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386 lines
12 KiB
386 lines
12 KiB
/////////////////////////////////////////////////////////////////////////////////// |
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/// OpenGL Mathematics (glm.g-truc.net) |
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/// |
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/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net) |
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/// Permission is hereby granted, free of charge, to any person obtaining a copy |
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/// of this software and associated documentation files (the "Software"), to deal |
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/// in the Software without restriction, including without limitation the rights |
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/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
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/// copies of the Software, and to permit persons to whom the Software is |
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/// furnished to do so, subject to the following conditions: |
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/// |
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/// The above copyright notice and this permission notice shall be included in |
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/// all copies or substantial portions of the Software. |
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/// |
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/// Restrictions: |
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/// By making use of the Software for military purposes, you choose to make |
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/// a Bunny unhappy. |
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/// |
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/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
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/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
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/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
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/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
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/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
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/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
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/// THE SOFTWARE. |
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/// |
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/// @ref gtx_dual_quaternion |
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/// @file glm/gtx/dual_quaternion.inl |
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/// @date 2013-02-10 / 2013-02-13 |
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/// @author Maksim Vorobiev (msomeone@gmail.com) |
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/////////////////////////////////////////////////////////////////////////////////// |
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#include "../geometric.hpp" |
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#include <limits> |
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namespace glm |
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{ |
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// -- Component accesses -- |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tdualquat<T, P>::length_type tdualquat<T, P>::length() const |
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{ |
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return 2; |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER typename tdualquat<T, P>::part_type & tdualquat<T, P>::operator[](typename tdualquat<T, P>::length_type i) |
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{ |
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assert(i >= 0 && i < this->length()); |
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return (&real)[i]; |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER typename tdualquat<T, P>::part_type const & tdualquat<T, P>::operator[](typename tdualquat<T, P>::length_type i) const |
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{ |
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assert(i >= 0 && i < this->length()); |
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return (&real)[i]; |
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} |
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// -- Implicit basic constructors -- |
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# if !GLM_HAS_DEFAULTED_FUNCTIONS || !defined(GLM_FORCE_NO_CTOR_INIT) |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat() |
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# ifndef GLM_FORCE_NO_CTOR_INIT |
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: real(tquat<T, P>()) |
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, dual(tquat<T, P>(0, 0, 0, 0)) |
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# endif |
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{} |
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# endif |
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# if !GLM_HAS_DEFAULTED_FUNCTIONS |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P>::tdualquat(tdualquat<T, P> const & d) |
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: real(d.real) |
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, dual(d.dual) |
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{} |
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# endif//!GLM_HAS_DEFAULTED_FUNCTIONS |
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template <typename T, precision P> |
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template <precision Q> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tdualquat<T, Q> const & d) |
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: real(d.real) |
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, dual(d.dual) |
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{} |
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// -- Explicit basic constructors -- |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(ctor) |
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{} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tquat<T, P> const & r) |
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: real(r), dual(tquat<T, P>(0, 0, 0, 0)) |
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{} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tquat<T, P> const & q, tvec3<T, P> const& p) |
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: real(q), dual( |
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T(-0.5) * ( p.x*q.x + p.y*q.y + p.z*q.z), |
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T(+0.5) * ( p.x*q.w + p.y*q.z - p.z*q.y), |
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T(+0.5) * (-p.x*q.z + p.y*q.w + p.z*q.x), |
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T(+0.5) * ( p.x*q.y - p.y*q.x + p.z*q.w)) |
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{} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tquat<T, P> const & r, tquat<T, P> const & d) |
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: real(r), dual(d) |
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{} |
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// -- Conversion constructors -- |
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template <typename T, precision P> |
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template <typename U, precision Q> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tdualquat<U, Q> const & q) |
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: real(q.real) |
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, dual(q.dual) |
