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QVM 背后的动机是什么？为什么不直接使用 uBLAS/Eigen/CML/GLM 等？

quat<float> rx = rotx_quat(3.14159f);
vec<float,3> v = {0,0,7};
mat<float,4,4> tr = translation_mat(v);
struct float3 { float a[3]; };

namespace boost { namespace qvm {

  template <>
  struct vec_traits<float3> {

    static int const dim=3;
    typedef float scalar_type;

    template <int I>
    static inline scalar_type & write_element( float3 & v ) {
      return v.a[I];
    }

    template <int I>
    static inline scalar_type read_element( float3 const & v ) {
      return v.a[I];
    }

    static inline scalar_type & write_element_idx( int i, float3 & v ) {
      return v.a[i];
    } //optional

    static inline scalar_type read_element_idx( int i, float3 const & v ) {
      return v.a[i];
    } //optional

  };

} }
namespace boost { namespace qvm {

  template <>
  struct vec_traits<float3>: vec_traits_defaults<float3,float,3> {

    template <int I>
    static inline scalar_type & write_element( float3 & v ) {
      return v.a[I];
    }

    static inline scalar_type & write_element_idx( int i, float3 & v ) {
      return v.a[i];
    } //optional

  };

} }
float3 v;
X(v) = 0;
Y(v) = 0;
Z(v) = 7;
float vmag = mag(v);
float33 m = rotx_mat<3>(3.14159f);
float3 vrot = m * v;
template <int I>
static inline void write_element( float3 & v, scalar_type s ) {
  v.a[I] = s;
}
float v[3] = {0,0,7};
float3 vrot = rotx_mat<3>(3.14159f) * v;
float v[3] = {0,0,7};
v *= 42;
float v[3] = {0,0,7};
vref(v) *= 42;
void multiply_column1( float33 & m, float scalar ) {
  col<1>(m) *= scalar;
}
float3 v = {0,0,7};
float3 vrot = transposed(rotx_mat<3>(3.14159f)) * v;
float3 v = {0,0,7};
YXZ(v) = rotx_mat<3>(3.14159f) * v;
float3 v = {0,0,7};
float4 point = XYZ1(v); //{0,0,7,1}
float4 vector = XYZ0(v); //{0,0,7,0}
float3 v = {0,0,7};
float4 v1 = ZZZZ(v); //{7,7,7,7}
float3 v = _00X(42.0f); //{0,0,42}
template <class Matrix,class Vector>
Vector operator*( Matrix const & m, Vector const & v );
template <class A,class B>
typename enable_if_c<
  is_mat<A>::value && is_vec<B>::value && mat_traits<A>::cols==vec_traits<B>::dim, //Condition
  B>::type //Return type
operator*( A const & a, B const & b );
using namespace boost::qvm;
auto & m = m1 * m2; // auto requires C++11
user_matrix1 m = m1 * m2;
namespace boost { namespace qvm {

  template <>
  struct deduce_mat2<user_matrix1,user_matrix2,3,3> {
    typedef user_matrix1 type;
  };

  template <>
  struct deduce_mat2<user_matrix2,user_matrix1,3,3> {
    typedef user_matrix1 type;
  };

} }
float m[3][3];
auto & inv = inverse(m);
user_matrix2 m=convert_to<user_matrix2>(m1 * m2);
#include <boost/qvm/quat_traits.hpp>
#include <boost/qvm/quat_traits_array.hpp>
#include <boost/qvm/deduce_quat.hpp>
#include <boost/qvm/quat_access.hpp>
#include <boost/qvm/quat_operations.hpp>
#include <boost/qvm/quat.hpp>
#include <boost/qvm/vec_traits.hpp>
#include <boost/qvm/vec_traits_array.hpp>
#include <boost/qvm/deduce_vec.hpp>
#include <boost/qvm/vec_access.hpp>
#include <boost/qvm/swizzle.hpp>
#include <boost/qvm/swizzle2.hpp>
#include <boost/qvm/swizzle3.hpp>
#include <boost/qvm/swizzle4.hpp>
#include <boost/qvm/vec_operations.hpp>
#include <boost/qvm/vec_operations2.hpp>
#include <boost/qvm/vec_operations3.hpp>
#include <boost/qvm/vec_operations4.hpp>
#include <boost/qvm/quat_vec_operations.hpp>
#include <boost/qvm/vec_mat_operations.hpp>
#include <boost/qvm/map_vec_mat.hpp>
#include <boost/qvm/vec.hpp>
#include <boost/qvm/mat_traits.hpp>
#include <boost/qvm/mat_traits_array.hpp>
#include <boost/qvm/deduce_mat.hpp>
#include <boost/qvm/mat_access.hpp>
#include <boost/qvm/mat_operations.hpp>
#include <boost/qvm/mat_operations2.hpp>
#include <boost/qvm/mat_operations3.hpp>
#include <boost/qvm/mat_operations4.hpp>
#include <boost/qvm/map_mat_mat.hpp>
#include <boost/qvm/map_mat_vec.hpp>
#include <boost/qvm/mat.hpp>
S operator*( S, S );
S operator/( S, S );
S operator+( S, S );
S operator-( S, S );

