| /////////////////////////////////////////////////////////////////////////////////////////////////// |
| // OpenGL Mathematics Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net) |
| /////////////////////////////////////////////////////////////////////////////////////////////////// |
| // Created : 2005-12-21 |
| // Updated : 2008-11-27 |
| // Licence : This source is under MIT License |
| // File : glm/gtx/quaternion.inl |
| /////////////////////////////////////////////////////////////////////////////////////////////////// |
| |
| #include <limits> |
| |
| namespace glm |
| { |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, P> cross |
| ( |
| detail::tvec3<T, P> const & v, |
| detail::tquat<T, P> const & q |
| ) |
| { |
| return inverse(q) * v; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, P> cross |
| ( |
| detail::tquat<T, P> const & q, |
| detail::tvec3<T, P> const & v |
| ) |
| { |
| return q * v; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> squad |
| ( |
| detail::tquat<T, P> const & q1, |
| detail::tquat<T, P> const & q2, |
| detail::tquat<T, P> const & s1, |
| detail::tquat<T, P> const & s2, |
| T const & h) |
| { |
| return mix(mix(q1, q2, h), mix(s1, s2, h), T(2) * (T(1) - h) * h); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> intermediate |
| ( |
| detail::tquat<T, P> const & prev, |
| detail::tquat<T, P> const & curr, |
| detail::tquat<T, P> const & next |
| ) |
| { |
| detail::tquat<T, P> invQuat = inverse(curr); |
| return exp((log(next + invQuat) + log(prev + invQuat)) / T(-4)) * curr; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> exp |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| detail::tvec3<T, P> u(q.x, q.y, q.z); |
| float Angle = glm::length(u); |
| detail::tvec3<T, P> v(u / Angle); |
| return detail::tquat<T, P>(cos(Angle), sin(Angle) * v); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> log |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| if((q.x == static_cast<T>(0)) && (q.y == static_cast<T>(0)) && (q.z == static_cast<T>(0))) |
| { |
| if(q.w > T(0)) |
| return detail::tquat<T, P>(log(q.w), T(0), T(0), T(0)); |
| else if(q.w < T(0)) |
| return detail::tquat<T, P>(log(-q.w), T(3.1415926535897932384626433832795), T(0),T(0)); |
| else |
| 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()); |
| } |
| else |
| { |
| T Vec3Len = sqrt(q.x * q.x + q.y * q.y + q.z * q.z); |
| T QuatLen = sqrt(Vec3Len * Vec3Len + q.w * q.w); |
| T t = atan(Vec3Len, T(q.w)) / Vec3Len; |
| return detail::tquat<T, P>(t * q.x, t * q.y, t * q.z, log(QuatLen)); |
| } |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> pow |
| ( |
| detail::tquat<T, P> const & x, |
| T const & y |
| ) |
| { |
| if(abs(x.w) > T(0.9999)) |
| return x; |
| float Angle = acos(y); |
| float NewAngle = Angle * y; |
| float Div = sin(NewAngle) / sin(Angle); |
| return detail::tquat<T, P>( |
| cos(NewAngle), |
| x.x * Div, |
| x.y * Div, |
| x.z * Div); |
| } |
| |
| //template <typename T, precision P> |
| //GLM_FUNC_QUALIFIER detail::tquat<T, P> sqrt |
| //( |
| // detail::tquat<T, P> const & q |
| //) |
| //{ |
| // T q0 = static_cast<T>(1) - dot(q, q); |
| // return T(2) * (T(1) + q0) * q; |
| //} |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, P> rotate |
| ( |
| detail::tquat<T, P> const & q, |
| detail::tvec3<T, P> const & v |
| ) |
| { |
| return q * v; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<T, P> rotate |
| ( |
| detail::tquat<T, P> const & q, |
| detail::tvec4<T, P> const & v |
| ) |
| { |
| return q * v; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T extractRealComponent |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| T w = static_cast<T>(1.0) - q.x * q.x - q.y * q.y - q.z * q.z; |
| if(w < T(0)) |
| return T(0); |
| else |
| return -sqrt(w); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T length2 |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| return q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> shortMix |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y, |
| T const & a |
| ) |
| { |
| if(a <= T(0)) return x; |
| if(a >= T(1)) return y; |
| |
| T fCos = dot(x, y); |
| detail::tquat<T, P> y2(y); //BUG!!! tquat<T> y2; |
| if(fCos < T(0)) |
| { |
| y2 = -y; |
| fCos = -fCos; |
| } |
| |
| //if(fCos > 1.0f) // problem |
| T k0, k1; |
| if(fCos > T(0.9999)) |
| { |
| k0 = static_cast<T>(1) - a; |
| k1 = static_cast<T>(0) + a; //BUG!!! 1.0f + a; |
| } |
| else |
| { |
| T fSin = sqrt(T(1) - fCos * fCos); |
| T fAngle = atan(fSin, fCos); |
| T fOneOverSin = static_cast<T>(1) / fSin; |
| k0 = sin((T(1) - a) * fAngle) * fOneOverSin; |
| k1 = sin((T(0) + a) * fAngle) * fOneOverSin; |
| } |
| |
| return detail::tquat<T, P>( |
| 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, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> fastMix |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y, |
| T const & a |
| ) |
| { |
| return glm::normalize(x * (T(1) - a) + (y * a)); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> rotation |
| ( |
| detail::tvec3<T, P> const & orig, |
| detail::tvec3<T, P> const & dest |
| ) |
| { |
| T cosTheta = dot(orig, dest); |
| detail::tvec3<T, P> rotationAxis; |
| |
| if(cosTheta < T(-1) + epsilon<T>()) |
| { |
| // special case when vectors in opposite directions : |
| // there is no "ideal" rotation axis |
| // So guess one; any will do as long as it's perpendicular to start |
| // This implementation favors a rotation around the Up axis (Y), |
| // since it's often what you want to do. |
| rotationAxis = cross(detail::tvec3<T, P>(0, 0, 1), orig); |
| if(length2(rotationAxis) < epsilon<T>()) // bad luck, they were parallel, try again! |
| rotationAxis = cross(detail::tvec3<T, P>(1, 0, 0), orig); |
| |
| rotationAxis = normalize(rotationAxis); |
| return angleAxis(pi<T>(), rotationAxis); |
| } |
| |
| // Implementation from Stan Melax's Game Programming Gems 1 article |
| rotationAxis = cross(orig, dest); |
| |
| T s = sqrt((T(1) + cosTheta) * T(2)); |
| T invs = static_cast<T>(1) / s; |
| |
| return detail::tquat<T, P>( |
| s * T(0.5f), |
| rotationAxis.x * invs, |
| rotationAxis.y * invs, |
| rotationAxis.z * invs); |
| } |
| |
| }//namespace glm |