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/* ----------------------------------------------------------------------- *

 * This file is part of GEL, http://www.imm.dtu.dk/GEL

 * Copyright (C) the authors and DTU Informatics

 * For license and list of authors, see ../../doc/intro.pdf

 * @brief Abstract vector class

 * ----------------------------------------------------------------------- */

/** @file ArithVec.h

 * @brief Abstract vector class

 */

#ifndef __CGLA_ARITHVEC_H__

#define __CGLA_ARITHVEC_H__

#include <array>

#include <algorithm>

#include <iostream>

#include "CGLA.h"

#include <numeric>

namespace CGLA

{

    /** \brief Template representing generic arithmetic vectors.

     The three parameters to the template are

     T - the scalar type (i.e. float, int, double etc.)

     V - the name of the vector type. This template is always (and

     only) used as ancestor of concrete types, and the name of the

     class _inheriting_ _from_ this class is used as the V argument.

     N - The final argument is the dimension N. For instance, N=3 for a

     3D vector.

     This class template contains all functions that are assumed to be

     the same for any arithmetic vector - regardless of dimension or

     the type of scalars used for coordinates.

     The template contains no virtual functions which is important

     since they add overhead.

     */

    template <class T, class V, unsigned int N>

    class ArithVec

    {

    protected:

        /// The actual contents of the vector.

        std::array<T,N> data;

    protected:

        //----------------------------------------------------------------------

        // Constructors

        //----------------------------------------------------------------------

        /// Construct uninitialized vector

        ArithVec() {}

        /// Construct a vector where all coordinates are identical

        explicit ArithVec(T _a)

        {

            std::fill_n(data, N, _a);

        }

        /// Construct a 2D vector

        ArithVec(T _a, T _b): data({_a,_b}) {assert(N==2);}

        /// Construct a 2D vector

        ArithVec(T _a, T _b, T _c): data({_a,_b,_c}) {assert(N==3);}

        /// Construct a 2D vector

        ArithVec(T _a, T _b, T _c, T _d): data({_a,_b,_c,_d}) {assert(N==4);}

    public:

        /// For convenience we define a more meaningful name for the scalar type

        typedef T ScalarType;

        /// A more meaningful name for vector type

        typedef V VectorType;

        /// Return dimension of vector

        static unsigned int get_dim() {return N;}

        /// Set all coordinates of a 2D vector.

        void set(T _a, T _b)

        {

            assert(N==2);

            data = {_a,_b};

        }

        /// Set all coordinates of a 3D vector.

        void set(T _a, T _b, T _c)

        {

            assert(N==3);

            data = {_a,_b,_c};

        }

        /// Set all coordinates of a 4D vector.

        void set(T _a, T _b, T _c, T _d)

        {

            assert(N==4);

            data = {_a,_b,_c,_d};

        }

        /// Const index operator

        const T& operator [] ( unsigned int i ) const

        {

            assert(i<N);

            return data[i];

        }

        /// Non-const index operator

        T& operator [] ( unsigned int i )

        {

            assert(i<N);

            return data[i];

        }

        /// Const index operator

        const T& operator () ( unsigned int i ) const

        {

            assert(i<N);

            return data[i];

        }

        /// Non-const index operator

        T& operator () ( unsigned int i )

        {

            assert(i<N);

            return data[i];

        }

        /** Get a pointer to first element in data array.

         This function may be useful when interfacing with some other API

         such as OpenGL (TM) */

        T* get() {return begin();}

        T* begin() {return data.begin();}

        T* end() {return data.end();}

        /** Get a const pointer to first element in data array.

         This function may be useful when interfacing with some other API

         such as OpenGL (TM). */

        const T* get() const {return data.begin();}

        const T* begin() const {return data.begin();}

        const T* end() const {return data.end();}

        //----------------------------------------------------------------------

        // Comparison operators

        //----------------------------------------------------------------------

        /// Equality operator

        bool operator==(const V& v) const

        {

            return std::equal(begin(),end(), v.begin());

        }

        /// Equality wrt scalar. True if all coords are equal to scalar

        bool operator==(T k) const

        {

            return std::count(begin(),end(), k)==N;

        }

        /// Inequality operator

        bool operator!=(const V& v) const

        {

            return !(*this==v);

        }

        /// Inequality wrt scalar. True if any coord not equal to scalar

        bool operator!=(T k) const

        {

            return !(*this==k);

