///////////////////////////////////////////////////////////////////////////

//

// Copyright (c) 2004-2012, Industrial Light & Magic, a division of Lucas

// Digital Ltd. LLC

// 

// All rights reserved.

// 

// Redistribution and use in source and binary forms, with or without

// modification, are permitted provided that the following conditions are

// met:

// *       Redistributions of source code must retain the above copyright

// notice, this list of conditions and the following disclaimer.

// *       Redistributions in binary form must reproduce the above

// copyright notice, this list of conditions and the following disclaimer

// in the documentation and/or other materials provided with the

// distribution.

// *       Neither the name of Industrial Light & Magic nor the names of

// its contributors may be used to endorse or promote products derived

// from this software without specific prior written permission. 

// 

// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS

// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT

// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR

// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT

// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,

// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT

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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

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///////////////////////////////////////////////////////////////////////////

#ifndef INCLUDED_IMATHVEC_H

#define INCLUDED_IMATHVEC_H

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

//

//	2D, 3D and 4D point/vector class templates

//

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

#include "ImathExc.h"

#include "ImathLimits.h"

#include "ImathMath.h"

#include "ImathNamespace.h"

#include <iostream>

#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER

// suppress exception specification warnings

#pragma warning(push)

#pragma warning(disable:4290)

#endif

IMATH_INTERNAL_NAMESPACE_HEADER_ENTER

template <class T> class Vec2;

template <class T> class Vec3;

template <class T> class Vec4;

enum InfException {INF_EXCEPTION};

template <class T> class Vec2

{

  public:

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

    // Access to elements

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

    T			x, y;

    T &			operator [] (int i);

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

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

    // Constructors

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

    Vec2 ();                        // no initialization

    explicit Vec2 (T a);            // (a a)

    Vec2 (T a, T b);                // (a b)

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

    // Copy constructors and assignment

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

    Vec2 (const Vec2 &v);

    template <class S> Vec2 (const Vec2<S> &v);

    const Vec2 &	operator = (const Vec2 &v);

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

    // Compatibility with Sb

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

    template <class S>

    void		setValue (S a, S b);

    template <class S>

    void		setValue (const Vec2<S> &v);

    template <class S>

    void		getValue (S &a, S &b) const;

    template <class S>

    void		getValue (Vec2<S> &v) const;

    T *			getValue ();

    const T *		getValue () const;

    //---------

    // Equality

    //---------

    template <class S>

    bool		operator == (const Vec2<S> &v) const;

    template <class S>

    bool		operator != (const Vec2<S> &v) const;

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

    // Compare two vectors and test if they are "approximately equal":

    //

    // equalWithAbsError (v, e)

    //

    //	    Returns true if the coefficients of this and v are the same with

    //	    an absolute error of no more than e, i.e., for all i

    //

    //      abs (this[i] - v[i]) <= e

    //

    // equalWithRelError (v, e)

    //

    //	    Returns true if the coefficients of this and v are the same with

    //	    a relative error of no more than e, i.e., for all i

    //

    //      abs (this[i] - v[i]) <= e * abs (this[i])

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

    bool		equalWithAbsError (const Vec2<T> &v, T e) const;

    bool		equalWithRelError (const Vec2<T> &v, T e) const;

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

    // Dot product

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

    T			dot (const Vec2 &v) const;

    T			operator ^ (const Vec2 &v) const;

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

    // Right-handed cross product, i.e. z component of

    // Vec3 (this->x, this->y, 0) % Vec3 (v.x, v.y, 0)

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

    T			cross (const Vec2 &v) const;

    T			operator % (const Vec2 &v) const;

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

    // Component-wise addition

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

    const Vec2 &	operator += (const Vec2 &v);

    Vec2		operator + (const Vec2 &v) const;

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

    // Component-wise subtraction

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

    const Vec2 &	operator -= (const Vec2 &v);

    Vec2		operator - (const Vec2 &v) const;

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

    // Component-wise multiplication by -1

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

    Vec2		operator - () const;

    const Vec2 &	negate ();

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

    // Component-wise multiplication

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

    const Vec2 &	operator *= (const Vec2 &v);

    const Vec2 &	operator *= (T a);

    Vec2		operator * (const Vec2 &v) const;

    Vec2		operator * (T a) const;

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

    // Component-wise division

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

    const Vec2 &	operator /= (const Vec2 &v);

    const Vec2 &	operator /= (T a);

    Vec2		operator / (const Vec2 &v) const;

    Vec2		operator / (T a) const;

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

    // Length and normalization:  If v.length() is 0.0, v.normalize()

    // and v.normalized() produce a null vector; v.normalizeExc() and

    // v.normalizedExc() throw a NullVecExc.

