///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2004, 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
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
///////////////////////////////////////////////////////////////////////////
#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 <iostream>
#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
// suppress exception specification warnings
#pragma warning(push)
#pragma warning(disable:4290)
#endif
namespace Imath {
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::MathExc);
const Vec2 & normalizeNonNull ();
Vec2<T> normalized () const; // does not modify *this
Vec2<T> normalizedExc () const throw (Iex::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::MathExc);
const Vec3 & normalizeNonNull ();
Vec3<T> normalized () const; // does not modify *this
Vec3<T> normalizedExc () const throw (Iex::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::MathExc);
const Vec4 & normalizeNonNull ();
Vec4<T> normalized () const; // does not modify *this
Vec4<T> normalizedExc () const throw (Iex::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::MathExc);
template <> const Vec2<short> &
Vec2<short>::normalizeNonNull ();
template <> Vec2<short>
Vec2<short>::normalized () const;
template <> Vec2<short>
Vec2<short>::normalizedExc () const throw (Iex::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::MathExc);
template <> const Vec2<int> &
Vec2<int>::normalizeNonNull ();
template <> Vec2<int>
Vec2<int>::normalized () const;
template <> Vec2<int>
Vec2<int>::normalizedExc () const throw (Iex::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::MathExc);
template <> const Vec3<short> &
Vec3<short>::normalizeNonNull ();
template <> Vec3<short>
Vec3<short>::normalized () const;
template <> Vec3<short>
Vec3<short>::normalizedExc () const throw (Iex::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::MathExc);
template <> const Vec3<int> &
Vec3<int>::normalizeNonNull ();
template <> Vec3<int>
Vec3<int>::normalized () const;
template <> Vec3<int>
Vec3<int>::normalizedExc () const throw (Iex::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::MathExc);
template <> const Vec4<short> &
Vec4<short>::normalizeNonNull ();
template <> Vec4<short>
Vec4<short>::normalized () const;
template <> Vec4<short>
Vec4<short>::normalizedExc () const throw (Iex::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::MathExc);
template <> const Vec4<int> &
Vec4<int>::normalizeNonNull ();
template <> Vec4<int>
Vec4<int>::normalized () const;
template <> Vec4<int>
Vec4<int>::normalizedExc () const throw (Iex::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>
inline
Vec2<T>::Vec2 (T a, T b)
{
x = a;
y = b;
}
template <class T>
inline
Vec2<T>::Vec2 (const Vec2 &v)
{
x = v.x;
y = v.y;
}
template <class T>
template <class S>
inline
Vec2<T>::Vec2 (const Vec2<S> &v)
{
x = T (v.x);
y = T (v.y);
}
template <class T>
inline const Vec2<T> &
Vec2<T>::operator = (const Vec2 &v)
{
x = v.x;
y = v.y;
return *this;
}
template <class T>
template <class S>
inline void
Vec2<T>::setValue (S a, S b)
{
x = T (a);
y = T (b);
}
template <class T>
template <class S>
inline void
Vec2<T>::setValue (const Vec2<S> &v)
{
x = T (v.x);
y = T (v.y);
}
template <class T>
template <class S>
inline void
Vec2<T>::getValue (S &a, S &b) const
{
a = S (x);
b = S (y);
}
template <class T>
template <class S>
inline void
Vec2<T>::getValue (Vec2<S> &v) const
{
v.x = S (x);
v.y = S (y);
}
template <class T>
inline T *
Vec2<T>::getValue()
