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ecency-mobile/ios/Pods/boost-for-react-native/boost/qvm/quat_operations.hpp

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//Copyright (c) 2008-2016 Emil Dotchevski and Reverge Studios, Inc.
//Distributed under the Boost Software License, Version 1.0. (See accompanying
//file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef UUID_E6519754D19211DFB8405F74DFD72085
#define UUID_E6519754D19211DFB8405F74DFD72085
#include <boost/qvm/inline.hpp>
#include <boost/qvm/enable_if.hpp>
#include <boost/qvm/deduce_quat.hpp>
#include <boost/qvm/mat_traits.hpp>
#include <boost/qvm/scalar_traits.hpp>
#include <boost/qvm/math.hpp>
#include <boost/qvm/assert.hpp>
#include <boost/qvm/error.hpp>
#include <boost/qvm/throw_exception.hpp>
#include <string>
namespace
boost
{
namespace
qvm
{
namespace
qvm_detail
{
BOOST_QVM_INLINE_CRITICAL
void const *
get_valid_ptr_quat_operations()
{
static int const obj=0;
return &obj;
}
}
////////////////////////////////////////////////
namespace
msvc_parse_bug_workaround
{
template <class A,class B>
struct
quats
{
static bool const value=is_quat<A>::value && is_quat<B>::value;
};
}
namespace
qvm_to_string_detail
{
template <class T>
std::string to_string( T const & x );
}
template <class A>
inline
typename boost::enable_if_c<
is_quat<A>::value,
std::string>::type
to_string( A const & a )
{
using namespace qvm_to_string_detail;
return '('+
to_string(quat_traits<A>::template read_element<0>(a))+','+
to_string(quat_traits<A>::template read_element<1>(a))+','+
to_string(quat_traits<A>::template read_element<2>(a))+','+
to_string(quat_traits<A>::template read_element<3>(a))+')';
}
////////////////////////////////////////////////
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value && is_quat<B>::value,
A &>::type
assign( A & a, B const & b )
{
quat_traits<A>::template write_element<0>(a) = quat_traits<B>::template read_element<0>(b);
quat_traits<A>::template write_element<1>(a) = quat_traits<B>::template read_element<1>(b);
quat_traits<A>::template write_element<2>(a) = quat_traits<B>::template read_element<2>(b);
quat_traits<A>::template write_element<3>(a) = quat_traits<B>::template read_element<3>(b);
return a;
}
template <class A,class B,class Cmp>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value && is_quat<B>::value,
bool>::type
cmp( A const & a, B const & b, Cmp f )
{
typedef typename deduce_scalar<
typename quat_traits<A>::scalar_type,
typename quat_traits<B>::scalar_type>::type T;
T q1[4] =
{
quat_traits<A>::template read_element<0>(a),
quat_traits<A>::template read_element<1>(a),
quat_traits<A>::template read_element<2>(a),
quat_traits<A>::template read_element<3>(a)
};
T q2[4] =
{
quat_traits<B>::template read_element<0>(b),
quat_traits<B>::template read_element<1>(b),
quat_traits<B>::template read_element<2>(b),
quat_traits<B>::template read_element<3>(b)
};
int i;
for( i=0; i!=4; ++i )
if( !f(q1[i],q2[i]) )
break;
if( i==4 )
return true;
for( i=0; i!=4; ++i )
if( !f(q1[i],-q2[i]) )
return false;
return true;
}
////////////////////////////////////////////////
template <class R,class A>
BOOST_QVM_INLINE_TRIVIAL
typename enable_if_c<
is_quat<R>::value && is_quat<A>::value,
R>::type
convert_to( A const & a )
{
R r;
quat_traits<R>::template write_element<0>(r) = quat_traits<A>::template read_element<0>(a);
quat_traits<R>::template write_element<1>(r) = quat_traits<A>::template read_element<1>(a);
quat_traits<R>::template write_element<2>(r) = quat_traits<A>::template read_element<2>(a);
quat_traits<R>::template write_element<3>(r) = quat_traits<A>::template read_element<3>(a);
return r;
}
template <class R,class A>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<R>::value && is_mat<A>::value &&
mat_traits<A>::rows==3 && mat_traits<A>::cols==3,
R>::type
convert_to( A const & a )
{
typedef typename mat_traits<A>::scalar_type T;
T const mat[3][3] =
{
{ mat_traits<A>::template read_element<0,0>(a), mat_traits<A>::template read_element<0,1>(a), mat_traits<A>::template read_element<0,2>(a) },
{ mat_traits<A>::template read_element<1,0>(a), mat_traits<A>::template read_element<1,1>(a), mat_traits<A>::template read_element<1,2>(a) },
{ mat_traits<A>::template read_element<2,0>(a), mat_traits<A>::template read_element<2,1>(a), mat_traits<A>::template read_element<2,2>(a) }
};
R r;
if( mat[0][0]+mat[1][1]+mat[2][2] > scalar_traits<T>::value(0) )
{
T t = mat[0][0] + mat[1][1] + mat[2][2] + scalar_traits<T>::value(1);
T s = (scalar_traits<T>::value(1)/sqrt<T>(t))/2;
quat_traits<R>::template write_element<0>(r)=s*t;
