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784 lines
18 KiB
784 lines
18 KiB
/////////////////////////////////////////////////////////////////////////////////// |
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/// OpenGL Mathematics (glm.g-truc.net) |
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/// |
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/// Copyright (c) 2005 - 2012 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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/// 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 gtc_quaternion |
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/// @file glm/gtc/quaternion.inl |
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/// @date 2009-05-21 / 2011-06-15 |
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/// @author Christophe Riccio |
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/////////////////////////////////////////////////////////////////////////////////// |
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#include <limits> |
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namespace glm{ |
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namespace detail |
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{ |
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template <typename T> |
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GLM_FUNC_QUALIFIER typename tquat<T>::size_type tquat<T>::length() const |
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{ |
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return 4; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER tquat<T>::tquat() : |
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x(0), |
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y(0), |
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z(0), |
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w(1) |
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{} |
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template <typename T> |
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GLM_FUNC_QUALIFIER tquat<T>::tquat |
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( |
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value_type const & s, |
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tvec3<T> const & v |
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) : |
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x(v.x), |
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y(v.y), |
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z(v.z), |
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w(s) |
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{} |
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template <typename T> |
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GLM_FUNC_QUALIFIER tquat<T>::tquat |
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( |
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value_type const & w, |
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value_type const & x, |
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value_type const & y, |
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value_type const & z |
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) : |
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x(x), |
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y(y), |
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z(z), |
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w(w) |
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{} |
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|
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////////////////////////////////////////////////////////////// |
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// tquat conversions |
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|
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//template <typename valType> |
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//GLM_FUNC_QUALIFIER tquat<valType>::tquat |
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//( |
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// valType const & pitch, |
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// valType const & yaw, |
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// valType const & roll |
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//) |
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//{ |
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// tvec3<valType> eulerAngle(pitch * valType(0.5), yaw * valType(0.5), roll * valType(0.5)); |
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// tvec3<valType> c = glm::cos(eulerAngle * valType(0.5)); |
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// tvec3<valType> s = glm::sin(eulerAngle * valType(0.5)); |
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// |
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// this->w = c.x * c.y * c.z + s.x * s.y * s.z; |
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// this->x = s.x * c.y * c.z - c.x * s.y * s.z; |
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// this->y = c.x * s.y * c.z + s.x * c.y * s.z; |
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// this->z = c.x * c.y * s.z - s.x * s.y * c.z; |
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//} |
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template <typename T> |
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GLM_FUNC_QUALIFIER tquat<T>::tquat |
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( |
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tvec3<T> const & eulerAngle |
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) |
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{ |
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tvec3<T> c = glm::cos(eulerAngle * value_type(0.5)); |
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tvec3<T> s = glm::sin(eulerAngle * value_type(0.5)); |
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|
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this->w = c.x * c.y * c.z + s.x * s.y * s.z; |
