QVM: Quaternions, Vectors, Matrices
Synopsis
#include <boost/qvm/all.hpp>
namespace boost
{
namespace qvm
{
//*** Type traits ***
template <class T>
struct is_quat
{
static bool const value=/*unspecified*/;
};
template <class Q>
struct quat_traits
{
/*main template members unspecified*/
};
/*
User-defined (possibly partial) specializations:
template <>
struct quat_traits<Q>
{
typedef /*user-defined*/ scalar_type;
template <int I> static inline scalar_type read_element( Quaternion const & q );
template <int I> static inline scalar_type & write_element( Quaternion & q );
};
*/
template <class QuatType,class ScalarType>
struct quat_traits_defaults
{
typedef QuatType quat_type;
typedef ScalarType scalar_type;
template <int I>
static BOOST_QVM_INLINE_CRITICAL
scalar_type read_element( quat_type const & x )
{
return quat_traits<quat_type>::template write_element<I>(const_cast<quat_type &>(x));
}
};
template <class T>
struct is_vec
{
static bool const value=/*unspecified*/;
};
template <class V>
struct vec_traits
{
/*main template members unspecified*/
};
/*
User-defined (possibly partial) specializations:
template <>
struct vec_traits<V>
{
static int const dim = /*user-defined*/;
typedef /*user-defined*/ scalar_type;
template <int I> static inline scalar_type read_element( Vector const & v );
template <int I> static inline scalar_type & write_element( Vector & v );
static inline scalar_type read_element_idx( int i, Vector const & v );
static inline scalar_type & write_element_idx( int i, Vector & v );
};
*/
template <class VecType,class ScalarType,int Dim>
struct vec_traits_defaults
{
typedef VecType vec_type;
typedef ScalarType scalar_type;
static int const dim=Dim;
template <int I>
static BOOST_QVM_INLINE_CRITICAL
scalar_type write_element( vec_type const & x )
{
return vec_traits<vec_type>::template write_element<I>(const_cast<vec_type &>(x));
}
static BOOST_QVM_INLINE_CRITICAL
scalar_type read_element_idx( int i, vec_type const & x )
{
return vec_traits<vec_type>::write_element_idx(i,const_cast<vec_type &>(x));
}
protected:
static BOOST_QVM_INLINE_TRIVIAL
scalar_type & write_element_idx( int i, vec_type & m )
{
/* unspecified */
}
};
template <class T>
struct is_mat
{
static bool const value=/*unspecified*/;
};
template <class M>
struct mat_traits
{
/*main template members unspecified*/
};
/*
User-defined (possibly partial) specializations:
template <>
struct mat_traits<M>
{
static int const rows = /*user-defined*/;
static int const cols = /*user-defined*/;
typedef /*user-defined*/ scalar_type;
template <int R,int C> static inline scalar_type read_element( Matrix const & m );
template <int R,int C> static inline scalar_type & write_element( Matrix & m );
static inline scalar_type read_element_idx( int r, int c, Matrix const & m );
static inline scalar_type & write_element_idx( int r, int c, Matrix & m );
};
*/
template <class MatType,class ScalarType,int Rows,int Cols>
struct mat_traits_defaults
{
typedef MatType mat_type;
typedef ScalarType scalar_type;
static int const rows=Rows;
static int const cols=Cols;
template <int Row,int Col>
static BOOST_QVM_INLINE_CRITICAL
scalar_type write_element( mat_type const & x )
{
return mat_traits<mat_type>::template write_element<Row,Col>(const_cast<mat_type &>(x));
}
static BOOST_QVM_INLINE_CRITICAL
scalar_type read_element_idx( int r, int c, mat_type const & x )
{
return mat_traits<mat_type>::write_element_idx(r,c,const_cast<mat_type &>(x));
}
protected:
static BOOST_QVM_INLINE_TRIVIAL
scalar_type & write_element_idx( int r, int c, mat_type & m )
{
/* unspecified */
}
};
//*** Quaternion, vector and matrix types ***
template <class T>
struct quat
{
T a[4];
template <class R>
operator R() const
{
R r;
assign(r,*this);
return r;
}
};
template <class Quaternion>
struct quat_traits;
template <class T>
struct quat_traits< quat<T> >
{
typedef T scalar_type;
template <int I> static scalar_type read_element( quat<T> const & x ) { return x.a[I]; }
template <int I> static scalar_type & write_element( quat<T> & x ) { return x.a[I]; }
};
template <class T,int Dim>
struct vec
{
T a[Dim];
