/****************************************************************************
* VCGLib                                                            o o     *
* Visual and Computer Graphics Library                            o     o   *
*                                                                _   O  _   *
* Copyright(C) 2004-2019                                           \/)\/    *
* Visual Computing Lab                                            /\/|      *
* ISTI - Italian National Research Council                           |      *
*                                                                    \      *
* All rights reserved.                                                      *
*                                                                           *
* This program is free software; you can redistribute it and/or modify      *
* it under the terms of the GNU General Public License as published by      *
* the Free Software Foundation; either version 2 of the License, or         *
* (at your option) any later version.                                       *
*                                                                           *
* This program is distributed in the hope that it will be useful,           *
* but WITHOUT ANY WARRANTY; without even the implied warranty of            *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the             *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt)          *
* for more details.                                                         *
*                                                                           *
****************************************************************************/


#ifndef __VCGLIB_POINT2
#define __VCGLIB_POINT2

#include <assert.h>
#include <vcg/math/base.h>

namespace vcg {

/** \addtogroup space */
/*@{*/
/**
   The templated class for representing a point in 2D space.
   The class is templated over the ScalarType class that is used to represent coordinates.
   All the usual operator overloading (* + - ...) is present.
 */
template <class P2ScalarType>
class Point2
{
protected:
/// The only data member. Hidden to user.
	P2ScalarType _v[2];
public:
	/// the scalar type
	typedef P2ScalarType ScalarType;
	enum {Dimension = 2};

//@{

	/** @name Access to Coords.
	 access to coords is done by overloading of [] or explicit naming of coords (X,Y,)
	 ("p[0]" or "p.X()" are equivalent) **/
	inline const ScalarType &X() const {return _v[0];}
	inline const ScalarType &Y() const {return _v[1];}
	inline ScalarType &X() {return _v[0];}
	inline ScalarType &Y() {return _v[1];}
	inline const ScalarType * V() const
	{
		return _v;
	}
	inline ScalarType * V()
	{
		return _v;
	}
	inline ScalarType & V( const int i )
	{
		assert(i>=0 && i<2);
		return _v[i];
	}
	inline const ScalarType & V( const int i ) const
	{
		assert(i>=0 && i<2);
		return _v[i];
	}
	inline const ScalarType & operator [] ( const int i ) const
	{
		assert(i>=0 && i<2);
		return _v[i];
	}
	inline ScalarType & operator [] ( const int i )
	{
		assert(i>=0 && i<2);
		return _v[i];
	}
//@}
	/// empty constructor (does nothing)
	inline Point2 () { }
	/// x,y constructor
	inline Point2 ( const ScalarType nx, const ScalarType ny )
	{
		_v[0] = nx; _v[1] = ny;
	}
	/// copy constructor
	inline Point2 ( const Point2 & p) = default;
	/// copy constructor
	template<class Q>
	inline Point2 ( const Point2<Q> & p)
	{
		_v[0]= p[0];    _v[1]= p[1];
	}
	/// copy
	inline Point2 & operator =( const Point2 & p) = default;
	/// copy
	template<class Q>
	inline Point2 & operator =( const Point2<Q> & p)
	{
		_v[0]= p[0]; _v[1]= p[1];
		return *this;
	}
	/// sets the point to (0,0)
	inline void SetZero()
	{ _v[0] = 0;_v[1] = 0;}
	/// dot product
	inline ScalarType operator * ( const Point2 & p ) const
	{
		return ( _v[0]*p._v[0] + _v[1]*p._v[1] );
	}
	inline ScalarType dot( const Point2 & p ) const { return (*this) * p; }
	/// cross product
	inline ScalarType operator ^ ( const Point2 & p ) const
	{
		return _v[0]*p._v[1] - _v[1]*p._v[0];
	}
//@{
	 /** @name Linearity for 2d points (operators +, -, *, /, *= ...) **/
	inline Point2 operator + ( const Point2 & p) const
	{
		return Point2<ScalarType>( _v[0]+p._v[0], _v[1]+p._v[1] );
	}
	inline Point2 operator - ( const Point2 & p) const
	{
		return Point2<ScalarType>( _v[0]-p._v[0], _v[1]-p._v[1] );
	}
	inline Point2 operator * ( const ScalarType s ) const
	{
		return Point2<ScalarType>( _v[0] * s, _v[1] * s );
	}
	inline Point2 operator / ( const ScalarType s ) const
	{
		return Point2<ScalarType>( _v[0] / s, _v[1] / s );
	}
	inline Point2 & operator += ( const Point2 & p)
	{
		_v[0] += p._v[0];
		_v[1] += p._v[1];
		return *this;
	}
	inline Point2 & operator -= ( const Point2 & p)
	{
		_v[0] -= p._v[0];
		_v[1] -= p._v[1];
		return *this;
	}
	inline Point2 & operator *= ( const ScalarType s )
	{
		_v[0] *= s;
		_v[1] *= s;
		return *this;
	}