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this->x = s.x * c.y * c.z - c.x * s.y * s.z; |
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this->y = c.x * s.y * c.z + s.x * c.y * s.z; |
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this->z = c.x * c.y * s.z - s.x * s.y * c.z; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER tquat<T>::tquat |
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( |
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tmat3x3<T> const & m |
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) |
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{ |
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*this = quat_cast(m); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER tquat<T>::tquat |
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( |
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tmat4x4<T> const & m |
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) |
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{ |
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*this = quat_cast(m); |
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} |
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////////////////////////////////////////////////////////////// |
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// tquat<T> accesses |
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template <typename T> |
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GLM_FUNC_QUALIFIER typename tquat<T>::value_type & tquat<T>::operator [] (int i) |
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{ |
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return (&x)[i]; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER typename tquat<T>::value_type const & tquat<T>::operator [] (int i) const |
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{ |
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return (&x)[i]; |
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} |
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////////////////////////////////////////////////////////////// |
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// tquat<valType> operators |
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template <typename T> |
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GLM_FUNC_QUALIFIER tquat<T> & tquat<T>::operator *= |
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( |
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value_type const & s |
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) |
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{ |
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this->w *= s; |
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this->x *= s; |
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this->y *= s; |
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this->z *= s; |
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return *this; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER tquat<T> & tquat<T>::operator /= |
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( |
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value_type const & s |
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) |
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{ |
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this->w /= s; |
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this->x /= s; |
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this->y /= s; |
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this->z /= s; |
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return *this; |
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} |
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////////////////////////////////////////////////////////////// |
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// tquat<valType> external operators |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> operator- |
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( |
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detail::tquat<T> const & q |
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) |
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{ |
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return detail::tquat<T>(-q.w, -q.x, -q.y, -q.z); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> operator+ |
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( |
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detail::tquat<T> const & q, |
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detail::tquat<T> const & p |
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) |
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{ |
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return detail::tquat<T>( |
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q.w + p.w, |
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q.x + p.x, |
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q.y + p.y, |
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q.z + p.z); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> operator* |
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( |
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detail::tquat<T> const & q, |
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detail::tquat<T> const & p |
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) |
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{ |
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return detail::tquat<T>( |
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q.w * p.w - q.x * p.x - q.y * p.y - q.z * p.z, |
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q.w * p.x + q.x * p.w + q.y * p.z - q.z * p.y, |
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q.w * p.y + q.y * p.w + q.z * p.x - q.x * p.z, |
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q.w * p.z + q.z * p.w + q.x * p.y - q.y * p.x); |
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} |
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// Transformation |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tvec3<T> operator* |