template <class R>
operator R() const
{
R r;
assign(r,*this);
return r;
}
};
template <class Vector>
struct vec_traits;
template <class T,int Dim>
struct vec_traits< vec<T,Dim> >
{
typedef T scalar_type;
static int const dim=Dim;
template <int I> static scalar_type read_element( vec<T,Dim> const & x ) { return x.a[I]; }
template <int I> static scalar_type & write_element( vec<T,Dim> & x ) { return x.a[I]; }
static scalar_type read_element_idx( int i, vec<T,Dim> const & x ) { return x.a[i]; }
static scalar_type & write_element_idx( int i, vec<T,Dim> & x ) { return x.a[i]; }
};
template <class T,int Rows,int Cols>
struct mat
{
T a[Rows][Cols];
template <class R>
operator R() const
{
R r;
assign(r,*this);
return r;
}
};
template <class Matrix>
struct mat_traits;
template <class T,int Rows,int Cols>
struct mat_traits< mat<T,Rows,Cols> >
{
typedef T scalar_type;
static int const rows=Rows;
static int const cols=Cols;
template <int Row,int Col> static scalar_type read_element( mat<T,Rows,Cols> const & x ) { return x.a[Row][Col]; }
template <int Row,int Col> static scalar_type & write_element( mat<T,Rows,Cols> & x ) { return x.a[Row][Col]; }
static scalar_type read_element_idx( int row, int col, mat<T,Rows,Cols> const & x ) { return x.a[row][col]; }
static scalar_type & write_element_idx( int row, int col, mat<T,Rows,Cols> & x ) { return x.a[row][col]; }
};
//*** Accessing quaternion elements ***
//Only enabled if:
// is_quat<Q>::value
template <class Q> -unspecified-return-type- S( Q & q );
template <class Q> -unspecified-return-type- V( Q & q );
template <class Q> -unspecified-return-type- X( Q & q );
template <class Q> -unspecified-return-type- Y( Q & q );
template <class Q> -unspecified-return-type- Z( Q & q );
//*** Accessing vector elements ***
//Only enabled if:
// is_vec<V>::value
template <int I,class V> -unspecified-return-type- A( V & v );
template <class V> -unspecified-return-type- A0( V & v );
template <class V> -unspecified-return-type- A1( V & v );
...
template <class V> -unspecified-return-type- A9( V & v );
template <class V> -unspecified-return-type- X( V & v );
template <class V> -unspecified-return-type- Y( V & v );
template <class V> -unspecified-return-type- Z( V & v );
template <class V> -unspecified-return-type- W( V & v );
//*** Accessing vector elements by swizzling ***
//2D view proxies, only enabled if:
// is_vec<V>::value
template <class V> -unspecified-2D-vector-type- XX( V & v );
template <class V> -unspecified-2D-vector-type- XY( V & v );
template <class V> -unspecified-2D-vector-type- XZ( V & v );
template <class V> -unspecified-2D-vector-type- XW( V & v );
template <class V> -unspecified-2D-vector-type- X0( V & v );
template <class V> -unspecified-2D-vector-type- X1( V & v );
template <class V> -unspecified-2D-vector-type- YX( V & v );
template <class V> -unspecified-2D-vector-type- YY( V & v );
template <class V> -unspecified-2D-vector-type- YZ( V & v );
template <class V> -unspecified-2D-vector-type- YW( V & v );
template <class V> -unspecified-2D-vector-type- Y0( V & v );
template <class V> -unspecified-2D-vector-type- Y1( V & v );
template <class V> -unspecified-2D-vector-type- ZX( V & v );
template <class V> -unspecified-2D-vector-type- ZY( V & v );
template <class V> -unspecified-2D-vector-type- ZZ( V & v );
template <class V> -unspecified-2D-vector-type- ZW( V & v );
template <class V> -unspecified-2D-vector-type- Z0( V & v );
template <class V> -unspecified-2D-vector-type- Z1( V & v );
template <class V> -unspecified-2D-vector-type- WX( V & v );
template <class V> -unspecified-2D-vector-type- WY( V & v );
template <class V> -unspecified-2D-vector-type- WZ( V & v );
template <class V> -unspecified-2D-vector-type- WW( V & v );
template <class V> -unspecified-2D-vector-type- W0( V & v );
template <class V> -unspecified-2D-vector-type- W1( V & v );
...
//2D view proxies, only enabled if:
// is_scalar<S>::value
template <class S> -unspecified-2D-vector-type- X0( S & s );
template <class S> -unspecified-2D-vector-type- X1( S & s );
template <class S> -unspecified-2D-vector-type- XX( S & s );
...