	inline Point2 & operator /= ( const ScalarType s )
	{
		_v[0] /= s;
		_v[1] /= s;
		return *this;
	}

	inline Point2 operator - (void) const
	{
		return Point2(-_v[0], -_v[1]);
	}

 //@}
	/// returns the norm (Euclidian)
	inline ScalarType Norm( void ) const
	{
		return math::Sqrt( _v[0]*_v[0] + _v[1]*_v[1] );
	}
	/// returns the squared norm (Euclidian)
	inline ScalarType SquaredNorm( void ) const
	{
		return ( _v[0]*_v[0] + _v[1]*_v[1] );
	}
	inline Point2 & Scale( const ScalarType sx, const ScalarType sy )
	{
		_v[0] *= sx;
		_v[1] *= sy;
		return * this;
	}

	/// normalizes, and returns itself as result (nonsense)
	inline Point2 & Normalize( void )
	{
		ScalarType n = math::Sqrt(_v[0]*_v[0] + _v[1]*_v[1]);
		if(n>0.0) {
			_v[0] /= n; _v[1] /= n;
		}
		return *this;
	}

	inline void normalize(void)
	{
		this->Normalize();
	}

	inline Point2 normalized(void) const
	{
		Point2<ScalarType> p = *this;
		p.normalize();
		return p;
	}

	/// points equality
	inline bool operator == ( const Point2 & p ) const
	{
		return (_v[0]==p._v[0] && _v[1]==p._v[1]);
	}
	/// disparity between points
	inline bool operator != ( const Point2 & p ) const
	{
		return ( (_v[0]!=p._v[0]) || (_v[1]!=p._v[1]) );
	}
	/// lexical ordering
	inline bool operator <  ( const Point2 & p ) const
	{
		return (_v[1]!=p._v[1])?(_v[1]<p._v[1]):
		       (_v[0]<p._v[0]);
	}
	/// lexical ordering
	inline bool operator >  ( const Point2 & p ) const
	{
		return (_v[1]!=p._v[1])?(_v[1]>p._v[1]):
		       (_v[0]>p._v[0]);
	}
	/// lexical ordering
	inline bool operator <= ( const Point2 & p ) const
	{
		return (_v[1]!=p._v[1])?(_v[1]< p._v[1]):
		       (_v[0]<=p._v[0]);
	}
	/// lexical ordering
	inline bool operator >= ( const Point2 & p ) const
	{
		return (_v[1]!=p._v[1])?(_v[1]> p._v[1]):
		       (_v[0]>=p._v[0]);
	}
	/// returns the distance to another point p
	inline ScalarType Distance( const Point2 & p ) const
	{
		return Norm(*this-p);
	}
	/// returns the suqared distance to another point p
	inline ScalarType SquaredDistance( const Point2 & p ) const
	{
		return (*this-p).SquaredNorm();
	}
	/// returns the angle with X axis (radiants, in [-PI, +PI] )
	inline ScalarType Angle() const
	{
		return math::Atan2(_v[1],_v[0]);
	}
	/// transform the point in cartesian coords into polar coords
	inline Point2 & Cartesian2Polar()
	{
		ScalarType t = Angle();
		_v[0] = Norm();
		_v[1] = t;
		return *this;
	}
	/// transform the point in polar coords into cartesian coords
	inline Point2 & Polar2Cartesian()
	{
		ScalarType l = _v[0];
		_v[0] = (ScalarType)(l*math::Cos(_v[1]));
		_v[1] = (ScalarType)(l*math::Sin(_v[1]));
		return *this;
	}
	/// rotates the point of an angle (radiants, counterclockwise)
	inline Point2 & Rotate( const ScalarType rad )
	{
		ScalarType t = _v[0];
		ScalarType s = math::Sin(rad);
		ScalarType c = math::Cos(rad);

