///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net)
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
///
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
///
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
/// THE SOFTWARE.
///
/// @ref gtx_dual_quaternion
/// @file glm/gtx/dual_quaternion.inl
/// @date 2013-02-10 / 2013-02-13
/// @author Maksim Vorobiev (msomeone@gmail.com)
///////////////////////////////////////////////////////////////////////////////////
#include "../geometric.hpp"
#include <limits>
namespace glm{
namespace detail
{
template <typename T, precision P>
GLM_FUNC_QUALIFIER GLM_CONSTEXPR int tdualquat<T, P>::length() const
{
return 8;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat() :
real(tquat<T, P>()),
dual(tquat<T, P>(T(0), T(0), T(0), T(0)))
{}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat
(
tquat<T, P> const & r
) :
real(r),
dual(tquat<T, P>(T(0), T(0), T(0), T(0)))
{}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat
(
tquat<T, P> const & r,
tquat<T, P> const & d
) :
real(r),
dual(d)
{}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat
(
tquat<T, P> const & q,
tvec3<T, P> const& p
) :
real(q),
dual(
T(-0.5) * ( p.x*q.x + p.y*q.y + p.z*q.z),
T(+0.5) * ( p.x*q.w + p.y*q.z - p.z*q.y),
T(+0.5) * (-p.x*q.z + p.y*q.w + p.z*q.x),
T(+0.5) * ( p.x*q.y - p.y*q.x + p.z*q.w))
{}
//////////////////////////////////////////////////////////////
// tdualquat conversions
template <typename T, precision P>
GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat
(
tmat2x4<T, P> const & m
)
{
*this = dualquat_cast(m);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat
(
tmat3x4<T, P> const & m
)
{
*this = dualquat_cast(m);
}
//////////////////////////////////////////////////////////////
// tdualquat<T, P> accesses
template <typename T, precision P>
GLM_FUNC_QUALIFIER typename tdualquat<T, P>::part_type & tdualquat<T, P>::operator [] (int i)
{
assert(i >= 0 && i < this->length());
return (&real)[i];
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER typename tdualquat<T, P>::part_type const & tdualquat<T, P>::operator [] (int i) const
{
assert(i >= 0 && i < this->length());
return (&real)[i];
}
//////////////////////////////////////////////////////////////
// tdualquat<valType> operators
template <typename T, precision P>
GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator *=
(
T const & s
)
{
this->real *= s;
this->dual *= s;
return *this;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator /=
(
T const & s
)
{
this->real /= s;
this->dual /= s;
return *this;
}
//////////////////////////////////////////////////////////////
// tquat<valType> external operators
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> operator-
(
detail::tdualquat<T, P> const & q
)
{
return detail::tdualquat<T, P>(-q.real,-q.dual);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> operator+
(
detail::tdualquat<T, P> const & q,
detail::tdualquat<T, P> const & p
)
{
return detail::tdualquat<T, P>(q.real + p.real,q.dual + p.dual);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> operator*
(
detail::tdualquat<T, P> const & p,
detail::tdualquat<T, P> const & o
)
{
return detail::tdualquat<T, P>(p.real * o.real,p.real * o.dual + p.dual * o.real);
}
// Transformation
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec3<T, P> operator*
(
detail::tdualquat<T, P> const & q,
detail::tvec3<T, P> const & v
)
{
detail::tvec3<T, P> const real_v3(q.real.x,q.real.y,q.real.z);
detail::tvec3<T, P> const dual_v3(q.dual.x,q.dual.y,q.dual.z);
return (cross(real_v3, cross(real_v3,v) + v * q.real.w + dual_v3) + dual_v3 * q.real.w - real_v3 * q.dual.w) * T(2) + v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec3<T, P> operator*
(
detail::tvec3<T, P> const & v,
detail::tdualquat<T, P> const & q
)
{
return glm::inverse(q) * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<T, P> operator*
(
detail::tdualquat<T, P> const & q,
detail::tvec4<T, P> const & v
)
{
return detail::tvec4<T, P>(q * detail::tvec3<T, P>(v), v.w);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tvec4<T, P> operator*
(
detail::tvec4<T, P> const & v,
detail::tdualquat<T, P> const & q
)
{
return glm::inverse(q) * v;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> operator*
(
detail::tdualquat<T, P> const & q,
T const & s
)
{
return detail::tdualquat<T, P>(q.real * s, q.dual * s);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> operator*
(
T const & s,
detail::tdualquat<T, P> const & q
)
{
return q * s;