S & operator*=( S &, S );
S & operator/=( S &, S );
S & operator+=( S &, S );
S & operator-=( S &, S );

bool operator==( S, S );
bool operator!=( S, S );
namespace boost { namespace qvm {

  template <class T>
  struct is_scalar {
    static bool const value=false;
  };

  template <> struct is_scalar<char>           { static bool const value=true; };
  template <> struct is_scalar<signed char>    { static bool const value=true; };
  template <> struct is_scalar<unsigned char>  { static bool const value=true; };
  template <> struct is_scalar<signed short>   { static bool const value=true; };
  template <> struct is_scalar<unsigned short> { static bool const value=true; };
  template <> struct is_scalar<signed int>     { static bool const value=true; };
  template <> struct is_scalar<unsigned int>   { static bool const value=true; };
  template <> struct is_scalar<signed long>    { static bool const value=true; };
  template <> struct is_scalar<unsigned long>  { static bool const value=true; };
  template <> struct is_scalar<float>          { static bool const value=true; };
  template <> struct is_scalar<double>         { static bool const value=true; };
  template <> struct is_scalar<long double>    { static bool const value=true; };

} }
namespace boost { namespace qvm {

  template <class Scalar>
  struct scalar_traits {

    BOOST_QVM_INLINE_CRITICAL
    static Scalar value( int v ) {
      return Scalar(v);
    }

  };

} }
namespace boost { namespace qvm {

  template <class A,class B>
  struct deduce_scalar
  {
    typedef typename /*exact definition unspecified*/ type;
  };

} }
namespace boost { namespace qvm {

  template <class T>
  struct scalar {
    typedef /*exact definition unspecified*/ type;
  };

} }
namespace boost { namespace qvm {

  template <class T>
  struct is_quat {

    static bool const value = false;

  };

} }
namespace boost { namespace qvm {

  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 );

    // Alternative signature for write_element:

    template <int I>
    static inline void write_element( Quaternion & q, scalar_type s );

  };
  */

} }
#include <boost/qvm/quat_traits.hpp>

struct fquat { float a[4]; };

namespace boost { namespace qvm {

  template <>
  struct quat_traits<fquat> {

    typedef float scalar_type;

    template <int I>
    static inline scalar_type & write_element( fquat & q ) {
      return q.a[I];
    }

    template <int I>
    static inline scalar_type read_element( fquat const & q ) {
      return q.a[I];
    }

  };

} }
namespace boost { namespace qvm {

  template <>
  struct quat_traits<fquat>: quat_traits_defaults<fquat,float> {

    template <int I>
    static inline scalar_type & write_element( fquat & q ) {
      return q.a[I];
    }

  };

} }
namespace boost { namespace qvm {

  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));
    }

  };

} }
namespace boost { namespace qvm {

  template <class Q,
    class S=typename quat_traits<Q>::scalar_type>
  struct deduce_quat {
    typedef Q type;
  };

} }
namespace boost { namespace qvm {

  template <class A,class B,
    class S=typename deduce_scalar<
      typename scalar<A>::type,
      typename scalar<B>::type>::type>
  struct deduce_quat2 {
    typedef /*unspecified*/ type;
  };

} }
namespace boost { namespace qvm {

  template <class T>
  struct is_vec {

    static bool const value = false;

  };

 } }
namespace boost { namespace qvm {

  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 );

    static inline scalar_type read_element_idx( int i, Vector const & v );

    template <int I>
    static inline scalar_type & write_element( Vector & v );

    static inline scalar_type & write_element_idx( int i, Vector & v );

    // Alternative signature for write_element and write_element_idx:

    template <int I>
    static inline void write_element( Vector & v, scalar_type s );

    static inline void write_element_idx( int i, Vector & v, scalar_type s );