    // v.normalizeNonNull() and v.normalizedNonNull() are slightly

    // faster than the other normalization routines, but if v.length()

    // is 0.0, the result is undefined.

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

    T			length () const;

    T			length2 () const;

    const Vec2 &	normalize ();           // modifies *this

    const Vec2 &	normalizeExc () throw (IEX_NAMESPACE::MathExc);

    const Vec2 &	normalizeNonNull ();

    Vec2<T>		normalized () const;	// does not modify *this

    Vec2<T>		normalizedExc () const throw (IEX_NAMESPACE::MathExc);

    Vec2<T>		normalizedNonNull () const;

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

    // Number of dimensions, i.e. number of elements in a Vec2

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

    static unsigned int	dimensions() {return 2;}

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

    // Limitations of type T (see also class limits<T>)

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

    static T		baseTypeMin()		{return limits<T>::min();}

    static T		baseTypeMax()		{return limits<T>::max();}

    static T		baseTypeSmallest()	{return limits<T>::smallest();}

    static T		baseTypeEpsilon()	{return limits<T>::epsilon();}

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

    // Base type -- in templates, which accept a parameter, V, which

    // could be either a Vec2<T>, a Vec3<T>, or a Vec4<T> you can 

    // refer to T as V::BaseType

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

    typedef T		BaseType;

  private:

    T			lengthTiny () const;

};

template <class T> class Vec3

{

  public:

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

    // Access to elements

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

    T			x, y, z;

    T &			operator [] (int i);

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

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

    // Constructors

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

    Vec3 ();			   // no initialization

    explicit Vec3 (T a);           // (a a a)

    Vec3 (T a, T b, T c);	   // (a b c)

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

    // Copy constructors and assignment

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

    Vec3 (const Vec3 &v);

    template <class S> Vec3 (const Vec3<S> &v);

    const Vec3 &	operator = (const Vec3 &v);

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

    // Vec4 to Vec3 conversion, divides x, y and z by w:

    //

    // The one-argument conversion function divides by w even

    // if w is zero.  The result depends on how the environment

    // handles floating-point exceptions.

    //

    // The two-argument version thows an InfPointExc exception

    // if w is zero or if division by w would overflow.

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

    template <class S> explicit Vec3 (const Vec4<S> &v);

    template <class S> explicit Vec3 (const Vec4<S> &v, InfException);

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

    // Compatibility with Sb

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

    template <class S>

    void		setValue (S a, S b, S c);

    template <class S>

    void		setValue (const Vec3<S> &v);

    template <class S>

    void		getValue (S &a, S &b, S &c) const;

    template <class S>

    void		getValue (Vec3<S> &v) const;

    T *			getValue();

    const T *		getValue() const;

    //---------

    // Equality

    //---------

    template <class S>

    bool		operator == (const Vec3<S> &v) const;

    template <class S>

    bool		operator != (const Vec3<S> &v) const;

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

    // Compare two vectors and test if they are "approximately equal":

    //

    // equalWithAbsError (v, e)

    //

    //	    Returns true if the coefficients of this and v are the same with

    //	    an absolute error of no more than e, i.e., for all i

    //

    //      abs (this[i] - v[i]) <= e

    //

    // equalWithRelError (v, e)

    //

    //	    Returns true if the coefficients of this and v are the same with

    //	    a relative error of no more than e, i.e., for all i

    //

    //      abs (this[i] - v[i]) <= e * abs (this[i])

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

    bool		equalWithAbsError (const Vec3<T> &v, T e) const;

    bool		equalWithRelError (const Vec3<T> &v, T e) const;

