/// @ref gtx_quaternion /// @file glm/gtx/quaternion.inl #include <limits> #include "../gtc/constants.hpp" namespace glm { template <typename T, precision P> GLM_FUNC_QUALIFIER tvec3<T, P> cross(tvec3<T, P> const& v, tquat<T, P> const& q) { return inverse(q) * v; } template <typename T, precision P> GLM_FUNC_QUALIFIER tvec3<T, P> cross(tquat<T, P> const& q, tvec3<T, P> const& v) { return q * v; } template <typename T, precision P> GLM_FUNC_QUALIFIER tquat<T, P> squad ( tquat<T, P> const & q1, tquat<T, P> const & q2, tquat<T, P> const & s1, tquat<T, P> const & s2, T const & h) { return mix(mix(q1, q2, h), mix(s1, s2, h), static_cast<T>(2) * (static_cast<T>(1) - h) * h); } template <typename T, precision P> GLM_FUNC_QUALIFIER tquat<T, P> intermediate ( tquat<T, P> const & prev, tquat<T, P> const & curr, tquat<T, P> const & next ) { tquat<T, P> invQuat = inverse(curr); return exp((log(next + invQuat) + log(prev + invQuat)) / static_cast<T>(-4)) * curr; } template <typename T, precision P> GLM_FUNC_QUALIFIER tquat<T, P> exp(tquat<T, P> const& q) { tvec3<T, P> u(q.x, q.y, q.z); T const Angle = glm::length(u); if (Angle < epsilon<T>()) return tquat<T, P>(); tvec3<T, P> const v(u / Angle); return tquat<T, P>(cos(Angle), sin(Angle) * v); } template <typename T, precision P> GLM_FUNC_QUALIFIER tquat<T, P> log(tquat<T, P> const& q) { tvec3<T, P> u(q.x, q.y, q.z); T Vec3Len = length(u); if (Vec3Len < epsilon<T>()) { if(q.w > static_cast<T>(0)) return tquat<T, P>(log(q.w), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0)); else if(q.w < static_cast<T>(0)) return tquat<T, P>(log(-q.w), pi<T>(), static_cast<T>(0), static_cast<T>(0)); else return 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 t = atan(Vec3Len, T(q.w)) / Vec3Len; T QuatLen2 = Vec3Len * Vec3Len + q.w * q.w; return tquat<T, P>(static_cast<T>(0.5) * log(QuatLen2), t * q.x, t * q.y, t * q.z); } } template <typename T, precision P> GLM_FUNC_QUALIFIER tquat<T, P> pow(tquat<T, P> const & x, T const & y) { //Raising to the power of 0 should yield 1 //Needed to prevent a division by 0 error later on if(y > -epsilon<T>() && y < epsilon<T>()) return tquat<T, P>(1,0,0,0); //To deal with non-unit quaternions T magnitude = sqrt(x.x * x.x + x.y * x.y + x.z * x.z + x.w *x.w); //Equivalent to raising a real number to a power //Needed to prevent a division by 0 error later on if(abs(x.w / magnitude) > static_cast<T>(1) - epsilon<T>() && abs(x.w / magnitude) < static_cast<T>(1) + epsilon<T>()) return tquat<T, P>(pow(x.w, y),0,0,0); T Angle = acos(x.w / magnitude); T NewAngle = Angle * y; T Div = sin(NewAngle) / sin(Angle); T Mag = pow(magnitude, y - static_cast<T>(1)); return tquat<T, P>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag); } template <typename T, precision P> GLM_FUNC_QUALIFIER tvec3<T, P> rotate(tquat<T, P> const& q, tvec3<T, P> const& v) { return q * v; } template <typename T, precision P> GLM_FUNC_QUALIFIER tvec4<T, P> rotate(tquat<T, P> const& q, tvec4<T, P> const& v) { return q * v; } template <typename T, precision P> GLM_FUNC_QUALIFIER T extractRealComponent(tquat<T, P> const& q) { T w = static_cast<T>(1) - 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(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 tquat<T, P> shortMix(tquat<T, P> const& x, tquat<T, P> const& y, T const& a) { if(a <= static_cast<T>(0)) return x; if(a >= static_cast<T>(1)) return y; T fCos = dot(x, y); tquat<T, P> y2(y); //BUG!!! tquat<T> y2; if(fCos < static_cast<T>(0)) { y2 = -y; fCos = -fCos; } //if(fCos > 1.0f) // problem T k0, k1; if(fCos > (static_cast<T>(1) - epsilon<T>())) { 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((static_cast<T>(1) - a) * fAngle) * fOneOverSin; k1 = sin((static_cast<T>(0) + a) * fAngle) * fOneOverSin; } return 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 tquat<T, P> fastMix(tquat<T, P> const& x, tquat<T, P> const& y, T const & a) { return glm::normalize(x * (static_cast<T>(1) - a) + (y * a)); } template <typename T, precision P> GLM_FUNC_QUALIFIER tquat<T, P> rotation(tvec3<T, P> const& orig, tvec3<T, P> const& dest) { T cosTheta = dot(orig, dest); tvec3<T, P> rotationAxis; if(cosTheta >= static_cast<T>(1) - epsilon<T>()) return quat(); if(cosTheta < static_cast<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(tvec3<T, P>(0, 0, 1), orig); if(length2(rotationAxis) < epsilon<T>()) // bad luck, they were parallel, try again! rotationAxis = cross(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) * static_cast<T>(2)); T invs = static_cast<T>(1) / s; return tquat<T, P>( s * static_cast<T>(0.5f), rotationAxis.x * invs, rotationAxis.y * invs, rotationAxis.z * invs); } }//namespace glm