  };
  */

} }
#include <boost/qvm/vec_traits.hpp>

struct float3 { float a[3]; };

namespace boost { namespace qvm {

  template <>
  struct vec_traits<float3> {

    static int const dim=3;

    typedef float scalar_type;

    template <int I>
    static inline scalar_type & write_element( float3 & v ) {
      return v.a[I];
    }

    template <int I>
    static inline scalar_type read_element( float3 const & v ) {
      return v.a[I];
    }

    static inline scalar_type & write_element_idx( int i, float3 & v ) {
      return v.a[i];
    } //optional

    static inline scalar_type read_element_idx( int i, float3 const & v ) {
      return v.a[i];
    } //optional

  };

} }
namespace boost { namespace qvm {

  template <>
  struct vec_traits<float3>: vec_traits_defaults<float3,float,3>
  {

    template <int I>
    static inline scalar_type & write_element( float3 & v ) {
      return v.a[I];
    }

    static inline scalar_type & write_element_idx( int i, float3 & v ) {
      return v.a[i];
    } //optional

  };

} }
namespace boost { namespace qvm {

  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 */
    }
  };

} }
namespace boost { namespace qvm {

  template <class V,
    int D=vec_traits<Vector>::dim,
    class S=typename vec_traits<V>::scalar_type>
  struct deduce_vec {

    typedef /*unspecified*/ type;

  };

} }
namespace boost { namespace qvm {

  template <class A,class B,int D,
    class S=typename deduce_scalar<
      typename scalar<A>::type,
      typename scalar<B>::type>::type>
  struct deduce_vec2 {
    typedef /*unspecified*/ type;
  };

} }
namespace boost { namespace qvm {

  template <class T>
  struct is_mat {

    static bool const value = false;

  };

} }
namespace boost { namespace qvm {

  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 );

    static inline scalar_typeread_element_idx( int r, int c, Matrix const & m );

    template <int R,int C>
    static inline scalar_type & write_element( Matrix & m );

    static inline scalar_type & write_element_idx( int r, int c, Matrix & m );

    // Alternative signature for write_element and write_element_idx:

    template <int R,int C>
    static inline void write_element( Matrix & m, scalar_type s );

    static inline void write_element_idx( int r, int c, Matrix & m, scalar_type s );

  };
  */

} }
#include <boost/qvm/mat_traits.hpp>

struct float33 { float a[3][3]; };

namespace boost { namespace qvm {

  template <>
  struct mat_traits<float33> {

    static int const rows=3;
    static int const cols=3;
    typedef float scalar_type;

    template <int R,int C>
    static inline scalar_type & write_element( float33 & m ) {
      return m.a[R][C];
    }

    template <int R,int C>
    static inline scalar_type read_element( float33 const & m ) {
      return m.a[R][C];
    }

    static inline scalar_type & write_element_idx( int r, int c, float33 & m ) {
      return m.a[r][c];
    }

    static inline scalar_type read_element_idx( int r, int c, float33 const & m ) {
      return m.a[r][c];
    }

  };

} }
namespace boost { namespace qvm {

  template <>
  struct mat_traits<float33>: mat_traits_defaults<float33,float,3,3> {

    template <int R,int C> static inline scalar_type & write_element( float33 & m ) { return m.a[R][C]; }

    static inline scalar_type & write_element_idx( int r, int c, float33 & m ) {
      return m.a[r][c];
    }

  };

} }
namespace boost { namespace qvm {

  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 */
    }
  };

} }
namespace boost { namespace qvm {

  template <
    class M,
    int R=mat_traits<Matrix>::rows,
    int C=mat_traits<Matrix>::cols,
    class S=typename mat_traits<M>::scalar_type>
  struct deduce_mat {

    typedef /*unspecified*/ type;

  };

} }
namespace boost { namespace qvm {

  template <class A,class B,int R,int C,
    class S = typename deduce_scalar<
      typename scalar<A>::type,
      typename scalar<B>::type>::type
  struct deduce_mat2 {

    typedef /*unspecified*/ type;

  };

} }
namespace boost { namespace qvm {

    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];
      }

    };

} }
namespace boost { namespace qvm {

    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];
      }
    };

} }
namespace boost { namespace qvm {

  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];
    }

  };

} }
namespace boost { namespace qvm {

  //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 );

} }
S(q) *= 42;
V(q) *= 42
namespace boost { namespace qvm {

  //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 );

} }
A<1>(v) *= 42;
A1(v) *= 42;
Y(v) *= 42;
namespace boost { namespace qvm {

  //*** 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();

} }
YX(v) = v2;
namespace boost { namespace qvm {

  //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 );

