CS计算机代考程序代写 ///////////////////////////////////////////////////////////////////////////////////

///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
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///
/// @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

namespace glm
{
//////////////////////////////////////
// Component accesses

# ifdef GLM_FORCE_SIZE_FUNC
template
GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tdualquat::size_type tdualquat::size() const
{
return 2;
}

template
GLM_FUNC_QUALIFIER typename tdualquat::part_type & tdualquat::operator[](typename tdualquat::size_type i)
{
assert(i >= 0 && static_cast(i) < detail::component_count(*this)); return (&real)[i]; } template
GLM_FUNC_QUALIFIER typename tdualquat::part_type const & tdualquat::operator[](typename tdualquat::size_type i) const
{
assert(i >= 0 && static_cast(i) < detail::component_count(*this)); return (&real)[i]; } # else template
GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tdualquat::length_type tdualquat::length() const
{
return 2;
}

template
GLM_FUNC_QUALIFIER typename tdualquat::part_type & tdualquat::operator[](typename tdualquat::length_type i)
{
assert(i >= 0 && static_cast(i) < detail::component_count(*this)); return (&real)[i]; } template
GLM_FUNC_QUALIFIER typename tdualquat::part_type const & tdualquat::operator[](typename tdualquat::length_type i) const
{
assert(i >= 0 && static_cast(i) < detail::component_count(*this)); return (&real)[i]; } # endif//GLM_FORCE_SIZE_FUNC ////////////////////////////////////// // Implicit basic constructors template
GLM_FUNC_QUALIFIER tdualquat::tdualquat()
# ifndef GLM_FORCE_NO_CTOR_INIT
: real(tquat())
, dual(tquat(0, 0, 0, 0))
# endif
{}

template
GLM_FUNC_QUALIFIER tdualquat::tdualquat(tdualquat const & d)
: real(d.real)
, dual(d.dual)
{}

template
template GLM_FUNC_QUALIFIER tdualquat::tdualquat(tdualquat const & d)
: real(d.real)
, dual(d.dual)
{}

//////////////////////////////////////
// Explicit basic constructors

template
GLM_FUNC_QUALIFIER tdualquat::tdualquat(ctor)
{}

template
GLM_FUNC_QUALIFIER tdualquat::tdualquat(tquat const & r)
: real(r), dual(tquat(0, 0, 0, 0))
{}

template
GLM_FUNC_QUALIFIER tdualquat::tdualquat(tquat const & q, tvec3 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))
{}

template
GLM_FUNC_QUALIFIER tdualquat::tdualquat(tquat const & r, tquat const & d)
: real(r), dual(d)
{}

//////////////////////////////////////////////////////////////
// tdualquat conversions

template
template
GLM_FUNC_QUALIFIER tdualquat::tdualquat(tdualquat const & q)
: real(q.real)
, dual(q.dual)
{}

template
GLM_FUNC_QUALIFIER tdualquat::tdualquat(tmat2x4 const & m)
{
*this = dualquat_cast(m);
}

template
GLM_FUNC_QUALIFIER tdualquat::tdualquat(tmat3x4 const & m)
{
*this = dualquat_cast(m);
}

//////////////////////////////////////////////////////////////
// tdualquat operators

template
GLM_FUNC_QUALIFIER tdualquat & tdualquat::operator=(tdualquat const & q)
{
this->real = q.real;
this->dual = q.dual;
return *this;
}

template
template
GLM_FUNC_QUALIFIER tdualquat & tdualquat::operator=(tdualquat const & q)
{
this->real = q.real;
this->dual = q.dual;
return *this;
}

template
template
GLM_FUNC_QUALIFIER tdualquat & tdualquat::operator*=(U s)
{
this->real *= static_cast(s);
this->dual *= static_cast(s);
return *this;
}

template
template
GLM_FUNC_QUALIFIER tdualquat & tdualquat::operator/=(U s)
{
this->real /= static_cast(s);
this->dual /= static_cast(s);
return *this;
}

//////////////////////////////////////////////////////////////
// tquat external operators

template
GLM_FUNC_QUALIFIER tdualquat operator-(tdualquat const & q)
{
return tdualquat(-q.real,-q.dual);
}

template
GLM_FUNC_QUALIFIER tdualquat operator+(tdualquat const & q, tdualquat const & p)
{
return tdualquat(q.real + p.real,q.dual + p.dual);
}

template
GLM_FUNC_QUALIFIER tdualquat operator*(tdualquat const & p, tdualquat const & o)
{
return tdualquat(p.real * o.real,p.real * o.dual + p.dual * o.real);
}

