b.y),
                        saturate_cast<_Tp>(a.z - b.z)); }

template<typename _Tp> static inline Point3_<_Tp> operator - (const Point3_<_Tp>& a)
{ return Point3_<_Tp>( saturate_cast<_Tp>(-a.x),
                      saturate_cast<_Tp>(-a.y),
                      saturate_cast<_Tp>(-a.z) ); }

template<typename _Tp> static inline Point3_<_Tp> operator * (const Point3_<_Tp>& a, int b)
{ return Point3_<_Tp>( saturate_cast<_Tp>(a.x*b),
                      saturate_cast<_Tp>(a.y*b),
                      saturate_cast<_Tp>(a.z*b) ); }

template<typename _Tp> static inline Point3_<_Tp> operator * (int a, const Point3_<_Tp>& b)
{ return Point3_<_Tp>( saturate_cast<_Tp>(b.x*a),
                      saturate_cast<_Tp>(b.y*a),
                      saturate_cast<_Tp>(b.z*a) ); }

template<typename _Tp> static inline Point3_<_Tp> operator * (const Point3_<_Tp>& a, float b)
{ return Point3_<_Tp>( saturate_cast<_Tp>(a.x*b),
                      saturate_cast<_Tp>(a.y*b),
                      saturate_cast<_Tp>(a.z*b) ); }

template<typename _Tp> static inline Point3_<_Tp> operator * (float a, const Point3_<_Tp>& b)
{ return Point3_<_Tp>( saturate_cast<_Tp>(b.x*a),
                      saturate_cast<_Tp>(b.y*a),
                      saturate_cast<_Tp>(b.z*a) ); }

template<typename _Tp> static inline Point3_<_Tp> operator * (const Point3_<_Tp>& a, double b)
{ return Point3_<_Tp>( saturate_cast<_Tp>(a.x*b),
                      saturate_cast<_Tp>(a.y*b),
                      saturate_cast<_Tp>(a.z*b) ); }

template<typename _Tp> static inline Point3_<_Tp> operator * (double a, const Point3_<_Tp>& b)
{ return Point3_<_Tp>( saturate_cast<_Tp>(b.x*a),
                      saturate_cast<_Tp>(b.y*a),
                      saturate_cast<_Tp>(b.z*a) ); }
    
//////////////////////////////// Size ////////////////////////////////

template<typename _Tp> inline Size_<_Tp>::Size_()
    : width(0), height(0) {}
template<typename _Tp> inline Size_<_Tp>::Size_(_Tp _width, _Tp _height)
    : width(_width), height(_height) {}
template<typename _Tp> inline Size_<_Tp>::Size_(const Size_& sz)
    : width(sz.width), height(sz.height) {}
template<typename _Tp> inline Size_<_Tp>::Size_(const CvSize& sz)
    : width(saturate_cast<_Tp>(sz.width)), height(saturate_cast<_Tp>(sz.height)) {}
template<typename _Tp> inline Size_<_Tp>::Size_(const CvSize2D32f& sz)
    : width(saturate_cast<_Tp>(sz.width)), height(saturate_cast<_Tp>(sz.height)) {}
template<typename _Tp> inline Size_<_Tp>::Size_(const Point_<_Tp>& pt) : width(pt.x), height(pt.y) {}

template<typename _Tp> template<typename _Tp2> inline Size_<_Tp>::operator Size_<_Tp2>() const
{ return Size_<_Tp2>(saturate_cast<_Tp2>(width), saturate_cast<_Tp2>(height)); }
template<typename _Tp> inline Size_<_Tp>::operator CvSize() const
{ return cvSize(saturate_cast<int>(width), saturate_cast<int>(height)); }
template<typename _Tp> inline Size_<_Tp>::operator CvSize2D32f() const
{ return cvSize2D32f((float)width, (float)height); }

template<typename _Tp> inline Size_<_Tp>& Size_<_Tp>::operator = (const Size_<_Tp>& sz)
{ width = sz.width; height = sz.height; return *this; }
template<typename _Tp> static inline Size_<_Tp> operator * (const Size_<_Tp>& a, _Tp b)
{ return Size_<_Tp>(a.width * b, a.height * b); }
template<typename _Tp> static inline Size_<_Tp> operator + (const Size_<_Tp>& a, const Size_<_Tp>& b)
{ return Size_<_Tp>(a.width + b.width, a.height + b.height); }
template<typename _Tp> static inline Size_<_Tp> operator - (const Size_<_Tp>& a, const Size_<_Tp>& b)
{ return Size_<_Tp>(a.width - b.width, a.height - b.height); }
template<typename _Tp> inline _Tp Size_<_Tp>::area() const { return width*height; }

template<typename _Tp> static inline Size_<_Tp>& operator += (Size_<_Tp>& a, const Size_<_Tp>& b)
{ a.width += b.width; a.height += b.height; return a; }
template<typename _Tp> static inline Size_<_Tp>& operator -= (Size_<_Tp>& a, const Size_<_Tp>& b)
{ a.width -= b.width; a.height -= b.height; return a; }

template<typename _Tp> static inline bool operator == (const Size_<_Tp>& a, const Size_<_Tp>& b)
{ return a.width == b.width && a.height == b.height; }
template<typename _Tp> static inline bool operator != (const Size_<_Tp>& a, const Size_<_Tp>& b)
{ return a.width != b.width || a.height != b.height; }

//////////////////////////////// Rect ////////////////////////////////


template<typename _Tp> inline Rect_<_Tp>::Rect_() : x(0), y(0), width(0), height(0) {}
template<typename _Tp> inline Rect_<_Tp>::Rect_(_Tp _x, _Tp _y, _Tp _width, _Tp _height) : x(_x), y(_y), width(_width), height(_height) {}
template<typename _Tp> inline Rect_<_Tp>::Rect_(const Rect_<_Tp>& r) : x(r.x), y(r.y), width(r.width), height(r.height) {}
template<typename _Tp> inline Rect_<_Tp>::Rect_(const CvRect& r) : x((_Tp)r.x), y((_Tp)r.y), width((_Tp)r.width), height((_Tp)r.height) {}
template<typename _Tp> inline Rect_<_Tp>::Rect_(const Point_<_Tp>& org, const Size_<_Tp>& sz) :
    x(org.x), y(org.y), width(sz.width), height(sz.height) {}
template<typename _Tp> inline Rect_<_Tp>::Rect_(const Point_<_Tp>& pt1, const Point_<_Tp>& pt2)
{
    x = std::min(pt1.x, pt2.x); y = std::min(pt1.y, pt2.y);
    width = std::max(pt1.x, pt2.x) - x; height = std::max(pt1.y, pt2.y) - y;
}
template<typename _Tp> inline Rect_<_Tp>& Rect_<_Tp>::operator = ( const Rect_<_Tp>& r )
{ x = r.x; y = r.y; width = r.width; height = r.height; return *this; }

template<typename _Tp> inline Point_<_Tp> Rect_<_Tp>::tl() const { return Point_<_Tp>(x,y); }
template<typename _Tp> inline Point_<_Tp> Rect_<_Tp>::br() const { return Point_<_Tp>(x+width, y+height); }

template<typename _Tp> static inline Rect_<_Tp>& operator += ( Rect_<_Tp>& a, const Point_<_Tp>& b )
{ a.x += b.x; a.y += b.y; return a; }
template<typename _Tp> static inline Rect_<_Tp>& operator -= ( Rect_<_Tp>& a, const Point_<_Tp>& b )
{ a.x -= b.x; a.y -= b.y; return a; }

template<typename _Tp> static inline Rect_<_Tp>& operator += ( Rect_<_Tp>& a, const Size_<_Tp>& b )
{ a.width += b.width; a.height += b.height; return a; }

template<typename _Tp> static inline Rect_<_Tp>& operator -= ( Rect_<_Tp>& a, const Size_<_Tp>& b )
{ a.width -= b.width; a.height -= b.height; return a; }

template<typename _Tp> static inline Rect_<_Tp>& operator &= ( Rect_<_Tp>& a, const Rect_<_Tp>& b )
{
    _Tp x1 = std::max(a.x, b.x), y1 = std::max(a.y, b.y);
    a.width = std::min(a.x + a.width, b.x + b.width) - x1;
    a.height = std::min(a.y + a.height, b.y + b.height) - y1;
    a.x = x1; a.y = y1;
    if( a.width <= 0 || a.height <= 0 )
        a = Rect();
    return a;
}

template<typename _Tp> static inline Rect_<_Tp>& operator |= ( Rect_<_Tp>& a, const Rect_<_Tp>& b )
{
    _Tp x1 = std::min(a.x, b.x), y1 = std::min(a.y, b.y);
    a.width = std::max(a.x + a.width, b.x + b.width) - x1;
    a.height = std::max(a.y + a.height, b.y + b.height) - y1;
    a.x = x1; a.y = y1;
    return a;
}

template<typename _Tp> inline Size_<_Tp> Rect_<_Tp>::size() const { return Size_<_Tp>(width, height); }
template<typename _Tp> inline _Tp Rect_<_Tp>::area() const { return width*height; }

template<typename _Tp> template<typename _Tp2> inline Rect_<_Tp>::operator Rect_<_Tp2>() const
{ return Rect_<_Tp2>(saturate_cast<_Tp2>(x), saturate_cast<_Tp2>(y),
                     saturate_cast<_Tp2>(width), saturate_cast<_Tp2>(height)); }
template<typename _Tp> inline Rect_<_Tp>::operator CvRect() const
{ return cvRect(saturate_cast<int>(x), saturate_cast<int>(y),
                saturate_cast<int>(width), saturate_cast<int>(height)); }