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( |
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detail::tquat<T> const & q, |
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detail::tvec3<T> const & v |
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) |
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{ |
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typename detail::tquat<T>::value_type Two(2); |
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detail::tvec3<T> uv, uuv; |
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detail::tvec3<T> QuatVector(q.x, q.y, q.z); |
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uv = glm::cross(QuatVector, v); |
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uuv = glm::cross(QuatVector, uv); |
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uv *= (Two * q.w); |
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uuv *= Two; |
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return v + uv + uuv; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tvec3<T> operator* |
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( |
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detail::tvec3<T> const & v, |
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detail::tquat<T> const & q |
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) |
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{ |
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return inverse(q) * v; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tvec4<T> operator* |
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( |
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detail::tquat<T> const & q, |
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detail::tvec4<T> const & v |
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) |
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{ |
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return detail::tvec4<T>(q * detail::tvec3<T>(v), v.w); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tvec4<T> operator* |
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( |
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detail::tvec4<T> const & v, |
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detail::tquat<T> const & q |
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) |
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{ |
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return inverse(q) * v; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> operator* |
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( |
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detail::tquat<T> const & q, |
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typename detail::tquat<T>::value_type const & s |
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) |
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{ |
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return detail::tquat<T>( |
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q.w * s, q.x * s, q.y * s, q.z * s); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> operator* |
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( |
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typename detail::tquat<T>::value_type const & s, |
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detail::tquat<T> const & q |
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) |
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{ |
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return q * s; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> operator/ |
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( |
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detail::tquat<T> const & q, |
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typename detail::tquat<T>::value_type const & s |
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) |
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{ |
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return detail::tquat<T>( |
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q.w / s, q.x / s, q.y / s, q.z / s); |
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} |
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////////////////////////////////////// |
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// Boolean operators |
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template <typename T> |
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GLM_FUNC_QUALIFIER bool operator== |
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( |
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detail::tquat<T> const & q1, |
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detail::tquat<T> const & q2 |
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) |
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{ |
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return (q1.x == q2.x) && (q1.y == q2.y) && (q1.z == q2.z) && (q1.w == q2.w); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER bool operator!= |
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( |
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detail::tquat<T> const & q1, |
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detail::tquat<T> const & q2 |
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) |
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{ |
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return (q1.x != q2.x) || (q1.y != q2.y) || (q1.z != q2.z) || (q1.w != q2.w); |
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} |
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}//namespace detail |
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//////////////////////////////////////////////////////// |
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template <typename T> |
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GLM_FUNC_QUALIFIER T length |
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( |
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detail::tquat<T> const & q |
