ImathShear.h

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//
// Copyright (c) 2004, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
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// 
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#ifndef INCLUDED_IMATHSHEAR_H
#define INCLUDED_IMATHSHEAR_H

//----------------------------------------------------
//
//  Shear6 class template.
//
//----------------------------------------------------

#include "ImathExc.h"
#include "ImathLimits.h"
#include "ImathMath.h"
#include "ImathVec.h"

#include <iostream>


namespace Imath {




template <class T> class Shear6
{
  public:

    //-------------------
    // Access to elements
    //-------------------

    T           xy, xz, yz, yx, zx, zy;

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


    //-------------
    // Constructors
    //-------------

    Shear6 ();             // (0 0 0 0 0 0)
    Shear6 (T XY, T XZ, T YZ);     // (XY XZ YZ 0 0 0)
    Shear6 (const Vec3<T> &v);     // (v.x v.y v.z 0 0 0)
    template <class S>             // (v.x v.y v.z 0 0 0)
    Shear6 (const Vec3<S> &v);
    Shear6 (T XY, T XZ, T YZ,      // (XY XZ YZ YX ZX ZY)
        T YX, T ZX, T ZY);  


    //---------------------------------
    // Copy constructors and assignment
    //---------------------------------

    Shear6 (const Shear6 &h);
    template <class S> Shear6 (const Shear6<S> &h);

    const Shear6 &  operator = (const Shear6 &h);
    template <class S> 
    const Shear6 &  operator = (const Vec3<S> &v);


    //----------------------
    // Compatibility with Sb
    //----------------------

    template <class S>
    void        setValue (S XY, S XZ, S YZ, S YX, S ZX, S ZY);

    template <class S>
    void        setValue (const Shear6<S> &h);

    template <class S>
    void        getValue (S &XY, S &XZ, S &YZ, 
                  S &YX, S &ZX, S &ZY) const;

    template <class S>
    void        getValue (Shear6<S> &h) const;

    T *         getValue();
    const T *       getValue() const;


    //---------
    // Equality
    //---------

    template <class S>
    bool        operator == (const Shear6<S> &h) const;

    template <class S>
    bool        operator != (const Shear6<S> &h) const;

    //-----------------------------------------------------------------------
    // Compare two shears and test if they are "approximately equal":
    //
    // equalWithAbsError (h, e)
    //
    //      Returns true if the coefficients of this and h are the same with
    //      an absolute error of no more than e, i.e., for all i
    //
    //      abs (this[i] - h[i]) <= e
    //
    // equalWithRelError (h, e)
    //
    //      Returns true if the coefficients of this and h are the same with
    //      a relative error of no more than e, i.e., for all i
    //
    //      abs (this[i] - h[i]) <= e * abs (this[i])
    //-----------------------------------------------------------------------

    bool        equalWithAbsError (const Shear6<T> &h, T e) const;
    bool        equalWithRelError (const Shear6<T> &h, T e) const;


    //------------------------
    // Component-wise addition
    //------------------------

    const Shear6 &  operator += (const Shear6 &h);
    Shear6      operator + (const Shear6 &h) const;


    //---------------------------
    // Component-wise subtraction
    //---------------------------

    const Shear6 &  operator -= (const Shear6 &h);
    Shear6      operator - (const Shear6 &h) const;


    //------------------------------------
    // Component-wise multiplication by -1
    //------------------------------------

    Shear6      operator - () const;
    const Shear6 &  negate ();


    //------------------------------
    // Component-wise multiplication
    //------------------------------

    const Shear6 &  operator *= (const Shear6 &h);
    const Shear6 &  operator *= (T a);
    Shear6      operator * (const Shear6 &h) const;
    Shear6      operator * (T a) const;


    //------------------------
    // Component-wise division
    //------------------------

    const Shear6 &  operator /= (const Shear6 &h);
    const Shear6 &  operator /= (T a);
    Shear6      operator / (const Shear6 &h) const;
    Shear6      operator / (T a) const;


    //----------------------------------------------------------
    // Number of dimensions, i.e. number of elements in a Shear6
    //----------------------------------------------------------

    static unsigned int dimensions() {return 6;}


    //-------------------------------------------------
    // 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> or a Shear6<T>, you can refer to T as
    // V::BaseType
    //--------------------------------------------------------------

    typedef T       BaseType;
};


//--------------
// Stream output
//--------------

template <class T>
std::ostream &  operator << (std::ostream &s, const Shear6<T> &h);


//----------------------------------------------------
// Reverse multiplication: scalar * Shear6<T>
//----------------------------------------------------

template <class S, class T> Shear6<T>   operator * (S a, const Shear6<T> &h);