-unspecified-2D-vector-type- _00();
-unspecified-2D-vector-type- _01();
-unspecified-2D-vector-type- _10();
-unspecified-2D-vector-type- _11();
//3D view proxies, only enabled if:
// is_vec<V>::value
template <class V> -unspecified-3D-vector-type- XXX( V & v );
...
template <class V> -unspecified-3D-vector-type- XXW( V & v );
template <class V> -unspecified-3D-vector-type- XX0( V & v );
template <class V> -unspecified-3D-vector-type- XX1( V & v );
template <class V> -unspecified-3D-vector-type- XYX( V & v );
...
template <class V> -unspecified-3D-vector-type- XY1( V & v );
...
template <class V> -unspecified-3D-vector-type- WW1( V & v );
...
//3D view proxies, only enabled if:
// is_scalar<S>::value
template <class S> -unspecified-3D-vector-type- X00( S & s );
template <class S> -unspecified-3D-vector-type- X01( S & s );
...
template <class S> -unspecified-3D-vector-type- XXX( S & s );
template <class S> -unspecified-3D-vector-type- XX0( S & s );
...
-unspecified-3D-vector-type- _000();
-unspecified-3D-vector-type- _001();
-unspecified-3D-vector-type- _010();
...
-unspecified-3D-vector-type- _111();
//4D view proxies, only enabled if:
// is_vec<V>::value
template <class V> -unspecified-4D-vector-type- XXXX( V & v );
...
template <class V> -unspecified-4D-vector-type- XXXW( V & v );
template <class V> -unspecified-4D-vector-type- XXX0( V & v );
template <class V> -unspecified-4D-vector-type- XXX1( V & v );
template <class V> -unspecified-4D-vector-type- XXYX( V & v );
...
template <class V> -unspecified-4D-vector-type- XXY1( V & v );
...
template <class V> -unspecified-4D-vector-type- WWW1( V & v );
...
//4D view proxies, only enabled if:
// is_scalar<S>::value
template <class S> -unspecified-4D-vector-type- X000( S & s );
template <class S> -unspecified-4D-vector-type- X001( S & s );
...
template <class S> -unspecified-4D-vector-type- XXXX( S & s );
template <class S> -unspecified-4D-vector-type- XX00( S & s );
...
-unspecified-4D-vector-type- _0000();
-unspecified-4D-vector-type- _0001();
-unspecified-4D-vector-type- _0010();
...
-unspecified-4D-vector-type- _1111();
//*** Accessing matrix elements ***
//Only enabled if:
// is_quat<Q>::value
template <int R,int C,class M> -unspecified-return-type- A( M & m );
template <class M> -unspecified-return-type- A00( M & m );
template <class M> -unspecified-return-type- A01( M & m );
...
template <class M> -unspecified-return-type- A09( M & m );
template <class M> -unspecified-return-type- A10( M & m );
...
template <class M> -unspecified-return-type- A99( M & m );
//*** Quaternion operations ***
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value
template <class A,class B>
A & assign( A & a, B const & b );
//Only enabled if:
// is_quat<R>::value && is_quat<A>::value
template <class R,class A>
R convert_to( A const & a );
//Only enabled if:
// is_quat<R>::value && is_mat<A>::value &&
// mat_traits<A>::rows==3 && mat_traits<A>::cols==3
template <class R,class A>
R convert_to( A const & m );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value
template <class A,class B>
A & operator-=( A & a, B const & b );
//Only enabled if: is_quat<A>::value
template <class A>
typename deduce_quat<A>::type
operator-( A const & a );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value &&
template <class A,class B>
typename deduce_quat2<A,B>::type
operator-( A const & a, B const & b );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value
template <class A,class B>
A & operator+=( A & a, B const & b );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value &&
template <class A,class B>
typename deduce_quat2<A,B>::type
operator+( A const & a, B const & b );
//Only enabled if: is_quat<A>::value && is_quat<B>::value
template <class A,class B>
A & operator/=( A & a, B b );
//Only enabled if: is_quat<A>::value && is_quat<B>::value
template <class A,class B>
typename deduce_quat<A>::type
operator/( A const & a, B b );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value
template <class A,class B>
A & operator*=( A & a, B const & b );
//Only enabled if: is_quat<A>::value && is_quat<B>::value
template <class A,class B>
A & operator*=( A & a, B b );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value
template <class A,class B>
typename deduce_quat2<A,B>::type
operator*( A const & a, B const & b );