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

    // Dot product

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

    T			dot (const Vec3 &v) const;

    T			operator ^ (const Vec3 &v) const;

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

    // Right-handed cross product

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

    Vec3		cross (const Vec3 &v) const;

    const Vec3 &	operator %= (const Vec3 &v);

    Vec3		operator % (const Vec3 &v) const;

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

    // Component-wise addition

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

    const Vec3 &	operator += (const Vec3 &v);

    Vec3		operator + (const Vec3 &v) const;

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

    // Component-wise subtraction

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

    const Vec3 &	operator -= (const Vec3 &v);

    Vec3		operator - (const Vec3 &v) const;

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

    // Component-wise multiplication by -1

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

    Vec3		operator - () const;

    const Vec3 &	negate ();

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

    // Component-wise multiplication

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

    const Vec3 &	operator *= (const Vec3 &v);

    const Vec3 &	operator *= (T a);

    Vec3		operator * (const Vec3 &v) const;

    Vec3		operator * (T a) const;

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

    // Component-wise division

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

    const Vec3 &	operator /= (const Vec3 &v);

    const Vec3 &	operator /= (T a);

    Vec3		operator / (const Vec3 &v) const;

    Vec3		operator / (T a) const;

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

    // Length and normalization:  If v.length() is 0.0, v.normalize()

    // and v.normalized() produce a null vector; v.normalizeExc() and

    // v.normalizedExc() throw a NullVecExc.

    // v.normalizeNonNull() and v.normalizedNonNull() are slightly

    // faster than the other normalization routines, but if v.length()

    // is 0.0, the result is undefined.

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

    T			length () const;

    T			length2 () const;

    const Vec3 &	normalize ();           // modifies *this

    const Vec3 &	normalizeExc () throw (IEX_NAMESPACE::MathExc);

    const Vec3 &	normalizeNonNull ();

    Vec3<T>		normalized () const;	// does not modify *this

    Vec3<T>		normalizedExc () const throw (IEX_NAMESPACE::MathExc);

    Vec3<T>		normalizedNonNull () const;

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

    // Number of dimensions, i.e. number of elements in a Vec3

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

    static unsigned int	dimensions() {return 3;}

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

    // Limitations of type T (see also class limits<T>)

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

    static T		baseTypeMin()		{return limits<T>::min();}

    static T		baseTypeMax()		{return limits<T>::max();}

    static T		baseTypeSmallest()	{return limits<T>::smallest();}

    static T		baseTypeEpsilon()	{return limits<T>::epsilon();}

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

    // Base type -- in templates, which accept a parameter, V, which

    // could be either a Vec2<T>, a Vec3<T>, or a Vec4<T> you can 

    // refer to T as V::BaseType

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

    typedef T		BaseType;

  private:

    T			lengthTiny () const;

};

template <class T> class Vec4

{

  public:

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

    // Access to elements

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

    T               x, y, z, w; 

    T &             operator [] (int i);

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

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

    // Constructors

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

    Vec4 ();			   // no initialization

    explicit Vec4 (T a);           // (a a a a)

    Vec4 (T a, T b, T c, T d);	   // (a b c d)

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

    // Copy constructors and assignment

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

    Vec4 (const Vec4 &v);

    template <class S> Vec4 (const Vec4<S> &v);

    const Vec4 &    operator = (const Vec4 &v);

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

    // Vec3 to Vec4 conversion, sets w to 1

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

    template <class S> explicit Vec4 (const Vec3<S> &v);

    //---------

    // Equality

    //---------

    template <class S>

    bool            operator == (const Vec4<S> &v) const;

    template <class S>

    bool            operator != (const Vec4<S> &v) const;

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

    // Compare two vectors and test if they are "approximately equal":

    //

    // equalWithAbsError (v, e)

    //

    //	    Returns true if the coefficients of this and v are the same with

    //	    an absolute error of no more than e, i.e., for all i

    //

    //      abs (this[i] - v[i]) <= e

    //

    // equalWithRelError (v, e)