quat_traits<R>::template write_element<1>(r)=(mat[2][1]-mat[1][2])*s;
quat_traits<R>::template write_element<2>(r)=(mat[0][2]-mat[2][0])*s;
quat_traits<R>::template write_element<3>(r)=(mat[1][0]-mat[0][1])*s;
}
else if( mat[0][0]>mat[1][1] && mat[0][0]>mat[2][2] )
{
T t = mat[0][0] - mat[1][1] - mat[2][2] + scalar_traits<T>::value(1);
T s = (scalar_traits<T>::value(1)/sqrt<T>(t))/2;
quat_traits<R>::template write_element<0>(r)=(mat[2][1]-mat[1][2])*s;
quat_traits<R>::template write_element<1>(r)=s*t;
quat_traits<R>::template write_element<2>(r)=(mat[1][0]+mat[0][1])*s;
quat_traits<R>::template write_element<3>(r)=(mat[0][2]+mat[2][0])*s;
}
else if( mat[1][1]>mat[2][2] )
{
T t = - mat[0][0] + mat[1][1] - mat[2][2] + scalar_traits<T>::value(1);
T s = (scalar_traits<T>::value(1)/sqrt<T>(t))/2;
quat_traits<R>::template write_element<0>(r)=(mat[0][2]-mat[2][0])*s;
quat_traits<R>::template write_element<1>(r)=(mat[1][0]+mat[0][1])*s;
quat_traits<R>::template write_element<2>(r)=s*t;
quat_traits<R>::template write_element<3>(r)=(mat[2][1]+mat[1][2])*s;
}
else
{
T t = - mat[0][0] - mat[1][1] + mat[2][2] + scalar_traits<T>::value(1);
T s = (scalar_traits<T>::value(1)/sqrt<T>(t))/2;
quat_traits<R>::template write_element<0>(r)=(mat[1][0]-mat[0][1])*s;
quat_traits<R>::template write_element<1>(r)=(mat[0][2]+mat[2][0])*s;
quat_traits<R>::template write_element<2>(r)=(mat[2][1]+mat[1][2])*s;
quat_traits<R>::template write_element<3>(r)=s*t;
}
return r;
}
////////////////////////////////////////////////
template <class A>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value,
deduce_quat<A> >::type
conjugate( A const & a )
{
typedef typename deduce_quat<A>::type R;
R r;
quat_traits<R>::template write_element<0>(r)=quat_traits<A>::template read_element<0>(a);
quat_traits<R>::template write_element<1>(r)=-quat_traits<A>::template read_element<1>(a);
quat_traits<R>::template write_element<2>(r)=-quat_traits<A>::template read_element<2>(a);
quat_traits<R>::template write_element<3>(r)=-quat_traits<A>::template read_element<3>(a);
return r;
}
////////////////////////////////////////////////
namespace
qvm_detail
{
template <class T>
class
identity_quat_
{
identity_quat_( identity_quat_ const & );
identity_quat_ & operator=( identity_quat_ const & );
~identity_quat_();
public:
template <class R>
BOOST_QVM_INLINE_TRIVIAL
operator R() const
{
R r;
assign(r,*this);
return r;
}
};
}
template <class T>
struct
quat_traits< qvm_detail::identity_quat_<T> >
{
typedef qvm_detail::identity_quat_<T> this_quaternion;
typedef T scalar_type;
template <int I>
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element( this_quaternion const & x )
{
BOOST_QVM_STATIC_ASSERT(I>=0);
BOOST_QVM_STATIC_ASSERT(I<4);
return scalar_traits<T>::value(I==0);
}
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element_idx( int i, this_quaternion const & x )
{
BOOST_QVM_ASSERT(i>=0);
BOOST_QVM_ASSERT(i<4);
return scalar_traits<T>::value(i==0);
}
};
template <class T>
struct
deduce_quat< qvm_detail::identity_quat_<T> >
{
typedef quat<T> type;
};
template <class T>
struct
deduce_quat2< qvm_detail::identity_quat_<T>, qvm_detail::identity_quat_<T> >
{
typedef quat<T> type;
};
template <class T>
BOOST_QVM_INLINE_TRIVIAL
qvm_detail::identity_quat_<T> const &
identity_quat()
{
return *(qvm_detail::identity_quat_<T> const *)qvm_detail::get_valid_ptr_quat_operations();
}
template <class A>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
void>::type
set_identity( A & a )
{
typedef typename quat_traits<A>::scalar_type T;
T const zero=scalar_traits<T>::value(0);
T const one=scalar_traits<T>::value(1);
quat_traits<A>::template write_element<0>(a) = one;
quat_traits<A>::template write_element<1>(a) = zero;
quat_traits<A>::template write_element<2>(a) = zero;
quat_traits<A>::template write_element<3>(a) = zero;
}
////////////////////////////////////////////////
namespace
qvm_detail
{
template <class OriginalType,class Scalar>
class
quaternion_scalar_cast_
{
quaternion_scalar_cast_( quaternion_scalar_cast_ const & );
quaternion_scalar_cast_ & operator=( quaternion_scalar_cast_ const & );
~quaternion_scalar_cast_();
public:
template <class T>
BOOST_QVM_INLINE_TRIVIAL
quaternion_scalar_cast_ &
operator=( T const & x )
{
assign(*this,x);
return *this;
}
template <class R>
BOOST_QVM_INLINE_TRIVIAL
operator R() const
{
R r;
assign(r,*this);
return r;
}
};
template <bool> struct scalar_cast_quaternion_filter { };
template <> struct scalar_cast_quaternion_filter<true> { typedef int type; };
}
template <class OriginalType,class Scalar>