//Only enabled if: is_quat<A>::value && is_quat<B>::value
template <class A,class B>
typename deduce_quat<A>::type
operator*( A const & a, B b );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value
template <class A,class B>
bool operator==( A const & a, B const & b );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value
template <class A,class B>
bool operator!=( A const & a, B const & b );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value
template <class A,class B,class Cmp>
bool cmp( A const & a, B const & b, Cmp pred );
//Only enabled if: is_quat<A>::value
template <class A>
typename quat_traits<A>::scalar_type
mag_sqr( A const & a );
//Only enabled if: is_quat<A>::value
template <class A>
typename quat_traits<A>::scalar_type
mag( A const & a );
//Only enabled if: is_quat<A>::value
template <class A>
typename deduce_quat<A>::type
normalized( A const & a );
//Only enabled if: is_quat<A>::value
template <class A>
void normalize( A & a );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value
template <class A,class B>
typename deduce_scalar<A,B>::type
dot( A const & a, B const & b );
//Only enabled if: is_quat<A>::value
template <class A>
typename deduce_quat<A>::type
conjugate( A const & a );
//Only enabled if: is_quat<A>::value
template <class A>
typename deduce_quat<A>::type
inverse( A const & a );
//Only enabled if:
// is_quat<A>::value && is_quat<B>::value && is_scalar<C>
template <class A,class B,class C>
typename deduce_quat2<A,B> >::type
slerp( A const & a, B const & b, C c );
template <class T>
-unspecified-return-type- zero_quat();
//Only enabled if: is_quat<A>::value
template <class A>
void set_zero( A & a );
template <class S>
-unspecified-return-type- identity_quat();
//Only enabled if: is_quat<A>::value
template <class A>
void set_identity( A & a );
//Only enabled if:
// is_vec<A>::value && vec_traits<A>::dim==3
template <class A>
-unspecified-return-type- rot_quat( A const & axis, typename vec_traits<A>::scalar_type angle );
//Only enabled if:
// is_quat<A>::value &&
// is_vec<B>::value && vec_traits<B>::dim==3
template <class A>
void set_rot( A & a, B const & axis, typename vec_traits<B>::scalar_type angle );
//Only enabled if:
// is_quat<A>::value &&
// is_vec<B>::value && vec_traits<B>::dim==3
template <class A,class B>
void rotate( A & a, B const & axis, typename quat_traits<A>::scalar_type angle );
template <class Angle>
-unspecified-return-type- rotx_quat( Angle const & angle );
//Only enabled if: is_quat<A>::value
template <class A>
void set_rotx( A & a, typename quat_traits<A>::scalar_type angle );
//Only enabled if: is_quat<A>::value
template <class A>
void rotate_x( A & a, typename quat_traits<A>::scalar_type angle );
template <class Angle>
-unspecified-return-type- roty_quat( Angle const & angle );
//Only enabled if: is_quat<A>::value
template <class A>
void set_rotz( A & a, typename quat_traits<A>::scalar_type angle );
//Only enabled if: is_quat<A>::value
template <class A>
void rotate_y( A & a, typename quat_traits<A>::scalar_type angle );
template <class Angle>
-unspecified-return-type- rotz_quat( Angle const & angle );
//Only enabled if: is_quat<A>::value
template <class A>
void set_rotz( A & a, typename quat_traits<A>::scalar_type angle );
//Only enabled if: is_quat<A>::value
template <class A>
void rotate_z( A & a, typename quat_traits<A>::scalar_type angle );
//Only enabled if: is_quat<A>::value
template <class Scalar,class A>
-unspecified-return_type- scalar_cast( A const & a );
//Only enabled if: is_quat<A>::value
template <class A>
-unspecified-return-type- qref( A & a );
//*** Vector operations ***
//Only enabled if:
// is_vec<A>::value && is_vec<B>::value &&
// vec_traits<A>::dim==vec_traits<B>::dim
template <class A,class B>
A & assign( A & a, B const & b );
//Only enabled if:
// is_vec<R>::value && is_vec<A>::value &&
// vec_traits<R>::dim==vec_traits<A>::dim
template <class R,class A>
R convert_to( A const & a );
//Only enabled if:
// is_vec<A>::value && is_vec<B>::value &&
// vec_traits<A>::dim==vec_traits<B>::dim
template <class A,class B>
A & operator-=( A & a, B const & b );
//Only enabled if: is_vec<A>::value
template <class A>
typename deduce_vec<A>::type
operator-( A const & a );
//Only enabled if:
// is_vec<A>::value && is_vec<B>::value &&
// vec_traits<A>::dim==vec_traits<B>::dim