//-------------------------
// Typedefs for convenience
//-------------------------

typedef Vec3   <float>  Shear3f;
typedef Vec3   <double> Shear3d;
typedef Shear6 <float>  Shear6f;
typedef Shear6 <double> Shear6d;




//-----------------------
// Implementation of Shear6
//-----------------------

template <class T>
inline T &
Shear6<T>::operator [] (int i)
{
    return (&xy)[i];
}

template <class T>
inline const T &
Shear6<T>::operator [] (int i) const
{
    return (&xy)[i];
}

template <class T>
inline
Shear6<T>::Shear6 ()
{
    xy = xz = yz = yx = zx = zy = 0;
}

template <class T>
inline
Shear6<T>::Shear6 (T XY, T XZ, T YZ)
{
    xy = XY;
    xz = XZ;
    yz = YZ;
    yx = 0;
    zx = 0;
    zy = 0;
}

template <class T>
inline
Shear6<T>::Shear6 (const Vec3<T> &v)
{
    xy = v.x;
    xz = v.y;
    yz = v.z;
    yx = 0;
    zx = 0;
    zy = 0;
}

template <class T>
template <class S>
inline
Shear6<T>::Shear6 (const Vec3<S> &v)
{
    xy = T (v.x);
    xz = T (v.y);
    yz = T (v.z);
    yx = 0;
    zx = 0;
    zy = 0;
}

template <class T>
inline
Shear6<T>::Shear6 (T XY, T XZ, T YZ, T YX, T ZX, T ZY)
{
    xy = XY;
    xz = XZ;
    yz = YZ;
    yx = YX;
    zx = ZX;
    zy = ZY;
}

template <class T>
inline
Shear6<T>::Shear6 (const Shear6 &h)
{
    xy = h.xy;
    xz = h.xz;
    yz = h.yz;
    yx = h.yx;
    zx = h.zx;
    zy = h.zy;
}

template <class T>
template <class S>
inline
Shear6<T>::Shear6 (const Shear6<S> &h)
{
    xy = T (h.xy);
    xz = T (h.xz);
    yz = T (h.yz);
    yx = T (h.yx);
    zx = T (h.zx);
    zy = T (h.zy);
}

template <class T>
inline const Shear6<T> &
Shear6<T>::operator = (const Shear6 &h)
{
    xy = h.xy;
    xz = h.xz;
    yz = h.yz;
    yx = h.yx;
    zx = h.zx;
    zy = h.zy;
    return *this;
}

template <class T>
template <class S>
inline const Shear6<T> &
Shear6<T>::operator = (const Vec3<S> &v)
{
    xy = T (v.x);
    xz = T (v.y);
    yz = T (v.z);
    yx = 0;
    zx = 0;
    zy = 0;
    return *this;
}

template <class T>
template <class S>
inline void
Shear6<T>::setValue (S XY, S XZ, S YZ, S YX, S ZX, S ZY)
{
    xy = T (XY);
    xz = T (XZ);
    yz = T (YZ);
    yx = T (YX);
    zx = T (ZX);
    zy = T (ZY);
}

template <class T>
template <class S>
inline void
Shear6<T>::setValue (const Shear6<S> &h)
{
    xy = T (h.xy);
    xz = T (h.xz);
    yz = T (h.yz);
    yx = T (h.yx);
    zx = T (h.zx);
    zy = T (h.zy);
}

template <class T>
template <class S>
inline void
Shear6<T>::getValue (S &XY, S &XZ, S &YZ, S &YX, S &ZX, S &ZY) const
{
    XY = S (xy);
    XZ = S (xz);
    YZ = S (yz);
    YX = S (yx);
    ZX = S (zx);
    ZY = S (zy);
}

template <class T>
template <class S>
inline void
Shear6<T>::getValue (Shear6<S> &h) const
{
    h.xy = S (xy);
    h.xz = S (xz);
    h.yz = S (yz);
    h.yx = S (yx);
    h.zx = S (zx);
    h.zy = S (zy);
}

template <class T>
inline T *
Shear6<T>::getValue()
{
    return (T *) &xy;
}

template <class T>
inline const T *
Shear6<T>::getValue() const
{
    return (const T *) &xy;
}

template <class T>
template <class S>
inline bool
Shear6<T>::operator == (const Shear6<S> &h) const
{
    return xy == h.xy  &&  xz == h.xz  &&  yz == h.yz  &&  
       yx == h.yx  &&  zx == h.zx  &&  zy == h.zy;
}

template <class T>
template <class S>
inline bool
Shear6<T>::operator != (const Shear6<S> &h) const
{
    return xy != h.xy  ||  xz != h.xz  ||  yz != h.yz  ||
       yx != h.yx  ||  zx != h.zx  ||  zy != h.zy;
}