        }

        //----------------------------------------------------------------------

        // Comparison functions ... of geometric significance

        //----------------------------------------------------------------------

        /** Compare all coordinates against other vector. ( < )

         Similar to testing whether we are on one side of three planes. */

        bool  all_l  (const V& v) const

        {

            return std::inner_product(begin(), end(), v.begin(), true,

                                      std::logical_and<bool>(), std::less<T>());

        }

        /** Compare all coordinates against other vector. ( <= )

         Similar to testing whether we are on one side of three planes. */

        bool  all_le (const V& v) const

        {

            return std::inner_product(begin(), end(), v.begin(), true,

                                      std::logical_and<bool>(), std::less_equal<T>());

        }

        /** Compare all coordinates against other vector. ( > )

         Similar to testing whether we are on one side of three planes. */

        bool  all_g  (const V& v) const

        {

            return std::inner_product(begin(), end(), v.begin(), true,

                                      std::logical_and<bool>(), std::greater<T>());

        }

        /** Compare all coordinates against other vector. ( >= )

         Similar to testing whether we are on one side of three planes. */

        bool  all_ge (const V& v) const

        {

            return std::inner_product(begin(), end(), v.begin(), true,

                                      std::logical_and<bool>(), std::greater_equal<T>());

        }

        //----------------------------------------------------------------------

        // Assignment operators

        //----------------------------------------------------------------------

        /// Assignment multiplication with scalar.

        const V& operator *=(T k)

        {

            std::for_each(begin(), end(), [k](T& x){x*=k;});

            return static_cast<const V&>(*this);

        }

        /// Assignment division with scalar.

        const V& operator /=(T k)

        {

            std::for_each(begin(), end(), [k](T& x){x/=k;});

            return static_cast<const V&>(*this);

        }

        /// Assignment addition with scalar. Adds scalar to each coordinate.

        const V& operator +=(T k)

        {

            std::for_each(begin(), end(), [k](T& x){x+=k;});

            return  static_cast<const V&>(*this);

        }

        /// Assignment subtraction with scalar. Subtracts scalar from each coord.

        const V& operator -=(T k)

        {

            std::for_each(begin(), end(), [k](T& x){x-=k;});

            return  static_cast<const V&>(*this);

        }

        /** Assignment multiplication with vector.

         Multiply each coord independently. */

        const V& operator *=(const V& v)

        {

            std::transform(begin(), end(), v.begin(), begin(), std::multiplies<T>());

            return  static_cast<const V&>(*this);

        }

        /// Assigment division with vector. Each coord divided independently.

        const V& operator /=(const V& v)

        {

            std::transform(begin(), end(),  v.begin(), begin(), std::divides<T>());

            return  static_cast<const V&>(*this);

        }

        /// Assignmment addition with vector.

        const V& operator +=(const V& v)

        {

            std::transform(begin(), end(), v.begin(), begin(), std::plus<T>());

            return  static_cast<const V&>(*this);

        }

        /// Assignment subtraction with vector.

        const V& operator -=(const V& v)

        {

            std::transform(begin(), end(), v.begin(), begin(), std::minus<T>());

            return  static_cast<const V&>(*this);

        }

        //----------------------------------------------------------------------

        // Unary operators on vectors

        //----------------------------------------------------------------------

        /// Negate vector.

        const V operator - () const

        {

            V v_new;

            std::transform(begin(), end(), v_new.begin(), std::negate<T>());

            return v_new;

        }

        //----------------------------------------------------------------------

        // Binary operators on vectors

        //----------------------------------------------------------------------

        /** Multiply vector with vector. Each coord multiplied independently

         Do not confuse this operation with dot product. */

        const V operator * (const V& v1) const

        {

            V v_new;

            std::transform(begin(), end(), v1.begin(), v_new.begin(), std::multiplies<T>());

            return v_new;

        }

        /// Add two vectors

        const V operator + (const V& v1) const

        {

            V v_new;

            std::transform(begin(), end(), v1.begin(), v_new.begin(), std::plus<T>());

            return v_new;

        }

        /// Subtract two vectors.

        const V operator - (const V& v1) const

        {

            V v_new;

            std::transform(begin(), end(), v1.begin(), v_new.begin(), std::minus<T>());

            return v_new;