template<typename _Tp> inline bool Rect_<_Tp>::contains(const Point_<_Tp>& pt) const
{ return x <= pt.x && pt.x < x + width && y <= pt.y && pt.y < y + height; }

template<typename _Tp> static inline bool operator == (const Rect_<_Tp>& a, const Rect_<_Tp>& b)
{
    return a.x == b.x && a.y == b.y && a.width == b.width && a.height == b.height;
}

template<typename _Tp> static inline bool operator != (const Rect_<_Tp>& a, const Rect_<_Tp>& b)
{
    return a.x != b.x || a.y != b.y || a.width != b.width || a.height != b.height;
}    
    
template<typename _Tp> static inline Rect_<_Tp> operator + (const Rect_<_Tp>& a, const Point_<_Tp>& b)
{
    return Rect_<_Tp>( a.x + b.x, a.y + b.y, a.width, a.height );
}

template<typename _Tp> static inline Rect_<_Tp> operator - (const Rect_<_Tp>& a, const Point_<_Tp>& b)
{
    return Rect_<_Tp>( a.x - b.x, a.y - b.y, a.width, a.height );
}

template<typename _Tp> static inline Rect_<_Tp> operator + (const Rect_<_Tp>& a, const Size_<_Tp>& b)
{
    return Rect_<_Tp>( a.x, a.y, a.width + b.width, a.height + b.height );
}

template<typename _Tp> static inline Rect_<_Tp> operator & (const Rect_<_Tp>& a, const Rect_<_Tp>& b)
{
    Rect_<_Tp> c = a;
    return c &= b;
}

template<typename _Tp> static inline Rect_<_Tp> operator | (const Rect_<_Tp>& a, const Rect_<_Tp>& b)
{
    Rect_<_Tp> c = a;
    return c |= b;
}

template<typename _Tp> inline bool Point_<_Tp>::inside( const Rect_<_Tp>& r ) const
{
    return r.contains(*this);
}

inline RotatedRect::RotatedRect() { angle = 0; }
inline RotatedRect::RotatedRect(const Point2f& _center, const Size2f& _size, float _angle)
    : center(_center), size(_size), angle(_angle) {}
inline RotatedRect::RotatedRect(const CvBox2D& box)
    : center(box.center), size(box.size), angle(box.angle) {}
inline RotatedRect::operator CvBox2D() const
{
    CvBox2D box; box.center = center; box.size = size; box.angle = angle;
    return box;
}
    
//////////////////////////////// Scalar_ ///////////////////////////////

template<typename _Tp> inline Scalar_<_Tp>::Scalar_()
{ this->val[0] = this->val[1] = this->val[2] = this->val[3] = 0; }

template<typename _Tp> inline Scalar_<_Tp>::Scalar_(_Tp v0, _Tp v1, _Tp v2, _Tp v3)
{ this->val[0] = v0; this->val[1] = v1; this->val[2] = v2; this->val[3] = v3; }

template<typename _Tp> inline Scalar_<_Tp>::Scalar_(const CvScalar& s)
{
    this->val[0] = saturate_cast<_Tp>(s.val[0]);
    this->val[1] = saturate_cast<_Tp>(s.val[1]);
    this->val[2] = saturate_cast<_Tp>(s.val[2]);
    this->val[3] = saturate_cast<_Tp>(s.val[3]);
}

template<typename _Tp> inline Scalar_<_Tp>::Scalar_(_Tp v0)
{ this->val[0] = v0; this->val[1] = this->val[2] = this->val[3] = 0; }

template<typename _Tp> inline Scalar_<_Tp> Scalar_<_Tp>::all(_Tp v0)
{ return Scalar_<_Tp>(v0, v0, v0, v0); }
template<typename _Tp> inline Scalar_<_Tp>::operator CvScalar() const
{ return cvScalar(this->val[0], this->val[1], this->val[2], this->val[3]); }

template<typename _Tp> template<typename T2> inline Scalar_<_Tp>::operator Scalar_<T2>() const
{
    return Scalar_<T2>(saturate_cast<T2>(this->val[0]),
                  saturate_cast<T2>(this->val[1]),
                  saturate_cast<T2>(this->val[2]),
                  saturate_cast<T2>(this->val[3]));
}

template<typename _Tp> static inline Scalar_<_Tp>& operator += (Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    a.val[0] = saturate_cast<_Tp>(a.val[0] + b.val[0]);
    a.val[1] = saturate_cast<_Tp>(a.val[1] + b.val[1]);
    a.val[2] = saturate_cast<_Tp>(a.val[2] + b.val[2]);
    a.val[3] = saturate_cast<_Tp>(a.val[3] + b.val[3]);
    return a;
}

template<typename _Tp> static inline Scalar_<_Tp>& operator -= (Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    a.val[0] = saturate_cast<_Tp>(a.val[0] - b.val[0]);
    a.val[1] = saturate_cast<_Tp>(a.val[1] - b.val[1]);
    a.val[2] = saturate_cast<_Tp>(a.val[2] - b.val[2]);
    a.val[3] = saturate_cast<_Tp>(a.val[3] - b.val[3]);
    return a;
}

template<typename _Tp> static inline Scalar_<_Tp>& operator *= ( Scalar_<_Tp>& a, _Tp v )
{
    a.val[0] = saturate_cast<_Tp>(a.val[0] * v);
    a.val[1] = saturate_cast<_Tp>(a.val[1] * v);
    a.val[2] = saturate_cast<_Tp>(a.val[2] * v);
    a.val[3] = saturate_cast<_Tp>(a.val[3] * v);
    return a;
}

template<typename _Tp> inline Scalar_<_Tp> Scalar_<_Tp>::mul(const Scalar_<_Tp>& t, double scale ) const
{
    return Scalar_<_Tp>( saturate_cast<_Tp>(this->val[0]*t.val[0]*scale),
                       saturate_cast<_Tp>(this->val[1]*t.val[1]*scale),
                       saturate_cast<_Tp>(this->val[2]*t.val[2]*scale),
                       saturate_cast<_Tp>(this->val[3]*t.val[3]*scale));
}

template<typename _Tp> static inline bool operator == ( const Scalar_<_Tp>& a, const Scalar_<_Tp>& b )
{
    return a.val[0] == b.val[0] && a.val[1] == b.val[1] &&
        a.val[2] == b.val[2] && a.val[3] == b.val[3];
}

template<typename _Tp> static inline bool operator != ( const Scalar_<_Tp>& a, const Scalar_<_Tp>& b )
{
    return a.val[0] != b.val[0] || a.val[1] != b.val[1] ||
        a.val[2] != b.val[2] || a.val[3] != b.val[3];
}

template<typename _Tp> static inline Scalar_<_Tp> operator + (const Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(a.val[0] + b.val[0]),
                      saturate_cast<_Tp>(a.val[1] + b.val[1]),
                      saturate_cast<_Tp>(a.val[2] + b.val[2]),
                      saturate_cast<_Tp>(a.val[3] + b.val[3]));
}

template<typename _Tp> static inline Scalar_<_Tp> operator - (const Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(a.val[0] - b.val[0]),
                      saturate_cast<_Tp>(a.val[1] - b.val[1]),
                      saturate_cast<_Tp>(a.val[2] - b.val[2]),
                      saturate_cast<_Tp>(a.val[3] - b.val[3]));
}

template<typename _Tp> static inline Scalar_<_Tp> operator * (const Scalar_<_Tp>& a, _Tp alpha)
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(a.val[0] * alpha),
                      saturate_cast<_Tp>(a.val[1] * alpha),
                      saturate_cast<_Tp>(a.val[2] * alpha),
                      saturate_cast<_Tp>(a.val[3] * alpha));
}

template<typename _Tp> static inline Scalar_<_Tp> operator * (_Tp alpha, const Scalar_<_Tp>& a)
{
    return a*alpha;
}

template<typename _Tp> static inline Scalar_<_Tp> operator - (const Scalar_<_Tp>& a)
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(-a.val[0]), saturate_cast<_Tp>(-a.val[1]),
                      saturate_cast<_Tp>(-a.val[2]), saturate_cast<_Tp>(-a.val[3]));
}

    
template<typename _Tp> static inline Scalar_<_Tp>
operator * (const Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(a[0]*b[0] - a[1]*b[1] - a[2]*b[2] - a[3]*b[3]),
                        saturate_cast<_Tp>(a[0]*b[1] + a[1]*b[0] + a[2]*b[3] - a[3]*b[2]),
                        saturate_cast<_Tp>(a[0]*b[2] - a[1]*b[3] + a[2]*b[0] - a[3]*b[1]),
                        saturate_cast<_Tp>(a[0]*b[3] + a[1]*b[2] - a[2]*b[1] - a[3]*b[0]));
}
    
template<typename _Tp> static inline Scalar_<_Tp>&
operator *= (Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    a = a*b;
    return a;
}    
    
template<typename _Tp> inline Scalar_<_Tp> Scalar_<_Tp>::conj() const
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(this->val[0]),
                        saturate_cast<_Tp>(-this->val[1]),
                        saturate_cast<_Tp>(-this->val[2]),
                        saturate_cast<_Tp>(-this->val[3]));
}

template<typename _Tp> inline bool Scalar_<_Tp>::isReal() const
{
    return this->val[1] == 0 && this->val[2] == 0 && this->val[3] == 0;
}
    
template<typename _Tp> static inline
Scalar_<_Tp> operator / (const Scalar_<_Tp>& a, _Tp alpha)
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(a.val[0] / alpha),
                        saturate_cast<_Tp>(a.val[1] / alpha),
                        saturate_cast<_Tp>(a.val[2] / alpha),
                        saturate_cast<_Tp>(a.val[3] / alpha));
}    

template<typename _Tp> static inline
Scalar_<float> operator / (const Scalar_<float>& a, float alpha)
{
    float s = 1/alpha;
    return Scalar_<float>(a.val[0]*s, a.val[1]*s, a.val[2]*s, a.val[3]*s);
}        

template<typename _Tp> static inline
Scalar_<double> operator / (const Scalar_<double>& a, double alpha)
{
    double s = 1/alpha;
    return Scalar_<double>(a.val[0]*s, a.val[1]*s, a.val[2]*s, a.val[3]*s);
}            
    
template<typename _Tp> static inline
Scalar_<_Tp>& operator /= (Scalar_<_Tp>& a, _Tp alpha)
{
    a = a/alpha;
    return a;
}
    
template<typename _Tp> static inline
Scalar_<_Tp> operator / (_Tp a, const Scalar_<_Tp>& b)
{
    _Tp s = a/(b[0]*b[0] + b[1]*b[1] + b[2]*b[2] + b[3]*b[3]);
    return b.conj()*s;
}    
    
template<typename _Tp> static inline
Scalar_<_Tp> operator / (const Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    return a*((_Tp)1/b);
}

template<typename _Tp> static inline
Scalar_<_Tp>& operator /= (Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    a = a/b;
    return a;
}
    