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{} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tmat2x4<T, P> const & m) |
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{ |
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*this = dualquat_cast(m); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER GLM_CONSTEXPR tdualquat<T, P>::tdualquat(tmat3x4<T, P> const & m) |
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{ |
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*this = dualquat_cast(m); |
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} |
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// -- Unary arithmetic operators -- |
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# if !GLM_HAS_DEFAULTED_FUNCTIONS |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator=(tdualquat<T, P> const & q) |
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{ |
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this->real = q.real; |
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this->dual = q.dual; |
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return *this; |
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} |
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# endif//!GLM_HAS_DEFAULTED_FUNCTIONS |
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template <typename T, precision P> |
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template <typename U> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator=(tdualquat<U, P> const & q) |
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{ |
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this->real = q.real; |
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this->dual = q.dual; |
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return *this; |
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} |
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template <typename T, precision P> |
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template <typename U> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator*=(U s) |
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{ |
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this->real *= static_cast<T>(s); |
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this->dual *= static_cast<T>(s); |
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return *this; |
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} |
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template <typename T, precision P> |
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template <typename U> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> & tdualquat<T, P>::operator/=(U s) |
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{ |
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this->real /= static_cast<T>(s); |
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this->dual /= static_cast<T>(s); |
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return *this; |
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} |
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// -- Unary bit operators -- |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> operator+(tdualquat<T, P> const & q) |
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{ |
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return q; |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> operator-(tdualquat<T, P> const & q) |
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{ |
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return tdualquat<T, P>(-q.real, -q.dual); |
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} |
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// -- Binary operators -- |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> operator+(tdualquat<T, P> const & q, tdualquat<T, P> const & p) |
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{ |
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return tdualquat<T, P>(q.real + p.real,q.dual + p.dual); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> operator*(tdualquat<T, P> const & p, tdualquat<T, P> const & o) |
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{ |
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return tdualquat<T, P>(p.real * o.real,p.real * o.dual + p.dual * o.real); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tdualquat<T, P> const & q, tvec3<T, P> const & v) |
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{ |
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tvec3<T, P> const real_v3(q.real.x,q.real.y,q.real.z); |
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tvec3<T, P> const dual_v3(q.dual.x,q.dual.y,q.dual.z); |
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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; |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tvec3<T, P> const & v, tdualquat<T, P> const & q) |
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{ |
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return glm::inverse(q) * v; |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tdualquat<T, P> const & q, tvec4<T, P> const & v) |
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{ |
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return tvec4<T, P>(q * tvec3<T, P>(v), v.w); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tvec4<T, P> const & v, tdualquat<T, P> const & q) |
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{ |
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return glm::inverse(q) * v; |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> operator*(tdualquat<T, P> const & q, T const & s) |
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{ |
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return tdualquat<T, P>(q.real * s, q.dual * s); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> operator*(T const & s, tdualquat<T, P> const & q) |
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{ |
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return q * s; |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> operator/(tdualquat<T, P> const & q, T const & s) |
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{ |
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return tdualquat<T, P>(q.real / s, q.dual / s); |
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} |
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// -- Boolean operators -- |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER bool operator==(tdualquat<T, P> const & q1, tdualquat<T, P> const & q2) |
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{ |
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return (q1.real == q2.real) && (q1.dual == q2.dual); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER bool operator!=(tdualquat<T, P> const & q1, tdualquat<T, P> const & q2) |
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{ |
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return (q1.real != q2.dual) || (q1.real != q2.dual); |
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} |
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// -- Operations -- |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> normalize(tdualquat<T, P> const & q) |
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{ |
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return q / length(q.real); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> lerp(tdualquat<T, P> const & x, tdualquat<T, P> const & y, T const & a) |
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{ |
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// Dual Quaternion Linear blend aka DLB: |
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// Lerp is only defined in [0, 1] |
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assert(a >= static_cast<T>(0)); |
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assert(a <= static_cast<T>(1)); |