        }

        /// Divide two vectors. Each coord separately

        const V operator / (const V& v1) const

        {

            V v_new;

            std::transform(begin(), end(), v1.begin(), v_new.begin(), std::divides<T>());

            return v_new;

        }

        //----------------------------------------------------------------------

        // Binary operators on vector and scalar

        //----------------------------------------------------------------------

        /// Multiply scalar onto vector.

        const V operator * (T k) const

        {

            V v_new;

            std::transform(begin(), end(), v_new.begin(), [k](T x){return x*k;});

            return v_new;

        }

        /// Divide vector by scalar.

        const V operator / (T k) const

        {

            V v_new;

            std::transform(begin(), end(), v_new.begin(), [k](T x){return x/k;});

            return v_new;

        }

        /// Return the smallest coordinate of the vector

        const T min_coord() const

        {

            return *std::min_element(begin(), end());

        }

        /// Return the largest coordinate of the vector

        const T max_coord() const

        {

            return *std::max_element(begin(), end());

        }

    };

    template <class T, class V, unsigned int N>

    inline std::ostream& operator<<(std::ostream&os, const ArithVec<T,V,N>& v)

    {

        os << "[ ";

        for(const T& x : v) os << x << " ";

        os << "]";

        return os;

        }

        /// Get from operator for ArithVec descendants.

        template <class T,class V, unsigned int N>

        inline std::istream& operator>>(std::istream&is, ArithVec<T,V,N>& v)

        {

            is >> std::ws;

            if (is.peek() == '[')

                is.ignore();

            is >> std::ws;

            for (int c=0; c<N; ++c)

            {

                is >> v(c) >> std::ws;

            }

            if (is.peek() == ']')

                is.ignore();

            return is;

        }

        /** Dot product for two vectors. The `*' operator is

         reserved for coordinatewise	multiplication of vectors. */

        template <class T,class V, unsigned int N>

        inline T dot(const ArithVec<T,V,N>& v0, const ArithVec<T,V,N>& v1)

        {

            return std::inner_product(v0.begin(), v0.end(), v1.begin(), T(0));

        }

        /** Compute the sqr length by taking dot product of vector with itself. */

        template <class T,class V, unsigned int N>

        inline T sqr_length(const ArithVec<T,V,N>& v)

        {

            return dot(v,v);

        }

        /** Multiply double onto vector. This operator handles the case

         where the vector is on the righ side of the `*'.

         \note It seems to be optimal to put the binary operators inside the

         ArithVec class template, but the operator functions whose

         left operand is _not_ a vector cannot be inside, hence they

         are here.

         We need three operators for scalar * vector although they are

         identical, because, if we use a separate template argument for

         the left operand, it will match any type. If we use just T as

         type for the left operand hoping that other built-in types will

         be automatically converted, we will be disappointed. It seems that

         a float * ArithVec<float,Vec3f,3> function is not found if the

         left operand is really a double.

         */

        template<class T, class V, unsigned int N>

        inline const V operator * (double k, const ArithVec<T,V,N>& v)

        {

            return v * k;

        }

        /** Multiply float onto vector. See the note in the documentation

         regarding multiplication of a double onto a vector. */

        template<class T, class V, unsigned int N>

        inline const V operator * (float k, const ArithVec<T,V,N>& v)

        {

            return v * k;

        }

        /** Multiply unsigned int onto vector. See the note in the documentation

         regarding multiplication of a double onto a vector. */

        template<class T, class V, unsigned int N>

        inline const V operator * (int k, const ArithVec<T,V,N>& v)

        {

            return v * k;

        }

        /** Returns the vector containing for each coordinate the smallest

         value from two vectors. */

        template <class T,class V, unsigned int N>

        inline V v_min(const ArithVec<T,V,N>& v0, const ArithVec<T,V,N>& v1)

        {

            V v;

            std::transform(v0.begin(), v0.end(), v1.begin(), v.begin(),

                           [](T a, T b){return std::min(a,b);});

            return v;

        }

        /** Returns the vector containing for each coordinate the largest

         value from two vectors. */

        template <class T,class V, unsigned int N>

        inline V v_max(const ArithVec<T,V,N>& v0, const ArithVec<T,V,N>& v1)

        {

            V v;

            std::transform(v0.begin(), v0.end(), v1.begin(), v.begin(),

                           [](T a, T b){return std::max(a,b);});

            return v;

        }

}

#endif