// -*- 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;

    // cross product
    Vector3<T> operator         %(const Vector3<T> &v) const;

    // gets the length of this vector squared
    T                           length_squared() const
    {
        return (T)(*this * *this);
    }

    // gets the length of this vector
    float           length(void) const;

    // 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 this vector and another vector
    T        angle(const Vector3<T> &v2)
    {
        return (T)acosf(((*this)*v2) / (this->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