struct
quat_traits< qvm_detail::quaternion_scalar_cast_<OriginalType,Scalar> >
{
typedef Scalar scalar_type;
typedef qvm_detail::quaternion_scalar_cast_<OriginalType,Scalar> this_quaternion;
template <int I>
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element( this_quaternion const & x )
{
BOOST_QVM_STATIC_ASSERT(I>=0);
BOOST_QVM_STATIC_ASSERT(I<4);
return scalar_type(quat_traits<OriginalType>::template read_element<I>(reinterpret_cast<OriginalType const &>(x)));
}
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element_idx( int i, this_quaternion const & x )
{
BOOST_QVM_ASSERT(i>=0);
BOOST_QVM_ASSERT(i<4);
return scalar_type(quat_traits<OriginalType>::read_element_idx(i,reinterpret_cast<OriginalType const &>(x)));
}
};
template <class Scalar,class T>
BOOST_QVM_INLINE_TRIVIAL
qvm_detail::quaternion_scalar_cast_<T,Scalar> const &
scalar_cast( T const & x, typename qvm_detail::scalar_cast_quaternion_filter<is_quat<T>::value>::type=0 )
{
return reinterpret_cast<qvm_detail::quaternion_scalar_cast_<T,Scalar> const &>(x);
}
////////////////////////////////////////////////
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value && is_scalar<B>::value,
A &>::type
operator/=( A & a, B b )
{
quat_traits<A>::template write_element<0>(a)/=b;
quat_traits<A>::template write_element<1>(a)/=b;
quat_traits<A>::template write_element<2>(a)/=b;
quat_traits<A>::template write_element<3>(a)/=b;
return a;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value && is_scalar<B>::value,
deduce_quat<A> >::type
operator/( A const & a, B b )
{
typedef typename deduce_quat<A>::type R;
R r;
quat_traits<R>::template write_element<0>(r) = quat_traits<A>::template read_element<0>(a)/b;
quat_traits<R>::template write_element<1>(r) = quat_traits<A>::template read_element<1>(a)/b;
quat_traits<R>::template write_element<2>(r) = quat_traits<A>::template read_element<2>(a)/b;
quat_traits<R>::template write_element<3>(r) = quat_traits<A>::template read_element<3>(a)/b;
return r;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value && is_quat<B>::value,
deduce_scalar<typename quat_traits<A>::scalar_type,typename quat_traits<B>::scalar_type> >::type
dot( A const & a, B const & b )
{
typedef typename quat_traits<A>::scalar_type Ta;
typedef typename quat_traits<B>::scalar_type Tb;
typedef typename deduce_scalar<Ta,Tb>::type Tr;
Ta const a0=quat_traits<A>::template read_element<0>(a);
Ta const a1=quat_traits<A>::template read_element<1>(a);
Ta const a2=quat_traits<A>::template read_element<2>(a);
Ta const a3=quat_traits<A>::template read_element<3>(a);
Tb const b0=quat_traits<B>::template read_element<0>(b);
Tb const b1=quat_traits<B>::template read_element<1>(b);
Tb const b2=quat_traits<B>::template read_element<2>(b);
Tb const b3=quat_traits<B>::template read_element<3>(b);
Tr const dp=a0*b0+a1*b1+a2*b2+a3*b3;
return dp;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value && is_quat<B>::value,
bool>::type
operator==( A const & a, B const & b )
{
return
quat_traits<A>::template read_element<0>(a)==quat_traits<B>::template read_element<0>(b) &&
quat_traits<A>::template read_element<1>(a)==quat_traits<B>::template read_element<1>(b) &&
quat_traits<A>::template read_element<2>(a)==quat_traits<B>::template read_element<2>(b) &&
quat_traits<A>::template read_element<3>(a)==quat_traits<B>::template read_element<3>(b);
}
template <class A>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value,
deduce_quat<A> >::type
inverse( A const & a )
{
typedef typename deduce_quat<A>::type R;
typedef typename quat_traits<A>::scalar_type TA;
TA aa = quat_traits<A>::template read_element<0>(a);
TA ab = quat_traits<A>::template read_element<1>(a);
TA ac = quat_traits<A>::template read_element<2>(a);
TA ad = quat_traits<A>::template read_element<3>(a);
TA m2 = ab*ab + ac*ac + ad*ad + aa*aa;
if( m2==scalar_traits<TA>::value(0) )
BOOST_QVM_THROW_EXCEPTION(zero_magnitude_error());
TA rm=scalar_traits<TA>::value(1)/m2;
R r;
quat_traits<R>::template write_element<0>(r) = aa*rm;
quat_traits<R>::template write_element<1>(r) = -ab*rm;
quat_traits<R>::template write_element<2>(r) = -ac*rm;
quat_traits<R>::template write_element<3>(r) = -ad*rm;
return r;
}
template <class A>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
typename quat_traits<A>::scalar_type>::type
mag_sqr( A const & a )
{
typedef typename quat_traits<A>::scalar_type T;
T x=quat_traits<A>::template read_element<0>(a);
T y=quat_traits<A>::template read_element<1>(a);
T z=quat_traits<A>::template read_element<2>(a);
