types.hpp

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#ifndef OPENCV_CORE_TYPES_HPP
#define OPENCV_CORE_TYPES_HPP
 
#ifndef __cplusplus
#  error types.hpp header must be compiled as C++
#endif
 
#include <climits>
#include <cfloat>
#include <vector>
#include <limits>
 
#include "opencv2/core/cvdef.h"
#include "opencv2/core/cvstd.hpp"
#include "opencv2/core/matx.hpp"
 
#ifdef _MSC_VER
#pragma warning(push)
#pragma warning(disable: 4459)  // declaration of '...' hides global declaration
#endif
 
namespace cv
{
 
 
 
template<typename _Tp> class Complex
{
public:
 
    Complex();
    Complex( _Tp _re, _Tp _im = 0 );
 
    template<typename T2> operator Complex<T2>() const;
    Complex conj() const;
 
    _Tp re, im; 
};
 
typedef Complex<float> Complexf;
typedef Complex<double> Complexd;
 
template<typename _Tp> class DataType< Complex<_Tp> >
{
public:
    typedef Complex<_Tp> value_type;
    typedef value_type   work_type;
    typedef _Tp          channel_type;
 
    enum { generic_type = 0,
           channels     = 2,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8)
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
           ,depth        = DataType<channel_type>::depth
           ,type         = CV_MAKETYPE(depth, channels)
#endif
    };
 
    typedef Vec<channel_type, channels> vec_type;
};
 
namespace traits {
template<typename _Tp>
struct Depth< Complex<_Tp> > { enum { value = Depth<_Tp>::value }; };
template<typename _Tp>
struct Type< Complex<_Tp> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, 2) }; };
} // namespace
 
 
 
template<typename _Tp> class Point_
{
public:
    typedef _Tp value_type;
 
    Point_();
    Point_(_Tp _x, _Tp _y);
#if (defined(__GNUC__) && __GNUC__ < 5) && !defined(__clang__)  // GCC 4.x bug. Details: https://github.com/opencv/opencv/pull/20837
    Point_(const Point_& pt);
    Point_(Point_&& pt) CV_NOEXCEPT = default;
#elif OPENCV_ABI_COMPATIBILITY < 500
    Point_(const Point_& pt) = default;
    Point_(Point_&& pt) CV_NOEXCEPT = default;
#endif
    Point_(const Size_<_Tp>& sz);
    Point_(const Vec<_Tp, 2>& v);
 
#if (defined(__GNUC__) && __GNUC__ < 5) && !defined(__clang__)  // GCC 4.x bug. Details: https://github.com/opencv/opencv/pull/20837
    Point_& operator = (const Point_& pt);
    Point_& operator = (Point_&& pt) CV_NOEXCEPT = default;
#elif OPENCV_ABI_COMPATIBILITY < 500
    Point_& operator = (const Point_& pt) = default;
    Point_& operator = (Point_&& pt) CV_NOEXCEPT = default;
#endif
    template<typename _Tp2> operator Point_<_Tp2>() const;
 
    operator Vec<_Tp, 2>() const;
 
    _Tp dot(const Point_& pt) const;
    double ddot(const Point_& pt) const;
    double cross(const Point_& pt) const;
    bool inside(const Rect_<_Tp>& r) const;
    _Tp x; 
    _Tp y; 
};
 
typedef Point_<int> Point2i;
typedef Point_<int64> Point2l;
typedef Point_<float> Point2f;
typedef Point_<double> Point2d;
typedef Point2i Point;
 
template<typename _Tp> class DataType< Point_<_Tp> >
{
public:
    typedef Point_<_Tp>                               value_type;
    typedef Point_<typename DataType<_Tp>::work_type> work_type;
    typedef _Tp                                       channel_type;
 
    enum { generic_type = 0,
           channels     = 2,
           fmt          = traits::SafeFmt<channel_type>::fmt + ((channels - 1) << 8)
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
           ,depth        = DataType<channel_type>::depth
           ,type         = CV_MAKETYPE(depth, channels)
#endif
         };
 
    typedef Vec<channel_type, channels> vec_type;
};
 
namespace traits {
template<typename _Tp>
struct Depth< Point_<_Tp> > { enum { value = Depth<_Tp>::value }; };
template<typename _Tp>
struct Type< Point_<_Tp> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, 2) }; };
} // namespace
 