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) |
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{ |
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return glm::sqrt(dot(q, q)); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> normalize |
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( |
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detail::tquat<T> const & q |
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) |
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{ |
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typename detail::tquat<T>::value_type len = length(q); |
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if(len <= typename detail::tquat<T>::value_type(0)) // Problem |
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return detail::tquat<T>(1, 0, 0, 0); |
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typename detail::tquat<T>::value_type oneOverLen = typename detail::tquat<T>::value_type(1) / len; |
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return detail::tquat<T>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER T dot |
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( |
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detail::tquat<T> const & q1, |
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detail::tquat<T> const & q2 |
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) |
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{ |
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return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> cross |
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( |
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detail::tquat<T> const & q1, |
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detail::tquat<T> const & q2 |
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) |
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{ |
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return detail::tquat<T>( |
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q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z, |
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q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y, |
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q1.w * q2.y + q1.y * q2.w + q1.z * q2.x - q1.x * q2.z, |
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q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x); |
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} |
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/* |
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// (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle)) |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> mix |
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( |
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detail::tquat<T> const & x, |
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detail::tquat<T> const & y, |
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typename detail::tquat<T>::value_type const & a |
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) |
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{ |
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if(a <= typename detail::tquat<T>::value_type(0)) return x; |
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if(a >= typename detail::tquat<T>::value_type(1)) return y; |
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|
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float fCos = dot(x, y); |
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detail::tquat<T> y2(y); //BUG!!! tquat<T> y2; |
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if(fCos < typename detail::tquat<T>::value_type(0)) |
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{ |
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y2 = -y; |
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fCos = -fCos; |
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} |
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|
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//if(fCos > 1.0f) // problem |
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float k0, k1; |
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if(fCos > typename detail::tquat<T>::value_type(0.9999)) |
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{ |
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k0 = typename detail::tquat<T>::value_type(1) - a; |
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k1 = typename detail::tquat<T>::value_type(0) + a; //BUG!!! 1.0f + a; |
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} |
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else |
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{ |
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typename detail::tquat<T>::value_type fSin = sqrt(T(1) - fCos * fCos); |
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typename detail::tquat<T>::value_type fAngle = atan(fSin, fCos); |
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typename detail::tquat<T>::value_type fOneOverSin = T(1) / fSin; |
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k0 = sin((typename detail::tquat<T>::value_type(1) - a) * fAngle) * fOneOverSin; |
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k1 = sin((typename detail::tquat<T>::value_type(0) + a) * fAngle) * fOneOverSin; |
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} |
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return detail::tquat<T>( |
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k0 * x.w + k1 * y2.w, |
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k0 * x.x + k1 * y2.x, |
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k0 * x.y + k1 * y2.y, |
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k0 * x.z + k1 * y2.z); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> mix2 |
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( |
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detail::tquat<T> const & x, |
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detail::tquat<T> const & y, |
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T const & a |