T w=quat_traits<A>::template read_element<3>(a);
return x*x+y*y+z*z+w*w;
}
template <class A>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
typename quat_traits<A>::scalar_type>::type
mag( A const & a )
{
typedef typename quat_traits<A>::scalar_type T;
T x=quat_traits<A>::template read_element<0>(a);
T y=quat_traits<A>::template read_element<1>(a);
T z=quat_traits<A>::template read_element<2>(a);
T w=quat_traits<A>::template read_element<3>(a);
return sqrt<T>(x*x+y*y+z*z+w*w);
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if<
msvc_parse_bug_workaround::quats<A,B>,
A &>::type
operator-=( A & a, B const & b )
{
quat_traits<A>::template write_element<0>(a)-=quat_traits<B>::template read_element<0>(b);
quat_traits<A>::template write_element<1>(a)-=quat_traits<B>::template read_element<1>(b);
quat_traits<A>::template write_element<2>(a)-=quat_traits<B>::template read_element<2>(b);
quat_traits<A>::template write_element<3>(a)-=quat_traits<B>::template read_element<3>(b);
return a;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value && is_quat<B>::value,
deduce_quat2<A,B> >::type
operator-( A const & a, B const & b )
{
typedef typename deduce_quat2<A,B>::type R;
R r;
quat_traits<R>::template write_element<0>(r)=quat_traits<A>::template read_element<0>(a)-quat_traits<B>::template read_element<0>(b);
quat_traits<R>::template write_element<1>(r)=quat_traits<A>::template read_element<1>(a)-quat_traits<B>::template read_element<1>(b);
quat_traits<R>::template write_element<2>(r)=quat_traits<A>::template read_element<2>(a)-quat_traits<B>::template read_element<2>(b);
quat_traits<R>::template write_element<3>(r)=quat_traits<A>::template read_element<3>(a)-quat_traits<B>::template read_element<3>(b);
return r;
}
template <class A>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value,
deduce_quat<A> >::type
operator-( A const & a )
{
typedef typename deduce_quat<A>::type R;
R r;
quat_traits<R>::template write_element<0>(r)=-quat_traits<A>::template read_element<0>(a);
quat_traits<R>::template write_element<1>(r)=-quat_traits<A>::template read_element<1>(a);
quat_traits<R>::template write_element<2>(r)=-quat_traits<A>::template read_element<2>(a);
quat_traits<R>::template write_element<3>(r)=-quat_traits<A>::template read_element<3>(a);
return r;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if<
msvc_parse_bug_workaround::quats<A,B>,
A &>::type
operator*=( A & a, B const & b )
{
typedef typename quat_traits<A>::scalar_type TA;
typedef typename quat_traits<B>::scalar_type TB;
TA const aa=quat_traits<A>::template read_element<0>(a);
TA const ab=quat_traits<A>::template read_element<1>(a);
TA const ac=quat_traits<A>::template read_element<2>(a);
TA const ad=quat_traits<A>::template read_element<3>(a);
TB const ba=quat_traits<B>::template read_element<0>(b);
TB const bb=quat_traits<B>::template read_element<1>(b);
TB const bc=quat_traits<B>::template read_element<2>(b);
TB const bd=quat_traits<B>::template read_element<3>(b);
quat_traits<A>::template write_element<0>(a) = aa*ba - ab*bb - ac*bc - ad*bd;
quat_traits<A>::template write_element<1>(a) = aa*bb + ab*ba + ac*bd - ad*bc;
quat_traits<A>::template write_element<2>(a) = aa*bc + ac*ba + ad*bb - ab*bd;
quat_traits<A>::template write_element<3>(a) = aa*bd + ad*ba + ab*bc - ac*bb;
return a;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value && is_scalar<B>::value,
A &>::type
operator*=( A & a, B b )
{
quat_traits<A>::template write_element<0>(a)*=b;
quat_traits<A>::template write_element<1>(a)*=b;
quat_traits<A>::template write_element<2>(a)*=b;
quat_traits<A>::template write_element<3>(a)*=b;
return a;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value && is_quat<B>::value,
deduce_quat2<A,B> >::type
operator*( A const & a, B const & b )
{
typedef typename deduce_quat2<A,B>::type R;
typedef typename quat_traits<A>::scalar_type TA;
typedef typename quat_traits<B>::scalar_type TB;
TA const aa=quat_traits<A>::template read_element<0>(a);
TA const ab=quat_traits<A>::template read_element<1>(a);
TA const ac=quat_traits<A>::template read_element<2>(a);
TA const ad=quat_traits<A>::template read_element<3>(a);
TB const ba=quat_traits<B>::template read_element<0>(b);
TB const bb=quat_traits<B>::template read_element<1>(b);
TB const bc=quat_traits<B>::template read_element<2>(b);
TB const bd=quat_traits<B>::template read_element<3>(b);
R r;
quat_traits<R>::template write_element<0>(r) = aa*ba - ab*bb - ac*bc - ad*bd;
quat_traits<R>::template write_element<1>(r) = aa*bb + ab*ba + ac*bd - ad*bc;