//////////////////////////////// Range /////////////////////////////////

inline Range::Range() : start(0), end(0) {}
inline Range::Range(int _start, int _end) : start(_start), end(_end) {}
inline Range::Range(const CvSlice& slice) : start(slice.start_index), end(slice.end_index)
{
    if( start == 0 && end == CV_WHOLE_SEQ_END_INDEX )
        *this = Range::all();
}

inline int Range::size() const { return end - start; }
inline bool Range::empty() const { return start == end; }
inline Range Range::all() { return Range(INT_MIN, INT_MAX); }

static inline bool operator == (const Range& r1, const Range& r2)
{ return r1.start == r2.start && r1.end == r2.end; }

static inline bool operator != (const Range& r1, const Range& r2)
{ return !(r1 == r2); }

static inline bool operator !(const Range& r)
{ return r.start == r.end; }

static inline Range operator & (const Range& r1, const Range& r2)
{
    Range r(std::max(r1.start, r2.start), std::min(r1.end, r2.end));
    r.end = std::max(r.end, r.start);
    return r;
}

static inline Range& operator &= (Range& r1, const Range& r2)
{
    r1 = r1 & r2;
    return r1;
}

static inline Range operator + (const Range& r1, int delta)
{
    return Range(r1.start + delta, r1.end + delta);
}

static inline Range operator + (int delta, const Range& r1)
{
    return Range(r1.start + delta, r1.end + delta);
}

static inline Range operator - (const Range& r1, int delta)
{
    return r1 + (-delta);
}

inline Range::operator CvSlice() const
{ return *this != Range::all() ? cvSlice(start, end) : CV_WHOLE_SEQ; }

    
    
//////////////////////////////// Vector ////////////////////////////////

// template vector class. It is similar to STL's vector,
// with a few important differences:
//   1) it can be created on top of user-allocated data w/o copying it
//   2) vector b = a means copying the header,
//      not the underlying data (use clone() to make a deep copy)
template <typename _Tp> class CV_EXPORTS Vector
{
public:
    typedef _Tp value_type;
    typedef _Tp* iterator;
    typedef const _Tp* const_iterator;
    typedef _Tp& reference;
    typedef const _Tp& const_reference;
    
    struct CV_EXPORTS Hdr
    {
        Hdr() : data(0), datastart(0), refcount(0), size(0), capacity(0) {};
        _Tp* data;
        _Tp* datastart;
        int* refcount;
        size_t size;
        size_t capacity;
    };
    
    Vector() {}
    Vector(size_t _size)  { resize(_size); }
    Vector(size_t _size, const _Tp& val)
    {
        resize(_size);
        for(size_t i = 0; i < _size; i++)
            hdr.data[i] = val;
    }
    Vector(_Tp* _data, size_t _size, bool _copyData=false)
    { set(_data, _size, _copyData); }
    
    template<int n> Vector(const Vec<_Tp, n>& vec)
    { set((_Tp*)&vec.val[0], n, true); }    
    
    Vector(const std::vector<_Tp>& vec, bool _copyData=false)
    { set((_Tp*)&vec[0], vec.size(), _copyData); }    
    
    Vector(const Vector& d) { *this = d; }
    
    Vector(const Vector& d, const Range& r_)
    {
        Range r = r_ == Range::all() ? Range(0, d.size()) : r_;
        /*if( r == Range::all() )
            r = Range(0, d.size());*/
        if( r.size() > 0 && r.start >= 0 && r.end <= d.size() )
        {
            if( d.hdr.refcount )
                CV_XADD(d.hdr.refcount, 1);
            hdr.refcount = d.hdr.refcount;
            hdr.datastart = d.hdr.datastart;
            hdr.data = d.hdr.data + r.start;
            hdr.capacity = hdr.size = r.size();
        }
    }
    
    Vector<_Tp>& operator = (const Vector& d)
    {
        if( this != &d )
        {
            if( d.hdr.refcount )
                CV_XADD(d.hdr.refcount, 1);
            release();
            hdr = d.hdr;
        }
        return *this;
    }
    
    ~Vector()  { release(); }
    
    Vector<_Tp> clone() const
    { return hdr.data ? Vector<_Tp>(hdr.data, hdr.size, true) : Vector<_Tp>(); }
    
    void copyTo(Vector<_Tp>& vec) const
    {
        size_t i, sz = size();
        vec.resize(sz);
        const _Tp* src = hdr.data;
        _Tp* dst = vec.hdr.data;
        for( i = 0; i < sz; i++ )
            dst[i] = src[i];
    }
    
    void copyTo(std::vector<_Tp>& vec) const
    {
        size_t i, sz = size();
        vec.resize(sz);
        const _Tp* src = hdr.data;
        _Tp* dst = sz ? &vec[0] : 0;
        for( i = 0; i < sz; i++ )
            dst[i] = src[i];
    }
    
    operator CvMat() const
    { return cvMat((int)size(), 1, type(), (void*)hdr.data); }
    
    _Tp& operator [] (size_t i) { CV_DbgAssert( i < size() ); return hdr.data[i]; }
    const _Tp& operator [] (size_t i) const { CV_DbgAssert( i < size() ); return hdr.data[i]; }
    Vector operator() (const Range& r) const { return Vector(*this, r); }
    _Tp& back() { CV_DbgAssert(!empty()); return hdr.data[hdr.size-1]; }
    const _Tp& back() const { CV_DbgAssert(!empty()); return hdr.data[hdr.size-1]; }
    _Tp& front() { CV_DbgAssert(!empty()); return hdr.data[0]; }
    const _Tp& front() const { CV_DbgAssert(!empty()); return hdr.data[0]; }
    
    _Tp* begin() { return hdr.data; }
    _Tp* end() { return hdr.data + hdr.size; }
    const _Tp* begin() const { return hdr.data; }
    const _Tp* end() const { return hdr.data + hdr.size; }
    
    void addref() { if( hdr.refcount ) CV_XADD(hdr.refcount, 1); }
    void release()
    {
        if( hdr.refcount && CV_XADD(hdr.refcount, -1) == 1 )
        {
            delete[] hdr.datastart;
            delete hdr.refcount;
        }
        hdr = Hdr();
    }
    
    void set(_Tp* _data, size_t _size, bool _copyData=false)
    {
        if( !_copyData )
        {
            release();
            hdr.data = hdr.datastart = _data;
            hdr.size = hdr.capacity = _size;
            hdr.refcount = 0;
        }
        else
        {
            reserve(_size);
            for( size_t i = 0; i < _size; i++ )
                hdr.data[i] = _data[i];
            hdr.size = _size;
        }
    }
    
    void reserve(size_t newCapacity)
    {
        _Tp* newData;
        int* newRefcount;
        size_t i, oldSize = hdr.size;
        if( (!hdr.refcount || *hdr.refcount == 1) && hdr.capacity >= newCapacity )
            return;
        newCapacity = std::max(newCapacity, oldSize);
        newData = new _Tp[newCapacity];
        newRefcount = new int(1);
        for( i = 0; i < oldSize; i++ )
            newData[i] = hdr.data[i];
        release();
        hdr.data = hdr.datastart = newData;
        hdr.capacity = newCapacity;
        hdr.size = oldSize;
        hdr.refcount = newRefcount;
    }
    
    void resize(size_t newSize)
    {
        size_t i;
        newSize = std::max(newSize, (size_t)0);
        if( (!hdr.refcount || *hdr.refcount == 1) && hdr.size == newSize )
            return;
        if( newSize > hdr.capacity )
            reserve(std::max(newSize, std::max((size_t)4, hdr.capacity*2)));
        for( i = hdr.size; i < newSize; i++ )
            hdr.data[i] = _Tp();
        hdr.size = newSize;
    }
    
    Vector<_Tp>& push_back(const _Tp& elem)
    {
        if( hdr.size == hdr.capacity )
            reserve( std::max((size_t)4, hdr.capacity*2) );
        hdr.data[hdr.size++] = elem;
        return *this;
    }
    