 
 
template<typename _Tp> class Point3_
{
public:
    typedef _Tp value_type;
 
    Point3_();
    Point3_(_Tp _x, _Tp _y, _Tp _z);
#if OPENCV_ABI_COMPATIBILITY < 500
    Point3_(const Point3_& pt) = default;
    Point3_(Point3_&& pt) CV_NOEXCEPT = default;
#endif
    explicit Point3_(const Point_<_Tp>& pt);
    Point3_(const Vec<_Tp, 3>& v);
 
#if OPENCV_ABI_COMPATIBILITY < 500
    Point3_& operator = (const Point3_& pt) = default;
    Point3_& operator = (Point3_&& pt) CV_NOEXCEPT = default;
#endif
    template<typename _Tp2> operator Point3_<_Tp2>() const;
    operator Vec<_Tp, 3>() const;
 
    _Tp dot(const Point3_& pt) const;
    double ddot(const Point3_& pt) const;
    Point3_ cross(const Point3_& pt) const;
    _Tp x; 
    _Tp y; 
    _Tp z; 
};
 
typedef Point3_<int> Point3i;
typedef Point3_<float> Point3f;
typedef Point3_<double> Point3d;
 
template<typename _Tp> class DataType< Point3_<_Tp> >
{
public:
    typedef Point3_<_Tp>                               value_type;
    typedef Point3_<typename DataType<_Tp>::work_type> work_type;
    typedef _Tp                                        channel_type;
 
    enum { generic_type = 0,
           channels     = 3,
           fmt          = traits::SafeFmt<channel_type>::fmt + ((channels - 1) << 8)
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
           ,depth        = DataType<channel_type>::depth
           ,type         = CV_MAKETYPE(depth, channels)
#endif
         };
 
    typedef Vec<channel_type, channels> vec_type;
};
 
namespace traits {
template<typename _Tp>
struct Depth< Point3_<_Tp> > { enum { value = Depth<_Tp>::value }; };
template<typename _Tp>
struct Type< Point3_<_Tp> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, 3) }; };
} // namespace
 
 
template<typename _Tp> class Size_
{
public:
    typedef _Tp value_type;
 
    Size_();
    Size_(_Tp _width, _Tp _height);
#if OPENCV_ABI_COMPATIBILITY < 500
    Size_(const Size_& sz) = default;
    Size_(Size_&& sz) CV_NOEXCEPT = default;
#endif
    Size_(const Point_<_Tp>& pt);
 
#if OPENCV_ABI_COMPATIBILITY < 500
    Size_& operator = (const Size_& sz) = default;
    Size_& operator = (Size_&& sz) CV_NOEXCEPT = default;
#endif
    _Tp area() const;
    double aspectRatio() const;
    bool empty() const;
 
    template<typename _Tp2> operator Size_<_Tp2>() const;
 
    _Tp width; 
    _Tp height; 
};
 
typedef Size_<int> Size2i;
typedef Size_<int64> Size2l;
typedef Size_<float> Size2f;
typedef Size_<double> Size2d;
typedef Size2i Size;
 
template<typename _Tp> class DataType< Size_<_Tp> >
{
public:
    typedef Size_<_Tp>                               value_type;
    typedef Size_<typename DataType<_Tp>::work_type> work_type;
    typedef _Tp                                      channel_type;
 
    enum { generic_type = 0,
           channels     = 2,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8)
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
           ,depth        = DataType<channel_type>::depth
           ,type         = CV_MAKETYPE(depth, channels)
#endif
         };
 
    typedef Vec<channel_type, channels> vec_type;
};
 
namespace traits {
template<typename _Tp>
struct Depth< Size_<_Tp> > { enum { value = Depth<_Tp>::value }; };
template<typename _Tp>
struct Type< Size_<_Tp> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, 2) }; };
} // namespace
 
 
template<typename _Tp> class Rect_
{
public:
    typedef _Tp value_type;
 
    Rect_();
    Rect_(_Tp _x, _Tp _y, _Tp _width, _Tp _height);
#if OPENCV_ABI_COMPATIBILITY < 500
    Rect_(const Rect_& r) = default;
    Rect_(Rect_&& r) CV_NOEXCEPT = default;
#endif
    Rect_(const Point_<_Tp>& org, const Size_<_Tp>& sz);
    Rect_(const Point_<_Tp>& pt1, const Point_<_Tp>& pt2);
 
