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256 lines
6.2 KiB
256 lines
6.2 KiB
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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// OpenGL Mathematics Copyright (c) 2005 - 2013 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 T, precision P> |
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GLM_FUNC_QUALIFIER detail::tvec3<T, P> cross |
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( |
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detail::tvec3<T, P> const & v, |
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detail::tquat<T, P> 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, precision P> |
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GLM_FUNC_QUALIFIER detail::tvec3<T, P> cross |
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( |
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detail::tquat<T, P> const & q, |
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detail::tvec3<T, P> 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, precision P> |
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GLM_FUNC_QUALIFIER detail::tquat<T, P> squad |
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( |
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detail::tquat<T, P> const & q1, |
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detail::tquat<T, P> const & q2, |
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detail::tquat<T, P> const & s1, |
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detail::tquat<T, P> 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) * (T(1) - h) * h); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER detail::tquat<T, P> intermediate |
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( |
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detail::tquat<T, P> const & prev, |
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detail::tquat<T, P> const & curr, |
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detail::tquat<T, P> const & next |
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) |
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{ |
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detail::tquat<T, P> invQuat = inverse(curr); |
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return exp((log(next + invQuat) + log(prev + invQuat)) / T(-4)) * curr; |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER detail::tquat<T, P> exp |
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( |
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detail::tquat<T, P> const & q |
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) |
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{ |
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detail::tvec3<T, P> u(q.x, q.y, q.z); |
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float Angle = glm::length(u); |
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detail::tvec3<T, P> v(u / Angle); |
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return detail::tquat<T, P>(cos(Angle), sin(Angle) * v); |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER detail::tquat<T, P> log |
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( |
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detail::tquat<T, P> const & q |
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) |
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{ |
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if((q.x == static_cast<T>(0)) && (q.y == static_cast<T>(0)) && (q.z == static_cast<T>(0))) |
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{ |
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if(q.w > T(0)) |
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return detail::tquat<T, P>(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, P>(log(-q.w), T(3.1415926535897932384626433832795), T(0),T(0)); |
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else |
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return detail::tquat<T, P>(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, P>(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, precision P> |
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GLM_FUNC_QUALIFIER detail::tquat<T, P> pow |
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( |
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detail::tquat<T, P> 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, P>( |
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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, precision P> |
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//GLM_FUNC_QUALIFIER detail::tquat<T, P> sqrt |
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//( |
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// detail::tquat<T, P> const & q |
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//) |
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//{ |
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// T q0 = static_cast<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, precision P> |
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GLM_FUNC_QUALIFIER detail::tvec3<T, P> rotate |
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( |
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detail::tquat<T, P> const & q, |
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detail::tvec3<T, P> 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, precision P> |
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GLM_FUNC_QUALIFIER detail::tvec4<T, P> rotate |
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( |
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detail::tquat<T, P> const & q, |
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detail::tvec4<T, P> 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, precision P> |
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GLM_FUNC_QUALIFIER T extractRealComponent |
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( |
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detail::tquat<T, P> const & q |
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) |
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{ |
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T w = static_cast<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 T, precision P> |
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GLM_FUNC_QUALIFIER T length2 |
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( |
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detail::tquat<T, P> const & q |
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) |
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{ |
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return q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w; |
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} |
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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER detail::tquat<T, P> shortMix |
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( |
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detail::tquat<T, P> const & x, |
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detail::tquat<T, P> const & y, |
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T const & a |
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) |
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{ |
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if(a <= T(0)) return x; |
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if(a >= T(1)) return y; |
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T fCos = dot(x, y); |
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detail::tquat<T, P> 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 = static_cast<T>(1) - a; |
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k1 = static_cast<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 = static_cast<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, P>( |
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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, precision P> |
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GLM_FUNC_QUALIFIER detail::tquat<T, P> fastMix |
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( |
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detail::tquat<T, P> const & x, |
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detail::tquat<T, P> 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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template <typename T, precision P> |
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GLM_FUNC_QUALIFIER detail::tquat<T, P> rotation |
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( |
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detail::tvec3<T, P> const & orig, |
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detail::tvec3<T, P> const & dest |
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) |
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{ |
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T cosTheta = dot(orig, dest); |
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detail::tvec3<T, P> rotationAxis; |
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if(cosTheta < T(-1) + epsilon<T>()) |
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{ |
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// special case when vectors in opposite directions : |
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// there is no "ideal" rotation axis |
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// So guess one; any will do as long as it's perpendicular to start |
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// This implementation favors a rotation around the Up axis (Y), |
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// since it's often what you want to do. |
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rotationAxis = cross(detail::tvec3<T, P>(0, 0, 1), orig); |
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if(length2(rotationAxis) < epsilon<T>()) // bad luck, they were parallel, try again! |
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rotationAxis = cross(detail::tvec3<T, P>(1, 0, 0), orig); |
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rotationAxis = normalize(rotationAxis); |
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return angleAxis(pi<T>(), rotationAxis); |
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} |
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// Implementation from Stan Melax's Game Programming Gems 1 article |
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rotationAxis = cross(orig, dest); |
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T s = sqrt((T(1) + cosTheta) * T(2)); |
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T invs = static_cast<T>(1) / s; |
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return detail::tquat<T, P>( |
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s * T(0.5f), |
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rotationAxis.x * invs, |
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rotationAxis.y * invs, |
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rotationAxis.z * invs); |
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} |
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}//namespace glm
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