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> operator/
(
detail::tdualquat<T, P> const & q,
T const & s
)
{
return detail::tdualquat<T, P>(q.real / s, q.dual / s);
}
//////////////////////////////////////
// Boolean operators
template <typename T, precision P>
GLM_FUNC_QUALIFIER bool operator==
(
detail::tdualquat<T, P> const & q1,
detail::tdualquat<T, P> const & q2
)
{
return (q1.real == q2.real) && (q1.dual == q2.dual);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER bool operator!=
(
detail::tdualquat<T, P> const & q1,
detail::tdualquat<T, P> const & q2
)
{
return (q1.real != q2.dual) || (q1.real != q2.dual);
}
}//namespace detail
////////////////////////////////////////////////////////
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> normalize
(
detail::tdualquat<T, P> const & q
)
{
return q / length(q.real);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> lerp
(
detail::tdualquat<T, P> const & x,
detail::tdualquat<T, P> const & y,
T const & a
)
{
// Dual Quaternion Linear blend aka DLB:
// Lerp is only defined in [0, 1]
assert(a >= static_cast<T>(0));
assert(a <= static_cast<T>(1));
T const k = dot(x.real,y.real) < static_cast<T>(0) ? -a : a;
T const one(1);
return detail::tdualquat<T, P>(x * (one - a) + y * k);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> inverse
(
detail::tdualquat<T, P> const & q
)
{
const glm::detail::tquat<T, P> real = conjugate(q.real);
const glm::detail::tquat<T, P> dual = conjugate(q.dual);
return detail::tdualquat<T, P>(real, dual + (real * (-2.0f * dot(real,dual))));
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tmat2x4<T, P> mat2x4_cast
(
detail::tdualquat<T, P> const & x
)
{
return detail::tmat2x4<T, P>( x[0].x, x[0].y, x[0].z, x[0].w, x[1].x, x[1].y, x[1].z, x[1].w );
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tmat3x4<T, P> mat3x4_cast
(
detail::tdualquat<T, P> const & x
)
{
detail::tquat<T, P> r = x.real / length2(x.real);
detail::tquat<T, P> const rr(r.w * x.real.w, r.x * x.real.x, r.y * x.real.y, r.z * x.real.z);
r *= static_cast<T>(2);
T const xy = r.x * x.real.y;
T const xz = r.x * x.real.z;
T const yz = r.y * x.real.z;
T const wx = r.w * x.real.x;
T const wy = r.w * x.real.y;
T const wz = r.w * x.real.z;
detail::tvec4<T, P> const a(
rr.w + rr.x - rr.y - rr.z,
xy - wz,
xz + wy,
-(x.dual.w * r.x - x.dual.x * r.w + x.dual.y * r.z - x.dual.z * r.y));
detail::tvec4<T, P> const b(
xy + wz,
rr.w + rr.y - rr.x - rr.z,
yz - wx,
-(x.dual.w * r.y - x.dual.x * r.z - x.dual.y * r.w + x.dual.z * r.x));
detail::tvec4<T, P> const c(
xz - wy,
yz + wx,
rr.w + rr.z - rr.x - rr.y,
-(x.dual.w * r.z + x.dual.x * r.y - x.dual.y * r.x - x.dual.z * r.w));
return detail::tmat3x4<T, P>(a, b, c);
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> dualquat_cast
(
detail::tmat2x4<T, P> const & x
)
{
return detail::tdualquat<T, P>(
detail::tquat<T, P>( x[0].w, x[0].x, x[0].y, x[0].z ),
detail::tquat<T, P>( x[1].w, x[1].x, x[1].y, x[1].z ));
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER detail::tdualquat<T, P> dualquat_cast
(
detail::tmat3x4<T, P> const & x
)
{
detail::tquat<T, P> real;
T const trace = x[0].x + x[1].y + x[2].z;
if(trace > T(0))
{
T const r = sqrt(T(1) + trace);
T const invr = static_cast<T>(0.5) / r;
real.w = static_cast<T>(0.5) * r;
real.x = (x[2].y - x[1].z) * invr;
real.y = (x[0].z - x[2].x) * invr;
real.z = (x[1].x - x[0].y) * invr;
}
else if(x[0].x > x[1].y && x[0].x > x[2].z)
{
T const r = sqrt(T(1) + x[0].x - x[1].y - x[2].z);
T const invr = static_cast<T>(0.5) / r;
real.x = static_cast<T>(0.5)*r;
real.y = (x[1].x + x[0].y) * invr;
real.z = (x[0].z + x[2].x) * invr;
real.w = (x[2].y - x[1].z) * invr;
}
else if(x[1].y > x[2].z)
{
T const r = sqrt(T(1) + x[1].y - x[0].x - x[2].z);
T const invr = static_cast<T>(0.5) / r;
real.x = (x[1].x + x[0].y) * invr;
real.y = static_cast<T>(0.5) * r;
real.z = (x[2].y + x[1].z) * invr;
real.w = (x[0].z - x[2].x) * invr;
}
else
{
T const r = sqrt(T(1) + x[2].z - x[0].x - x[1].y);
T const invr = static_cast<T>(0.5) / r;
real.x = (x[0].z + x[2].x) * invr;
real.y = (x[2].y + x[1].z) * invr;
real.z = static_cast<T>(0.5) * r;
real.w = (x[1].x - x[0].y) * invr;
}
detail::tquat<T, P> dual;
dual.x = T(0.5) * ( x[0].w * real.w + x[1].w * real.z - x[2].w * real.y);
dual.y = T(0.5) * (-x[0].w * real.z + x[1].w * real.w + x[2].w * real.x);
dual.z = T(0.5) * ( x[0].w * real.y - x[1].w * real.x + x[2].w * real.w);
dual.w = -T(0.5) * ( x[0].w * real.x + x[1].w * real.y + x[2].w * real.z);
return detail::tdualquat<T, P>(real, dual);
}
}//namespace glm