// Transformation
template
GLM_FUNC_QUALIFIER tvec3 operator*(tdualquat const & q, tvec3 const & v)
{
tvec3 const real_v3(q.real.x,q.real.y,q.real.z);
tvec3 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
GLM_FUNC_QUALIFIER tvec3 operator*(tvec3 const & v, tdualquat const & q)
{
return glm::inverse(q) * v;
}

template
GLM_FUNC_QUALIFIER tvec4 operator*(tdualquat const & q, tvec4 const & v)
{
return tvec4(q * tvec3(v), v.w);
}

template
GLM_FUNC_QUALIFIER tvec4 operator*(tvec4 const & v, tdualquat const & q)
{
return glm::inverse(q) * v;
}

template
GLM_FUNC_QUALIFIER tdualquat operator*(tdualquat const & q, T const & s)
{
return tdualquat(q.real * s, q.dual * s);
}

template
GLM_FUNC_QUALIFIER tdualquat operator*(T const & s, tdualquat const & q)
{
return q * s;
}

template
GLM_FUNC_QUALIFIER tdualquat operator/(tdualquat const & q, T const & s)
{
return tdualquat(q.real / s, q.dual / s);
}

//////////////////////////////////////
// Boolean operators
template
GLM_FUNC_QUALIFIER bool operator==(tdualquat const & q1, tdualquat const & q2)
{
return (q1.real == q2.real) && (q1.dual == q2.dual);
}

template
GLM_FUNC_QUALIFIER bool operator!=(tdualquat const & q1, tdualquat const & q2)
{
return (q1.real != q2.dual) || (q1.real != q2.dual);
}

////////////////////////////////////////////////////////
template
GLM_FUNC_QUALIFIER tdualquat normalize(tdualquat const & q)
{
return q / length(q.real);
}

template
GLM_FUNC_QUALIFIER tdualquat lerp(tdualquat const & x, tdualquat const & y, T const & a)
{
// Dual Quaternion Linear blend aka DLB:
// Lerp is only defined in [0, 1]
assert(a >= static_cast(0));
assert(a <= static_cast(1));
T const k = dot(x.real,y.real) < static_cast(0) ? -a : a;
T const one(1);
return tdualquat(x * (one – a) + y * k);
}

template
GLM_FUNC_QUALIFIER tdualquat inverse(tdualquat const & q)
{
const glm::tquat real = conjugate(q.real);
const glm::tquat dual = conjugate(q.dual);
return tdualquat(real, dual + (real * (-2.0f * dot(real,dual))));
}

template
GLM_FUNC_QUALIFIER tmat2x4 mat2x4_cast(tdualquat const & x)
{
return tmat2x4( 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
GLM_FUNC_QUALIFIER tmat3x4 mat3x4_cast(tdualquat const & x)
{
tquat r = x.real / length2(x.real);

tquat 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(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;

tvec4 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));

tvec4 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));

tvec4 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 tmat3x4(a, b, c);
}

template
GLM_FUNC_QUALIFIER tdualquat dualquat_cast(tmat2x4 const & x)
{
return tdualquat(
tquat( x[0].w, x[0].x, x[0].y, x[0].z ),
tquat( x[1].w, x[1].x, x[1].y, x[1].z ));
}

template
GLM_FUNC_QUALIFIER tdualquat dualquat_cast(tmat3x4 const & x)
{
tquat real(uninitialize);

T const trace = x[0].x + x[1].y + x[2].z;
if(trace > static_cast(0))
{
T const r = sqrt(T(1) + trace);
T const invr = static_cast(0.5) / r;
real.w = static_cast(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(0.5) / r;
real.x = static_cast(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(0.5) / r;
real.x = (x[1].x + x[0].y) * invr;
real.y = static_cast(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(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(0.5) * r;
real.w = (x[1].x – x[0].y) * invr;
}

tquat dual(uninitialize);
dual.x = static_cast(0.5) * ( x[0].w * real.w + x[1].w * real.z – x[2].w * real.y);
dual.y = static_cast(0.5) * (-x[0].w * real.z + x[1].w * real.w + x[2].w * real.x);
dual.z = static_cast(0.5) * ( x[0].w * real.y – x[1].w * real.x + x[2].w * real.w);
dual.w = -static_cast(0.5) * ( x[0].w * real.x + x[1].w * real.y + x[2].w * real.z);
return tdualquat(real, dual);
}
}//namespace glm