#if OPENCV_ABI_COMPATIBILITY < 500
    Rect_& operator = (const Rect_& r) = default;
    Rect_& operator = (Rect_&& r) CV_NOEXCEPT = default;
#endif
    Point_<_Tp> tl() const;
    Point_<_Tp> br() const;
 
    Size_<_Tp> size() const;
    _Tp area() const;
    bool empty() const;
 
    template<typename _Tp2> operator Rect_<_Tp2>() const;
 
    bool contains(const Point_<_Tp>& pt) const;
 
    _Tp x; 
    _Tp y; 
    _Tp width; 
    _Tp height; 
};
 
typedef Rect_<int> Rect2i;
typedef Rect_<float> Rect2f;
typedef Rect_<double> Rect2d;
typedef Rect2i Rect;
 
template<typename _Tp> class DataType< Rect_<_Tp> >
{
public:
    typedef Rect_<_Tp>                               value_type;
    typedef Rect_<typename DataType<_Tp>::work_type> work_type;
    typedef _Tp                                      channel_type;
 
    enum { generic_type = 0,
           channels     = 4,
           fmt          = traits::SafeFmt<channel_type>::fmt + ((channels - 1) << 8)
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
           ,depth        = DataType<channel_type>::depth
           ,type         = CV_MAKETYPE(depth, channels)
#endif
         };
 
    typedef Vec<channel_type, channels> vec_type;
};
 
namespace traits {
template<typename _Tp>
struct Depth< Rect_<_Tp> > { enum { value = Depth<_Tp>::value }; };
template<typename _Tp>
struct Type< Rect_<_Tp> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, 4) }; };
} // namespace
 
 
class CV_EXPORTS_W_SIMPLE RotatedRect
{
public:
    CV_WRAP RotatedRect();
    CV_WRAP RotatedRect(const Point2f& center, const Size2f& size, float angle);
    CV_WRAP RotatedRect(const Point2f& point1, const Point2f& point2, const Point2f& point3);
 
    void points(Point2f pts[]) const;
 
    CV_WRAP void points(CV_OUT std::vector<Point2f>& pts) const;
 
    CV_WRAP Rect boundingRect() const;
    CV_WRAP Rect2f boundingRect2f() const;
    CV_PROP_RW Point2f center;
    CV_PROP_RW Size2f size;
    CV_PROP_RW float angle;
};
 
template<> class DataType< RotatedRect >
{
public:
    typedef RotatedRect  value_type;
    typedef value_type   work_type;
    typedef float        channel_type;
 
    enum { generic_type = 0,
           channels     = (int)sizeof(value_type)/sizeof(channel_type), // 5
           fmt          = traits::SafeFmt<channel_type>::fmt + ((channels - 1) << 8)
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
           ,depth        = DataType<channel_type>::depth
           ,type         = CV_MAKETYPE(depth, channels)
#endif
         };
 
    typedef Vec<channel_type, channels> vec_type;
};
 
namespace traits {
template<>
struct Depth< RotatedRect > { enum { value = Depth<float>::value }; };
template<>
struct Type< RotatedRect > { enum { value = CV_MAKETYPE(Depth<float>::value, (int)sizeof(RotatedRect)/sizeof(float)) }; };
} // namespace
 
 
 
class CV_EXPORTS Range
{
public:
    Range();
    Range(int _start, int _end);
    int size() const;
    bool empty() const;
    static Range all();
 
    int start, end;
};
 
template<> class DataType<Range>
{
public:
    typedef Range      value_type;
    typedef value_type work_type;
    typedef int        channel_type;
 
    enum { generic_type = 0,
           channels     = 2,
           fmt          = traits::SafeFmt<channel_type>::fmt + ((channels - 1) << 8)
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
           ,depth        = DataType<channel_type>::depth
           ,type         = CV_MAKETYPE(depth, channels)
#endif
         };
 
    typedef Vec<channel_type, channels> vec_type;
};
 
namespace traits {
template<>
struct Depth< Range > { enum { value = Depth<int>::value }; };
template<>
struct Type< Range > { enum { value = CV_MAKETYPE(Depth<int>::value, 2) }; };
} // namespace
 