		_v[0] = _v[0]*c - _v[1]*s;
		_v[1] =     t*s + _v[1]*c;

		return *this;
	}

	/// This function extends the vector to any arbitrary domension
	/// virtually padding missing elements with zeros
	inline ScalarType Ext( const int i ) const
	{
		if(i>=0 && i<2)
			return _v[i];
		else
			return 0;
	}
	/// imports from 2D points of different types
	template <class T>
	inline void Import( const Point2<T> & b )
	{
		_v[0] = ScalarType(b.X());
		_v[1] = ScalarType(b.Y());
	}
	template <class EigenVector>
	inline void FromEigenVector(const EigenVector & b)
	{
		_v[0] = ScalarType(b[0]);
		_v[1] = ScalarType(b[1]);
	}
	template <class EigenVector>
	inline void ToEigenVector(EigenVector & b) const
	{
		b[0]=_v[0];
		b[1]=_v[1];
	}
	template <class EigenVector>
	inline EigenVector ToEigenVector(void) const
	{
		assert(EigenVector::RowsAtCompileTime == 2);
		EigenVector b;
		b << _v[0], _v[1];
		return b;
	}
	/// constructs a 2D points from an existing one of different type
	template <class T>
	static Point2 Construct( const Point2<T> & b )
	{
		return Point2(ScalarType(b.X()), ScalarType(b.Y()));
	}
	static Point2 Construct( const Point2<ScalarType> & b )
	{
		return b;
	}
	template <class T>
	static Point2 Construct( const T & x, const T & y)
	{
		return Point2(ScalarType(x), ScalarType(y));
	}

	static inline Point2 Zero(void)
	{
		return Point2(0,0);
	}

	static inline Point2 One(void)
	{
		return Point2(1,1);
	}
}; // end class definition


template <class T>
inline T Angle( Point2<T> const & p0, Point2<T> const & p1 )
{
	return p1.Angle() - p0.Angle();
}

template <class T>
inline Point2<T> operator * ( const T s, Point2<T> const & p )
{
	return Point2<T>( p[0] * s, p[1] * s );
}

template <class T>
inline T Norm( Point2<T> const & p )
{
	return p.Norm();
}

template <class T>
inline T SquaredNorm( Point2<T> const & p )
{
	return p.SquaredNorm();
}

template <class T>
inline Point2<T> & Normalize( Point2<T> & p )
{
	return p.Normalize();
}

template <typename Scalar>
inline Point2<Scalar> Normalized(const Point2<Scalar> & p )
{
	return p.normalized();
}

template <class T>
inline T Distance( Point2<T> const & p1,Point2<T> const & p2 )
{
	return Norm(p1-p2);
}

template <class T>
inline T SquaredDistance( Point2<T> const & p1,Point2<T> const & p2 )
{
	return SquaredNorm(p1-p2);
}

template <class T>
inline Point2<T> Abs(const Point2<T> & p)
{
	return (Point2<T>(math::Abs(p[0]), math::Abs(p[1])));
}

typedef Point2<short>  Point2s;
typedef Point2<int>	   Point2i;
typedef Point2<float>  Point2f;
typedef Point2<double> Point2d;

/*@}*/
} // end namespace
#endif