} }
A<4,2>(m) *= 42;
A42(m) *= 42;
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_quat<A>::value && is_quat<B>::value
  template <class A,class B>
  A & assign( A & a, B const & b );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_quat<A>::value && is_quat<B>::value
  template <class A,class B>
  A & operator-=( A & a, B const & b );

} }
namespace boost { namespace qvm {

   //Only enabled if: is_quat<A>::value
  template <class A>
  typename deduce_quat<A>::type
  operator-( A const & a );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_quat<A>::value && is_quat<B>::value
  template <class A,class B>
  A & operator+=( A & a, B const & b );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value && is_scalar<B>::value
  template <class A,class B>
  A & operator/=( A & a, B b );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value && is_scalar<B>::value
  template <class A,class B>
  typename deduce_quat2<A,B>>::type
  operator/( A const & a, B b );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value && is_scalar<B>::value
  template <class A,class B>
  A & operator*=( A & a, B b );

} }
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_quat<A>::value && is_quat<B>::value
  template <class A,class B>
  A & operator*=( A & a, B const & b );

} }
A tmp(a);
a = tmp * b;
return a;
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value && is_scalar<B>::value
  template <class A,class B>
  typename deduce_quat2<A,B>::type
  operator*( A const & a, B b );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_quat<A>::value && is_quat<B>::value
  template <class A,class B>
  bool operator==( A const & a, B const & b );

} }
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_quat<A>::value && is_quat<B>::value
  template <class A,class B>
  bool operator!=( A const & a, B const & b );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A>
  typename quat_traits<A>::scalar_type
  mag_sqr( A const & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A>
  typename quat_traits<A>::scalar_type
  mag( A const & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A>
  typename deduce_quat<A>::type
  normalized( A const & a );

} }
typename deduce_quat<A>::type tmp;
assign(tmp,a);
normalize(tmp);
return tmp;
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A>
  void normalize( A & a );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A>
  typename deduce_quat<A>::type
  conjugate( A const & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A>
  typename deduce_quat<A>::type
  inverse( A const & a );

} }
namespace boost { namespace qvm {

  //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
  slerp180( A const & a, B const & b, C c );

  //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
  slerp360( A const & a, B const & b, C c );

  //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 ) // Deprecated
    {
    return slerp360(a, b, t);
    }

} }
auto q = slerp180(a, b, t);
auto q = slerp360(dot(a, b) < 0 ? -a : a, b, t);
namespace boost { namespace qvm {

  template <class T>
  -unspecified-return-type- zero_quat();

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A>
  void set_zero( A & a );

} }
assign(a,
  zero_quat<typename quat_traits<A>::scalar_type>());
namespace boost { namespace qvm {

  template <class S>
  -unspecified-return-type- identity_quat();

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A>
  void set_identity( A & a );

} }
assign(
  a,
  identity_quat<typename quat_traits<A>::scalar_type>());
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_vec<A>::value && vec_traits<A>::dim==3
  template <class A,class Angle>
  -unspecified-return-type- rot_quat( A const & axis, Angle angle );

} }
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_quat<A>::value &&
  //  is_vec<B>::value && vec_traits<B>::dim==3
  template <class A,class B, class Angle>
  void set_rot( A & a, B const & axis, Angle angle );

} }
assign(
  a,
  rot_quat(axis,angle));
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_quat<A>::value &&
  //  is_vec<B>::value && vec_traits<B>::dim==3
  template <class A,class B,class Angle>
  void rotate( A & a, B const & axis, Angle angle );

} }
namespace boost { namespace qvm {

  template <class Angle>
  -unspecified-return-type- rotx_quat( Angle const & angle );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A,class Angle>
  void set_rotx( A & a, Angle angle );

} }
assign(
  a,
  rotx_quat(angle));
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A,class Angle>
  void rotate_x( A & a, Angle angle );

} }
namespace boost { namespace qvm {

  template <class Angle>
  -unspecified-return-type- roty_quat( Angle const & angle );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A,class Angle>
  void set_rotz( A & a, Angle angle );

} }
assign(
  a,
  roty_quat(angle));
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A,class Angle>
  void rotate_y( A & a, Angleangle );

} }
namespace boost { namespace qvm {

    template <class Angle>
    -unspecified-return-type- rotz_quat( Angle const & angle );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A,class Angle>
  void set_rotz( A & a, Angle angle );

