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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>() {memset(this, 0, sizeof(*this));}

        // 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();        }

        // 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);  }

};

typedef Vector3<int>                    Vector3i;
typedef Vector3<unsigned int>   Vector3ui;
typedef Vector3<long>                   Vector3l;
typedef Vector3<unsigned long>  Vector3ul;
typedef Vector3<float>                  Vector3f;

#endif // VECTOR3_H