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+/// @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