} }
assign(
  a,
  rotz_quat(angle));
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A,class Angle>
  void rotate_z( A & a, Angle angle );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class Scalar,class A>
  -unspecified-return_type- scalar_cast( A const & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A>
  std::string to_string( A const & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_quat<A>::value
  template <class A>
  -unspecified-return-type- qref( A & a );

} }
namespace boost { namespace qvm {

    //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 );

} }
namespace boost { namespace qvm {

    //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 );

} }
namespace boost { namespace qvm {

    //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 );

} }
namespace boost { namespace qvm {

    //Only enabled if: is_vec<A>::value
    template <class A>
    typename deduce_vec<A>::type
    operator-( A const & a );

} }
namespace boost { namespace qvm {

    //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 );

} }
namespace boost { namespace qvm {

    //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 );

} }
namespace boost { namespace qvm {

    //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 );

} }
namespace boost { namespace qvm {

    //Only enabled if: is_vec<A>::value && is_scalar<B>::value
    template <class A,class B>
    A & operator/=( A & a, B b );

} }
namespace boost { namespace qvm {

    //Only enabled if: is_vec<A>::value && is_scalar<B>::value
    template <class A,class B>
    typename deduce_vec2<A,B,vec_traits<A>::dim>::type
    operator/( A const & a, B b );

} }
namespace boost { namespace qvm {

    //Only enabled if: is_vec<A>::value && is_scalar<B>::value
    template <class A,class B>
    A & operator*=( A & a, B b );

} }
namespace boost { namespace qvm {

    //Only enabled if: is_vec<A>::value && is_scalar<B>::value
    template <class A,class B>
    typename deduce_vec2<A,B,vec_traits<A>::dim>::type
    operator*( A const & a, B b );

    //Only enabled if: is_scalar<B>::value && is_vec<A>::value
    template <class B,class A>
    typename deduce_vec2<A,B,vec_traits<A>::dim>::type
    operator*( B b, A const & a );

} }
namespace boost { namespace qvm {

    //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 );

} }
namespace boost { namespace qvm {

    //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 );

} }
.#include <boost/qvm/mat_operations.hpp>

namespace boost
{
  namespace qvm
  {
    //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 );

} }
namespace boost { namespace qvm {

    //Only enabled if:
    //  is_vec<A>::value
    template <class A>
    typename vec_traits<A>::scalar_type
    mag_sqr( A const & a );

} }
namespace boost { namespace qvm {

    //Only enabled if:
    //  is_vec<A>::value
    template <class A>
    typename vec_traits<A>::scalar_type
    mag( A const & a );

} }
namespace boost { namespace qvm {

    //Only enabled if:
    //  is_vec<A>::value
    template <class A>
    typename deduce_vec<A>::type
    normalized( A const & a );

} }
typename deduce_vec<A>::type tmp;
assign(tmp,a);
normalize(tmp);
return tmp;
namespace boost { namespace qvm {

    //Only enabled if:
    //  is_vec<A>::value
    template <class A>
    void normalize( A & a );

} }
namespace boost { namespace qvm {

    //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 );

} }
namespace boost { namespace qvm {

    //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 );

    //Only enabled if:
    //  is_vec<A>::value && is_vec<B>::value &&
    //  vec_traits<A>::dim==2 && vec_traits<B>::dim==2
    template <class A,class B>
    typename deduce_scalar<
      typename vec_traits<A>::scalar_type,
      typename vec_traits<B>::scalar_type>::type
    cross( A const & a, B const & b );

} }
namespace boost { namespace qvm {

    template <class T,int S>
    -unspecified-return-type- zero_vec();

} }
namespace boost { namespace qvm {

    //Only enabled if:
    //  is_vec<A>::value
    template <class A>
    void set_zero( A & a );

} }
assign(a,
  zero_vec<
    typename vec_traits<A>::scalar_type,
    vec_traits<A>::dim>());
namespace boost { namespace qvm {

    //Only enabled if: is_vec<A>::value
    template <class Scalar,class A>
    -unspecified-return_type- scalar_cast( A const & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_vec<A>::value
  template <class A>
  std::string to_string( A const & a );

} }
namespace boost { namespace qvm {

    //Only enabled if: is_vec<A>::value
    template <class A>
    -unspecified-return-type- vref( A & a );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value
  template <class A>
  typename deduce_mat<A>::type
  operator-( A const & a );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value && is_scalar<B>::value
  template <class A,class B>
  A & operator/=( A & a, B b );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value && is_scalar<B>::value
  template <class A,class B>
  typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type
  operator/( A const & a, B b );

} }
namespace boost { namespace qvm {

  //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 );