 
 
template<typename _Tp> class Scalar_ : public Vec<_Tp, 4>
{
public:
    Scalar_();
    Scalar_(_Tp v0, _Tp v1, _Tp v2=0, _Tp v3=0);
    Scalar_(_Tp v0);
 
    Scalar_(const Scalar_& s);
    Scalar_(Scalar_&& s) CV_NOEXCEPT;
 
    Scalar_& operator=(const Scalar_& s);
    Scalar_& operator=(Scalar_&& s) CV_NOEXCEPT;
 
    template<typename _Tp2, int cn>
    Scalar_(const Vec<_Tp2, cn>& v);
 
    static Scalar_<_Tp> all(_Tp v0);
 
    template<typename T2> operator Scalar_<T2>() const;
 
    Scalar_<_Tp> mul(const Scalar_<_Tp>& a, double scale=1 ) const;
 
    Scalar_<_Tp> conj() const;
 
    bool isReal() const;
};
 
typedef Scalar_<double> Scalar;
 
template<typename _Tp> class DataType< Scalar_<_Tp> >
{
public:
    typedef Scalar_<_Tp>                               value_type;
    typedef Scalar_<typename DataType<_Tp>::work_type> work_type;
    typedef _Tp                                        channel_type;
 
    enum { generic_type = 0,
           channels     = 4,
           fmt          = traits::SafeFmt<channel_type>::fmt + ((channels - 1) << 8)
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
           ,depth        = DataType<channel_type>::depth
           ,type         = CV_MAKETYPE(depth, channels)
#endif
         };
 
    typedef Vec<channel_type, channels> vec_type;
};
 
namespace traits {
template<typename _Tp>
struct Depth< Scalar_<_Tp> > { enum { value = Depth<_Tp>::value }; };
template<typename _Tp>
struct Type< Scalar_<_Tp> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, 4) }; };
} // namespace
 
 
 
class CV_EXPORTS_W_SIMPLE KeyPoint
{
public:
    CV_WRAP KeyPoint();
    KeyPoint(Point2f pt, float size, float angle=-1, float response=0, int octave=0, int class_id=-1);
    CV_WRAP KeyPoint(float x, float y, float size, float angle=-1, float response=0, int octave=0, int class_id=-1);
 
    size_t hash() const;
 
    CV_WRAP static void convert(const std::vector<KeyPoint>& keypoints,
                                CV_OUT std::vector<Point2f>& points2f,
                                const std::vector<int>& keypointIndexes=std::vector<int>());
    CV_WRAP static void convert(const std::vector<Point2f>& points2f,
                                CV_OUT std::vector<KeyPoint>& keypoints,
                                float size=1, float response=1, int octave=0, int class_id=-1);
 
    CV_WRAP static float overlap(const KeyPoint& kp1, const KeyPoint& kp2);
 
    CV_PROP_RW Point2f pt; 
    CV_PROP_RW float size; 
    CV_PROP_RW float angle; 
    CV_PROP_RW float response; 
    CV_PROP_RW int octave; 
    CV_PROP_RW int class_id; 
};
 
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
template<> class DataType<KeyPoint>
{
public:
    typedef KeyPoint      value_type;
    typedef float         work_type;
    typedef float         channel_type;
 
    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = (int)(sizeof(value_type)/sizeof(channel_type)), // 7
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };
 
    typedef Vec<channel_type, channels> vec_type;
};
#endif
 
 
 
class CV_EXPORTS_W_SIMPLE DMatch
{
public:
    CV_WRAP DMatch();
    CV_WRAP DMatch(int _queryIdx, int _trainIdx, float _distance);
    CV_WRAP DMatch(int _queryIdx, int _trainIdx, int _imgIdx, float _distance);
 
    CV_PROP_RW int queryIdx; 
    CV_PROP_RW int trainIdx; 
    CV_PROP_RW int imgIdx;   
 
    CV_PROP_RW float distance;
 
    // less is better
    bool operator<(const DMatch &m) const;
};
 
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
template<> class DataType<DMatch>
{
public:
    typedef DMatch      value_type;
    typedef int         work_type;
    typedef int         channel_type;
 
    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = (int)(sizeof(value_type)/sizeof(channel_type)), // 4
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };
 
    typedef Vec<channel_type, channels> vec_type;
};
#endif
 
 
 
class CV_EXPORTS TermCriteria
{
public:
    enum Type
    {
        COUNT=1, 
        MAX_ITER=COUNT, 
        EPS=2 
    };
 