quat_traits<R>::template write_element<2>(r) = aa*bc + ac*ba + ad*bb - ab*bd;
quat_traits<R>::template write_element<3>(r) = aa*bd + ad*ba + ab*bc - ac*bb;
return r;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value && is_scalar<B>::value,
deduce_quat<A> >::type
operator*( A const & a, B b )
{
typedef typename deduce_quat<A>::type R;
R r;
quat_traits<R>::template write_element<0>(r)=quat_traits<A>::template read_element<0>(a)*b;
quat_traits<R>::template write_element<1>(r)=quat_traits<A>::template read_element<1>(a)*b;
quat_traits<R>::template write_element<2>(r)=quat_traits<A>::template read_element<2>(a)*b;
quat_traits<R>::template write_element<3>(r)=quat_traits<A>::template read_element<3>(a)*b;
return r;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value && is_quat<B>::value,
bool>::type
operator!=( A const & a, B const & b )
{
return
quat_traits<A>::template read_element<0>(a)!=quat_traits<B>::template read_element<0>(b) ||
quat_traits<A>::template read_element<1>(a)!=quat_traits<B>::template read_element<1>(b) ||
quat_traits<A>::template read_element<2>(a)!=quat_traits<B>::template read_element<2>(b) ||
quat_traits<A>::template read_element<3>(a)!=quat_traits<B>::template read_element<3>(b);
}
template <class A>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value,
deduce_quat<A> >::type
normalized( A const & a )
{
typedef typename quat_traits<A>::scalar_type T;
T const a0=quat_traits<A>::template read_element<0>(a);
T const a1=quat_traits<A>::template read_element<1>(a);
T const a2=quat_traits<A>::template read_element<2>(a);
T const a3=quat_traits<A>::template read_element<3>(a);
T const m2=a0*a0+a1*a1+a2*a2+a3*a3;
if( m2==scalar_traits<typename quat_traits<A>::scalar_type>::value(0) )
BOOST_QVM_THROW_EXCEPTION(zero_magnitude_error());
T const rm=scalar_traits<T>::value(1)/sqrt<T>(m2);
typedef typename deduce_quat<A>::type R;
R r;
quat_traits<R>::template write_element<0>(r)=a0*rm;
quat_traits<R>::template write_element<1>(r)=a1*rm;
quat_traits<R>::template write_element<2>(r)=a2*rm;
quat_traits<R>::template write_element<3>(r)=a3*rm;
return r;
}
template <class A>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
void>::type
normalize( A & a )
{
typedef typename quat_traits<A>::scalar_type T;
T const a0=quat_traits<A>::template read_element<0>(a);
T const a1=quat_traits<A>::template read_element<1>(a);
T const a2=quat_traits<A>::template read_element<2>(a);
T const a3=quat_traits<A>::template read_element<3>(a);
T const m2=a0*a0+a1*a1+a2*a2+a3*a3;
if( m2==scalar_traits<typename quat_traits<A>::scalar_type>::value(0) )
BOOST_QVM_THROW_EXCEPTION(zero_magnitude_error());
T const rm=scalar_traits<T>::value(1)/sqrt<T>(m2);
quat_traits<A>::template write_element<0>(a)*=rm;
quat_traits<A>::template write_element<1>(a)*=rm;
quat_traits<A>::template write_element<2>(a)*=rm;
quat_traits<A>::template write_element<3>(a)*=rm;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if<
msvc_parse_bug_workaround::quats<A,B>,
A &>::type
operator+=( A & a, B const & b )
{
quat_traits<A>::template write_element<0>(a)+=quat_traits<B>::template read_element<0>(b);
quat_traits<A>::template write_element<1>(a)+=quat_traits<B>::template read_element<1>(b);
quat_traits<A>::template write_element<2>(a)+=quat_traits<B>::template read_element<2>(b);
quat_traits<A>::template write_element<3>(a)+=quat_traits<B>::template read_element<3>(b);
return a;
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value && is_quat<B>::value,
deduce_quat2<A,B> >::type
operator+( A const & a, B const & b )
{
typedef typename deduce_quat2<A,B>::type R;
R r;
quat_traits<R>::template write_element<0>(r)=quat_traits<A>::template read_element<0>(a)+quat_traits<B>::template read_element<0>(b);
quat_traits<R>::template write_element<1>(r)=quat_traits<A>::template read_element<1>(a)+quat_traits<B>::template read_element<1>(b);
quat_traits<R>::template write_element<2>(r)=quat_traits<A>::template read_element<2>(a)+quat_traits<B>::template read_element<2>(b);
quat_traits<R>::template write_element<3>(r)=quat_traits<A>::template read_element<3>(a)+quat_traits<B>::template read_element<3>(b);
return r;
}
template <class A,class B,class C>
BOOST_QVM_INLINE_OPERATIONS
typename lazy_enable_if_c<
is_quat<A>::value && is_quat<B>::value && is_scalar<C>::value,
deduce_quat2<A,B> >::type
slerp( A const & a, B const & b, C t )
{
typedef typename deduce_quat2<A,B>::type R;
typedef typename quat_traits<R>::scalar_type TR;
TR const one = scalar_traits<TR>::value(1);
TR dp = dot(a,b);
TR sc=one;
if( dp < one )
{
TR const theta = acosf(dp);