    Vector<_Tp>& pop_back()
    {
        if( hdr.size > 0 )
            --hdr.size;
        return *this;
    }
    
    size_t size() const { return hdr.size; }
    size_t capacity() const { return hdr.capacity; }
    bool empty() const { return hdr.size == 0; }
    void clear() { resize(0); }
    int type() const { return DataType<_Tp>::type; }
    
protected:
    Hdr hdr;
};    

    
template<typename _Tp> inline typename DataType<_Tp>::work_type
dot(const Vector<_Tp>& v1, const Vector<_Tp>& v2)
{
    typedef typename DataType<_Tp>::work_type _Tw;
    size_t i, n = v1.size();
    assert(v1.size() == v2.size());

    _Tw s = 0;
    const _Tp *ptr1 = &v1[0], *ptr2 = &v2[0];
    for( i = 0; i <= n - 4; i += 4 )
        s += (_Tw)ptr1[i]*ptr2[i] + (_Tw)ptr1[i+1]*ptr2[i+1] +
            (_Tw)ptr1[i+2]*ptr2[i+2] + (_Tw)ptr1[i+3]*ptr2[i+3];
    for( ; i < n; i++ )
        s += (_Tw)ptr1[i]*ptr2[i];
    return s;
}
    
// Multiply-with-Carry RNG
inline RNG::RNG() { state = 0xffffffff; }
inline RNG::RNG(uint64 _state) { state = _state ? _state : 0xffffffff; }
inline unsigned RNG::next()
{
    state = (uint64)(unsigned)state*CV_RNG_COEFF + (unsigned)(state >> 32);
    return (unsigned)state;
}

inline RNG::operator uchar() { return (uchar)next(); }
inline RNG::operator schar() { return (schar)next(); }
inline RNG::operator ushort() { return (ushort)next(); }
inline RNG::operator short() { return (short)next(); }
inline RNG::operator unsigned() { return next(); }
inline unsigned RNG::operator ()(unsigned N) {return (unsigned)uniform(0,N);}
inline unsigned RNG::operator ()() {return next();}
inline RNG::operator int() { return (int)next(); }
// * (2^32-1)^-1
inline RNG::operator float() { return next()*2.3283064365386962890625e-10f; }
inline RNG::operator double()
{
    unsigned t = next();
    return (((uint64)t << 32) | next())*5.4210108624275221700372640043497e-20;
}
inline int RNG::uniform(int a, int b) { return a == b ? a : next()%(b - a) + a; }
inline float RNG::uniform(float a, float b) { return ((float)*this)*(b - a) + a; }
inline double RNG::uniform(double a, double b) { return ((double)*this)*(b - a) + a; }

inline TermCriteria::TermCriteria() : type(0), maxCount(0), epsilon(0) {}
inline TermCriteria::TermCriteria(int _type, int _maxCount, double _epsilon)
    : type(_type), maxCount(_maxCount), epsilon(_epsilon) {}
inline TermCriteria::TermCriteria(const CvTermCriteria& criteria)
    : type(criteria.type), maxCount(criteria.max_iter), epsilon(criteria.epsilon) {}
inline TermCriteria::operator CvTermCriteria() const
{ return cvTermCriteria(type, maxCount, epsilon); }

inline uchar* LineIterator::operator *() { return ptr; }
inline LineIterator& LineIterator::operator ++()
{
    int mask = err < 0 ? -1 : 0;
    err += minusDelta + (plusDelta & mask);
    ptr += minusStep + (plusStep & mask);
    return *this;
}
inline LineIterator LineIterator::operator ++(int)
{
    LineIterator it = *this;
    ++(*this);
    return it;
}
inline Point LineIterator::pos() const
{
    Point p;
    p.y = (int)((ptr - ptr0)/step);
    p.x = (int)(((ptr - ptr0) - p.y*step)/elemSize);
    return p;
}
    
/////////////////////////////// AutoBuffer ////////////////////////////////////////

template<typename _Tp, size_t fixed_size> inline AutoBuffer<_Tp, fixed_size>::AutoBuffer()
{
    ptr = buf;
    size = fixed_size;
}

template<typename _Tp, size_t fixed_size> inline AutoBuffer<_Tp, fixed_size>::AutoBuffer(size_t _size)
{
    ptr = buf;
    size = fixed_size;
    allocate(_size);
}

template<typename _Tp, size_t fixed_size> inline AutoBuffer<_Tp, fixed_size>::~AutoBuffer()
{ deallocate(); }

template<typename _Tp, size_t fixed_size> inline void AutoBuffer<_Tp, fixed_size>::allocate(size_t _size)
{
    if(_size <= size)
        return;
    deallocate();
    if(_size > fixed_size)
    {
        ptr = cv::allocate<_Tp>(_size);
        size = _size;
    }
}

template<typename _Tp, size_t fixed_size> inline void AutoBuffer<_Tp, fixed_size>::deallocate()
{
    if( ptr != buf )
    {
        cv::deallocate<_Tp>(ptr, size);
        ptr = buf;
        size = fixed_size;
    }
}

template<typename _Tp, size_t fixed_size> inline AutoBuffer<_Tp, fixed_size>::operator _Tp* ()
{ return ptr; }

template<typename _Tp, size_t fixed_size> inline AutoBuffer<_Tp, fixed_size>::operator const _Tp* () const
{ return ptr; }


/////////////////////////////////// Ptr ////////////////////////////////////////

template<typename _Tp> inline Ptr<_Tp>::Ptr() : obj(0), refcount(0) {}
template<typename _Tp> inline Ptr<_Tp>::Ptr(_Tp* _obj) : obj(_obj)
{
    if(obj)
    {
        refcount = (int*)fastMalloc(sizeof(*refcount));
        *refcount = 1;
    }
    else
        refcount = 0;
}

template<typename _Tp> inline void Ptr<_Tp>::addref()
{ if( refcount ) CV_XADD(refcount, 1); }

template<typename _Tp> inline void Ptr<_Tp>::release()
{
    if( refcount && CV_XADD(refcount, -1) == 1 )
    {
        delete_obj();
        fastFree(refcount);
    }
    refcount = 0;
    obj = 0;
}

template<typename _Tp> inline void Ptr<_Tp>::delete_obj()
{
    if( obj ) delete obj;
}

template<typename _Tp> inline Ptr<_Tp>::~Ptr() { release(); }

template<typename _Tp> inline Ptr<_Tp>::Ptr(const Ptr<_Tp>& ptr)
{
    obj = ptr.obj;
    refcount = ptr.refcount;
    addref();
}

template<typename _Tp> inline Ptr<_Tp>& Ptr<_Tp>::operator = (const Ptr<_Tp>& ptr)
{
    int* _refcount = ptr.refcount;
    if( _refcount )
        CV_XADD(_refcount, 1);
    release();
    obj = ptr.obj;
    refcount = _refcount;
    return *this;
}

template<typename _Tp> inline _Tp* Ptr<_Tp>::operator -> () { return obj; }
template<typename _Tp> inline const _Tp* Ptr<_Tp>::operator -> () const { return obj; }

template<typename _Tp> inline Ptr<_Tp>::operator _Tp* () { return obj; }
template<typename _Tp> inline Ptr<_Tp>::operator const _Tp*() const { return obj; }

template<typename _Tp> inline bool Ptr<_Tp>::empty() const { return obj == 0; }

//// specializied implementations of Ptr::delete_obj() for classic OpenCV types

template<> CV_EXPORTS void Ptr<CvMat>::delete_obj();
template<> CV_EXPORTS void Ptr<IplImage>::delete_obj();
template<> CV_EXPORTS void Ptr<CvMatND>::delete_obj();
template<> CV_EXPORTS void Ptr<CvSparseMat>::delete_obj();
template<> CV_EXPORTS void Ptr<CvMemStorage>::delete_obj();
template<> CV_EXPORTS void Ptr<CvFileStorage>::delete_obj();
    
//////////////////////////////////////// XML & YAML I/O ////////////////////////////////////

CV_EXPORTS_W void write( FileStorage& fs, const string& name, int value );
CV_EXPORTS_W void write( FileStorage& fs, const string& name, float value );
CV_EXPORTS_W void write( FileStorage& fs, const string& name, double value );
CV_EXPORTS_W void write( FileStorage& fs, const string& name, const string& value );

template<typename _Tp> inline void write(FileStorage& fs, const _Tp& value)
{ write(fs, string(), value); }