    TermCriteria();
    TermCriteria(int type, int maxCount, double epsilon);
 
    inline bool isValid() const
    {
        const bool isCount = (type & COUNT) && maxCount > 0;
        const bool isEps = (type & EPS) && !cvIsNaN(epsilon);
        return isCount || isEps;
    }
 
    int type; 
    int maxCount; 
    double epsilon; 
};
 
 
 
 
 
class CV_EXPORTS_W_MAP Moments
{
public:
    Moments();
    Moments(double m00, double m10, double m01, double m20, double m11,
            double m02, double m30, double m21, double m12, double m03 );
    //Moments( const CvMoments& moments );
    //operator CvMoments() const;
 
    CV_PROP_RW double  m00, m10, m01, m20, m11, m02, m30, m21, m12, m03;
 
    CV_PROP_RW double  mu20, mu11, mu02, mu30, mu21, mu12, mu03;
 
    CV_PROP_RW double  nu20, nu11, nu02, nu30, nu21, nu12, nu03;
};
 
template<> class DataType<Moments>
{
public:
    typedef Moments     value_type;
    typedef double      work_type;
    typedef double      channel_type;
 
    enum { generic_type = 0,
           channels     = (int)(sizeof(value_type)/sizeof(channel_type)), // 24
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8)
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
           ,depth        = DataType<channel_type>::depth
           ,type         = CV_MAKETYPE(depth, channels)
#endif
         };
 
    typedef Vec<channel_type, channels> vec_type;
};
 
namespace traits {
template<>
struct Depth< Moments > { enum { value = Depth<double>::value }; };
template<>
struct Type< Moments > { enum { value = CV_MAKETYPE(Depth<double>::value, (int)(sizeof(Moments)/sizeof(double))) }; };
} // namespace
 
 
 
 
 
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)
{
    a = a / b;
    return a;
}
 
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;
}
 
 
 
 
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) {}
 
#if (defined(__GNUC__) && __GNUC__ < 5) && !defined(__clang__)  // GCC 4.x bug. Details: https://github.com/opencv/opencv/pull/20837
template<typename _Tp> inline
Point_<_Tp>::Point_(const Point_& pt)
    : x(pt.x), y(pt.y) {}
#endif
 
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]) {}
 
#if (defined(__GNUC__) && __GNUC__ < 5) && !defined(__clang__)  // GCC 4.x bug. Details: https://github.com/opencv/opencv/pull/20837
template<typename _Tp> inline
Point_<_Tp>& Point_<_Tp>::operator = (const Point_& pt)
{
    x = pt.x; y = pt.y;
    return *this;
}
#endif
 
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 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*(double)(pt.x) + (double)y*(double)(pt.y);
}
 
template<typename _Tp> inline
double Point_<_Tp>::cross(const Point_& pt) const
{
    return (double)x*pt.y - (double)y*pt.x;
}
 
template<typename _Tp> inline bool
Point_<_Tp>::inside( const Rect_<_Tp>& r ) const
{
    return r.contains(*this);
}
 
 
template<typename _Tp> static inline
Point_<_Tp>& operator += (Point_<_Tp>& a, const Point_<_Tp>& b)
{
    a.x += b.x;
    a.y += b.y;
    return a;
}
 
template<typename _Tp> static inline
Point_<_Tp>& operator -= (Point_<_Tp>& a, const Point_<_Tp>& b)
{
    a.x -= b.x;
    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
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) );
}
 
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 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
Point_<_Tp> operator / (const Point_<_Tp>& a, int b)
{
    Point_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}
 
template<typename _Tp> static inline
Point_<_Tp> operator / (const Point_<_Tp>& a, float b)
{
    Point_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}
 
template<typename _Tp> static inline
Point_<_Tp> operator / (const Point_<_Tp>& a, double b)
{
    Point_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}
 
 
template<typename _AccTp> static inline _AccTp normL2Sqr(const Point_<int>& pt);
template<typename _AccTp> static inline _AccTp normL2Sqr(const Point_<int64>& pt);
template<typename _AccTp> static inline _AccTp normL2Sqr(const Point_<float>& pt);
template<typename _AccTp> static inline _AccTp normL2Sqr(const Point_<double>& pt);
 
template<> inline int normL2Sqr<int>(const Point_<int>& pt) { return pt.dot(pt); }
template<> inline int64 normL2Sqr<int64>(const Point_<int64>& pt) { return pt.dot(pt); }
template<> inline float normL2Sqr<float>(const Point_<float>& pt) { return pt.dot(pt); }
template<> inline double normL2Sqr<double>(const Point_<int>& pt) { return pt.dot(pt); }
 
template<> inline double normL2Sqr<double>(const Point_<float>& pt) { return pt.ddot(pt); }
template<> inline double normL2Sqr<double>(const Point_<double>& pt) { return pt.ddot(pt); }
 