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T const k = dot(x.real,y.real) < static_cast<T>(0) ? -a : a; |
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T const one(1); |
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return tdualquat<T, P>(x * (one - a) + y * k); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> inverse(tdualquat<T, P> const & q) |
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{ |
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const glm::tquat<T, P> real = conjugate(q.real); |
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const glm::tquat<T, P> dual = conjugate(q.dual); |
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return tdualquat<T, P>(real, dual + (real * (-2.0f * dot(real,dual)))); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tmat2x4<T, P> mat2x4_cast(tdualquat<T, P> const & x) |
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{ |
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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 ); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tmat3x4<T, P> mat3x4_cast(tdualquat<T, P> const & x) |
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{ |
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tquat<T, P> r = x.real / length2(x.real); |
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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); |
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r *= static_cast<T>(2); |
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T const xy = r.x * x.real.y; |
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T const xz = r.x * x.real.z; |
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T const yz = r.y * x.real.z; |
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T const wx = r.w * x.real.x; |
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T const wy = r.w * x.real.y; |
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T const wz = r.w * x.real.z; |
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tvec4<T, P> const a( |
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rr.w + rr.x - rr.y - rr.z, |
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xy - wz, |
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xz + wy, |
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-(x.dual.w * r.x - x.dual.x * r.w + x.dual.y * r.z - x.dual.z * r.y)); |
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tvec4<T, P> const b( |
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xy + wz, |
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rr.w + rr.y - rr.x - rr.z, |
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yz - wx, |
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-(x.dual.w * r.y - x.dual.x * r.z - x.dual.y * r.w + x.dual.z * r.x)); |
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tvec4<T, P> const c( |
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xz - wy, |
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yz + wx, |
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rr.w + rr.z - rr.x - rr.y, |
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-(x.dual.w * r.z + x.dual.x * r.y - x.dual.y * r.x - x.dual.z * r.w)); |
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return tmat3x4<T, P>(a, b, c); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> dualquat_cast(tmat2x4<T, P> const & x) |
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{ |
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return tdualquat<T, P>( |
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tquat<T, P>( x[0].w, x[0].x, x[0].y, x[0].z ), |
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tquat<T, P>( x[1].w, x[1].x, x[1].y, x[1].z )); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER tdualquat<T, P> dualquat_cast(tmat3x4<T, P> const & x) |
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{ |
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tquat<T, P> real(uninitialize); |
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T const trace = x[0].x + x[1].y + x[2].z; |
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if(trace > static_cast<T>(0)) |
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{ |
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T const r = sqrt(T(1) + trace); |
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T const invr = static_cast<T>(0.5) / r; |
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real.w = static_cast<T>(0.5) * r; |
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real.x = (x[2].y - x[1].z) * invr; |
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real.y = (x[0].z - x[2].x) * invr; |
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real.z = (x[1].x - x[0].y) * invr; |
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} |
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else if(x[0].x > x[1].y && x[0].x > x[2].z) |
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{ |
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T const r = sqrt(T(1) + x[0].x - x[1].y - x[2].z); |
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T const invr = static_cast<T>(0.5) / r; |
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real.x = static_cast<T>(0.5)*r; |
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real.y = (x[1].x + x[0].y) * invr; |
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real.z = (x[0].z + x[2].x) * invr; |
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real.w = (x[2].y - x[1].z) * invr; |
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} |
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else if(x[1].y > x[2].z) |
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{ |
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T const r = sqrt(T(1) + x[1].y - x[0].x - x[2].z); |
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T const invr = static_cast<T>(0.5) / r; |
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real.x = (x[1].x + x[0].y) * invr; |
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real.y = static_cast<T>(0.5) * r; |
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real.z = (x[2].y + x[1].z) * invr; |
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real.w = (x[0].z - x[2].x) * invr; |
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} |
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else |
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{ |
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T const r = sqrt(T(1) + x[2].z - x[0].x - x[1].y); |
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T const invr = static_cast<T>(0.5) / r; |
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real.x = (x[0].z + x[2].x) * invr; |
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real.y = (x[2].y + x[1].z) * invr; |
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real.z = static_cast<T>(0.5) * r; |
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real.w = (x[1].x - x[0].y) * invr; |
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} |
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tquat<T, P> dual(uninitialize); |
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dual.x = static_cast<T>(0.5) * ( x[0].w * real.w + x[1].w * real.z - x[2].w * real.y); |
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dual.y = static_cast<T>(0.5) * (-x[0].w * real.z + x[1].w * real.w + x[2].w * real.x); |
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dual.z = static_cast<T>(0.5) * ( x[0].w * real.y - x[1].w * real.x + x[2].w * real.w); |
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dual.w = -static_cast<T>(0.5) * ( x[0].w * real.x + x[1].w * real.y + x[2].w * real.z); |
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return tdualquat<T, P>(real, dual); |
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} |
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}//namespace glm
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