TR const invsintheta = one/sin<TR>(theta);
TR const scale = sin<TR>(theta*(one-t)) * invsintheta;
TR const invscale = sin<TR>(theta*t) * invsintheta * sc;
return a*scale + b*invscale;
}
else
return normalized(a+(b-a)*t);
}
////////////////////////////////////////////////
namespace
qvm_detail
{
template <class T>
class
qref_
{
qref_( qref_ const & );
qref_ & operator=( qref_ const & );
~qref_();
public:
template <class R>
BOOST_QVM_INLINE_TRIVIAL
qref_ &
operator=( R const & x )
{
assign(*this,x);
return *this;
}
template <class R>
BOOST_QVM_INLINE_TRIVIAL
operator R() const
{
R r;
assign(r,*this);
return r;
}
};
}
template <class Q>
struct quat_traits;
template <class Q>
struct
quat_traits< qvm_detail::qref_<Q> >
{
typedef typename quat_traits<Q>::scalar_type scalar_type;
typedef qvm_detail::qref_<Q> this_quaternion;
template <int I>
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element( this_quaternion const & x )
{
BOOST_QVM_STATIC_ASSERT(I>=0);
BOOST_QVM_STATIC_ASSERT(I<4);
return quat_traits<Q>::template read_element<I>(reinterpret_cast<Q const &>(x));
}
template <int I>
static
BOOST_QVM_INLINE_CRITICAL
scalar_type &
write_element( this_quaternion & x )
{
BOOST_QVM_STATIC_ASSERT(I>=0);
BOOST_QVM_STATIC_ASSERT(I<4);
return quat_traits<Q>::template write_element<I>(reinterpret_cast<Q &>(x));
}
};
template <class Q>
struct
deduce_quat< qvm_detail::qref_<Q> >
{
typedef quat<typename quat_traits<Q>::scalar_type> type;
};
template <class Q>
BOOST_QVM_INLINE_TRIVIAL
typename enable_if_c<
is_quat<Q>::value,
qvm_detail::qref_<Q> const &>::type
qref( Q const & a )
{
return reinterpret_cast<qvm_detail::qref_<Q> const &>(a);
}
template <class Q>
BOOST_QVM_INLINE_TRIVIAL
typename enable_if_c<
is_quat<Q>::value,
qvm_detail::qref_<Q> &>::type
qref( Q & a )
{
return reinterpret_cast<qvm_detail::qref_<Q> &>(a);
}
////////////////////////////////////////////////
namespace
qvm_detail
{
template <class T>
class
zero_q_
{
zero_q_( zero_q_ const & );
zero_q_ & operator=( zero_q_ const & );
~zero_q_();
public:
template <class R>
BOOST_QVM_INLINE_TRIVIAL
operator R() const
{
R r;
assign(r,*this);
return r;
}
};
}
template <class T>
struct
quat_traits< qvm_detail::zero_q_<T> >
{
typedef qvm_detail::zero_q_<T> this_quaternion;
typedef T scalar_type;
template <int I>
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element( this_quaternion const & x )
{
BOOST_QVM_STATIC_ASSERT(I>=0);
BOOST_QVM_STATIC_ASSERT(I<4);
return scalar_traits<scalar_type>::value(0);
}
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element_idx( int i, this_quaternion const & x )
{
BOOST_QVM_ASSERT(i>=0);
BOOST_QVM_ASSERT(i<4);
return scalar_traits<scalar_type>::value(0);
}
};
template <class T>
BOOST_QVM_INLINE_TRIVIAL
qvm_detail::zero_q_<T> const &
zero_quat()
{
return *(qvm_detail::zero_q_<T> const *)qvm_detail::get_valid_ptr_quat_operations();
}
template <class A>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
void>::type
set_zero( A & a )
{
typedef typename quat_traits<A>::scalar_type T;
T const zero=scalar_traits<T>::value(0);
quat_traits<A>::template write_element<0>(a) = zero;
quat_traits<A>::template write_element<1>(a) = zero;
quat_traits<A>::template write_element<2>(a) = zero;
quat_traits<A>::template write_element<3>(a) = zero;
}
////////////////////////////////////////////////
namespace
qvm_detail
{
template <class V>
struct
rot_quat_
{
typedef typename vec_traits<V>::scalar_type scalar_type;
scalar_type a[4];
template <class Angle>
BOOST_QVM_INLINE
rot_quat_( V const & axis, Angle angle )
{
scalar_type const x=vec_traits<V>::template read_element<0>(axis);
scalar_type const y=vec_traits<V>::template read_element<1>(axis);
scalar_type const z=vec_traits<V>::template read_element<2>(axis);
scalar_type const m2=x*x+y*y+z*z;
if( m2==scalar_traits<scalar_type>::value(0) )
BOOST_QVM_THROW_EXCEPTION(zero_magnitude_error());
scalar_type const rm=scalar_traits<scalar_type>::value(1)/sqrt<scalar_type>(m2);
angle/=2;
scalar_type const s=sin<Angle>(angle);
a[0] = cos<Angle>(angle);
a[1] = rm*x*s;
a[2] = rm*y*s;
a[3] = rm*z*s;
}
template <class R>
BOOST_QVM_INLINE_TRIVIAL
operator R() const
{
R r;
assign(r,*this);
return r;
}
};
}
template <class V>
struct
quat_traits< qvm_detail::rot_quat_<V> >
{
typedef qvm_detail::rot_quat_<V> this_quaternion;
typedef typename this_quaternion::scalar_type scalar_type;
template <int I>
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element( this_quaternion const & x )
{
BOOST_QVM_STATIC_ASSERT(I>=0);
BOOST_QVM_STATIC_ASSERT(I<4);
return x.a[I];
}
};
template <class V>