 
 
 
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 Point_<_Tp>& pt)
    : x(pt.x), y(pt.y), z(_Tp()) {}
 
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 Vec<_Tp, 3>() const
{
    return Vec<_Tp, 3>(x, y, z);
}
 
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 += b.x;
    a.y += b.y;
    a.z += b.z;
    return a;
}
 
template<typename _Tp> static inline
Point3_<_Tp>& operator -= (Point3_<_Tp>& a, const Point3_<_Tp>& b)
{
    a.x -= b.x;
    a.y -= b.y;
    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
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) );
}
 
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
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
Point3_<_Tp> operator / (const Point3_<_Tp>& a, int b)
{
    Point3_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}
 
template<typename _Tp> static inline
Point3_<_Tp> operator / (const Point3_<_Tp>& a, float b)
{
    Point3_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}
 
template<typename _Tp> static inline
Point3_<_Tp> operator / (const Point3_<_Tp>& a, double b)
{
    Point3_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}
 
 
 
 
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 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
_Tp Size_<_Tp>::area() const
{
    const _Tp result = width * height;
    CV_DbgAssert(!std::numeric_limits<_Tp>::is_integer
        || width == 0 || result / width == height); // make sure the result fits in the return value
    return result;
}
 
template<typename _Tp> inline
double Size_<_Tp>::aspectRatio() const
{
    return width / static_cast<double>(height);
}
 
template<typename _Tp> inline
bool Size_<_Tp>::empty() const
{
    return width <= 0 || height <= 0;
}
 
 
template<typename _Tp> static inline
Size_<_Tp>& operator *= (Size_<_Tp>& a, _Tp b)
{
    a.width *= b;
    a.height *= b;
    return a;
}
 
template<typename _Tp> static inline
Size_<_Tp> operator * (const Size_<_Tp>& a, _Tp b)
{
    Size_<_Tp> tmp(a);
    tmp *= b;
    return tmp;
}
 
template<typename _Tp> static inline
Size_<_Tp>& operator /= (Size_<_Tp>& a, _Tp b)
{
    a.width /= b;
    a.height /= b;
    return a;
}
 
template<typename _Tp> static inline
Size_<_Tp> operator / (const Size_<_Tp>& a, _Tp b)
{
    Size_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}
 
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 + (const Size_<_Tp>& a, const Size_<_Tp>& b)
{
    Size_<_Tp> tmp(a);
    tmp += b;
    return tmp;
}
 
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 - (const Size_<_Tp>& a, const Size_<_Tp>& b)
{
    Size_<_Tp> tmp(a);
    tmp -= b;
    return tmp;
}
 
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 == b);
}
 
 
 
 
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 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
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> inline
Size_<_Tp> Rect_<_Tp>::size() const
{
    return Size_<_Tp>(width, height);
}
 
template<typename _Tp> inline
_Tp Rect_<_Tp>::area() const
{
    const _Tp result = width * height;
    CV_DbgAssert(!std::numeric_limits<_Tp>::is_integer
        || width == 0 || result / width == height); // make sure the result fits in the return value
    return result;
}
 
template<typename _Tp> inline
bool Rect_<_Tp>::empty() const
{
    return width <= 0 || height <= 0;
}
 