{
return (T *) &x;
}
template <class T>
inline const T *
Vec2<T>::getValue() const
{
return (const T *) &x;
}
template <class T>
template <class S>
inline bool
Vec2<T>::operator == (const Vec2<S> &v) const
{
return x == v.x && y == v.y;
}
template <class T>
template <class S>
inline bool
Vec2<T>::operator != (const Vec2<S> &v) const
{
return x != v.x || y != v.y;
}
template <class T>
bool
Vec2<T>::equalWithAbsError (const Vec2<T> &v, T e) const
{
for (int i = 0; i < 2; i++)
if (!Imath::equalWithAbsError ((*this)[i], v[i], e))
return false;
return true;
}
template <class T>
bool
Vec2<T>::equalWithRelError (const Vec2<T> &v, T e) const
{
for (int i = 0; i < 2; i++)
if (!Imath::equalWithRelError ((*this)[i], v[i], e))
return false;
return true;
}
template <class T>
inline T
Vec2<T>::dot (const Vec2 &v) const
{
return x * v.x + y * v.y;
}
template <class T>
inline T
Vec2<T>::operator ^ (const Vec2 &v) const
{
return dot (v);
}
template <class T>
inline T
Vec2<T>::cross (const Vec2 &v) const
{
return x * v.y - y * v.x;
}
template <class T>
inline T
Vec2<T>::operator % (const Vec2 &v) const
{
return x * v.y - y * v.x;
}
template <class T>
inline const Vec2<T> &
Vec2<T>::operator += (const Vec2 &v)
{
x += v.x;
y += v.y;
return *this;
}
template <class T>
inline Vec2<T>
Vec2<T>::operator + (const Vec2 &v) const
{
return Vec2 (x + v.x, y + v.y);
}
template <class T>
inline const Vec2<T> &
Vec2<T>::operator -= (const Vec2 &v)
{
x -= v.x;
y -= v.y;
return *this;
}
template <class T>
inline Vec2<T>
Vec2<T>::operator - (const Vec2 &v) const
{
return Vec2 (x - v.x, y - v.y);
}
template <class T>
inline Vec2<T>
Vec2<T>::operator - () const
{
return Vec2 (-x, -y);
}
template <class T>
inline const Vec2<T> &
Vec2<T>::negate ()
{
x = -x;
y = -y;
return *this;
}
template <class T>
inline const Vec2<T> &
Vec2<T>::operator *= (const Vec2 &v)
{
x *= v.x;
y *= v.y;
return *this;
}
template <class T>
inline const Vec2<T> &
Vec2<T>::operator *= (T a)
{
x *= a;
y *= a;
return *this;
}
template <class T>
inline Vec2<T>
Vec2<T>::operator * (const Vec2 &v) const
{
return Vec2 (x * v.x, y * v.y);
}
template <class T>
inline Vec2<T>
Vec2<T>::operator * (T a) const
{
return Vec2 (x * a, y * a);
}
template <class T>
inline const Vec2<T> &
Vec2<T>::operator /= (const Vec2 &v)
{
x /= v.x;
y /= v.y;
return *this;
}
template <class T>
inline const Vec2<T> &
Vec2<T>::operator /= (T a)
{
x /= a;
y /= a;
return *this;
}
template <class T>
inline Vec2<T>
Vec2<T>::operator / (const Vec2 &v) const
{
return Vec2 (x / v.x, y / v.y);
}
template <class T>
inline Vec2<T>
Vec2<T>::operator / (T a) const
{
return Vec2 (x / a, y / a);
}
template <class T>
T
Vec2<T>::lengthTiny () const
{
T absX = (x >= T (0))? x: -x;
T absY = (y >= T (0))? y: -y;
T max = absX;
if (max < absY)
max = absY;
if (max == T (0))
return T (0);
//
// Do not replace the divisions by max with multiplications by 1/max.
// Computing 1/max can overflow but the divisions below will always
// produce results less than or equal to 1.
//
absX /= max;
absY /= max;
return max * Math<T>::sqrt (absX * absX + absY * absY);
}
template <class T>
inline T
Vec2<T>::length () const
{
T length2 = dot (*this);
if (length2 < T (2) * limits<T>::smallest())
return lengthTiny();
return Math<T>::sqrt (length2);
}
template <class T>
inline T
Vec2<T>::length2 () const
{
return dot (*this);
}
template <class T>
const Vec2<T> &
Vec2<T>::normalize ()
{
T l = length();
if (l != T (0))
{
//
// Do not replace the divisions by l with multiplications by 1/l.