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) |
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{ |
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bool flip = false; |
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if(a <= T(0)) return x; |
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if(a >= T(1)) return y; |
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|
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T cos_t = dot(x, y); |
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if(cos_t < T(0)) |
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{ |
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cos_t = -cos_t; |
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flip = true; |
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} |
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T alpha(0), beta(0); |
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|
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if(T(1) - cos_t < 1e-7) |
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beta = T(1) - alpha; |
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else |
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{ |
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T theta = acos(cos_t); |
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T sin_t = sin(theta); |
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beta = sin(theta * (T(1) - alpha)) / sin_t; |
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alpha = sin(alpha * theta) / sin_t; |
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} |
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|
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if(flip) |
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alpha = -alpha; |
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|
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return normalize(beta * x + alpha * y); |
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} |
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*/ |
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|
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> mix |
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( |
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detail::tquat<T> const & x, |
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detail::tquat<T> const & y, |
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T const & a |
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) |
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{ |
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T cosTheta = dot(x, y); |
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|
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// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator |
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if(cosTheta > T(1) - epsilon<T>()) |
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{ |
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// Linear interpolation |
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return detail::tquat<T>( |
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mix(x.w, y.w, a), |
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mix(x.x, y.x, a), |
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mix(x.y, y.y, a), |
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mix(x.z, y.z, a)); |
|
} |
|
else |
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{ |
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// Essential Mathematics, page 467 |
|
T angle = acos(cosTheta); |
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return (sin((T(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle); |
|
} |
|
} |
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|
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> lerp |
|
( |
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detail::tquat<T> const & x, |
|
detail::tquat<T> const & y, |
|
T const & a |
|
) |
|
{ |
|
return x * (T(1) - a) + (y * a); |
|
} |
|
|
|
template <typename T> |
|
GLM_FUNC_QUALIFIER detail::tquat<T> slerp |
|
( |
|
detail::tquat<T> const & x, |
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detail::tquat<T> const & y, |
|
T const & a |
|
) |
|
{ |
|
detail::tquat<T> z = y; |
|
|
|
T cosTheta = dot(x, y); |
|
|
|
// If cosTheta < 0, the interpolation will take the long way around the sphere. |
|
// To fix this, one quat must be negated. |
|
if (cosTheta < T(0)) |
|
{ |
|
z = -y; |
|
cosTheta = -cosTheta; |
|
} |
|
|
|
// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator |
|
if(cosTheta > T(1) - epsilon<T>()) |
|
{ |
|
// Linear interpolation |
|
return detail::tquat<T>( |
|
mix(x.w, y.w, a), |
|
mix(x.x, y.x, a), |
|
mix(x.y, y.y, a), |
|
mix(x.z, y.z, a)); |
|
} |
|
else |
|
{ |
|
// Essential Mathematics, page 467 |
|
T angle = acos(cosTheta); |
|
return (sin((T(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle); |
|
} |
|
} |
|
|
|
template <typename T> |
|
GLM_FUNC_QUALIFIER detail::tquat<T> conjugate |
|
( |
|
detail::tquat<T> const & q |
|
) |
|
{ |
|
return detail::tquat<T>(q.w, -q.x, -q.y, -q.z); |
|
} |
|
|
|
template <typename T> |
|
GLM_FUNC_QUALIFIER detail::tquat<T> inverse |
|
( |
|
detail::tquat<T> const & q |
|
) |
|
{ |
|
return conjugate(q) / dot(q, q); |
|
} |
|
|
|
template <typename T> |
|
GLM_FUNC_QUALIFIER detail::tquat<T> rotate |
|
( |
|
detail::tquat<T> const & q, |
|
typename detail::tquat<T>::value_type const & angle, |
|
detail::tvec3<T> const & v |
|
) |
|
{ |
|
detail::tvec3<T> Tmp = v; |
|
|
|
// Axis of rotation must be normalised |
|
typename detail::tquat<T>::value_type len = glm::length(Tmp); |
|
if(abs(len - T(1)) > T(0.001)) |
|
{ |
|
T oneOverLen = T(1) / len; |
|
Tmp.x *= oneOverLen; |
|
Tmp.y *= oneOverLen; |
|
Tmp.z *= oneOverLen; |
|
} |
|
|
|
#ifdef GLM_FORCE_RADIANS |
|
typename detail::tquat<T>::value_type const AngleRad(angle); |
|
#else |
|
typename detail::tquat<T>::value_type const AngleRad = radians(angle); |
|
#endif |
|
typename detail::tquat<T>::value_type const Sin = sin(AngleRad * T(0.5)); |
|
|
|