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
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
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 )
{
    const _Tp width = a.width - b.width;
    const _Tp height = a.height - b.height;
    CV_DbgAssert(width >= 0 && height >= 0);
    a.width = width;
    a.height = height;
    return a;
}
 
template<typename _Tp> static inline
Rect_<_Tp>& operator &= ( Rect_<_Tp>& a, const Rect_<_Tp>& b )
{
    if (a.empty() || b.empty()) {
        a = Rect();
        return a;
    }
    const Rect_<_Tp>& Rx_min = (a.x < b.x) ? a : b;
    const Rect_<_Tp>& Rx_max = (a.x < b.x) ? b : a;
    const Rect_<_Tp>& Ry_min = (a.y < b.y) ? a : b;
    const Rect_<_Tp>& Ry_max = (a.y < b.y) ? b : a;
    // Looking at the formula below, we will compute Rx_min.width - (Rx_max.x - Rx_min.x)
    // but we want to avoid overflows. Rx_min.width >= 0 and (Rx_max.x - Rx_min.x) >= 0
    // by definition so the difference does not overflow. The only thing that can overflow
    // is (Rx_max.x - Rx_min.x). And it can only overflow if Rx_min.x < 0.
    // Let us first deal with the following case.
    if ((Rx_min.x < 0 && Rx_min.x + Rx_min.width < Rx_max.x) ||
        (Ry_min.y < 0 && Ry_min.y + Ry_min.height < Ry_max.y)) {
        a = Rect();
        return a;
    }
    // We now know that either Rx_min.x >= 0, or
    // Rx_min.x < 0 && Rx_min.x + Rx_min.width >= Rx_max.x and therefore
    // Rx_min.width >= (Rx_max.x - Rx_min.x) which means (Rx_max.x - Rx_min.x)
    // is inferior to a valid int and therefore does not overflow.
    a.width = std::min(Rx_min.width - (Rx_max.x - Rx_min.x), Rx_max.width);
    a.height = std::min(Ry_min.height - (Ry_max.y - Ry_min.y), Ry_max.height);
    a.x = Rx_max.x;
    a.y = Ry_max.y;
    if (a.empty())
        a = Rect();
    return a;
}
 
template<typename _Tp> static inline
Rect_<_Tp>& operator |= ( Rect_<_Tp>& a, const Rect_<_Tp>& b )
{
    if (a.empty()) {
        a = b;
    }
    else if (!b.empty()) {
        _Tp x1 = std::min(a.x, b.x);
        _Tp 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> 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 Size_<_Tp>& b)
{
    const _Tp width = a.width - b.width;
    const _Tp height = a.height - b.height;
    CV_DbgAssert(width >= 0 && height >= 0);
    return Rect_<_Tp>( a.x, a.y, width, 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> static inline
double jaccardDistance(const Rect_<_Tp>& a, const Rect_<_Tp>& b) {
    _Tp Aa = a.area();
    _Tp Ab = b.area();
 
    if ((Aa + Ab) <= std::numeric_limits<_Tp>::epsilon()) {
        // jaccard_index = 1 -> distance = 0
        return 0.0;
    }
 
    double Aab = (a & b).area();
    // distance = 1 - jaccard_index
    return 1.0 - Aab / (Aa + Ab - Aab);
}
 
CV_EXPORTS_W inline double rectangleIntersectionArea(const Rect2d& a, const Rect2d& b) { return (a & b).area(); }
 
 
inline
RotatedRect::RotatedRect()
    : center(), size(), angle(0) {}
 
inline
RotatedRect::RotatedRect(const Point2f& _center, const Size2f& _size, float _angle)
    : center(_center), size(_size), angle(_angle) {}
 
 
inline
Range::Range()
    : start(0), end(0) {}
 
inline
Range::Range(int _start, int _end)
    : start(_start), end(_end) {}
 
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);
}
 
 
 
 
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 Scalar_<_Tp>& s) : Vec<_Tp, 4>(s) {
}
 
template<typename _Tp> inline
Scalar_<_Tp>::Scalar_(Scalar_<_Tp>&& s) CV_NOEXCEPT {
    this->val[0] = std::move(s.val[0]);
    this->val[1] = std::move(s.val[1]);
    this->val[2] = std::move(s.val[2]);
    this->val[3] = std::move(s.val[3]);
}
 
template<typename _Tp> inline
Scalar_<_Tp>& Scalar_<_Tp>::operator=(const Scalar_<_Tp>& s) {
    this->val[0] = s.val[0];
    this->val[1] = s.val[1];
    this->val[2] = s.val[2];
    this->val[3] = s.val[3];
    return *this;
}
 
template<typename _Tp> inline
Scalar_<_Tp>& Scalar_<_Tp>::operator=(Scalar_<_Tp>&& s) CV_NOEXCEPT {
    this->val[0] = std::move(s.val[0]);
    this->val[1] = std::move(s.val[1]);
    this->val[2] = std::move(s.val[2]);
    this->val[3] = std::move(s.val[3]);
    return *this;
}
 
template<typename _Tp> template<typename _Tp2, int cn> inline
Scalar_<_Tp>::Scalar_(const Vec<_Tp2, cn>& v)
{
    int i;
    for( i = 0; i < (cn < 4 ? cn : 4); i++ )
        this->val[i] = cv::saturate_cast<_Tp>(v.val[i]);
    for( ; i < 4; i++ )
        this->val[i] = 0;
}
 