// Computing 1/l can overflow but the divisions below will always
// produce results less than or equal to 1.
//
x /= l;
y /= l;
}
return *this;
}
template <class T>
const Vec2<T> &
Vec2<T>::normalizeExc () throw (Iex::MathExc)
{
T l = length();
if (l == T (0))
throw NullVecExc ("Cannot normalize null vector.");
x /= l;
y /= l;
return *this;
}
template <class T>
inline
const Vec2<T> &
Vec2<T>::normalizeNonNull ()
{
T l = length();
x /= l;
y /= l;
return *this;
}
template <class T>
Vec2<T>
Vec2<T>::normalized () const
{
T l = length();
if (l == T (0))
return Vec2 (T (0));
return Vec2 (x / l, y / l);
}
template <class T>
Vec2<T>
Vec2<T>::normalizedExc () const throw (Iex::MathExc)
{
T l = length();
if (l == T (0))
throw NullVecExc ("Cannot normalize null vector.");
return Vec2 (x / l, y / l);
}
template <class T>
inline
Vec2<T>
Vec2<T>::normalizedNonNull () const
{
T l = length();
return Vec2 (x / l, y / l);
}
//-----------------------
// Implementation of Vec3
//-----------------------
template <class T>
inline T &
Vec3<T>::operator [] (int i)
{
return (&x)[i];
}
template <class T>
inline const T &
Vec3<T>::operator [] (int i) const
{
return (&x)[i];
}
template <class T>
inline
Vec3<T>::Vec3 ()
{
// empty
}
template <class T>
inline
Vec3<T>::Vec3 (T a)
{
x = y = z = a;
}
template <class T>
inline
Vec3<T>::Vec3 (T a, T b, T c)
{
x = a;
y = b;
z = c;
}
template <class T>
inline
Vec3<T>::Vec3 (const Vec3 &v)
{
x = v.x;
y = v.y;
z = v.z;
}
template <class T>
template <class S>
inline
Vec3<T>::Vec3 (const Vec3<S> &v)
{
x = T (v.x);
y = T (v.y);
z = T (v.z);
}
template <class T>
inline const Vec3<T> &
Vec3<T>::operator = (const Vec3 &v)
{
x = v.x;
y = v.y;
z = v.z;
return *this;
}
template <class T>
template <class S>
inline
Vec3<T>::Vec3 (const Vec4<S> &v)
{
x = T (v.x / v.w);
y = T (v.y / v.w);
z = T (v.z / v.w);
}
template <class T>
template <class S>
Vec3<T>::Vec3 (const Vec4<S> &v, InfException)
{
T vx = T (v.x);
T vy = T (v.y);
T vz = T (v.z);
T vw = T (v.w);
T absW = (vw >= T (0))? vw: -vw;
if (absW < 1)
{
T m = baseTypeMax() * absW;
if (vx <= -m || vx >= m || vy <= -m || vy >= m || vz <= -m || vz >= m)
throw InfPointExc ("Cannot normalize point at infinity.");
}
x = vx / vw;
y = vy / vw;
z = vz / vw;
}
template <class T>
template <class S>
inline void
Vec3<T>::setValue (S a, S b, S c)
{
x = T (a);
y = T (b);
z = T (c);
}
template <class T>
template <class S>
inline void
Vec3<T>::setValue (const Vec3<S> &v)
{
x = T (v.x);
y = T (v.y);
z = T (v.z);
}
template <class T>
template <class S>
inline void
Vec3<T>::getValue (S &a, S &b, S &c) const
{
a = S (x);
b = S (y);
c = S (z);
}
template <class T>
template <class S>
inline void
Vec3<T>::getValue (Vec3<S> &v) const
{
v.x = S (x);
v.y = S (y);
v.z = S (z);
}
template <class T>
inline T *
Vec3<T>::getValue()
{
return (T *) &x;
}
template <class T>
inline const T *
Vec3<T>::getValue() const
{
return (const T *) &x;
}
template <class T>
template <class S>
inline bool
Vec3<T>::operator == (const Vec3<S> &v) const
{
return x == v.x && y == v.y && z == v.z;
}
template <class T>
template <class S>
inline bool