template <class A,class B>
typename deduce_vec2<A,B,vec_traits<A>::dim>::type
operator-( A const & a, B const & b );
//Only enabled if:
// is_vec<A>::value && is_vec<B>::value &&
// vec_traits<A>::dim==vec_traits<B>::dim
template <class A,class B>
A & operator+=( A & a, B const & b );
//Only enabled if:
// is_vec<A>::value && is_vec<B>::value &&
// vec_traits<A>::dim==vec_traits<B>::dim
template <class A,class B>
typename deduce_vec2<A,B,vec_traits<A>::dim>::type
operator+( A const & a, B const & b );
//Only enabled if: is_vec<A>::value && is_scalar<B>::value
template <class A,class B>
A & operator/=( A & a, B b );
//Only enabled if: is_vec<A>::value && is_scalar<B>::value
template <class A,class B>
typename deduce_vec<A>::type
operator/( A const & a, B b );
//Only enabled if: is_vec<A>::value && is_scalar<B>::value
template <class A,class B>
A & operator*=( A & a, B b );
//Only enabled if: is_vec<A>::value && is_scalar<B>::value
template <class A>
typename deduce_vec<A>::type
operator*( A const & a, B b );
//Only enabled if: is_scalar<A>::value && is_vec<B>::value
template <class A>
typename deduce_vec<B>::type
operator*( A a, B const & b );
//Only enabled if:
// is_vec<A>::value && is_vec<B>::value &&
// vec_traits<A>::dim==vec_traits<B>::dim
template <class A,class B>
bool operator==( A const & a, B const & b );
//Only enabled if:
// is_vec<A>::value && is_vec<B>::value &&
// vec_traits<A>::dim==vec_traits<B>::dim
template <class A,class B>
bool operator!=( A const & a, B const & b );
//Only enabled if:
// is_vec<A>::value && is_vec<B>::value &&
// vec_traits<A>::dim==vec_traits<B>::dim
template <class A,class B,class Cmp>
bool cmp( A const & a, B const & b, Cmp pred );
//Only enabled if:
// is_vec<A>::value
template <class A>
typename vec_traits<A>::scalar_type
mag_sqr( A const & a );
//Only enabled if:
// is_vec<A>::value
template <class A>
typename vec_traits<A>::scalar_type
mag( A const & a );
//Only enabled if:
// is_vec<A>::value
template <class A>
typename deduce_vec<A>::type
normalized( A const & a );
//Only enabled if:
// is_vec<A>::value
template <class A>
void normalize( A & a );
//Only enabled if:
// is_vec<A>::value && is_vec<B>::value &&
// vec_traits<A>::dim==vec_traits<B>::dim
template <class A,class B>
typename deduce_scalar<A,B>::type
dot( A const & a, B const & b );
//Only enabled if:
// is_vec<A>::value && is_vec<B>::value &&
// vec_traits<A>::dim==3 && vec_traits<B>::dim==3
template <class A,class B>
typename deduce_vec2<A,B,3>::type
cross( A const & a, B const & b );
template <class T,int S>
-unspecified-return-type- zero_vec();
//Only enabled if:
// is_vec<A>::value
template <class A>
void set_zero( A & a );
//Only enabled if: is_vec<A>::value
template <class A>
-unspecified-return-type- vref( A & a );
//Only enabled if: is_vec<A>::value
template <class Scalar,class A>
-unspecified-return_type- scalar_cast( A const & a );
//*** Matrix operations ***
//Only enabled if:
// is_mat<A>::value && is_mat<B>::value &&
// mat_traits<A>::rows==mat_traits<B>::rows &&
// mat_traits<A>::cols==mat_traits<B>::cols
template <class A,class B>
A & assign( A & a, B const & b );
//Only enabled if:
// is_mat<R>::value && is_mat<A>::value &&
// mat_traits<R>::rows==mat_traits<A>::rows &&
// mat_traits<R>::cols==mat_traits<A>::cols
template <class R,class A>
R convert_to( A const & a );
//Only enabled if:
// is_mat<A>::value && is_mat<B>::value &&
// mat_traits<A>::rows==mat_traits<B>::rows &&
// mat_traits<A>::cols==mat_traits<B>::cols
template <class A,class B>
A & operator-=( A & a, B const & b );
//Only enabled if: is_mat<A>::value
template <class A>
typename deduce_mat<A>::type
operator-( A const & a );
//Only enabled if:
// is_mat<A>::value && is_mat<B>::value &&
// mat_traits<A>::rows==mat_traits<B>::rows &&
// mat_traits<A>::cols==mat_traits<B>::cols
template <class A,class B>
typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type
operator-( A const & a, B const & b );
//Only enabled if:
// is_mat<A>::value && is_mat<B>::value &&
// mat_traits<A>::rows==mat_traits<B>::rows &&
// mat_traits<A>::cols==mat_traits<B>::cols
template <class A,class B>
A & operator+=( A & a, B const & b );
//Only enabled if:
// is_mat<A>::value && is_mat<B>::value &&
// mat_traits<A>::rows==mat_traits<B>::rows &&