template <class T>
bool
Shear6<T>::equalWithAbsError (const Shear6<T> &h, T e) const
{
    for (int i = 0; i < 6; i++)
    if (!Imath::equalWithAbsError ((*this)[i], h[i], e))
        return false;

    return true;
}

template <class T>
bool
Shear6<T>::equalWithRelError (const Shear6<T> &h, T e) const
{
    for (int i = 0; i < 6; i++)
    if (!Imath::equalWithRelError ((*this)[i], h[i], e))
        return false;

    return true;
}


template <class T>
inline const Shear6<T> &
Shear6<T>::operator += (const Shear6 &h)
{
    xy += h.xy;
    xz += h.xz;
    yz += h.yz;
    yx += h.yx;
    zx += h.zx;
    zy += h.zy;
    return *this;
}

template <class T>
inline Shear6<T>
Shear6<T>::operator + (const Shear6 &h) const
{
    return Shear6 (xy + h.xy, xz + h.xz, yz + h.yz,
           yx + h.yx, zx + h.zx, zy + h.zy);
}

template <class T>
inline const Shear6<T> &
Shear6<T>::operator -= (const Shear6 &h)
{
    xy -= h.xy;
    xz -= h.xz;
    yz -= h.yz;
    yx -= h.yx;
    zx -= h.zx;
    zy -= h.zy;
    return *this;
}

template <class T>
inline Shear6<T>
Shear6<T>::operator - (const Shear6 &h) const
{
    return Shear6 (xy - h.xy, xz - h.xz, yz - h.yz,
           yx - h.yx, zx - h.zx, zy - h.zy);
}

template <class T>
inline Shear6<T>
Shear6<T>::operator - () const
{
    return Shear6 (-xy, -xz, -yz, -yx, -zx, -zy);
}

template <class T>
inline const Shear6<T> &
Shear6<T>::negate ()
{
    xy = -xy;
    xz = -xz;
    yz = -yz;
    yx = -yx;
    zx = -zx;
    zy = -zy;
    return *this;
}

template <class T>
inline const Shear6<T> &
Shear6<T>::operator *= (const Shear6 &h)
{
    xy *= h.xy;
    xz *= h.xz;
    yz *= h.yz;
    yx *= h.yx;
    zx *= h.zx;
    zy *= h.zy;
    return *this;
}

template <class T>
inline const Shear6<T> &
Shear6<T>::operator *= (T a)
{
    xy *= a;
    xz *= a;
    yz *= a;
    yx *= a;
    zx *= a;
    zy *= a;
    return *this;
}

template <class T>
inline Shear6<T>
Shear6<T>::operator * (const Shear6 &h) const
{
    return Shear6 (xy * h.xy, xz * h.xz, yz * h.yz, 
           yx * h.yx, zx * h.zx, zy * h.zy);
}

template <class T>
inline Shear6<T>
Shear6<T>::operator * (T a) const
{
    return Shear6 (xy * a, xz * a, yz * a,
           yx * a, zx * a, zy * a);
}

template <class T>
inline const Shear6<T> &
Shear6<T>::operator /= (const Shear6 &h)
{
    xy /= h.xy;
    xz /= h.xz;
    yz /= h.yz;
    yx /= h.yx;
    zx /= h.zx;
    zy /= h.zy;
    return *this;
}

template <class T>
inline const Shear6<T> &
Shear6<T>::operator /= (T a)
{
    xy /= a;
    xz /= a;
    yz /= a;
    yx /= a;
    zx /= a;
    zy /= a;
    return *this;
}

template <class T>
inline Shear6<T>
Shear6<T>::operator / (const Shear6 &h) const
{
    return Shear6 (xy / h.xy, xz / h.xz, yz / h.yz,
           yx / h.yx, zx / h.zx, zy / h.zy);
}

template <class T>
inline Shear6<T>
Shear6<T>::operator / (T a) const
{
    return Shear6 (xy / a, xz / a, yz / a,
           yx / a, zx / a, zy / a);
}


//-----------------------------
// Stream output implementation
//-----------------------------

template <class T>
std::ostream &
operator << (std::ostream &s, const Shear6<T> &h)
{
    return s << '(' 
         << h.xy << ' ' << h.xz << ' ' << h.yz 
         << h.yx << ' ' << h.zx << ' ' << h.zy 
         << ')';
}


//-----------------------------------------
// Implementation of reverse multiplication
//-----------------------------------------

template <class S, class T>
inline Shear6<T>
operator * (S a, const Shear6<T> &h)
{
    return Shear6<T> (a * h.xy, a * h.xz, a * h.yz,
              a * h.yx, a * h.zx, a * h.zy);
}


} // namespace Imath

#endif