Vec3<T>::operator != (const Vec3<S> &v) const
{
return x != v.x || y != v.y || z != v.z;
}
template <class T>
bool
Vec3<T>::equalWithAbsError (const Vec3<T> &v, T e) const
{
for (int i = 0; i < 3; i++)
if (!Imath::equalWithAbsError ((*this)[i], v[i], e))
return false;
return true;
}
template <class T>
bool
Vec3<T>::equalWithRelError (const Vec3<T> &v, T e) const
{
for (int i = 0; i < 3; i++)
if (!Imath::equalWithRelError ((*this)[i], v[i], e))
return false;
return true;
}
template <class T>
inline T
Vec3<T>::dot (const Vec3 &v) const
{
return x * v.x + y * v.y + z * v.z;
}
template <class T>
inline T
Vec3<T>::operator ^ (const Vec3 &v) const
{
return dot (v);
}
template <class T>
inline Vec3<T>
Vec3<T>::cross (const Vec3 &v) const
{
return Vec3 (y * v.z - z * v.y,
z * v.x - x * v.z,
x * v.y - y * v.x);
}
template <class T>
inline const Vec3<T> &
Vec3<T>::operator %= (const Vec3 &v)
{
T a = y * v.z - z * v.y;
T b = z * v.x - x * v.z;
T c = x * v.y - y * v.x;
x = a;
y = b;
z = c;
return *this;
}
template <class T>
inline Vec3<T>
Vec3<T>::operator % (const Vec3 &v) const
{
return Vec3 (y * v.z - z * v.y,
z * v.x - x * v.z,
x * v.y - y * v.x);
}
template <class T>
inline const Vec3<T> &
Vec3<T>::operator += (const Vec3 &v)
{
x += v.x;
y += v.y;
z += v.z;
return *this;
}
template <class T>
inline Vec3<T>
Vec3<T>::operator + (const Vec3 &v) const
{
return Vec3 (x + v.x, y + v.y, z + v.z);
}
template <class T>
inline const Vec3<T> &
Vec3<T>::operator -= (const Vec3 &v)
{
x -= v.x;
y -= v.y;
z -= v.z;
return *this;
}
template <class T>
inline Vec3<T>
Vec3<T>::operator - (const Vec3 &v) const
{
return Vec3 (x - v.x, y - v.y, z - v.z);
}
template <class T>
inline Vec3<T>
Vec3<T>::operator - () const
{
return Vec3 (-x, -y, -z);
}
template <class T>
inline const Vec3<T> &
Vec3<T>::negate ()
{
x = -x;
y = -y;
z = -z;
return *this;
}
template <class T>
inline const Vec3<T> &
Vec3<T>::operator *= (const Vec3 &v)
{
x *= v.x;
y *= v.y;
z *= v.z;
return *this;
}
template <class T>
inline const Vec3<T> &
Vec3<T>::operator *= (T a)
{
x *= a;
y *= a;
z *= a;
return *this;
}
template <class T>
inline Vec3<T>
Vec3<T>::operator * (const Vec3 &v) const
{
return Vec3 (x * v.x, y * v.y, z * v.z);
}
template <class T>
inline Vec3<T>
Vec3<T>::operator * (T a) const
{
return Vec3 (x * a, y * a, z * a);
}
template <class T>
inline const Vec3<T> &
Vec3<T>::operator /= (const Vec3 &v)
{
x /= v.x;
y /= v.y;
z /= v.z;
return *this;
}
template <class T>
inline const Vec3<T> &
Vec3<T>::operator /= (T a)
{
x /= a;
y /= a;
z /= a;
return *this;
}
template <class T>
inline Vec3<T>
Vec3<T>::operator / (const Vec3 &v) const
{
return Vec3 (x / v.x, y / v.y, z / v.z);
}
template <class T>
inline Vec3<T>
Vec3<T>::operator / (T a) const
{
return Vec3 (x / a, y / a, z / a);
}
template <class T>
T
Vec3<T>::lengthTiny () const
{
T absX = (x >= T (0))? x: -x;
T absY = (y >= T (0))? y: -y;
T absZ = (z >= T (0))? z: -z;
T max = absX;
if (max < absY)
max = absY;
if (max < absZ)
max = absZ;
if (max == T (0))
return T (0);
//
// Do not replace the divisions by max with multiplications by 1/max.