    //

    //	    Returns true if the coefficients of this and v are the same with

    //	    a relative error of no more than e, i.e., for all i

    //

    //      abs (this[i] - v[i]) <= e * abs (this[i])

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

    bool		equalWithAbsError (const Vec4<T> &v, T e) const;

    bool		equalWithRelError (const Vec4<T> &v, T e) const;

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

    // Dot product

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

    T			dot (const Vec4 &v) const;

    T			operator ^ (const Vec4 &v) const;

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

    // Cross product is not defined in 4D

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

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

    // Component-wise addition

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

    const Vec4 &    operator += (const Vec4 &v);

    Vec4            operator + (const Vec4 &v) const;

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

    // Component-wise subtraction

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

    const Vec4 &    operator -= (const Vec4 &v);

    Vec4            operator - (const Vec4 &v) const;

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

    // Component-wise multiplication by -1

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

    Vec4            operator - () const;

    const Vec4 &    negate ();

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

    // Component-wise multiplication

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

    const Vec4 &    operator *= (const Vec4 &v);

    const Vec4 &    operator *= (T a);

    Vec4            operator * (const Vec4 &v) const;

    Vec4            operator * (T a) const;

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

    // Component-wise division

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

    const Vec4 &    operator /= (const Vec4 &v);

    const Vec4 &    operator /= (T a);

    Vec4            operator / (const Vec4 &v) const;

    Vec4            operator / (T a) const;

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

    // Length and normalization:  If v.length() is 0.0, v.normalize()

    // and v.normalized() produce a null vector; v.normalizeExc() and

    // v.normalizedExc() throw a NullVecExc.

    // v.normalizeNonNull() and v.normalizedNonNull() are slightly

    // faster than the other normalization routines, but if v.length()

    // is 0.0, the result is undefined.

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

    T               length () const;

    T               length2 () const;

    const Vec4 &    normalize ();           // modifies *this

    const Vec4 &    normalizeExc () throw (IEX_NAMESPACE::MathExc);

    const Vec4 &    normalizeNonNull ();

    Vec4<T>         normalized () const;	// does not modify *this

    Vec4<T>         normalizedExc () const throw (IEX_NAMESPACE::MathExc);

    Vec4<T>         normalizedNonNull () const;

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

    // Number of dimensions, i.e. number of elements in a Vec4

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

    static unsigned int	dimensions() {return 4;}

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

    // Limitations of type T (see also class limits<T>)

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

    static T		baseTypeMin()		{return limits<T>::min();}

    static T		baseTypeMax()		{return limits<T>::max();}

    static T		baseTypeSmallest()	{return limits<T>::smallest();}

    static T		baseTypeEpsilon()	{return limits<T>::epsilon();}

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

    // Base type -- in templates, which accept a parameter, V, which

    // could be either a Vec2<T>, a Vec3<T>, or a Vec4<T> you can 

    // refer to T as V::BaseType

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

    typedef T		BaseType;

  private:

    T			lengthTiny () const;

};

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

// Stream output

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

template <class T>

std::ostream &	operator << (std::ostream &s, const Vec2<T> &v);

template <class T>

std::ostream &	operator << (std::ostream &s, const Vec3<T> &v);

template <class T>

std::ostream &	operator << (std::ostream &s, const Vec4<T> &v);

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

// Reverse multiplication: S * Vec2<T> and S * Vec3<T>

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

template <class T> Vec2<T>	operator * (T a, const Vec2<T> &v);

template <class T> Vec3<T>	operator * (T a, const Vec3<T> &v);

template <class T> Vec4<T>	operator * (T a, const Vec4<T> &v);

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

// Typedefs for convenience

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

typedef Vec2 <short>  V2s;

typedef Vec2 <int>    V2i;

typedef Vec2 <float>  V2f;

typedef Vec2 <double> V2d;

typedef Vec3 <short>  V3s;

typedef Vec3 <int>    V3i;

typedef Vec3 <float>  V3f;

typedef Vec3 <double> V3d;

typedef Vec4 <short>  V4s;

typedef Vec4 <int>    V4i;

typedef Vec4 <float>  V4f;

typedef Vec4 <double> V4d;