struct
deduce_quat< qvm_detail::rot_quat_<V> >
{
typedef quat<typename vec_traits<V>::scalar_type> type;
};
template <class A,class Angle>
BOOST_QVM_INLINE
typename enable_if_c<
is_vec<A>::value && vec_traits<A>::dim==3,
qvm_detail::rot_quat_<A> >::type
rot_quat( A const & axis, Angle angle )
{
return qvm_detail::rot_quat_<A>(axis,angle);
}
template <class A,class B,class Angle>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value &&
is_vec<B>::value && vec_traits<B>::dim==3,
void>::type
set_rot( A & a, B const & axis, Angle angle )
{
assign(a,rot_quat(axis,angle));
}
template <class A,class B,class Angle>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value &&
is_vec<B>::value && vec_traits<B>::dim==3,
void>::type
rotate( A & a, B const & axis, Angle angle )
{
a *= rot_quat(axis,angle);
}
////////////////////////////////////////////////
namespace
qvm_detail
{
template <class T>
struct
rotx_quat_
{
BOOST_QVM_INLINE_TRIVIAL
rotx_quat_()
{
}
template <class R>
BOOST_QVM_INLINE_TRIVIAL
operator R() const
{
R r;
assign(r,*this);
return r;
}
private:
rotx_quat_( rotx_quat_ const & );
rotx_quat_ & operator=( rotx_quat_ const & );
~rotx_quat_();
};
template <int I>
struct
rotx_q_get
{
template <class T>
static
BOOST_QVM_INLINE_CRITICAL
T
get( T const & )
{
return scalar_traits<T>::value(0);
}
};
template <>
struct
rotx_q_get<1>
{
template <class T>
static
BOOST_QVM_INLINE_CRITICAL
T
get( T const & angle )
{
return sin<T>(angle/2);
}
};
template <>
struct
rotx_q_get<0>
{
template <class T>
static
BOOST_QVM_INLINE_CRITICAL
T
get( T const & angle )
{
return cos<T>(angle/2);
}
};
}
template <class Angle>
struct
quat_traits< qvm_detail::rotx_quat_<Angle> >
{
typedef qvm_detail::rotx_quat_<Angle> this_quaternion;
typedef Angle scalar_type;
template <int I>
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element( this_quaternion const & x )
{
BOOST_QVM_STATIC_ASSERT(I>=0);
BOOST_QVM_STATIC_ASSERT(I<4);
return qvm_detail::rotx_q_get<I>::get(reinterpret_cast<Angle const &>(x));
}
};
template <class Angle>
struct
deduce_quat< qvm_detail::rotx_quat_<Angle> >
{
typedef quat<Angle> type;
};
template <class Angle>
struct
deduce_quat2< qvm_detail::rotx_quat_<Angle>, qvm_detail::rotx_quat_<Angle> >
{
typedef quat<Angle> type;
};
template <class Angle>
BOOST_QVM_INLINE_TRIVIAL
qvm_detail::rotx_quat_<Angle> const &
rotx_quat( Angle const & angle )
{
return reinterpret_cast<qvm_detail::rotx_quat_<Angle> const &>(angle);
}
template <class A,class Angle>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
void>::type
set_rotx( A & a, Angle angle )
{
assign(a,rotx_quat(angle));
}
template <class A,class Angle>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
void>::type
rotate_x( A & a, Angle angle )
{
a *= rotx_quat(angle);
}
////////////////////////////////////////////////
namespace
qvm_detail
{
template <class T>
struct
roty_quat_
{
BOOST_QVM_INLINE_TRIVIAL
roty_quat_()
{
}
template <class R>
BOOST_QVM_INLINE_TRIVIAL
operator R() const
{
R r;
assign(r,*this);
return r;
}
private:
roty_quat_( roty_quat_ const & );
roty_quat_ & operator=( roty_quat_ const & );
~roty_quat_();
};
template <int I>
struct
roty_q_get
{
template <class T>
static
BOOST_QVM_INLINE_CRITICAL
T
get( T const & )
{
return scalar_traits<T>::value(0);
}
};
template <>
struct
roty_q_get<2>
{
template <class T>
static
BOOST_QVM_INLINE_CRITICAL
T
get( T const & angle )
{
return sin<T>(angle/2);
}
};
template <>
struct
roty_q_get<0>
{
template <class T>
static
BOOST_QVM_INLINE_CRITICAL
T
get( T const & angle )
{
return cos<T>(angle/2);
}
};
}
template <class Angle>
struct
quat_traits< qvm_detail::roty_quat_<Angle> >
{
typedef qvm_detail::roty_quat_<Angle> this_quaternion;
typedef Angle scalar_type;
template <int I>
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element( this_quaternion const & x )
{
BOOST_QVM_STATIC_ASSERT(I>=0);
BOOST_QVM_STATIC_ASSERT(I<4);
return qvm_detail::roty_q_get<I>::get(reinterpret_cast<Angle const &>(x));
}
};
template <class Angle>
struct
deduce_quat< qvm_detail::roty_quat_<Angle> >
{
typedef quat<Angle> type;
};
template <class Angle>
struct
deduce_quat2< qvm_detail::roty_quat_<Angle>, qvm_detail::roty_quat_<Angle> >
{
typedef quat<Angle> type;
};
template <class Angle>
BOOST_QVM_INLINE_TRIVIAL
qvm_detail::roty_quat_<Angle> const &
roty_quat( Angle const & angle )
{
return reinterpret_cast<qvm_detail::roty_quat_<Angle> const &>(angle);
}
template <class A,class Angle>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
void>::type
set_roty( A & a, Angle angle )
{
assign(a,roty_quat(angle));