// mat_traits<A>::cols==mat_traits<B>::cols
template <class A,class B>
typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type
operator+( A const & a, B const & b );
//Only enabled if: is_mat<A>::value && is_scalar<B>::value
template <class A,class B>
A & operator/=( A & a, B b );
//Only enabled if: is_mat<A>::value && is_scalar<B>::value
template <class A,class B>
typename deduce_mat<A>::type
operator/( A const & a, B b );
//Only enabled if:
// is_mat<A>::value && is_mat<B>::value &&
// mat_traits<A>::rows==mat_traits<A>::cols &&
// mat_traits<A>::rows==mat_traits<B>::rows &&
// mat_traits<A>::cols==mat_traits<B>::cols
template <class A,class B>
A & operator*=( A & a, B const & b );
//Only enabled if: is_mat<A>::value && is_scalar<B>::value
template <class A,class B>
A & operator*=( A & a, B b );
//Only enabled if:
// is_mat<A>::value && is_mat<B>::value &&
// mat_traits<A>::cols==mat_traits<B>::rows
template <class A,class B>
typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<B>::cols>::type
operator*( A const & a, B const & b );
//Only enabled if: is_mat<A>::value && is_scalar<B>::value
template <class A,class B>
typename deduce_mat<A>::type
operator*( A const & a, B b );
//Only enabled if: is_scalar<A>::value && is_mat<B>::value
template <class A,class B>
typename deduce_mat<B>::type
operator*( A a, B const & b );
//Only enabled if:
// is_mat<A>::value && is_mat<B>::value &&
// mat_traits<A>::rows==mat_traits<B>::rows &&
// mat_traits<A>::cols==mat_traits<B>::cols
template <class A,class B>
bool operator==( A const & a, B const & b );
//Only enabled if:
// is_mat<A>::value && is_mat<B>::value &&
// mat_traits<A>::rows==mat_traits<B>::rows &&
// mat_traits<A>::cols==mat_traits<B>::cols
template <class A,class B>
bool operator!=( A const & a, B const & b );
//Only enabled if:
// is_mat<A>::value && is_mat<B>::value &&
// mat_traits<A>::rows==mat_traits<B>::rows &&
// mat_traits<A>::cols==mat_traits<B>::cols
template <class A,class B,class Cmp>
bool cmp( A const & a, B const & b, Cmp pred );
//Only enabled if:
// is_mat<A>::value && is_scalar<B>::value
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class B>
typename deduce_mat<A>::type
inverse( A const & a, B det );
template <class A>
typename deduce_mat<A>::type
inverse( A const & a );
template <class T,int D>
-unspecified-return-type- zero_mat();
template <class T,int R,int C>
-unspecified-return-type- zero_mat();
//Only enabled if:
// is_mat<A>::value
template <class A>
void set_zero( A & a );
template <class S,int D>
-unspecified-return-type- identity_mat();
//Only enabled if:
// is_mat<A>::value &&
// mat_traits<A>::cols==mat_traits<A>::rows
template <class A>
void set_identity( A & a );
//Only enabled if:
// is_vec<A>::value && vec_traits<A>::dim==3
template <int Dim,class A,class Angle>
-unspecified-return-type-
rot_mat( A const & axis, Angle angle );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_xzy( Angle x1, Angle z2, Angle y3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_xyz( Angle x1, Angle y2, Angle z3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_yxz( Angle y1, Angle x2, Angle z3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_yzx( Angle y1, Angle z2, Angle x3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_zyx( Angle z1, Angle y2, Angle x3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_zxy( Angle z1, Angle x2, Angle y3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_xzx( Angle x1, Angle z2, Angle x3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_xyx( Angle x1, Angle y2, Angle x3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_yxy( Angle y1, Angle x2, Angle y3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_yzy( Angle y1, Angle z2, Angle y3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_zyz( Angle z1, Angle y2, Angle z3 );
template <int Dim,class Angle>
-unspecified-return-type-
rot_mat_zxz( Angle z1, Angle y2, Angle z3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols &&
// is_vec<B>::value && vec_traits<B>::dim==3
template <class A>