return q * detail::tquat<T>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin); |
|
//return gtc::quaternion::cross(q, detail::tquat<T>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin)); |
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} |
|
|
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template <typename T> |
|
GLM_FUNC_QUALIFIER detail::tvec3<T> eulerAngles |
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( |
|
detail::tquat<T> const & x |
|
) |
|
{ |
|
return detail::tvec3<T>(pitch(x), yaw(x), roll(x)); |
|
} |
|
|
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template <typename valType> |
|
GLM_FUNC_QUALIFIER valType roll |
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( |
|
detail::tquat<valType> const & q |
|
) |
|
{ |
|
#ifdef GLM_FORCE_RADIANS |
|
return valType(atan2(valType(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z)); |
|
#else |
|
return glm::degrees(atan(valType(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z)); |
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#endif |
|
} |
|
|
|
template <typename valType> |
|
GLM_FUNC_QUALIFIER valType pitch |
|
( |
|
detail::tquat<valType> const & q |
|
) |
|
{ |
|
#ifdef GLM_FORCE_RADIANS |
|
return valType(atan2(valType(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z)); |
|
#else |
|
return glm::degrees(atan(valType(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z)); |
|
#endif |
|
} |
|
|
|
template <typename valType> |
|
GLM_FUNC_QUALIFIER valType yaw |
|
( |
|
detail::tquat<valType> const & q |
|
) |
|
{ |
|
#ifdef GLM_FORCE_RADIANS |
|
return asin(valType(-2) * (q.x * q.z - q.w * q.y)); |
|
#else |
|
return glm::degrees(asin(valType(-2) * (q.x * q.z - q.w * q.y))); |
|
#endif |
|
} |
|
|
|
template <typename T> |
|
GLM_FUNC_QUALIFIER detail::tmat3x3<T> mat3_cast |
|
( |
|
detail::tquat<T> const & q |
|
) |
|
{ |
|
detail::tmat3x3<T> Result(T(1)); |
|
Result[0][0] = 1 - 2 * q.y * q.y - 2 * q.z * q.z; |
|
Result[0][1] = 2 * q.x * q.y + 2 * q.w * q.z; |
|
Result[0][2] = 2 * q.x * q.z - 2 * q.w * q.y; |
|
|
|
Result[1][0] = 2 * q.x * q.y - 2 * q.w * q.z; |
|
Result[1][1] = 1 - 2 * q.x * q.x - 2 * q.z * q.z; |
|
Result[1][2] = 2 * q.y * q.z + 2 * q.w * q.x; |
|
|
|
Result[2][0] = 2 * q.x * q.z + 2 * q.w * q.y; |
|
Result[2][1] = 2 * q.y * q.z - 2 * q.w * q.x; |
|
Result[2][2] = 1 - 2 * q.x * q.x - 2 * q.y * q.y; |
|
return Result; |
|
} |
|
|
|
template <typename T> |
|
GLM_FUNC_QUALIFIER detail::tmat4x4<T> mat4_cast |
|
( |
|
detail::tquat<T> const & q |
|
) |
|
{ |
|
return detail::tmat4x4<T>(mat3_cast(q)); |
|
} |
|
|
|
template <typename T> |
|
GLM_FUNC_QUALIFIER detail::tquat<T> quat_cast |
|
( |
|
detail::tmat3x3<T> const & m |
|
) |
|
{ |
|
typename detail::tquat<T>::value_type fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2]; |
|
typename detail::tquat<T>::value_type fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2]; |
|
typename detail::tquat<T>::value_type fourZSquaredMinus1 = m[2][2] - m[0][0] - m[1][1]; |
|
typename detail::tquat<T>::value_type fourWSquaredMinus1 = m[0][0] + m[1][1] + m[2][2]; |
|
|
|
int biggestIndex = 0; |
|
typename detail::tquat<T>::value_type fourBiggestSquaredMinus1 = fourWSquaredMinus1; |
|
if(fourXSquaredMinus1 > fourBiggestSquaredMinus1) |
|
{ |
|
fourBiggestSquaredMinus1 = fourXSquaredMinus1; |
|
biggestIndex = 1; |
|
} |
|
if(fourYSquaredMinus1 > fourBiggestSquaredMinus1) |
|
{ |
|
fourBiggestSquaredMinus1 = fourYSquaredMinus1; |
|
biggestIndex = 2; |
|
} |
|
if(fourZSquaredMinus1 > fourBiggestSquaredMinus1) |
|
{ |
|
fourBiggestSquaredMinus1 = fourZSquaredMinus1; |
|
biggestIndex = 3; |
|
} |
|
|
|
typename detail::tquat<T>::value_type biggestVal = sqrt(fourBiggestSquaredMinus1 + T(1)) * T(0.5); |
|
typename detail::tquat<T>::value_type mult = T(0.25) / biggestVal; |
|
|
|
detail::tquat<T> Result; |
|
switch(biggestIndex) |
|
{ |
|
case 0: |
|
Result.w = biggestVal; |
|
Result.x = (m[1][2] - m[2][1]) * mult; |
|
Result.y = (m[2][0] - m[0][2]) * mult; |
|
Result.z = (m[0][1] - m[1][0]) * mult; |
|
break; |
|
case 1: |
|
Result.w = (m[1][2] - m[2][1]) * mult; |
|
Result.x = biggestVal; |
|
Result.y = (m[0][1] + m[1][0]) * mult; |
|
Result.z = (m[2][0] + m[0][2]) * mult; |
|
break; |
|
case 2: |
|
Result.w = (m[2][0] - m[0][2]) * mult; |
|
Result.x = (m[0][1] + m[1][0]) * mult; |
|
Result.y = biggestVal; |
|
Result.z = (m[1][2] + m[2][1]) * mult; |
|
break; |
|
case 3: |
|
Result.w = (m[0][1] - m[1][0]) * mult; |
|
Result.x = (m[2][0] + m[0][2]) * mult; |
|
Result.y = (m[1][2] + m[2][1]) * mult; |
|
Result.z = biggestVal; |
|
break; |
|
} |
|
return Result; |
|
} |
|
|
|
template <typename T> |
|
GLM_FUNC_QUALIFIER detail::tquat<T> quat_cast |
|
( |
|
detail::tmat4x4<T> const & m4 |
|
) |
|
{ |
|
return quat_cast(detail::tmat3x3<T>(m4)); |
|
} |
|
|
|
template <typename T> |
|
GLM_FUNC_QUALIFIER T angle |
|
( |
|
detail::tquat<T> const & x |
|
) |
|
{ |
|
#ifdef GLM_FORCE_RADIANS |
|
return acos(x.w) * T(2); |
|
#else |
|
return glm::degrees(acos(x.w) * T(2)); |
|
#endif |
|
} |
|
|
|
template <typename T> |
|
GLM_FUNC_QUALIFIER detail::tvec3<T> axis |
|
( |
|
detail::tquat<T> const & x |
|
) |
|
{ |
|
T tmp1 = T(1) - x.w * x.w; |
|
if(tmp1 <= T(0)) |
|
return detail::tvec3<T>(0, 0, 1); |
|
T tmp2 = T(1) / sqrt(tmp1); |
|
return detail::tvec3<T>(x.x * tmp2, x.y * tmp2, x.z * tmp2); |
|
} |
|
|
|
template <typename valType> |
|
GLM_FUNC_QUALIFIER detail::tquat<valType> angleAxis |
|
( |
|
valType const & angle, |
|
valType const & x, |
|
valType const & y, |
|
valType const & z |
|
) |
|
{ |
|
return angleAxis(angle, detail::tvec3<valType>(x, y, z)); |
|
} |
|
|
|
template <typename valType> |
|
GLM_FUNC_QUALIFIER detail::tquat<valType> angleAxis |
|
( |
|
valType const & angle, |
|
detail::tvec3<valType> const & v |
|
) |
|
{ |
|
detail::tquat<valType> result; |
|
|
|
#ifdef GLM_FORCE_RADIANS |
|
valType a(angle); |
|
#else |
|
valType a(glm::radians(angle)); |
|
#endif |
|
valType s = glm::sin(a * valType(0.5)); |
|
|
|
result.w = glm::cos(a * valType(0.5)); |
|
result.x = v.x * s; |
|
result.y = v.y * s; |
|
result.z = v.z * s; |
|
return result; |
|
} |
|
|
|
}//namespace glm
|
|
|