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571 lines
15 KiB
Text
571 lines
15 KiB
Text
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// OpenGL Mathematics Copyright (c) 2005 - 2011 G-Truc Creation (www.g-truc.net)
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// Created : 2009-05-21
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// Updated : 2010-02-04
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// Licence : This source is under MIT License
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// File : glm/gtc/quaternion.inl
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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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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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// tquat conversions
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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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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 = toQuat(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 = toQuat(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 - 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 gtc::quaternion::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 gtc::quaternion::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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namespace gtc{
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namespace quaternion{
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////////////////////////////////////////////////////////
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template <typename T>
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GLM_FUNC_QUALIFIER typename detail::tquat<T>::value_type 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 typename detail::tquat<T>::value_type 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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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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//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;
|
||
|
|
}
|
||
|
|
|
||
|
|
return detail::tquat<T>(
|
||
|
|
k0 * x.w + k1 * y2.w,
|
||
|
|
k0 * x.x + k1 * y2.x,
|
||
|
|
k0 * x.y + k1 * y2.y,
|
||
|
|
k0 * x.z + k1 * y2.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER detail::tquat<T> mix2
|
||
|
|
(
|
||
|
|
detail::tquat<T> const & x,
|
||
|
|
detail::tquat<T> const & y,
|
||
|
|
T const & a
|
||
|
|
)
|
||
|
|
{
|
||
|
|
bool flip = false;
|
||
|
|
if(a <= T(0)) return x;
|
||
|
|
if(a >= T(1)) return y;
|
||
|
|
|
||
|
|
T cos_t = dot(x, y);
|
||
|
|
if(cos_t < T(0))
|
||
|
|
{
|
||
|
|
cos_t = -cos_t;
|
||
|
|
flip = true;
|
||
|
|
}
|
||
|
|
|
||
|
|
T alpha(0), beta(0);
|
||
|
|
|
||
|
|
if(T(1) - cos_t < 1e-7)
|
||
|
|
beta = T(1) - alpha;
|
||
|
|
else
|
||
|
|
{
|
||
|
|
T theta = acos(cos_t);
|
||
|
|
T sin_t = sin(theta);
|
||
|
|
beta = sin(theta * (T(1) - alpha)) / sin_t;
|
||
|
|
alpha = sin(alpha * theta) / sin_t;
|
||
|
|
}
|
||
|
|
|
||
|
|
if(flip)
|
||
|
|
alpha = -alpha;
|
||
|
|
|
||
|
|
return normalize(beta * x + alpha * y);
|
||
|
|
}
|
||
|
|
*/
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER detail::tquat<T> mix
|
||
|
|
(
|
||
|
|
detail::tquat<T> const & x,
|
||
|
|
detail::tquat<T> const & y,
|
||
|
|
T const & a
|
||
|
|
)
|
||
|
|
{
|
||
|
|
T angle = acos(dot(x, y));
|
||
|
|
return (sin((1 - a) * angle) * x + sin(a * angle) * y) / 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 gtc::quaternion::conjugate(q) / gtc::quaternion::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::core::function::geometric::length(Tmp);
|
||
|
|
if(abs(len - typename detail::tquat<T>::value_type(1)) > typename detail::tquat<T>::value_type(0.001))
|
||
|
|
{
|
||
|
|
T oneOverLen = T(1) / len;
|
||
|
|
Tmp.x *= oneOverLen;
|
||
|
|
Tmp.y *= oneOverLen;
|
||
|
|
Tmp.z *= oneOverLen;
|
||
|
|
}
|
||
|
|
|
||
|
|
typename detail::tquat<T>::value_type AngleRad = radians(angle);
|
||
|
|
typename detail::tquat<T>::value_type fSin = sin(AngleRad * T(0.5));
|
||
|
|
|
||
|
|
return gtc::quaternion::cross(q, detail::tquat<T>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
GLM_FUNC_QUALIFIER detail::tmat3x3<T> mat3_cast
|
||
|
|
(
|
||
|
|
detail::tquat<T> const & q
|
||
|
|
)
|
||
|
|
{
|
||
|
|
detail::tmat3x3<T> Result(typename detail::tquat<T>::value_type(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 + typename detail::tquat<T>::value_type(1)) * typename detail::tquat<T>::value_type(0.5);
|
||
|
|
typename detail::tquat<T>::value_type mult = typename detail::tquat<T>::value_type(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));
|
||
|
|
}
|
||
|
|
|
||
|
|
}//namespace quaternion
|
||
|
|
}//namespace gtc
|
||
|
|
}//namespace glm
|