CV_EXPORTS void writeScalar( FileStorage& fs, int value );
CV_EXPORTS void writeScalar( FileStorage& fs, float value );
CV_EXPORTS void writeScalar( FileStorage& fs, double value );
CV_EXPORTS void writeScalar( FileStorage& fs, const string& value );

template<> inline void write( FileStorage& fs, const int& value )
{
    writeScalar(fs, value);
}

template<> inline void write( FileStorage& fs, const float& value )
{
    writeScalar(fs, value);
}

template<> inline void write( FileStorage& fs, const double& value )
{
    writeScalar(fs, value);
}

template<> inline void write( FileStorage& fs, const string& value )
{
    writeScalar(fs, value);
}

template<typename _Tp> inline void write(FileStorage& fs, const Point_<_Tp>& pt )
{
    write(fs, pt.x);
    write(fs, pt.y);
}

template<typename _Tp> inline void write(FileStorage& fs, const Point3_<_Tp>& pt )
{
    write(fs, pt.x);
    write(fs, pt.y);
    write(fs, pt.z);
}

template<typename _Tp> inline void write(FileStorage& fs, const Size_<_Tp>& sz )
{
    write(fs, sz.width);
    write(fs, sz.height);
}

template<typename _Tp> inline void write(FileStorage& fs, const Complex<_Tp>& c )
{
    write(fs, c.re);
    write(fs, c.im);
}

template<typename _Tp> inline void write(FileStorage& fs, const Rect_<_Tp>& r )
{
    write(fs, r.x);
    write(fs, r.y);
    write(fs, r.width);
    write(fs, r.height);
}

template<typename _Tp, int cn> inline void write(FileStorage& fs, const Vec<_Tp, cn>& v )
{
    for(int i = 0; i < cn; i++)
        write(fs, v.val[i]);
}

template<typename _Tp> inline void write(FileStorage& fs, const Scalar_<_Tp>& s )
{
    write(fs, s.val[0]);
    write(fs, s.val[1]);
    write(fs, s.val[2]);
    write(fs, s.val[3]);
}

inline void write(FileStorage& fs, const Range& r )
{
    write(fs, r.start);
    write(fs, r.end);
}

class CV_EXPORTS WriteStructContext
{
public:
    WriteStructContext(FileStorage& _fs, const string& name,
        int flags, const string& typeName=string());
    ~WriteStructContext();
    FileStorage* fs;
};

template<typename _Tp> inline void write(FileStorage& fs, const string& name, const Point_<_Tp>& pt )
{
    WriteStructContext ws(fs, name, CV_NODE_SEQ+CV_NODE_FLOW);
    write(fs, pt.x);
    write(fs, pt.y);
}

template<typename _Tp> inline void write(FileStorage& fs, const string& name, const Point3_<_Tp>& pt )
{
    WriteStructContext ws(fs, name, CV_NODE_SEQ+CV_NODE_FLOW);
    write(fs, pt.x);
    write(fs, pt.y);
    write(fs, pt.z);
}

template<typename _Tp> inline void write(FileStorage& fs, const string& name, const Size_<_Tp>& sz )
{
    WriteStructContext ws(fs, name, CV_NODE_SEQ+CV_NODE_FLOW);
    write(fs, sz.width);
    write(fs, sz.height);
}

template<typename _Tp> inline void write(FileStorage& fs, const string& name, const Complex<_Tp>& c )
{
    WriteStructContext ws(fs, name, CV_NODE_SEQ+CV_NODE_FLOW);
    write(fs, c.re);
    write(fs, c.im);
}

template<typename _Tp> inline void write(FileStorage& fs, const string& name, const Rect_<_Tp>& r )
{
    WriteStructContext ws(fs, name, CV_NODE_SEQ+CV_NODE_FLOW);
    write(fs, r.x);
    write(fs, r.y);
    write(fs, r.width);
    write(fs, r.height);
}

template<typename _Tp, int cn> inline void write(FileStorage& fs, const string& name, const Vec<_Tp, cn>& v )
{
    WriteStructContext ws(fs, name, CV_NODE_SEQ+CV_NODE_FLOW);
    for(int i = 0; i < cn; i++)
        write(fs, v.val[i]);
}

template<typename _Tp> inline void write(FileStorage& fs, const string& name, const Scalar_<_Tp>& s )
{
    WriteStructContext ws(fs, name, CV_NODE_SEQ+CV_NODE_FLOW);
    write(fs, s.val[0]);
    write(fs, s.val[1]);
    write(fs, s.val[2]);
    write(fs, s.val[3]);
}

inline void write(FileStorage& fs, const string& name, const Range& r )
{
    WriteStructContext ws(fs, name, CV_NODE_SEQ+CV_NODE_FLOW);
    write(fs, r.start);
    write(fs, r.end);
}

template<typename _Tp, int numflag> class CV_EXPORTS VecWriterProxy
{
public:
    VecWriterProxy( FileStorage* _fs ) : fs(_fs) {}
    void operator()(const vector<_Tp>& vec) const
    {
        size_t i, count = vec.size();
        for( i = 0; i < count; i++ )
            write( *fs, vec[i] );
    }
    FileStorage* fs;
};

template<typename _Tp> class CV_EXPORTS VecWriterProxy<_Tp,1>
{
public:
    VecWriterProxy( FileStorage* _fs ) : fs(_fs) {}
    void operator()(const vector<_Tp>& vec) const
    {
        int _fmt = DataType<_Tp>::fmt;
        char fmt[] = { (char)((_fmt>>8)+'1'), (char)_fmt, '\0' };
        fs->writeRaw( string(fmt), (uchar*)&vec[0], vec.size()*sizeof(_Tp) );
    }
    FileStorage* fs;
};


template<typename _Tp> static inline void write( FileStorage& fs, const vector<_Tp>& vec )
{
    VecWriterProxy<_Tp, DataType<_Tp>::fmt != 0> w(&fs);
    w(vec);
}

template<typename _Tp> static inline FileStorage&
operator << ( FileStorage& fs, const vector<_Tp>& vec )
{
    VecWriterProxy<_Tp, DataType<_Tp>::generic_type == 0> w(&fs);
    w(vec);
    return fs;
}

CV_EXPORTS_W void write( FileStorage& fs, const string& name, const Mat& value );
CV_EXPORTS void write( FileStorage& fs, const string& name, const SparseMat& value );

template<typename _Tp> static inline FileStorage& operator << (FileStorage& fs, const _Tp& value)
{
    if( !fs.isOpened() )
        return fs;
    if( fs.state == FileStorage::NAME_EXPECTED + FileStorage::INSIDE_MAP )
        CV_Error( CV_StsError, "No element name has been given" );
    write( fs, fs.elname, value );
    if( fs.state & FileStorage::INSIDE_MAP )
        fs.state = FileStorage::NAME_EXPECTED + FileStorage::INSIDE_MAP;
    return fs;
}

CV_EXPORTS FileStorage& operator << (FileStorage& fs, const string& str);

static inline FileStorage& operator << (FileStorage& fs, const char* str)
{ return (fs << string(str)); }

inline FileNode::FileNode() : fs(0), node(0) {}
inline FileNode::FileNode(const CvFileStorage* _fs, const CvFileNode* _node)
    : fs(_fs), node(_node) {}

inline FileNode::FileNode(const FileNode& _node) : fs(_node.fs), node(_node.node) {}

inline int FileNode::type() const { return !node ? NONE : (node->tag & TYPE_MASK); }
inline bool FileNode::empty() const { return node == 0; }
inline bool FileNode::isNone() const { return type() == NONE; }
inline bool FileNode::isSeq() const { return type() == SEQ; }
inline bool FileNode::isMap() const { return type() == MAP; }
inline bool FileNode::isInt() const { return type() == INT; }
inline bool FileNode::isReal() const { return type() == REAL; }
inline bool FileNode::isString() const { return type() == STR; }
inline bool FileNode::isNamed() const { return !node ? false : (node->tag & NAMED) != 0; }
inline size_t FileNode::size() const
{
    int t = type();
    return t == MAP ? ((CvSet*)node->data.map)->active_count :
        t == SEQ ? node->data.seq->total : node != 0;
}

inline CvFileNode* FileNode::operator *() { return (CvFileNode*)node; }
inline const CvFileNode* FileNode::operator* () const { return node; }

static inline void read(const FileNode& node, int& value, int default_value)
{
    value = !node.node ? default_value :
    CV_NODE_IS_INT(node.node->tag) ? node.node->data.i :
    CV_NODE_IS_REAL(node.node->tag) ? cvRound(node.node->data.f) : 0x7fffffff;
}
    
static inline void read(const FileNode& node, bool& value, bool default_value)
{
    int temp; read(node, temp, (int)default_value);
    value = temp != 0;
}

static inline void read(const FileNode& node, uchar& value, uchar default_value)
{
    int temp; read(node, temp, (int)default_value);
    value = saturate_cast<uchar>(temp);
}

static inline void read(const FileNode& node, schar& value, schar default_value)
{
    int temp; read(node, temp, (int)default_value);
    value = saturate_cast<schar>(temp);
}

static inline void read(const FileNode& node, ushort& value, ushort default_value)
{
    int temp; read(node, temp, (int)default_value);
    value = saturate_cast<ushort>(temp);
}

static inline void read(const FileNode& node, short& value, short default_value)
{
    int temp; read(node, temp, (int)default_value);
    value = saturate_cast<short>(temp);
}
    
static inline void read(const FileNode& node, float& value, float default_value)
{
    value = !node.node ? default_value :
        CV_NODE_IS_INT(node.node->tag) ? (float)node.node->data.i :
        CV_NODE_IS_REAL(node.node->tag) ? (float)node.node->data.f : 1e30f;
}

static inline void read(const FileNode& node, double& value, double default_value)
{
    value = !node.node ? default_value :
        CV_NODE_IS_INT(node.node->tag) ? (double)node.node->data.i :
        CV_NODE_IS_REAL(node.node->tag) ? node.node->data.f : 1e300;
}

static inline void read(const FileNode& node, string& value, const string& default_value)
{
    value = !node.node ? default_value : CV_NODE_IS_STRING(node.node->tag) ? string(node.node->data.str.ptr) : string("");
}