// Computing 1/max can overflow but the divisions below will always
// produce results less than or equal to 1.
//
absX /= max;
absY /= max;
absZ /= max;
return max * Math<T>::sqrt (absX * absX + absY * absY + absZ * absZ);
}
template <class T>
inline T
Vec3<T>::length () const
{
T length2 = dot (*this);
if (length2 < T (2) * limits<T>::smallest())
return lengthTiny();
return Math<T>::sqrt (length2);
}
template <class T>
inline T
Vec3<T>::length2 () const
{
return dot (*this);
}
template <class T>
const Vec3<T> &
Vec3<T>::normalize ()
{
T l = length();
if (l != T (0))
{
//
// Do not replace the divisions by l with multiplications by 1/l.
// Computing 1/l can overflow but the divisions below will always
// produce results less than or equal to 1.
//
x /= l;
y /= l;
z /= l;
}
return *this;
}
template <class T>
const Vec3<T> &
Vec3<T>::normalizeExc () throw (Iex::MathExc)
{
T l = length();
if (l == T (0))
throw NullVecExc ("Cannot normalize null vector.");
x /= l;
y /= l;
z /= l;
return *this;
}
template <class T>
inline
const Vec3<T> &
Vec3<T>::normalizeNonNull ()
{
T l = length();
x /= l;
y /= l;
z /= l;
return *this;
}
template <class T>
Vec3<T>
Vec3<T>::normalized () const
{
T l = length();
if (l == T (0))
return Vec3 (T (0));
return Vec3 (x / l, y / l, z / l);
}
template <class T>
Vec3<T>
Vec3<T>::normalizedExc () const throw (Iex::MathExc)
{
T l = length();
if (l == T (0))
throw NullVecExc ("Cannot normalize null vector.");
return Vec3 (x / l, y / l, z / l);
}
template <class T>
inline
Vec3<T>
Vec3<T>::normalizedNonNull () const
{
T l = length();
return Vec3 (x / l, y / l, z / l);
}
//-----------------------
// Implementation of Vec4
//-----------------------
template <class T>
inline T &
Vec4<T>::operator [] (int i)
{
return (&x)[i];
}
template <class T>
inline const T &
Vec4<T>::operator [] (int i) const
{
return (&x)[i];
}
template <class T>
inline
Vec4<T>::Vec4 ()
{
// empty
}
template <class T>
inline
Vec4<T>::Vec4 (T a)
{
x = y = z = w = a;
}
template <class T>
inline
Vec4<T>::Vec4 (T a, T b, T c, T d)
{
x = a;
y = b;
z = c;
w = d;
}
template <class T>
inline
Vec4<T>::Vec4 (const Vec4 &v)
{
x = v.x;
y = v.y;
z = v.z;
w = v.w;
}
template <class T>
template <class S>
inline
Vec4<T>::Vec4 (const Vec4<S> &v)
{
x = T (v.x);
y = T (v.y);
z = T (v.z);
w = T (v.w);
}
template <class T>
inline const Vec4<T> &
Vec4<T>::operator = (const Vec4 &v)
{
x = v.x;
y = v.y;
z = v.z;
w = v.w;
return *this;
}
template <class T>
template <class S>
inline
Vec4<T>::Vec4 (const Vec3<S> &v)
{
x = T (v.x);
y = T (v.y);
z = T (v.z);
w = T (1);
}
template <class T>
template <class S>
inline bool
Vec4<T>::operator == (const Vec4<S> &v) const
{
return x == v.x && y == v.y && z == v.z && w == v.w;
}
template <class T>
template <class S>
inline bool