void set_rot( A & a, B const & axis, typename vec_traits<B>::scalar_type angle );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_xzy( A & a, Angle x1, Angle z2, Angle y3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_xyz( A & a, Angle x1, Angle y2, Angle z3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_yxz( A & a, Angle y1, Angle x2, Angle z3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_yzx( A & a, Angle y1, Angle z2, Angle x3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_zyx( A & a, Angle z1, Angle y2, Angle x3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_zxy( A & a, Angle z1, Angle x2, Angle y3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_xzx( A & a, Angle x1, Angle z2, Angle x3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_xyx( A & a, Angle x1, Angle y2, Angle x3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_yxy( A & a, Angle y1, Angle x2, Angle y3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_yzy( A & a, Angle y1, Angle z2, Angle y3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_zyz( A & a, Angle z1, Angle y2, Angle z3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_zxz( A & a, Angle z1, Angle x2, Angle z3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void set_rot_xzy( A & a, Angle x1, Angle z2, Angle y3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols &&
// is_vec<B>::value && vec_traits<B>::dim==3
template <class A,class B>
void rotate( A & a, B const & axis, typename mat_traits<A>::scalar_type angle );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_xzy( A & a, Angle x1, Angle z2, Angle y3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_xyz( A & a, Angle x1, Angle y2, Angle z3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_yxz( A & a, Angle y1, Angle x2, Angle z3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_yzx( A & a, Angle y1, Angle z2, Angle x3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_zyx( A & a, Angle z1, Angle y2, Angle x3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_zxy( A & a, Angle z1, Angle x2, Angle y3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_xzx( A & a, Angle x1, Angle z2, Angle x3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_xyx( A & a, Angle x1, Angle y2, Angle x3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_yxy( A & a, Angle y1, Angle x2, Angle y3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_yzy( A & a, Angle y1, Angle z2, Angle y3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_zyz( A & a, Angle z1, Angle y2, Angle z3 );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A,class Angle>
void rotate_zxz( A & a, Angle z1, Angle x2, Angle z3 );
template <int Dim,class Angle>
-unspecified-return-type- rotx_mat( Angle const & angle );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A>
void set_rotx( A & a, typename mat_traits<A>::scalar_type angle );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A>
void rotate_x( A & a, typename mat_traits<A>::scalar_type angle );
template <int Dim,class Angle>
-unspecified-return-type- roty_mat( Angle const & angle );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A>
void set_roty( A & a, typename mat_traits<A>::scalar_type angle );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A>
void rotate_y( A & a, typename mat_traits<A>::scalar_type angle );
template <int Dim,class Angle>
-unspecified-return-type- rotz_mat( Angle const & angle );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A>
void set_rotz( A & a, typename mat_traits<A>::scalar_type angle );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows>=3 &&
// mat_traits<A>::rows==mat_traits<A>::cols
template <class A>
void rotate_z( A & a, typename mat_traits<A>::scalar_type angle );
//Only enabled if:
// is_mat<A>::value && mat_traits<A>::rows==mat_traits<A>::cols
template <class A>
mat_traits<A>::scalar_type
determinant( A const & a );
template <class T>
-unspecified-return-type
perspective_lh( T fov_y, T aspect, T zn, T zf );
template <class T>
-unspecified-return-type
perspective_rh( T fov_y, T aspect, T zn, T zf );
//Only enabled if: is_mat<A>::value
template <class A>
-unspecified-return-type- mref( A & a );
//Only enabled if: is_mat<A>::value
template <class Scalar,class A>
-unspecified-return_type- scalar_cast( A const & a );
//*** Quaternion-Vector operations ***
//Only enabled if:
// is_quat<A>::value &&
// is_vec<B>::value && vec_traits<B>::dim==3
template <class A,class B>
typename deduce_vec2<A,B,3>::type
operator*( A const & a, B const & b );
//*** Vector-Matrix operations ***
//Only enabled if:
// is_mat<A>::value && is_vec<B>::value &&
// mat_traits<A>::cols==vec_traits<B>::dim
template <class A,class B>
typename deduce_vec2<A,B,mat_traits<A>::rows>::type
operator*( A const & a, B const & b );
//Only enabled if:
// is_mat<A>::value && is_vec<B>::value &&
// mat_traits<A>::rows==4 && mat_traits<A>::cols==4 &&
// vec_traits<B>::dim==3
template <class A,class B>
deduce_vec2<A,B,3> >::type
transform_vector( A const & a, B const & b );
//Only enabled if:
// is_mat<A>::value && is_vec<B>::value &&
// mat_traits<A>::rows==4 && mat_traits<A>::cols==4 &&
// vec_traits<B>::dim==3
template <class A,class B>
deduce_vec2<A,B,3> >::type
transform_point( A const & a, B const & b );
//*** Matrix-to-matrix view proxies ***
template <int R>
-unspecified-return-type- del_row();
template <int C>
-unspecified-return-type- del_col();
template <int R,int C>
-unspecified-return-type- del_row_col();
template <int R>
-unspecified-return-type- neg_row();
template <int C>
-unspecified-return-type- neg_col();
template <int R1,int R2>
-unspecified-return-type- swap_rows();
template <int C1,int C2>
-unspecified-return-type- swap_cols();
-unspecified-return-type- transposed();
//*** Vector-to-matrix view proxies ***
//Only enabled if: is_vec<A>::value
template <iclass A>
-unspecified-return-type- col_mat( A & a );
//Only enabled if: is_vec<A>::value
template <iclass A>
-unspecified-return-type- row_mat( A & a );
//Only enabled if: is_vec<A>::value
template <iclass A>
-unspecified-return-type- translation_mat( A & a );
//Only enabled if: is_vec<A>::value
template <iclass A>
-unspecified-return-type- diag_mat( A & a );
//*** Matrix-to-vector view proxies ***
//Only enabled if: is_mat<A>::value
template <int C,class A>
-unspecified-return-type- col( A & a );
//Only enabled if: is_mat<A>::value
template <int C,class A>
-unspecified-return-type- row( A & a );
//Only enabled if: is_mat<A>::value
template <class A>
-unspecified-return-type- diag( A & a );
//Only enabled if:
// is_mat<A>::value &&
// mat_traits<A>::rows==mat_traits<A>::cols && mat_traits<A>::rows>=3
template <class A>
-unspecified-return-type- translation( A & a );
//*** Generic programming utilities ***
template <class Q>
struct deduce_quat
{
typedef Q type;
};
template <class A,class B>
struct deduce_quat2
{
typedef /*unspecified*/ type;
};
template <
class V,
int Dim=vec_traits<Vector>::dim>
struct deduce_vec
{
typedef /*unspecified*/ type;
};
template <class A,class B,int Dim>
struct deduce_vec2
{
typedef /*unspecified*/ type;
};
template <
class M,
int Rows=mat_traits<Matrix>::rows,
int Cols=mat_traits<Matrix>::cols>
struct deduce_mat
{
typedef /*unspecified*/ type;
};
template <class A,class B,int Rows,int Cols>
struct deduce_mat2
{
typedef /*unspecified*/ type;
};
template <class A,class B>
struct deduce_scalar
{
typedef typename impl<A,B>::type type;
};
template <class Scalar>
struct scalar_traits
{
BOOST_QVM_INLINE_CRITICAL
static Scalar value( int v )
{
return Scalar(v);
}
};
template <class T>
struct scalar
{
typedef /*exact definition unspecified*/ type;
};
//*** Exception types ***
struct error:
virtual boost::exception,
virtual std::exception
{
};
struct zero_determinant_error: virtual error { };
struct zero_magnitude_error: virtual error { };
}
}
//*** Macros ***
#ifndef BOOST_QVM_FORCE_INLINE
#define BOOST_QVM_FORCE_INLINE /*platform-specific*/
#endif
#ifndef BOOST_QVM_INLINE
#define BOOST_QVM_INLINE inline
#endif
#ifndef BOOST_QVM_INLINE_TRIVIAL
#define BOOST_QVM_INLINE_TRIVIAL BOOST_QVM_FORCE_INLINE
#endif
#ifndef BOOST_QVM_INLINE_CRITICAL
#define BOOST_QVM_INLINE_CRITICAL BOOST_QVM_FORCE_INLINE
#endif
#ifndef BOOST_QVM_INLINE_OPERATIONS
#define BOOST_QVM_INLINE_OPERATIONS BOOST_QVM_INLINE
#endif
#ifndef BOOST_QVM_INLINE_RECURSION
#define BOOST_QVM_INLINE_RECURSION BOOST_QVM_INLINE_OPERATIONS
#endif
#ifndef BOOST_QVM_ASSERT
#include <boost/assert.hpp>
#define BOOST_QVM_ASSERT BOOST_ASSERT
#endif
#ifndef BOOST_QVM_STATIC_ASSERT
#include <boost/static_assert.hpp>
#define BOOST_QVM_STATIC_ASSERT BOOST_STATIC_ASSERT
#endif
#ifndef BOOST_QVM_THROW_EXCEPTION
#include <boost/throw_exception.hpp>
#define BOOST_QVM_THROW_EXCEPTION BOOST_THROW_EXCEPTION
#endif
Copyright (c) 2008-2018 by Emil Dotchevski and Reverge Studios, Inc.
Distributed under the Boost Software License, Version 1.0.