CV_EXPORTS_W void read(const FileNode& node, Mat& mat, const Mat& default_mat=Mat() );
CV_EXPORTS void read(const FileNode& node, SparseMat& mat, const SparseMat& default_mat=SparseMat() );    
    
inline FileNode::operator int() const
{
    int value;
    read(*this, value, 0);
    return value;
}
inline FileNode::operator float() const
{
    float value;
    read(*this, value, 0.f);
    return value;
}
inline FileNode::operator double() const
{
    double value;
    read(*this, value, 0.);
    return value;
}
inline FileNode::operator string() const
{
    string value;
    read(*this, value, value);
    return value;
}

inline void FileNode::readRaw( const string& fmt, uchar* vec, size_t len ) const
{
    begin().readRaw( fmt, vec, len );
}

template<typename _Tp, int numflag> class CV_EXPORTS VecReaderProxy
{
public:
    VecReaderProxy( FileNodeIterator* _it ) : it(_it) {}
    void operator()(vector<_Tp>& vec, size_t count) const
    {
        count = std::min(count, it->remaining);
        vec.resize(count);
        for( size_t i = 0; i < count; i++, ++(*it) )
            read(**it, vec[i], _Tp());
    }
    FileNodeIterator* it;
};
    
template<typename _Tp> class CV_EXPORTS VecReaderProxy<_Tp,1>
{
public:
    VecReaderProxy( FileNodeIterator* _it ) : it(_it) {}
    void operator()(vector<_Tp>& vec, size_t count) const
    {
        size_t remaining = it->remaining, cn = DataType<_Tp>::channels;
        int _fmt = DataType<_Tp>::fmt;
        char fmt[] = { (char)((_fmt>>8)+'1'), (char)_fmt, '\0' };
		size_t remaining1 = remaining/cn;
		count = count < remaining1 ? count : remaining1;
        vec.resize(count);
        it->readRaw( string(fmt), (uchar*)&vec[0], count*sizeof(_Tp) );
    }
    FileNodeIterator* it;
};

template<typename _Tp> static inline void
read( FileNodeIterator& it, vector<_Tp>& vec, size_t maxCount=(size_t)INT_MAX )
{
    VecReaderProxy<_Tp, DataType<_Tp>::fmt != 0> r(&it);
    r(vec, maxCount);
}

template<typename _Tp> static inline void
read( FileNode& node, vector<_Tp>& vec, const vector<_Tp>& default_value=vector<_Tp>() )
{
    read( node.begin(), vec );
}
    
inline FileNodeIterator FileNode::begin() const
{
    return FileNodeIterator(fs, node);
}

inline FileNodeIterator FileNode::end() const
{
    return FileNodeIterator(fs, node, size());
}

inline FileNode FileNodeIterator::operator *() const
{ return FileNode(fs, (const CvFileNode*)reader.ptr); }

inline FileNode FileNodeIterator::operator ->() const
{ return FileNode(fs, (const CvFileNode*)reader.ptr); }

template<typename _Tp> static inline FileNodeIterator& operator >> (FileNodeIterator& it, _Tp& value)
{ read( *it, value, _Tp()); return ++it; }

template<typename _Tp> static inline
FileNodeIterator& operator >> (FileNodeIterator& it, vector<_Tp>& vec)
{
    VecReaderProxy<_Tp, DataType<_Tp>::fmt != 0> r(&it);
    r(vec, (size_t)INT_MAX);
    return it;
}

template<typename _Tp> static inline void operator >> (const FileNode& n, _Tp& value)
{ read( n, value, _Tp()); }

template<typename _Tp> static inline void operator >> (const FileNode& n, vector<_Tp>& vec)
{ FileNodeIterator it = n.begin(); it >> vec; }

static inline bool operator == (const FileNodeIterator& it1, const FileNodeIterator& it2)
{
    return it1.fs == it2.fs && it1.container == it2.container &&
        it1.reader.ptr == it2.reader.ptr && it1.remaining == it2.remaining;
}

static inline bool operator != (const FileNodeIterator& it1, const FileNodeIterator& it2)
{
    return !(it1 == it2);
}

static inline ptrdiff_t operator - (const FileNodeIterator& it1, const FileNodeIterator& it2)
{
    return it2.remaining - it1.remaining;
}

static inline bool operator < (const FileNodeIterator& it1, const FileNodeIterator& it2)
{
    return it1.remaining > it2.remaining;
}

inline FileNode FileStorage::getFirstTopLevelNode() const
{
    FileNode r = root();
    FileNodeIterator it = r.begin();
    return it != r.end() ? *it : FileNode();
}

//////////////////////////////////////// Various algorithms ////////////////////////////////////

template<typename _Tp> static inline _Tp gcd(_Tp a, _Tp b)
{
    if( a < b )
        std::swap(a, b);
    while( b > 0 )
    {
        _Tp r = a % b;
        a = b;
        b = r;
    }
    return a;
}

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

  Generic implementation of QuickSort algorithm
  Use it as: vector<_Tp> a; ... sort(a,<less_than_predictor>);

  The current implementation was derived from *BSD system qsort():

    * Copyright (c) 1992, 1993
    *  The Regents of the University of California.  All rights reserved.
    *
    * Redistribution and use in source and binary forms, with or without
    * modification, are permitted provided that the following conditions
    * are met:
    * 1. Redistributions of source code must retain the above copyright
    *    notice, this list of conditions and the following disclaimer.
    * 2. Redistributions in binary form must reproduce the above copyright
    *    notice, this list of conditions and the following disclaimer in the
    *    documentation and/or other materials provided with the distribution.
    * 3. All advertising materials mentioning features or use of this software
    *    must display the following acknowledgement:
    *  This product includes software developed by the University of
    *  California, Berkeley and its contributors.
    * 4. Neither the name of the University nor the names of its contributors
    *    may be used to endorse or promote products derived from this software
    *    without specific prior written permission.
    *
    * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
    * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
    * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
    * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
    * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
    * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
    * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
    * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
    * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
    * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
    * SUCH DAMAGE.

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

template<typename _Tp, class _LT> void sort( vector<_Tp>& vec, _LT LT=_LT() )
{
    int isort_thresh = 7;
    int sp = 0;

    struct
    {
        _Tp *lb;
        _Tp *ub;
    } stack[48];

    size_t total = vec.size();

    if( total <= 1 )
        return;

    _Tp* arr = &vec[0];
    stack[0].lb = arr;
    stack[0].ub = arr + (total - 1);

    while( sp >= 0 )
    {
        _Tp* left = stack[sp].lb;
        _Tp* right = stack[sp--].ub;

        for(;;)
        {
            int i, n = (int)(right - left) + 1, m;
            _Tp* ptr;
            _Tp* ptr2;

            if( n <= isort_thresh )
            {
            insert_sort:
                for( ptr = left + 1; ptr <= right; ptr++ )
                {
                    for( ptr2 = ptr; ptr2 > left && LT(ptr2[0],ptr2[-1]); ptr2--)
                        std::swap( ptr2[0], ptr2[-1] );
                }
                break;
            }
            else
            {
                _Tp* left0;
                _Tp* left1;
                _Tp* right0;
                _Tp* right1;
                _Tp* pivot;
                _Tp* a;
                _Tp* b;
                _Tp* c;
                int swap_cnt = 0;

                left0 = left;
                right0 = right;
                pivot = left + (n/2);

                if( n > 40 )
                {
                    int d = n / 8;
                    a = left, b = left + d, c = left + 2*d;
                    left = LT(*a, *b) ? (LT(*b, *c) ? b : (LT(*a, *c) ? c : a))
                                      : (LT(*c, *b) ? b : (LT(*a, *c) ? a : c));

                    a = pivot - d, b = pivot, c = pivot + d;
                    pivot = LT(*a, *b) ? (LT(*b, *c) ? b : (LT(*a, *c) ? c : a))
                                      : (LT(*c, *b) ? b : (LT(*a, *c) ? a : c));

                    a = right - 2*d, b = right - d, c = right;
                    right = LT(*a, *b) ? (LT(*b, *c) ? b : (LT(*a, *c) ? c : a))
                                      : (LT(*c, *b) ? b : (LT(*a, *c) ? a : c));
                }

                a = left, b = pivot, c = right;
                pivot = LT(*a, *b) ? (LT(*b, *c) ? b : (LT(*a, *c) ? c : a))
                                   : (LT(*c, *b) ? b : (LT(*a, *c) ? a : c));
                if( pivot != left0 )
                {
                    std::swap( *pivot, *left0 );
                    pivot = left0;
                }
                left = left1 = left0 + 1;
                right = right1 = right0;

                for(;;)
                {
                    while( left <= right && !LT(*pivot, *left) )
                    {
                        if( !LT(*left, *pivot) )
                        {
                            if( left > left1 )
                                std::swap( *left1, *left );
                            swap_cnt = 1;
                            left1++;
                        }
                        left++;
                    }

                    while( left <= right && !LT(*right, *pivot) )
                    {
                        if( !LT(*pivot, *right) )
                        {
                            if( right < right1 )
                                std::swap( *right1, *right );
                            swap_cnt = 1;
                            right1--;
                        }
                        right--;
                    }

                    if( left > right )
                        break;
                    std::swap( *left, *right );
                    swap_cnt = 1;
                    left++;
                    right--;
                }

                if( swap_cnt == 0 )
                {
                    left = left0, right = right0;
                    goto insert_sort;
                }

                n = std::min( (int)(left1 - left0), (int)(left - left1) );
                for( i = 0; i < n; i++ )
                    std::swap( left0[i], left[i-n] );

                n = std::min( (int)(right0 - right1), (int)(right1 - right) );
                for( i = 0; i < n; i++ )
                    std::swap( left[i], right0[i-n+1] );
                n = (int)(left - left1);
                m = (int)(right1 - right);
                if( n > 1 )
                {
                    if( m > 1 )
                    {
                        if( n > m )
                        {
                            stack[++sp].lb = left0;
                            stack[sp].ub = left0 + n - 1;
                            left = right0 - m + 1, right = right0;
                        }
                        else
                        {
                            stack[++sp].lb = right0 - m + 1;
                            stack[sp].ub = right0;
                            left = left0, right = left0 + n - 1;
                        }
                    }
                    else
                        left = left0, right = left0 + n - 1;
                }
                else if( m > 1 )
                    left = right0 - m + 1, right = right0;
                else
                    break;
            }
        }
    }
}

template<typename _Tp> class CV_EXPORTS LessThan
{
public:
    bool operator()(const _Tp& a, const _Tp& b) const { return a < b; }
};

template<typename _Tp> class CV_EXPORTS GreaterEq
{
public:
    bool operator()(const _Tp& a, const _Tp& b) const { return a >= b; }
};

template<typename _Tp> class CV_EXPORTS LessThanIdx
{
public:
    LessThanIdx( const _Tp* _arr ) : arr(_arr) {}
    bool operator()(int a, int b) const { return arr[a] < arr[b]; }
    const _Tp* arr;
};

template<typename _Tp> class CV_EXPORTS GreaterEqIdx
{
public:
    GreaterEqIdx( const _Tp* _arr ) : arr(_arr) {}
    bool operator()(int a, int b) const { return arr[a] >= arr[b]; }
    const _Tp* arr;
};