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

// Specializations for VecN<short>, VecN<int>

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

// Vec2<short>

template <> short

Vec2<short>::length () const;

template <> const Vec2<short> &

Vec2<short>::normalize ();

template <> const Vec2<short> &

Vec2<short>::normalizeExc () throw (IEX_NAMESPACE::MathExc);

template <> const Vec2<short> &

Vec2<short>::normalizeNonNull ();

template <> Vec2<short>

Vec2<short>::normalized () const;

template <> Vec2<short>

Vec2<short>::normalizedExc () const throw (IEX_NAMESPACE::MathExc);

template <> Vec2<short>

Vec2<short>::normalizedNonNull () const;

// Vec2<int>

template <> int

Vec2<int>::length () const;

template <> const Vec2<int> &

Vec2<int>::normalize ();

template <> const Vec2<int> &

Vec2<int>::normalizeExc () throw (IEX_NAMESPACE::MathExc);

template <> const Vec2<int> &

Vec2<int>::normalizeNonNull ();

template <> Vec2<int>

Vec2<int>::normalized () const;

template <> Vec2<int>

Vec2<int>::normalizedExc () const throw (IEX_NAMESPACE::MathExc);

template <> Vec2<int>

Vec2<int>::normalizedNonNull () const;

// Vec3<short>

template <> short

Vec3<short>::length () const;

template <> const Vec3<short> &

Vec3<short>::normalize ();

template <> const Vec3<short> &

Vec3<short>::normalizeExc () throw (IEX_NAMESPACE::MathExc);

template <> const Vec3<short> &

Vec3<short>::normalizeNonNull ();

template <> Vec3<short>

Vec3<short>::normalized () const;

template <> Vec3<short>

Vec3<short>::normalizedExc () const throw (IEX_NAMESPACE::MathExc);

template <> Vec3<short>

Vec3<short>::normalizedNonNull () const;

// Vec3<int>

template <> int

Vec3<int>::length () const;

template <> const Vec3<int> &

Vec3<int>::normalize ();

template <> const Vec3<int> &

Vec3<int>::normalizeExc () throw (IEX_NAMESPACE::MathExc);

template <> const Vec3<int> &

Vec3<int>::normalizeNonNull ();

template <> Vec3<int>

Vec3<int>::normalized () const;

template <> Vec3<int>

Vec3<int>::normalizedExc () const throw (IEX_NAMESPACE::MathExc);

template <> Vec3<int>

Vec3<int>::normalizedNonNull () const;

// Vec4<short>

template <> short

Vec4<short>::length () const;

template <> const Vec4<short> &

Vec4<short>::normalize ();

template <> const Vec4<short> &

Vec4<short>::normalizeExc () throw (IEX_NAMESPACE::MathExc);

template <> const Vec4<short> &

Vec4<short>::normalizeNonNull ();

template <> Vec4<short>

Vec4<short>::normalized () const;

template <> Vec4<short>

Vec4<short>::normalizedExc () const throw (IEX_NAMESPACE::MathExc);

template <> Vec4<short>

Vec4<short>::normalizedNonNull () const;

// Vec4<int>

template <> int

Vec4<int>::length () const;

template <> const Vec4<int> &

Vec4<int>::normalize ();

template <> const Vec4<int> &

Vec4<int>::normalizeExc () throw (IEX_NAMESPACE::MathExc);

template <> const Vec4<int> &

Vec4<int>::normalizeNonNull ();

template <> Vec4<int>

Vec4<int>::normalized () const;

template <> Vec4<int>

Vec4<int>::normalizedExc () const throw (IEX_NAMESPACE::MathExc);

template <> Vec4<int>

Vec4<int>::normalizedNonNull () const;

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

// Implementation of Vec2:

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

template <class T>

inline T &

Vec2<T>::operator [] (int i)

{

    return (&x)[i];

}

template <class T>

inline const T &

Vec2<T>::operator [] (int i) const

{

    return (&x)[i];

}

template <class T>

inline

Vec2<T>::Vec2 ()

{

    // empty

}

template <class T>

inline

Vec2<T>::Vec2 (T a)

{

    x = y = a;

}

template <class T>