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// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: t -*-

// Copyright 2010 Michael Smith, all rights reserved.

//      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.

// Derived closely from:

/****************************************

 * 3D Vector Classes

 * By Bill Perone (billperone@yahoo.com)

 * Original: 9-16-2002

 * Revised: 19-11-2003

 *          11-12-2003

 *          18-12-2003

 *          06-06-2004

 *

 * © 2003, This code is provided "as is" and you can use it freely as long as

 * credit is given to Bill Perone in the application it is used in

 *

 * Notes:

 * if a*b = 0 then a & b are orthogonal

 * a%b = -b%a

 * a*(b%c) = (a%b)*c

 * a%b = a(cast to matrix)*b

 * (a%b).length() = area of parallelogram formed by a & b

 * (a%b).length() = a.length()*b.length() * sin(angle between a & b)

 * (a%b).length() = 0 if angle between a & b = 0 or a.length() = 0 or b.length() = 0

 * a * (b%c) = volume of parallelpiped formed by a, b, c

 * vector triple product: a%(b%c) = b*(a*c) - c*(a*b)

 * scalar triple product: a*(b%c) = c*(a%b) = b*(c%a)

 * vector quadruple product: (a%b)*(c%d) = (a*c)*(b*d) - (a*d)*(b*c)

 * if a is unit vector along b then a%b = -b%a = -b(cast to matrix)*a = 0

 * vectors a1...an are linearly dependant if there exists a vector of scalars (b) where a1*b1 + ... + an*bn = 0

 *           or if the matrix (A) * b = 0

 *

 ****************************************/

#ifndef VECTOR3_H

#define VECTOR3_H

#include <math.h>

#include <string.h>

template <typename T>

class Vector3

{

public:

        T x, y, z;

        // trivial ctor

        Vector3<T>() { x = y = z = 0; }

        // setting ctor

        Vector3<T>(const T x0, const T y0, const T z0): x(x0), y(y0), z(z0) {}

        // function call operator

        void operator ()(const T x0, const T y0, const T z0)

        {       x= x0; y= y0; z= z0;  }

        // test for equality

        bool operator==(const Vector3<T> &v)

        {       return (x==v.x && y==v.y && z==v.z);    }

        // test for inequality

        bool operator!=(const Vector3<T> &v)

        {       return (x!=v.x || y!=v.y || z!=v.z);    }

        // negation

        Vector3<T> operator -(void) const

        {       return Vector3<T>(-x,-y,-z);    }

        // addition

        Vector3<T> operator +(const Vector3<T> &v) const

        {   return Vector3<T>(x+v.x, y+v.y, z+v.z);      }

        // subtraction

        Vector3<T> operator -(const Vector3<T> &v) const

        {   return Vector3<T>(x-v.x, y-v.y, z-v.z);      }

        // uniform scaling

        Vector3<T> operator *(const T num) const

        {

                Vector3<T> temp(*this);

                return temp*=num;

        }

        // uniform scaling

        Vector3<T> operator /(const T num) const

        {

                Vector3<T> temp(*this);

                return temp/=num;

        }

        // addition

        Vector3<T> &operator +=(const Vector3<T> &v)

        {

                x+=v.x; y+=v.y; z+=v.z;

                return *this;

        }

        // subtraction

        Vector3<T> &operator -=(const Vector3<T> &v)

        {

                x-=v.x; y-=v.y; z-=v.z;

                return *this;

        }

        // uniform scaling

        Vector3<T> &operator *=(const T num)

        {

                x*=num; y*=num; z*=num;

                return *this;

        }

        // uniform scaling

        Vector3<T> &operator /=(const T num)

        {

                x/=num; y/=num; z/=num;

                return *this;

        }

        // dot product

        T operator *(const Vector3<T> &v) const

        {       return x*v.x + y*v.y + z*v.z;   }

        // cross product

        Vector3<T> operator %(const Vector3<T> &v) const

        {

                Vector3<T> temp(y*v.z - z*v.y, z*v.x - x*v.z, x*v.y - y*v.x);

                return temp;

        }

        // gets the length of this vector squared

        T length_squared() const

        {       return (T)(*this * *this);   }

        // gets the length of this vector

        float length() const

        {       return (T)sqrt(*this * *this);   }

        // normalizes this vector

        void normalize()

        {       *this/=length();        }

        // zero the vector

        void zero()

        {       x = y = z = 0.0; }

        // returns the normalized version of this vector

        Vector3<T> normalized() const

        {   return  *this/length();  }

        // reflects this vector about n

        void reflect(const Vector3<T> &n)

        {

                Vector3<T> orig(*this);

                project(n);

                *this= *this*2 - orig;

        }

        // projects this vector onto v

        void project(const Vector3<T> &v)

        {       *this= v * (*this * v)/(v*v);   }

        // returns this vector projected onto v

        Vector3<T> projected(const Vector3<T> &v)

        {   return v * (*this * v)/(v*v);       }

        // computes the angle between 2 arbitrary vectors

        T angle(const Vector3<T> &v1, const Vector3<T> &v2)

        {   return (T)acosf((v1*v2) / (v1.length()*v2.length()));  }

        // computes the angle between 2 arbitrary normalized vectors

        T angle_normalized(const Vector3<T> &v1, const Vector3<T> &v2)

        {   return (T)acosf(v1*v2);  }

        // check if any elements are NAN

        bool is_nan(void)

                {   return isnan(x) || isnan(y) || isnan(z); }

        // check if any elements are infinity

        bool is_inf(void)

                {   return isinf(x) || isinf(y) || isinf(z); }

        // rotate by a standard rotation

        void rotate(enum Rotation rotation);

};

typedef Vector3<int16_t>                Vector3i;

typedef Vector3<uint16_t>               Vector3ui;

typedef Vector3<int32_t>                Vector3l;

typedef Vector3<uint32_t>               Vector3ul;

typedef Vector3<float>                  Vector3f;

#endif // VECTOR3_H