// This function splits the input sequence or set into one or more equivalence classes and
// returns the vector of labels - 0-based class indexes for each element.
// predicate(a,b) returns true if the two sequence elements certainly belong to the same class.
//
// The algorithm is described in "Introduction to Algorithms"
// by Cormen, Leiserson and Rivest, the chapter "Data structures for disjoint sets"
template<typename _Tp, class _EqPredicate> int
partition( const vector<_Tp>& _vec, vector<int>& labels,
           _EqPredicate predicate=_EqPredicate())
{
    int i, j, N = (int)_vec.size();
    const _Tp* vec = &_vec[0];

    const int PARENT=0;
    const int RANK=1;

    vector<int> _nodes(N*2);
    int (*nodes)[2] = (int(*)[2])&_nodes[0];

    // The first O(N) pass: create N single-vertex trees
    for(i = 0; i < N; i++)
    {
        nodes[i][PARENT]=-1;
        nodes[i][RANK] = 0;
    }

    // The main O(N^2) pass: merge connected components
    for( i = 0; i < N; i++ )
    {
        int root = i;

        // find root
        while( nodes[root][PARENT] >= 0 )
            root = nodes[root][PARENT];

        for( j = 0; j < N; j++ )
        {
            if( i == j || !predicate(vec[i], vec[j]))
                continue;
            int root2 = j;

            while( nodes[root2][PARENT] >= 0 )
                root2 = nodes[root2][PARENT];

            if( root2 != root )
            {
                // unite both trees
                int rank = nodes[root][RANK], rank2 = nodes[root2][RANK];
                if( rank > rank2 )
                    nodes[root2][PARENT] = root;
                else
                {
                    nodes[root][PARENT] = root2;
                    nodes[root2][RANK] += rank == rank2;
                    root = root2;
                }
                assert( nodes[root][PARENT] < 0 );

                int k = j, parent;

                // compress the path from node2 to root
                while( (parent = nodes[k][PARENT]) >= 0 )
                {
                    nodes[k][PARENT] = root;
                    k = parent;
                }

                // compress the path from node to root
                k = i;
                while( (parent = nodes[k][PARENT]) >= 0 )
                {
                    nodes[k][PARENT] = root;
                    k = parent;
                }
            }
        }
    }

    // Final O(N) pass: enumerate classes
    labels.resize(N);
    int nclasses = 0;

    for( i = 0; i < N; i++ )
    {
        int root = i;
        while( nodes[root][PARENT] >= 0 )
            root = nodes[root][PARENT];
        // re-use the rank as the class label
        if( nodes[root][RANK] >= 0 )
            nodes[root][RANK] = ~nclasses++;
        labels[i] = ~nodes[root][RANK];
    }

    return nclasses;
}

    
//////////////////////////////////////////////////////////////////////////////

// bridge C++ => C Seq API
CV_EXPORTS schar*  seqPush( CvSeq* seq, const void* element=0);
CV_EXPORTS schar*  seqPushFront( CvSeq* seq, const void* element=0);
CV_EXPORTS void  seqPop( CvSeq* seq, void* element=0);
CV_EXPORTS void  seqPopFront( CvSeq* seq, void* element=0);
CV_EXPORTS void  seqPopMulti( CvSeq* seq, void* elements,
                              int count, int in_front=0 );
CV_EXPORTS void  seqRemove( CvSeq* seq, int index );
CV_EXPORTS void  clearSeq( CvSeq* seq );
CV_EXPORTS schar*  getSeqElem( const CvSeq* seq, int index );
CV_EXPORTS void  seqRemoveSlice( CvSeq* seq, CvSlice slice );
CV_EXPORTS void  seqInsertSlice( CvSeq* seq, int before_index, const CvArr* from_arr );    

template<typename _Tp> inline Seq<_Tp>::Seq() : seq(0) {}
template<typename _Tp> inline Seq<_Tp>::Seq( const CvSeq* _seq ) : seq((CvSeq*)_seq)
{
    CV_Assert(!_seq || _seq->elem_size == sizeof(_Tp));
}

template<typename _Tp> inline Seq<_Tp>::Seq( MemStorage& storage,
                                             int headerSize )
{
    CV_Assert(headerSize >= (int)sizeof(CvSeq));
    seq = cvCreateSeq(DataType<_Tp>::type, headerSize, sizeof(_Tp), storage);
}

template<typename _Tp> inline _Tp& Seq<_Tp>::operator [](int idx)
{ return *(_Tp*)getSeqElem(seq, idx); }

template<typename _Tp> inline const _Tp& Seq<_Tp>::operator [](int idx) const
{ return *(_Tp*)getSeqElem(seq, idx); }

template<typename _Tp> inline SeqIterator<_Tp> Seq<_Tp>::begin() const
{ return SeqIterator<_Tp>(*this); }

template<typename _Tp> inline SeqIterator<_Tp> Seq<_Tp>::end() const
{ return SeqIterator<_Tp>(*this, true); }

template<typename _Tp> inline size_t Seq<_Tp>::size() const
{ return seq ? seq->total : 0; }

template<typename _Tp> inline int Seq<_Tp>::type() const
{ return seq ? CV_MAT_TYPE(seq->flags) : 0; }

template<typename _Tp> inline int Seq<_Tp>::depth() const
{ return seq ? CV_MAT_DEPTH(seq->flags) : 0; }

template<typename _Tp> inline int Seq<_Tp>::channels() const
{ return seq ? CV_MAT_CN(seq->flags) : 0; }

template<typename _Tp> inline size_t Seq<_Tp>::elemSize() const
{ return seq ? seq->elem_size : 0; }

template<typename _Tp> inline size_t Seq<_Tp>::index(const _Tp& elem) const
{ return cvSeqElemIdx(seq, &elem); }

template<typename _Tp> inline void Seq<_Tp>::push_back(const _Tp& elem)
{ cvSeqPush(seq, &elem); }

template<typename _Tp> inline void Seq<_Tp>::push_front(const _Tp& elem)
{ cvSeqPushFront(seq, &elem); }

template<typename _Tp> inline void Seq<_Tp>::push_back(const _Tp* elem, size_t count)
{ cvSeqPushMulti(seq, elem, (int)count, 0); }

template<typename _Tp> inline void Seq<_Tp>::push_front(const _Tp* elem, size_t count)
{ cvSeqPushMulti(seq, elem, (int)count, 1); }    
    
template<typename _Tp> inline _Tp& Seq<_Tp>::back()
{ return *(_Tp*)getSeqElem(seq, -1); }

template<typename _Tp> inline const _Tp& Seq<_Tp>::back() const
{ return *(const _Tp*)getSeqElem(seq, -1); }

template<typename _Tp> inline _Tp& Seq<_Tp>::front()
{ return *(_Tp*)getSeqElem(seq, 0); }

template<typename _Tp> inline const _Tp& Seq<_Tp>::front() const
{ return *(const _Tp*)getSeqElem(seq, 0); }

template<typename _Tp> inline bool Seq<_Tp>::empty() const
{ return !seq || seq->total == 0; }

template<typename _Tp> inline void Seq<_Tp>::clear()
{ if(seq) clearSeq(seq); }

template<typename _Tp> inline void Seq<_Tp>::pop_back()
{ seqPop(seq); }

template<typename _Tp> inline void Seq<_Tp>::pop_front()
{ seqPopFront(seq); }

template<typename _Tp> inline void Seq<_Tp>::pop_back(_Tp* elem, size_t count)
{ seqPopMulti(seq, elem, (int)count, 0); }

template<typename _Tp> inline void Seq<_Tp>::pop_front(_Tp* elem, size_t count)
{ seqPopMulti(seq, elem, (int)count, 1); }    

template<typename _Tp> inline void Seq<_Tp>::insert(int idx, const _Tp& elem)
{ seqInsert(seq, idx, &elem); }
    
template<typename _Tp> inline void Seq<_Tp>::insert(int idx, const _Tp* elems, size_t count)
{
    CvMat m = cvMat(1, count, DataType<_Tp>::type, elems);
    seqInsertSlice(seq, idx, &m);
}
    
template<typename _Tp> inline void Seq<_Tp>::remove(int idx)
{ seqRemove(seq, idx); }
    
template<typename _Tp> inline void Seq<_Tp>::remove(const Range& r)
{ seqRemoveSlice(seq, r); }
    
template<typename _Tp> inline void Seq<_Tp>::copyTo(vector<_Tp>& vec, const Range& range) const
{
    size_t len = !seq ? 0 : range == Range::all() ? seq->total : range.end - range.start;
    vec.resize(len);
    if( seq && len )
        cvCvtSeqToArray(seq, &vec[0], range);
}