}
template <class A,class Angle>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
void>::type
rotate_y( A & a, Angle angle )
{
a *= roty_quat(angle);
}
////////////////////////////////////////////////
namespace
qvm_detail
{
template <class T>
struct
rotz_quat_
{
BOOST_QVM_INLINE_TRIVIAL
rotz_quat_()
{
}
template <class R>
BOOST_QVM_INLINE_TRIVIAL
operator R() const
{
R r;
assign(r,*this);
return r;
}
private:
rotz_quat_( rotz_quat_ const & );
rotz_quat_ & operator=( rotz_quat_ const & );
~rotz_quat_();
};
template <int I>
struct
rotz_q_get
{
template <class T>
static
BOOST_QVM_INLINE_CRITICAL
T
get( T const & )
{
return scalar_traits<T>::value(0);
}
};
template <>
struct
rotz_q_get<3>
{
template <class T>
static
BOOST_QVM_INLINE_CRITICAL
T
get( T const & angle )
{
return sin<T>(angle/2);
}
};
template <>
struct
rotz_q_get<0>
{
template <class T>
static
BOOST_QVM_INLINE_CRITICAL
T
get( T const & angle )
{
return cos<T>(angle/2);
}
};
}
template <class Angle>
struct
quat_traits< qvm_detail::rotz_quat_<Angle> >
{
typedef qvm_detail::rotz_quat_<Angle> this_quaternion;
typedef Angle scalar_type;
template <int I>
static
BOOST_QVM_INLINE_CRITICAL
scalar_type
read_element( this_quaternion const & x )
{
BOOST_QVM_STATIC_ASSERT(I>=0);
BOOST_QVM_STATIC_ASSERT(I<4);
return qvm_detail::rotz_q_get<I>::get(reinterpret_cast<Angle const &>(x));
}
};
template <class Angle>
struct
deduce_quat< qvm_detail::rotz_quat_<Angle> >
{
typedef quat<Angle> type;
};
template <class Angle>
struct
deduce_quat2< qvm_detail::rotz_quat_<Angle>, qvm_detail::rotz_quat_<Angle> >
{
typedef quat<Angle> type;
};
template <class Angle>
BOOST_QVM_INLINE_TRIVIAL
qvm_detail::rotz_quat_<Angle> const &
rotz_quat( Angle const & angle )
{
return reinterpret_cast<qvm_detail::rotz_quat_<Angle> const &>(angle);
}
template <class A,class Angle>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
void>::type
set_rotz( A & a, Angle angle )
{
assign(a,rotz_quat(angle));
}
template <class A,class Angle>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value,
void>::type
rotate_z( A & a, Angle angle )
{
a *= rotz_quat(angle);
}
template <class A,class B>
BOOST_QVM_INLINE_OPERATIONS
typename enable_if_c<
is_quat<A>::value && is_vec<B>::value && vec_traits<B>::dim==3,
typename quat_traits<A>::scalar_type>::type
axis_angle( A const & a, B & b )
{
typedef typename quat_traits<A>::scalar_type T;
T a0=quat_traits<A>::template read_element<0>(a);
T a1=quat_traits<A>::template read_element<1>(a);
T a2=quat_traits<A>::template read_element<2>(a);
T a3=quat_traits<A>::template read_element<3>(a);
if( a0>1 )
{
T const m2=a0*a0+a1*a1+a2*a2+a3*a3;
if( m2==scalar_traits<T>::value(0) )
BOOST_QVM_THROW_EXCEPTION(zero_magnitude_error());
T const s=sqrt<T>(m2);
a0/=s;
a1/=s;
a2/=s;
a3/=s;
}
if( T s=sqrt<T>(1-a0*a0) )
{
vec_traits<B>::template write_element<0>(b) = a1/s;
vec_traits<B>::template write_element<1>(b) = a2/s;
vec_traits<B>::template write_element<2>(b) = a3/s;
}
else
{
typedef typename vec_traits<B>::scalar_type T;
vec_traits<B>::template write_element<0>(b) = scalar_traits<T>::value(1);
vec_traits<B>::template write_element<1>(b) = vec_traits<B>::template write_element<2>(b) = scalar_traits<T>::value(0);
}
return scalar_traits<T>::value(2) * qvm::acos(a0);
}
////////////////////////////////////////////////
namespace
sfinae
{
using ::boost::qvm::assign;
using ::boost::qvm::cmp;
using ::boost::qvm::convert_to;
using ::boost::qvm::conjugate;
using ::boost::qvm::set_identity;
using ::boost::qvm::set_zero;
using ::boost::qvm::scalar_cast;
using ::boost::qvm::operator/=;
using ::boost::qvm::operator/;
using ::boost::qvm::dot;
using ::boost::qvm::operator==;
using ::boost::qvm::inverse;
using ::boost::qvm::mag_sqr;
using ::boost::qvm::mag;
using ::boost::qvm::slerp;
using ::boost::qvm::operator-=;
using ::boost::qvm::operator-;
using ::boost::qvm::operator*=;
using ::boost::qvm::operator*;
using ::boost::qvm::operator!=;
using ::boost::qvm::normalized;
using ::boost::qvm::normalize;
using ::boost::qvm::operator+=;
using ::boost::qvm::operator+;
using ::boost::qvm::qref;
using ::boost::qvm::rot_quat;
using ::boost::qvm::set_rot;
using ::boost::qvm::rotate;
using ::boost::qvm::rotx_quat;
using ::boost::qvm::set_rotx;
using ::boost::qvm::rotate_x;
using ::boost::qvm::roty_quat;
using ::boost::qvm::set_roty;
using ::boost::qvm::rotate_y;
using ::boost::qvm::rotz_quat;
using ::boost::qvm::set_rotz;
using ::boost::qvm::rotate_z;
}
////////////////////////////////////////////////
}
}
#endif
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