Vec4<T>::operator != (const Vec4<S> &v) const
{
return x != v.x || y != v.y || z != v.z || w != v.w;
}
template <class T>
bool
Vec4<T>::equalWithAbsError (const Vec4<T> &v, T e) const
{
for (int i = 0; i < 4; i++)
if (!Imath::equalWithAbsError ((*this)[i], v[i], e))
return false;
return true;
}
template <class T>
bool
Vec4<T>::equalWithRelError (const Vec4<T> &v, T e) const
{
for (int i = 0; i < 4; i++)
if (!Imath::equalWithRelError ((*this)[i], v[i], e))
return false;
return true;
}
template <class T>
inline T
Vec4<T>::dot (const Vec4 &v) const
{
return x * v.x + y * v.y + z * v.z + w * v.w;
}
template <class T>
inline T
Vec4<T>::operator ^ (const Vec4 &v) const
{
return dot (v);
}
template <class T>
inline const Vec4<T> &
Vec4<T>::operator += (const Vec4 &v)
{
x += v.x;
y += v.y;
z += v.z;
w += v.w;
return *this;
}
template <class T>
inline Vec4<T>
Vec4<T>::operator + (const Vec4 &v) const
{
return Vec4 (x + v.x, y + v.y, z + v.z, w + v.w);
}
template <class T>
inline const Vec4<T> &
Vec4<T>::operator -= (const Vec4 &v)
{
x -= v.x;
y -= v.y;
z -= v.z;
w -= v.w;
return *this;
}
template <class T>
inline Vec4<T>
Vec4<T>::operator - (const Vec4 &v) const
{
return Vec4 (x - v.x, y - v.y, z - v.z, w - v.w);
}
template <class T>
inline Vec4<T>
Vec4<T>::operator - () const
{
return Vec4 (-x, -y, -z, -w);
}
template <class T>
inline const Vec4<T> &
Vec4<T>::negate ()
{
x = -x;
y = -y;
z = -z;
w = -w;
return *this;
}
template <class T>
inline const Vec4<T> &
Vec4<T>::operator *= (const Vec4 &v)
{
x *= v.x;
y *= v.y;
z *= v.z;
w *= v.w;
return *this;
}
template <class T>
inline const Vec4<T> &
Vec4<T>::operator *= (T a)
{
x *= a;
y *= a;
z *= a;
w *= a;
return *this;
}
template <class T>
inline Vec4<T>
Vec4<T>::operator * (const Vec4 &v) const
{
return Vec4 (x * v.x, y * v.y, z * v.z, w * v.w);
}
template <class T>
inline Vec4<T>
Vec4<T>::operator * (T a) const
{
return Vec4 (x * a, y * a, z * a, w * a);
}
template <class T>
inline const Vec4<T> &
Vec4<T>::operator /= (const Vec4 &v)
{
x /= v.x;
y /= v.y;
z /= v.z;
w /= v.w;
return *this;
}
template <class T>
inline const Vec4<T> &
Vec4<T>::operator /= (T a)
{
x /= a;
y /= a;
z /= a;
w /= a;
return *this;
}
template <class T>
inline Vec4<T>
Vec4<T>::operator / (const Vec4 &v) const
{
return Vec4 (x / v.x, y / v.y, z / v.z, w / v.w);
}
template <class T>
inline Vec4<T>
Vec4<T>::operator / (T a) const
{
return Vec4 (x / a, y / a, z / a, w / a);
}
template <class T>
T
Vec4<T>::lengthTiny () const
{
T absX = (x >= T (0))? x: -x;
T absY = (y >= T (0))? y: -y;
T absZ = (z >= T (0))? z: -z;
T absW = (w >= T (0))? w: -w;
T max = absX;
if (max < absY)
max = absY;
if (max < absZ)
max = absZ;
if (max < absW)
max = absW;
if (max == T (0))
return T (0);
//
// Do not replace the divisions by max with multiplications by 1/max.