template<typename _Tp> inline Seq<_Tp>::operator vector<_Tp>() const
{
    vector<_Tp> vec;
    copyTo(vec);
    return vec;
}

template<typename _Tp> inline SeqIterator<_Tp>::SeqIterator()
{ memset(this, 0, sizeof(*this)); }

template<typename _Tp> inline SeqIterator<_Tp>::SeqIterator(const Seq<_Tp>& seq, bool seekEnd)
{
    cvStartReadSeq(seq.seq, this);
    index = seekEnd ? seq.seq->total : 0;
}

template<typename _Tp> inline void SeqIterator<_Tp>::seek(size_t pos)
{
    cvSetSeqReaderPos(this, (int)pos, false);
    index = pos;
}

template<typename _Tp> inline size_t SeqIterator<_Tp>::tell() const
{ return index; }

template<typename _Tp> inline _Tp& SeqIterator<_Tp>::operator *()
{ return *(_Tp*)ptr; }

template<typename _Tp> inline const _Tp& SeqIterator<_Tp>::operator *() const
{ return *(const _Tp*)ptr; }

template<typename _Tp> inline SeqIterator<_Tp>& SeqIterator<_Tp>::operator ++()
{
    CV_NEXT_SEQ_ELEM(sizeof(_Tp), *this);
    if( ++index >= seq->total*2 )
        index = 0;
    return *this;
}

template<typename _Tp> inline SeqIterator<_Tp> SeqIterator<_Tp>::operator ++(int) const
{
    SeqIterator<_Tp> it = *this;
    ++*this;
    return it;
}

template<typename _Tp> inline SeqIterator<_Tp>& SeqIterator<_Tp>::operator --()
{
    CV_PREV_SEQ_ELEM(sizeof(_Tp), *this);
    if( --index < 0 )
        index = seq->total*2-1;
    return *this;
}

template<typename _Tp> inline SeqIterator<_Tp> SeqIterator<_Tp>::operator --(int) const
{
    SeqIterator<_Tp> it = *this;
    --*this;
    return it;
}

template<typename _Tp> inline SeqIterator<_Tp>& SeqIterator<_Tp>::operator +=(int delta)
{
    cvSetSeqReaderPos(this, delta, 1);
    index += delta;
    int n = seq->total*2;
    if( index < 0 )
        index += n;
    if( index >= n )
        index -= n;
    return *this;
}

template<typename _Tp> inline SeqIterator<_Tp>& SeqIterator<_Tp>::operator -=(int delta)
{
    return (*this += -delta);
}

template<typename _Tp> inline ptrdiff_t operator - (const SeqIterator<_Tp>& a,
                                                    const SeqIterator<_Tp>& b)
{
    ptrdiff_t delta = a.index - b.index, n = a.seq->total;
    if( std::abs(static_cast<long>(delta)) > n )
        delta += delta < 0 ? n : -n;
    return delta;
}

template<typename _Tp> inline bool operator == (const SeqIterator<_Tp>& a,
                                                const SeqIterator<_Tp>& b)
{
    return a.seq == b.seq && a.index == b.index;
}

template<typename _Tp> inline bool operator != (const SeqIterator<_Tp>& a,
                                                const SeqIterator<_Tp>& b)
{
    return !(a == b);
}


template<typename _ClsName> struct CV_EXPORTS RTTIImpl
{
public:
    static int isInstance(const void* ptr)
    {
        static _ClsName dummy;
        union
        {
            const void* p;
            const void** pp;
        } a, b;
        a.p = &dummy;
        b.p = ptr;
        return *a.pp == *b.pp;
    }
    static void release(void** dbptr)
    {
        if(dbptr && *dbptr)
        {
            delete (_ClsName*)*dbptr;
            *dbptr = 0;
        }
    }
    static void* read(CvFileStorage* fs, CvFileNode* n)
    {
        FileNode fn(fs, n);
        _ClsName* obj = new _ClsName;
        if(obj->read(fn))
            return obj;
        delete obj;
        return 0;
    }
    
    static void write(CvFileStorage* _fs, const char* name, const void* ptr, CvAttrList)
    {
        if(ptr && _fs)
        {
            FileStorage fs(_fs);
            fs.fs.addref();
            ((const _ClsName*)ptr)->write(fs, string(name));
        }
    }
    
    static void* clone(const void* ptr)
    {
        if(!ptr)
            return 0;
        return new _ClsName(*(const _ClsName*)ptr);
    }
};

    
class CV_EXPORTS Formatter
{
public:
    virtual ~Formatter() {}
    virtual void write(std::ostream& out, const Mat& m, const int* params=0, int nparams=0) const = 0;
    virtual void write(std::ostream& out, const void* data, int nelems, int type,
                       const int* params=0, int nparams=0) const = 0;
    static const Formatter* get(const char* fmt="");
    static const Formatter* setDefault(const Formatter* fmt);
};


struct CV_EXPORTS Formatted
{
    Formatted(const Mat& m, const Formatter* fmt,
              const vector<int>& params);
    Formatted(const Mat& m, const Formatter* fmt,
              const int* params=0);
    Mat mtx;
    const Formatter* fmt;
    vector<int> params;
};

    
/** Writes a point to an output stream in Matlab notation
 */
template<typename _Tp> inline std::ostream& operator<<(std::ostream& out, const Point_<_Tp>& p)
{
    out << "[" << p.x << ", " << p.y << "]";
    return out;
}

/** Writes a point to an output stream in Matlab notation
 */
template<typename _Tp> inline std::ostream& operator<<(std::ostream& out, const Point3_<_Tp>& p)
{
    out << "[" << p.x << ", " << p.y << ", " << p.z << "]";
    return out;
}        

static inline Formatted format(const Mat& mtx, const char* fmt,
                               const vector<int>& params=vector<int>())
{
    return Formatted(mtx, Formatter::get(fmt), params);
}

template<typename _Tp> static inline Formatted format(const vector<Point_<_Tp> >& vec,
                                                      const char* fmt, const vector<int>& params=vector<int>())
{
    return Formatted(Mat(vec), Formatter::get(fmt), params);
}

template<typename _Tp> static inline Formatted format(const vector<Point3_<_Tp> >& vec,
                                                      const char* fmt, const vector<int>& params=vector<int>())
{
    return Formatted(Mat(vec), Formatter::get(fmt), params);
}

/** \brief prints Mat to the output stream in Matlab notation
 * use like
 @verbatim
 Mat my_mat = Mat::eye(3,3,CV_32F);
 std::cout << my_mat;
 @endverbatim
 */    
static inline std::ostream& operator << (std::ostream& out, const Mat& mtx)
{
    Formatter::get()->write(out, mtx);
    return out;
}

/** \brief prints Mat to the output stream allows in the specified notation (see format)
 * use like
 @verbatim
 Mat my_mat = Mat::eye(3,3,CV_32F);
 std::cout << my_mat;
 @endverbatim
 */    
static inline std::ostream& operator << (std::ostream& out, const Formatted& fmtd)
{
    fmtd.fmt->write(out, fmtd.mtx);
    return out;
}


template<typename _Tp> static inline std::ostream& operator << (std::ostream& out,
                                                                const vector<Point_<_Tp> >& vec)
{
    Formatter::get()->write(out, Mat(vec));
    return out;
}


template<typename _Tp> static inline std::ostream& operator << (std::ostream& out,
                                                                const vector<Point3_<_Tp> >& vec)
{
    Formatter::get()->write(out, Mat(vec));
    return out;
}
    
/*template<typename _Tp> struct AlgorithmParamType {};
template<> struct AlgorithmParamType<int> { enum { type = CV_PARAM_TYPE_INT }; };
template<> struct AlgorithmParamType<double> { enum { type = CV_PARAM_TYPE_REAL }; };
template<> struct AlgorithmParamType<string> { enum { type = CV_PARAM_TYPE_STRING }; };
template<> struct AlgorithmParamType<Mat> { enum { type = CV_PARAM_TYPE_MAT }; };
    
template<typename _Tp> _Tp Algorithm::get(int paramId) const
{
    _Tp value = _Tp();
    get_(paramId, AlgorithmParamType<_Tp>::type, &value);
    return value;
}
    
template<typename _Tp> bool Algorithm::set(int paramId, const _Tp& value)
{
    set_(paramId, AlgorithmParamType<_Tp>::type, &value);
    return value;
}
    
template<typename _Tp> _Tp Algorithm::paramDefaultValue(int paramId) const
{
    _Tp value = _Tp();
    paramDefaultValue_(paramId, AlgorithmParamType<_Tp>::type, &value);
    return value;
}
    
template<typename _Tp> bool Algorithm::paramRange(int paramId, _Tp& minVal, _Tp& maxVal) const
{
    return paramRange_(paramId, AlgorithmParamType<_Tp>::type, &minVal, &maxVal);
}

template<typename _Tp> void Algorithm::addParam(int propId, _Tp& value, bool readOnly, const string& name,
                                         const string& help, const _Tp& defaultValue,
                                         _Tp (Algorithm::*getter)(), bool (Algorithm::*setter)(const _Tp&))
{
    addParam_(propId, AlgorithmParamType<_Tp>::type, &value, readOnly, name, help, &defaultValue,
             (void*)getter, (void*)setter);
}
    
template<typename _Tp> void Algorithm::setParamRange(int propId, const _Tp& minVal, const _Tp& maxVal)
{
    setParamRange_(propId, AlgorithmParamType<_Tp>::type, &minVal, &maxVal);
}*/
    
}

#endif // __cplusplus
#endif