} }
A tmp(a);
a = tmp * b;
return a;
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value && is_scalar<B>::value
  template <class A,class B>
  A & operator*=( A & a, B b );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value && is_scalar<B>::value
  template <class A,class B>
  typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type
  operator*( A const & a, B b );

  //Only enabled if: is_scalar<B>::value && is_mat<A>::value
  template <class B,class A>
  typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type
  operator*( B b, A const & a );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //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_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type
  inverse( A const & a, B det );

  template <class A>
  typename deduce_mat<A>::type
  inverse( A const & a );

} }
namespace boost { namespace qvm {

  template <class T,int D>
  -unspecified-return-type- zero_mat();

  template <class T,int R,int C>
  -unspecified-return-type- zero_mat();

} }
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_mat<A>::value
  template <class A>
  void set_zero( A & a );

} }
assign(a,
  zero_mat<
    typename mat_traits<A>::scalar_type,
    mat_traits<A>::rows,
    mat_traits<A>::cols>());
namespace boost { namespace qvm {

  template <class S,int D>
  -unspecified-return-type- identity_mat();

} }
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_mat<A>::value &&
  //  mat_traits<A>::cols==mat_traits<A>::rows
  template <class A>
  void set_identity( A & a );

} }
assign(
  a,
  identity_mat<
    typename mat_traits<A>::scalar_type,
    mat_traits<A>::rows,
    mat_traits<A>::cols>());
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //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, class Angle>
  void set_rot( A & a, B const & axis, Angle 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 );

} }
namespace boost { namespace qvm {

  //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,class Angle>
  void rotate( A & a, B const & axis, Angle 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 );

} }
namespace boost { namespace qvm {

  template <int Dim,class Angle>
  -unspecified-return-type- rotx_mat( Angle const & angle );

} }
namespace boost { namespace qvm {

  //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_rotx( A & a, Angle angle );

} }
assign(
  a,
  rotx_mat<mat_traits<A>::rows>(angle));
namespace boost { namespace qvm {

  //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_x( A & a, Angle angle );

} }
namespace boost { namespace qvm {

  template <int Dim,class Angle>
  -unspecified-return-type- roty_mat( Angle const & angle );

} }
namespace boost { namespace qvm {

  //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_roty( A & a, Angle angle );

} }
assign(
  a,
  roty_mat<mat_traits<A>::rows>(angle));
namespace boost { namespace qvm {

  //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_y( A & a, Angle angle );

} }
namespace boost { namespace qvm {

  template <int Dim,class Angle>
  -unspecified-return-type- rotz_mat( Angle const & angle );

} }
namespace boost { namespace qvm {

  //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_rotz( A & a, Angle angle );

} }
assign(
  a,
  rotz_mat<mat_traits<A>::rows>(angle));
namespace boost { namespace qvm {

  //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_z( A & a, Angle angle );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  template <class T>
  -unspecified-return-type-
  perspective_lh( T fov_y, T aspect, T zn, T zf );

} }
namespace boost { namespace qvm {

  template <class T>
  -unspecified-return-type-
  perspective_rh( T fov_y, T aspect, T zn, T zf );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value
  template <class Scalar,class A>
  -unspecified-return_type- scalar_cast( A const & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value
  template <class A>
  std::string to_string( A const & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value
  template <class A>
  -unspecified-return-type- mref( A & a );

} }
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_quat<A>::value && is_vec<B>::value &&
  //  is_vec<B>::value && vec_traits<B>::dim==3
  template <class A,class B>
  typename deduce_vec2<A,B,mat_traits<A>::rows>::type
  operator*( A const & a, B const & b );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  //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 );

} }
namespace boost { namespace qvm {

  template <int R>
  -unspecified-return-type- del_row();

} }
namespace boost { namespace qvm {

  template <int C>
  -unspecified-return-type- del_col();

} }
namespace boost { namespace qvm {

  template <int R,int C>
  -unspecified-return-type- del_row_col();

} }
namespace boost { namespace qvm {

  template <int R>
  -unspecified-return-type- neg_row();

} }
namespace boost { namespace qvm {

  template <int C>
  -unspecified-return-type- neg_col();

} }
The expression `neg_col<C>(m)` returns a read-only <<view_proxy,`view proxy`>> that looks like the matrix `m` with column `C` negated.
namespace boost { namespace qvm {

  template <int R1,int R2>
  -unspecified-return-type- swap_rows();

} }
namespace boost { namespace qvm {

  template <int C1,int C2>
  -unspecified-return-type- swap_cols();

