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-///////////////////////////////////////////////////////////////////////////////////
-/// OpenGL Mathematics (glm.g-truc.net)
-///
-/// Copyright (c) 2005 - 2015 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.
-///
-/// Restrictions:
-/// By making use of the Software for military purposes, you choose to make
-/// a Bunny unhappy.
-///
-/// 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
-{
- //////////////////////////////////////
- // Component accesses
-
-# ifdef GLM_FORCE_SIZE_FUNC
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tdualquat<T, P>::size_type tdualquat<T, P>::size() const
- {
- return 2;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER typename tdualquat<T, P>::part_type & tdualquat<T, P>::operator[](typename tdualquat<T, P>::size_type i)
- {
- assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
- return (&real)[i];
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER typename tdualquat<T, P>::part_type const & tdualquat<T, P>::operator[](typename tdualquat<T, P>::size_type i) const
- {
- assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
- return (&real)[i];
- }
-# else
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tdualquat<T, P>::length_type tdualquat<T, P>::length() const
- {
- return 2;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER typename tdualquat<T, P>::part_type & tdualquat<T, P>::operator[](typename tdualquat<T, P>::length_type i)
- {
- assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
- return (&real)[i];
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER typename tdualquat<T, P>::part_type const & tdualquat<T, P>::operator[](typename tdualquat<T, P>::length_type i) const
- {
- assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
- return (&real)[i];
- }
-# endif//GLM_FORCE_SIZE_FUNC
-
- //////////////////////////////////////
- // Implicit basic constructors
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat()
-# ifndef GLM_FORCE_NO_CTOR_INIT
- : real(tquat<T, P>())
- , dual(tquat<T, P>(0, 0, 0, 0))
-# endif
- {}
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat(tdualquat<T, P> const & d)
- : real(d.real)
- , dual(d.dual)
- {}
-
- template <typename T, precision P>
- template <precision Q>
- GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat(tdualquat<T, Q> const & d)
- : real(d.real)
- , dual(d.dual)
- {}
-
- //////////////////////////////////////
- // Explicit basic constructors
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat(ctor)
- {}
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat(tquat<T, P> const & r)
- : real(r), dual(tquat<T, P>(0, 0, 0, 0))
- {}
-
- 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))
- {}
-
- 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)
- {}
-
- //////////////////////////////////////////////////////////////
- // tdualquat conversions
-
- template <typename T, precision P>
- template <typename U, precision Q>
- GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat(tdualquat<U, Q> const & q)
- : real(q.real)
- , dual(q.dual)
- {}
-
- 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 operators
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator=(tdualquat<T, P> const & q)
- {
- this->real = q.real;
- this->dual = q.dual;
- return *this;
- }
-
- template <typename T, precision P>
- template <typename U>
- GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator=(tdualquat<U, P> const & q)
- {
- this->real = q.real;
- this->dual = q.dual;
- return *this;
- }
-
- template <typename T, precision P>
- template <typename U>
- GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator*=(U s)
- {
- this->real *= static_cast<T>(s);
- this->dual *= static_cast<T>(s);
- return *this;
- }
-
- template <typename T, precision P>
- template <typename U>
- GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator/=(U s)
- {
- this->real /= static_cast<T>(s);
- this->dual /= static_cast<T>(s);
- return *this;
- }
-
- //////////////////////////////////////////////////////////////
- // tquat<valType> external operators
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> operator-(tdualquat<T, P> const & q)
- {
- return tdualquat<T, P>(-q.real,-q.dual);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> operator+(tdualquat<T, P> const & q, tdualquat<T, P> const & p)
- {
- return tdualquat<T, P>(q.real + p.real,q.dual + p.dual);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> operator*(tdualquat<T, P> const & p, tdualquat<T, P> const & o)
- {
- return tdualquat<T, P>(p.real * o.real,p.real * o.dual + p.dual * o.real);
- }
-
- // Transformation
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tdualquat<T, P> const & q, tvec3<T, P> const & v)
- {
- tvec3<T, P> const real_v3(q.real.x,q.real.y,q.real.z);
- 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 tvec3<T, P> operator*(tvec3<T, P> const & v, tdualquat<T, P> const & q)
- {
- return glm::inverse(q) * v;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tdualquat<T, P> const & q, tvec4<T, P> const & v)
- {
- return tvec4<T, P>(q * tvec3<T, P>(v), v.w);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tvec4<T, P> const & v, tdualquat<T, P> const & q)
- {
- return glm::inverse(q) * v;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> operator*(tdualquat<T, P> const & q, T const & s)
- {
- return tdualquat<T, P>(q.real * s, q.dual * s);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> operator*(T const & s, tdualquat<T, P> const & q)
- {
- return q * s;
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> operator/(tdualquat<T, P> const & q, T const & s)
- {
- return tdualquat<T, P>(q.real / s, q.dual / s);
- }
-
- //////////////////////////////////////
- // Boolean operators
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER bool operator==(tdualquat<T, P> const & q1, tdualquat<T, P> const & q2)
- {
- return (q1.real == q2.real) && (q1.dual == q2.dual);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER bool operator!=(tdualquat<T, P> const & q1, tdualquat<T, P> const & q2)
- {
- return (q1.real != q2.dual) || (q1.real != q2.dual);
- }
-
- ////////////////////////////////////////////////////////
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> normalize(tdualquat<T, P> const & q)
- {
- return q / length(q.real);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> lerp(tdualquat<T, P> const & x, 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 tdualquat<T, P>(x * (one - a) + y * k);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> inverse(tdualquat<T, P> const & q)
- {
- const glm::tquat<T, P> real = conjugate(q.real);
- const glm::tquat<T, P> dual = conjugate(q.dual);
- return tdualquat<T, P>(real, dual + (real * (-2.0f * dot(real,dual))));
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tmat2x4<T, P> mat2x4_cast(tdualquat<T, P> const & x)
- {
- return 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 tmat3x4<T, P> mat3x4_cast(tdualquat<T, P> const & x)
- {
- tquat<T, P> r = x.real / length2(x.real);
-
- 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;
-
- 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));
-
- 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));
-
- 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 tmat3x4<T, P>(a, b, c);
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> dualquat_cast(tmat2x4<T, P> const & x)
- {
- return tdualquat<T, P>(
- tquat<T, P>( x[0].w, x[0].x, x[0].y, x[0].z ),
- tquat<T, P>( x[1].w, x[1].x, x[1].y, x[1].z ));
- }
-
- template <typename T, precision P>
- GLM_FUNC_QUALIFIER tdualquat<T, P> dualquat_cast(tmat3x4<T, P> const & x)
- {
- tquat<T, P> real(uninitialize);
-
- T const trace = x[0].x + x[1].y + x[2].z;
- if(trace > static_cast<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;
- }
-
- tquat<T, P> dual(uninitialize);
- dual.x = static_cast<T>(0.5) * ( x[0].w * real.w + x[1].w * real.z - x[2].w * real.y);
- dual.y = static_cast<T>(0.5) * (-x[0].w * real.z + x[1].w * real.w + x[2].w * real.x);
- dual.z = static_cast<T>(0.5) * ( x[0].w * real.y - x[1].w * real.x + x[2].w * real.w);
- dual.w = -static_cast<T>(0.5) * ( x[0].w * real.x + x[1].w * real.y + x[2].w * real.z);
- return tdualquat<T, P>(real, dual);
- }
-}//namespace glm