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> Scalar_<_Tp>::mul(const Scalar_<_Tp>& a, double scale ) const
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(this->val[0] * a.val[0] * scale),
                        saturate_cast<_Tp>(this->val[1] * a.val[1] * scale),
                        saturate_cast<_Tp>(this->val[2] * a.val[2] * scale),
                        saturate_cast<_Tp>(this->val[3] * a.val[3] * scale));
}
 
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> 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] += b.val[0];
    a.val[1] += b.val[1];
    a.val[2] += b.val[2];
    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] -= b.val[0];
    a.val[1] -= b.val[1];
    a.val[2] -= b.val[2];
    a.val[3] -= b.val[3];
    return a;
}
 
template<typename _Tp> static inline
Scalar_<_Tp>& operator *= ( Scalar_<_Tp>& a, _Tp v )
{
    a.val[0] *= v;
    a.val[1] *= v;
    a.val[2] *= v;
    a.val[3] *= v;
    return a;
}
 
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>(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, _Tp alpha)
{
    return Scalar_<_Tp>(a.val[0] * alpha,
                        a.val[1] * alpha,
                        a.val[2] * alpha,
                        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> static inline
Scalar_<_Tp> operator / (const Scalar_<_Tp>& a, _Tp alpha)
{
    return Scalar_<_Tp>(a.val[0] / alpha,
                        a.val[1] / alpha,
                        a.val[2] / alpha,
                        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;
}
 
template<typename _Tp> static inline
Scalar operator * (const Matx<_Tp, 4, 4>& a, const Scalar& b)
{
    Matx<double, 4, 1> c((Matx<double, 4, 4>)a, b, Matx_MatMulOp());
    return reinterpret_cast<const Scalar&>(c);
}
 
template<> inline
Scalar operator * (const Matx<double, 4, 4>& a, const Scalar& b)
{
    Matx<double, 4, 1> c(a, b, Matx_MatMulOp());
    return reinterpret_cast<const Scalar&>(c);
}
 
 
 
 
inline
KeyPoint::KeyPoint()
    : pt(0,0), size(0), angle(-1), response(0), octave(0), class_id(-1) {}
 
inline
KeyPoint::KeyPoint(Point2f _pt, float _size, float _angle, float _response, int _octave, int _class_id)
    : pt(_pt), size(_size), angle(_angle), response(_response), octave(_octave), class_id(_class_id) {}
 
inline
KeyPoint::KeyPoint(float x, float y, float _size, float _angle, float _response, int _octave, int _class_id)
    : pt(x, y), size(_size), angle(_angle), response(_response), octave(_octave), class_id(_class_id) {}
 
 
 
 
inline
DMatch::DMatch()
    : queryIdx(-1), trainIdx(-1), imgIdx(-1), distance(FLT_MAX) {}
 
inline
DMatch::DMatch(int _queryIdx, int _trainIdx, float _distance)
    : queryIdx(_queryIdx), trainIdx(_trainIdx), imgIdx(-1), distance(_distance) {}
 
inline
DMatch::DMatch(int _queryIdx, int _trainIdx, int _imgIdx, float _distance)
    : queryIdx(_queryIdx), trainIdx(_trainIdx), imgIdx(_imgIdx), distance(_distance) {}
 
inline
bool DMatch::operator < (const DMatch &m) const
{
    return distance < m.distance;
}
 
 
 
 
inline
TermCriteria::TermCriteria()
    : type(0), maxCount(0), epsilon(0) {}
 
inline
TermCriteria::TermCriteria(int _type, int _maxCount, double _epsilon)
    : type(_type), maxCount(_maxCount), epsilon(_epsilon) {}
 
 
} // cv
 
#ifdef _MSC_VER
#pragma warning(pop)
#endif
 
#endif //OPENCV_CORE_TYPES_HPP