} }
namespace boost { namespace qvm {

  -unspecified-return-type- transposed();

} }
namespace boost { namespace qvm {

  //Only enabled if: is_vec<A>::value
  template <iclass A>
  -unspecified-return-type- col_mat( A & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_vec<A>::value
  template <iclass A>
  -unspecified-return-type- row_mat( A & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_vec<A>::value
  template <iclass A>
  -unspecified-return-type- translation_mat( A & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_vec<A>::value
  template <iclass A>
  -unspecified-return-type- diag_mat( A & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value
  template <int C,class A>
  -unspecified-return-type- col( A & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value
  template <int C,class A>
  -unspecified-return-type- row( A & a );

} }
namespace boost { namespace qvm {

  //Only enabled if: is_mat<A>::value
  template <class A>
  -unspecified-return-type- diag( A & a );

} }
namespace boost { namespace qvm {

  //Only enabled if:
  //  is_mat<A>::value &&
  //  (mat_traits<A>::rows==mat_traits<A>::cols || mat_traits<A>::rows+1==mat_traits<A>::cols) &&
  //  mat_traits<A>::cols>=3
  template <class A>
  -unspecified-return-type- translation( A & a );

} }
namespace boost { namespace qvm {

  struct error: virtual boost::exception, virtual std::exception { };

} }
namespace boost { namespace qvm {

  struct zero_magnitude_error: virtual error { };

} }
namespace boost { namespace qvm {

  struct zero_determinant_error: virtual error { };

} }
namespace boost { namespace qvm {

  #ifndef BOOST_QVM_INLINE
  #define BOOST_QVM_INLINE inline
  #endif

} }
namespace boost { namespace qvm {

  #ifndef BOOST_QVM_FORCE_INLINE
  #define BOOST_QVM_FORCE_INLINE /*platform-specific*/
  #endif

} }
namespace boost { namespace qvm {

  #ifndef BOOST_QVM_INLINE_TRIVIAL
  #define BOOST_QVM_INLINE_TRIVIAL BOOST_QVM_FORCE_INLINE
  #endif

} }
namespace boost { namespace qvm {

  #ifndef BOOST_QVM_INLINE_CRITICAL
  #define BOOST_QVM_INLINE_CRITICAL BOOST_QVM_FORCE_INLINE
  #endif

} }
namespace boost { namespace qvm {

  #ifndef BOOST_QVM_INLINE_OPERATIONS
  #define BOOST_QVM_INLINE_OPERATIONS BOOST_QVM_INLINE
  #endif

} }
namespace boost { namespace qvm {

  #ifndef BOOST_QVM_INLINE_RECURSION
  #define BOOST_QVM_INLINE_RECURSION BOOST_QVM_INLINE_OPERATIONS
  #endif

} }
namespace boost { namespace qvm {

#ifndef BOOST_QVM_ASSERT
#include <boost/assert.hpp>
#define BOOST_QVM_ASSERT BOOST_ASSERT
#endif

} }
namespace boost { namespace qvm {

  #ifndef BOOST_QVM_STATIC_ASSERT
  #include <boost/static_assert.hpp>
  #define BOOST_QVM_STATIC_ASSERT BOOST_STATIC_ASSERT
  #endif

} }
namespace boost { namespace qvm {

  #ifndef BOOST_QVM_THROW_EXCEPTION
  #include <boost/throw_exception.hpp>
  #define BOOST_QVM_THROW_EXCEPTION BOOST_THROW_EXCEPTION
  #endif

} }
auto tr = transposed(m); //Error: the return type of transposed can not be copied.
auto & tr = transposed(m);
namespace ns1 {

  struct float2 { float x, y; };

}

namespace ns2 {

  using namespace boost::qvm;

  void f() {
    ns1::float2 a, b;
    a==b; //OK
    ns1::float2 arr1[2], arr2[2];
    std::equal(arr1,arr1+2,arr2); //Error: operator== is inaccessible from namespace std
  }

}
namespace ns1 {

  using boost::qvm::operator==;

}

`xs`	0	0	0
0	`ys`	0	0
0	0	`zf`/(`zf`-`zn`)	-`zn`*`zf`/(`zf`-`zn`)
0	0	1	0

`xs`	0	0	0
0	`ys`	0	0
0	0	`zf`/(`zn`-`zf`)	`zn`*`zf`/(`zn`-`zf`)
0	0	-1	0

四元数特征	#include <boost/qvm/quat_traits.hpp> #include <boost/qvm/quat_traits_array.hpp> #include <boost/qvm/deduce_quat.hpp>
四元数元素访问	#include <boost/qvm/quat_access.hpp>
四元数运算	#include <boost/qvm/quat_operations.hpp>
`quat` 类模板	#include <boost/qvm/quat.hpp>

