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/*******************************************************************************
 * CGoGN: Combinatorial and Geometric modeling with Generic N-dimensional Maps  *
 * version 0.1                                                                  *
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 * Copyright (C) 2009-2012, IGG Team, LSIIT, University of Strasbourg           *
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 *                                                                              *
 * This library is free software; you can redistribute it and/or modify it      *
 * under the terms of the GNU Lesser General Public License as published by the *
 * Free Software Foundation; either version 2.1 of the License, or (at your     *
 * option) any later version.                                                   *
 *                                                                              *
 * This library 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 Lesser General Public License  *
 * for more details.                                                            *
 *                                                                              *
 * You should have received a copy of the GNU Lesser General Public License     *
 * along with this library; if not, write to the Free Software Foundation,      *
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301 USA.           *
 *                                                                              *
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 * Web site: http://cgogn.unistra.fr/                                           *
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 * Contact information: cgogn@unistra.fr                                        *
 *                                                                              *
 *******************************************************************************/

#ifndef __VECTOR_GEN__
#define __VECTOR_GEN__

#include <cassert>
#include <iostream>
#include <math.h>
#include <string.h>

#include "Utils/static_assert.h"
#include "Utils/nameTypes.h"

namespace CGoGN
{

namespace Geom
{

/*
 * Class for the representation of vectors
 */
template <unsigned int DIM, typename T>
class Vector
{
public:
	typedef T DATA_TYPE ;
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	enum
	{
		DIMENSION = DIM
	} ;
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	static std::string CGoGNnameOfType() ;

	/**********************************************/
	/*                CONSTRUCTORS                */
	/**********************************************/

	Vector() ;

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	Vector(const Vector<DIM, T>& v) ;
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	template <typename T2>
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	Vector(const Vector<DIM, T2>& v) ;
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	Vector(T x, T y) ;

	Vector(T x, T y, T z) ;

	Vector(T x, T y, T z, T w) ;

	/**
	 * constructor that initialize all component to a given value
	 * @param x the value to assign to all component
	 */
	Vector(T x) ;

	void set(T a) ;

	void zero() ;

	/**********************************************/
	/*                 ACCESSORS                  */
	/**********************************************/

	T& operator[](unsigned int index) ;

	const T& operator[](unsigned int index) const ;

	unsigned int dimension() const ;

	T* data() ;

	const T* data() const ;

	/**********************************************/
	/*         ARITHMETIC SELF-OPERATORS          */
	/**********************************************/

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	Vector<DIM, T>& operator+=(const Vector<DIM, T>& v) ;
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	Vector<DIM, T>& operator-=(const Vector<DIM, T>& v) ;
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	Vector<DIM, T>& operator*=(T a) ;
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	Vector<DIM, T>& operator/=(T a) ;
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	/**********************************************/
	/*            ARITHMETIC OPERATORS            */
	/**********************************************/

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	Vector<DIM, T> operator+(const Vector<DIM, T>& v) const ;
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	Vector<DIM, T> operator-(const Vector<DIM, T>& v) const ;
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	Vector<DIM, T> operator*(T a) const ;
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	Vector<DIM, T> operator/(T a) const ;
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	/**********************************************/
	/*             UTILITY FUNCTIONS              */
	/**********************************************/

	T norm2() const ;

	double norm() const ;

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	/*
	 * normalize the vector and returns its norm
	 */
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	double normalize() ;

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	/*
	 * Return a normalized copy
	 */
	Vector<DIM, T> normalized() const;

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	// dot product
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	T operator*(const Vector<DIM, T> v) const ;
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	// cross product
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	Vector<DIM, T> operator^(const Vector<DIM, T> v) const ;
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	// Equal
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	bool operator==(const Vector<DIM, T>& v) const ;
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	// Different
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	bool operator!=(const Vector<DIM, T>& v) const ;
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	bool hasNan() const ;

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	bool isFinite() const ;
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	/**
	 * Tests if the vector is normalized
	 * @param epsilon tolerated error
	 * @return true if the given vector has a unit norm +/- epsilon
	 */
	bool isNormalized(const T& epsilon) const ;

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	/**
	 * Tests if current and given vectors are near within 1/precision (equal if precision is zero)
	 * @param V a vector
	 * @param epsilon tolerated error
	 * @return true if orthogonal
	 */
	bool isNear(const Vector<DIM, T>& v, int precision) const ;

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	/**
	 * Tests if current and given vectors are orthogonal
	 * @param V a vector
	 * @param epsilon tolerated error
	 * @return true if orthogonal
	 */
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	bool isOrthogonal(const Vector<DIM, T>& v, const T& epsilon = 1e-5) const ;
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	/**********************************************/
	/*             STREAM OPERATORS               */
	/**********************************************/

	template <unsigned int DD, typename TT>
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	friend std::ostream& operator<<(std::ostream& out, const Vector<DD, TT>& v) ;
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	template <unsigned int DD, typename TT>
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	friend std::istream& operator>>(std::istream& in, Vector<DD, TT>& v) ;
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private:
	T m_data[DIM] ;
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} ;
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/***
 * Test if x is null within precision.
 * Two cases are possible :
 *  - precision == 0 : x is null if (x == 0)
 *  - precision > 0 : x is null if (|x| < 1/precision) or (precision * |x| < 1)
 */
template <typename T>
bool isNull(T x, int precision = 0) ;

/***
 * Test if the square root of x is null within precision.
 * In other words, test if x is null within precision*precision
 */
template <typename T>
bool isNull2(T x, int precision = 0) ;

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template <unsigned int DIM, typename T>
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Vector<DIM, T> operator*(T a, const Vector<DIM, T>& v) ;
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template <unsigned int DIM, typename T>
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Vector<DIM, T> operator/(T a, const Vector<DIM, T>& v) ;
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// returns the signed volume of the parallelepiped spanned by vectors v1, v2 and v3
template <unsigned int DIM, typename T>
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T tripleProduct(const Vector<DIM, T>& v1, const Vector<DIM, T>& v2, const Vector<DIM, T>& v3) ;
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// returns a spherical interpolation of two vectors considering parameter t ((0 <= t <= 1) => result between v1 and v2)
template <unsigned int DIM, typename T>
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Vector<DIM, T> slerp(const Vector<DIM, T> &v1, const Vector<DIM, T> &v2, const T &t) ;
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/**********************************************/
/*           SOME USEFUL TYPEDEFS             */
/**********************************************/

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typedef Vector<2, float> Vec2f ;
typedef Vector<2, double> Vec2d ;
typedef Vector<2, unsigned int> Vec2ui ;
typedef Vector<2, int> Vec2i ;
typedef Vector<2, unsigned char> Vec2uc ;

typedef Vector<3, float> Vec3f ;
typedef Vector<3, double> Vec3d ;
typedef Vector<3, unsigned int> Vec3ui ;
typedef Vector<3, int> Vec3i ;
typedef Vector<3, unsigned char> Vec3uc ;

typedef Vector<4, float> Vec4f ;
typedef Vector<4, double> Vec4d ;
typedef Vector<4, unsigned int> Vec4ui ;
typedef Vector<4, int> Vec4i ;
typedef Vector<4, unsigned char> Vec4uc ;
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}

}

#include "vector_gen.hpp"

#endif