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289 lines
6.3 KiB
289 lines
6.3 KiB
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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// OpenGL Mathematics Copyright (c) 2005 - 2012 G-Truc Creation (www.g-truc.net) |
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/////////////////////////////////////////////////////////////////////////////////////////////////// |
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// Created : 2005-12-21 |
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// Updated : 2008-11-27 |
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// Licence : This source is under MIT License |
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// File : glm/gtx/quaternion.inl |
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/////////////////////////////////////////////////////////////////////////////////////////////////// |
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#include <limits> |
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namespace glm |
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{ |
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template <typename valType> |
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GLM_FUNC_QUALIFIER detail::tvec3<valType> cross |
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( |
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detail::tvec3<valType> const & v, |
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detail::tquat<valType> 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 valType> |
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GLM_FUNC_QUALIFIER detail::tvec3<valType> cross |
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( |
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detail::tquat<valType> const & q, |
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detail::tvec3<valType> const & v |
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) |
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{ |
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return q * v; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> squad |
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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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detail::tquat<T> const & s1, |
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detail::tquat<T> const & s2, |
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T const & h) |
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{ |
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return mix(mix(q1, q2, h), mix(s1, s2, h), T(2) * h (T(1) - h)); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> intermediate |
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( |
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detail::tquat<T> const & prev, |
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detail::tquat<T> const & curr, |
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detail::tquat<T> const & next |
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) |
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{ |
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detail::tquat<T> invQuat = inverse(curr); |
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return ext((log(next + invQuat) + log(prev + invQuat)) / T(-4)) * curr; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> exp |
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( |
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detail::tquat<T> const & q, |
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T const & exponent |
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) |
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{ |
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detail::tvec3<T> u(q.x, q.y, q.z); |
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float a = glm::length(u); |
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detail::tvec3<T> v(u / a); |
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return detail::tquat<T>(cos(a), sin(a) * v); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> log |
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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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if((q.x == T(0)) && (q.y == T(0)) && (q.z == T(0))) |
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{ |
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if(q.w > T(0)) |
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return detail::tquat<T>(log(q.w), T(0), T(0), T(0)); |
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else if(q.w < T(0)) |
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return detail::tquat<T>(log(-q.w), T(3.1415926535897932384626433832795), T(0),T(0)); |
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else |
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return detail::tquat<T>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity()); |
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} |
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else |
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{ |
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T Vec3Len = sqrt(q.x * q.x + q.y * q.y + q.z * q.z); |
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T QuatLen = sqrt(Vec3Len * Vec3Len + q.w * q.w); |
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T t = atan(Vec3Len, T(q.w)) / Vec3Len; |
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return detail::tquat<T>(t * q.x, t * q.y, t * q.z, log(QuatLen)); |
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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> pow |
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( |
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detail::tquat<T> const & x, |
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T const & y |
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) |
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{ |
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if(abs(x.w) > T(0.9999)) |
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return x; |
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float Angle = acos(y); |
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float NewAngle = Angle * y; |
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float Div = sin(NewAngle) / sin(Angle); |
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return detail::tquat<T>( |
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cos(NewAngle), |
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x.x * Div, |
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x.y * Div, |
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x.z * Div); |
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} |
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//template <typename T> |
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//GLM_FUNC_QUALIFIER detail::tquat<T> sqrt |
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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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// T q0 = T(1) - dot(q, q); |
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// return T(2) * (T(1) + q0) * q; |
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//} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tvec3<T> rotate |
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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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return q * v; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tvec4<T> rotate |
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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 q * v; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER T angle |
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( |
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detail::tquat<T> const & x |
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) |
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{ |
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return glm::degrees(acos(x.w) * T(2)); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tvec3<T> axis |
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( |
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detail::tquat<T> const & x |
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) |
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{ |
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T tmp1 = T(1) - x.w * x.w; |
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if(tmp1 <= T(0)) |
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return detail::tvec3<T>(0, 0, 1); |
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T tmp2 = T(1) / sqrt(tmp1); |
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return detail::tvec3<T>(x.x * tmp2, x.y * tmp2, x.z * tmp2); |
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} |
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template <typename valType> |
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GLM_FUNC_QUALIFIER detail::tquat<valType> angleAxis |
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( |
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valType const & angle, |
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valType const & x, |
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valType const & y, |
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valType const & z |
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) |
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{ |
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return angleAxis(angle, detail::tvec3<valType>(x, y, z)); |
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} |
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template <typename valType> |
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GLM_FUNC_QUALIFIER detail::tquat<valType> angleAxis |
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( |
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valType const & angle, |
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detail::tvec3<valType> const & v |
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) |
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{ |
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detail::tquat<valType> result; |
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valType a = glm::radians(angle); |
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valType s = glm::sin(a * valType(0.5)); |
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result.w = glm::cos(a * valType(0.5)); |
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result.x = v.x * s; |
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result.y = v.y * s; |
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result.z = v.z * s; |
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return result; |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER T extractRealComponent |
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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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T w = T(1.0) - q.x * q.x - q.y * q.y - q.z * q.z; |
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if(w < T(0)) |
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return T(0); |
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else |
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return -sqrt(w); |
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} |
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template <typename valType> |
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GLM_FUNC_QUALIFIER valType roll |
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( |
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detail::tquat<valType> const & q |
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) |
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{ |
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return glm::degrees(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)); |
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} |
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template <typename valType> |
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GLM_FUNC_QUALIFIER valType pitch |
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( |
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detail::tquat<valType> const & q |
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) |
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{ |
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return glm::degrees(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)); |
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} |
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template <typename valType> |
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GLM_FUNC_QUALIFIER valType yaw |
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( |
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detail::tquat<valType> const & q |
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) |
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{ |
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return glm::degrees(asin(valType(-2) * (q.x * q.z - q.w * q.y))); |
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} |
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template <typename T> |
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GLM_FUNC_QUALIFIER detail::tquat<T> shortMix |
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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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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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T fCos = dot(x, y); |
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detail::tquat<T> y2(y); //BUG!!! tquat<T> y2; |
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if(fCos < T(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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T k0, k1; |
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if(fCos > T(0.9999)) |
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{ |
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k0 = T(1) - a; |
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k1 = T(0) + a; //BUG!!! 1.0f + a; |
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} |
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else |
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{ |
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T fSin = sqrt(T(1) - fCos * fCos); |
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T fAngle = atan(fSin, fCos); |
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T fOneOverSin = T(1) / fSin; |
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k0 = sin((T(1) - a) * fAngle) * fOneOverSin; |
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k1 = sin((T(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> fastMix |
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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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return glm::normalize(x * (T(1) - a) + (y * a)); |
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} |
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}//namespace glm
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