向量特征	#include <boost/qvm/vec_traits.hpp> #include <boost/qvm/vec_traits_array.hpp> #include <boost/qvm/deduce_vec.hpp>
向量元素访问	#include <boost/qvm/vec_access.hpp>
向量混合	#include <boost/qvm/swizzle.hpp> #include <boost/qvm/swizzle2.hpp> #include <boost/qvm/swizzle3.hpp> #include <boost/qvm/swizzle4.hpp>
向量运算	#include <boost/qvm/vec_operations.hpp> #include <boost/qvm/vec_operations2.hpp> #include <boost/qvm/vec_operations3.hpp> #include <boost/qvm/vec_operations4.hpp>
四元数-向量运算	#include <boost/qvm/quat_vec_operations.hpp>
向量-矩阵运算	#include <boost/qvm/vec_mat_operations.hpp>
向量-矩阵视图代理	#include <boost/qvm/map_vec_mat.hpp>
`vec` 类模板	#include <boost/qvm/vec.hpp>

矩阵特征	#include <boost/qvm/mat_traits.hpp> #include <boost/qvm/mat_traits_array.hpp> #include <boost/qvm/deduce_mat.hpp>
矩阵元素访问	#include <boost/qvm/mat_access.hpp>
矩阵运算	#include <boost/qvm/mat_operations.hpp> #include <boost/qvm/mat_operations2.hpp> #include <boost/qvm/mat_operations3.hpp> #include <boost/qvm/mat_operations4.hpp>
矩阵-矩阵视图代理	#include <boost/qvm/map_mat_mat.hpp>
矩阵-向量视图代理	#include <boost/qvm/map_mat_vec.hpp>
`mat` 类模板	#include <boost/qvm/mat.hpp>

Boost C++ 库

QVM

摘要

支持

可移植性

发行

教程

四元数、向量、矩阵

C/C++ 数组

视图代理

混合

SFINAE/enable_if

互操作性

为二元运算指定返回类型

为一元运算指定返回类型

在不同的四元数、向量和矩阵类型之间转换

参考

头文件

类型特征系统

标量要求

is_scalar

scalar_traits

deduce_scalar

scalar

is_quat

quat_traits

quat_traits_defaults

deduce_quat

deduce_quat2

is_vec

vec_traits

vec_traits_defaults

deduce_vec

deduce_vec2

is_mat

mat_traits

mat_traits_defaults

deduce_mat

deduce_mat2

内置四元数、向量和矩阵类型

quat

vec

mat

元素访问

四元数

向量

向量元素混合

矩阵

四元数运算

assign

convert_to

operator-=

operator- (一元)

operator- (二元)

operator+=

operator+

operator/= (标量)

operator/ (标量)

operator*= (标量)

operator*=

operator* (标量)

operator*

operator==

operator!=

cmp

mag_sqr

mag

normalized

normalize

dot

conjugate

inverse

slerp180 / slerp360

zero_quat

set_zero

identity_quat

set_identity

rot_quat

set_rot

rotate

`is_scalar`

`scalar_traits`

`deduce_scalar`

`scalar`

`is_quat`

`quat_traits`

`quat_traits_defaults`

`deduce_quat`

`deduce_quat2`

`is_vec`

`vec_traits`

`vec_traits_defaults`

`deduce_vec`

`deduce_vec2`

`is_mat`

`mat_traits`

`mat_traits_defaults`

`deduce_mat`

`deduce_mat2`

`quat`

`vec`

`mat`

`assign`

`convert_to`

`operator-=`

`operator-` (一元)

`operator-` (二元)

`operator+=`

`operator+`

`operator/=` (标量)

`operator/` (标量)

`operator*=` (标量)

`operator*=`

`operator*` (标量)

`operator*`

`operator==`

`operator!=`

`cmp`

`mag_sqr`

`mag`

`normalized`

`normalize`

`dot`

`conjugate`

`inverse`

`slerp180` / `slerp360`

`zero_quat`

`set_zero`

`identity_quat`

`set_identity`

`rot_quat`

`set_rot`

`rotate`

`rotx_quat`

`set_rotx`

`rotate_x`

`roty_quat`

`set_roty`

`rotate_y`

`rotz_quat`

`set_rotz`

`rotate_z`

`scalar_cast`

`to_string`

`qref`