// Computing 1/max can overflow but the divisions below will always
// produce results less than or equal to 1.
//
absX /= max;
absY /= max;
absZ /= max;
absW /= max;
return max *
Math<T>::sqrt (absX * absX + absY * absY + absZ * absZ + absW * absW);
}
template <class T>
inline T
Vec4<T>::length () const
{
T length2 = dot (*this);
if (length2 < T (2) * limits<T>::smallest())
return lengthTiny();
return Math<T>::sqrt (length2);
}
template <class T>
inline T
Vec4<T>::length2 () const
{
return dot (*this);
}
template <class T>
const Vec4<T> &
Vec4<T>::normalize ()
{
T l = length();
if (l != T (0))
{
//
// Do not replace the divisions by l with multiplications by 1/l.
// Computing 1/l can overflow but the divisions below will always
// produce results less than or equal to 1.
//
x /= l;
y /= l;
z /= l;
w /= l;
}
return *this;
}
template <class T>
const Vec4<T> &
Vec4<T>::normalizeExc () throw (Iex::MathExc)
{
T l = length();
if (l == T (0))
throw NullVecExc ("Cannot normalize null vector.");
x /= l;
y /= l;
z /= l;
w /= l;
return *this;
}
template <class T>
inline
const Vec4<T> &
Vec4<T>::normalizeNonNull ()
{
T l = length();
x /= l;
y /= l;
z /= l;
w /= l;
return *this;
}
template <class T>
Vec4<T>
Vec4<T>::normalized () const
{
T l = length();
if (l == T (0))
return Vec4 (T (0));
return Vec4 (x / l, y / l, z / l, w / l);
}
template <class T>
Vec4<T>
Vec4<T>::normalizedExc () const throw (Iex::MathExc)
{
T l = length();
if (l == T (0))
throw NullVecExc ("Cannot normalize null vector.");
return Vec4 (x / l, y / l, z / l, w / l);
}
template <class T>
inline
Vec4<T>
Vec4<T>::normalizedNonNull () const
{
T l = length();
return Vec4 (x / l, y / l, z / l, w / l);
}
//-----------------------------
// Stream output implementation
//-----------------------------
template <class T>
std::ostream &
operator << (std::ostream &s, const Vec2<T> &v)
{
return s << '(' << v.x << ' ' << v.y << ')';
}
template <class T>
std::ostream &
operator << (std::ostream &s, const Vec3<T> &v)
{
return s << '(' << v.x << ' ' << v.y << ' ' << v.z << ')';
}
template <class T>
std::ostream &
operator << (std::ostream &s, const Vec4<T> &v)
{
return s << '(' << v.x << ' ' << v.y << ' ' << v.z << ' ' << v.w << ')';
}
//-----------------------------------------
// Implementation of reverse multiplication
//-----------------------------------------
template <class T>
inline Vec2<T>
operator * (T a, const Vec2<T> &v)
{
return Vec2<T> (a * v.x, a * v.y);
}
template <class T>
inline Vec3<T>
operator * (T a, const Vec3<T> &v)
{
return Vec3<T> (a * v.x, a * v.y, a * v.z);
}
template <class T>
inline Vec4<T>
operator * (T a, const Vec4<T> &v)
{
return Vec4<T> (a * v.x, a * v.y, a * v.z, a * v.w);
}
#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
#pragma warning(pop)
#endif
} // namespace Imath
#endif