254 lines
6.9 KiB
Text
254 lines
6.9 KiB
Text
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/// @ref gtx_quaternion
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#include <limits>
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#include "../gtc/constants.hpp"
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namespace glm
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{
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> quat_identity()
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{
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return qua<T, Q>(static_cast<T>(1), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<3, T, Q> cross(vec<3, T, Q> const& v, qua<T, Q> const& q)
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{
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return inverse(q) * v;
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<3, T, Q> cross(qua<T, Q> const& q, vec<3, T, Q> const& v)
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{
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return q * v;
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> squad
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(
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qua<T, Q> const& q1,
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qua<T, Q> const& q2,
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qua<T, Q> const& s1,
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qua<T, Q> 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), static_cast<T>(2) * (static_cast<T>(1) - h) * h);
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> intermediate
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(
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qua<T, Q> const& prev,
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qua<T, Q> const& curr,
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qua<T, Q> const& next
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)
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{
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qua<T, Q> invQuat = inverse(curr);
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return exp((log(next * invQuat) + log(prev * invQuat)) / static_cast<T>(-4)) * curr;
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> exp(qua<T, Q> const& q)
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{
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vec<3, T, Q> u(q.x, q.y, q.z);
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T const Angle = glm::length(u);
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if (Angle < epsilon<T>())
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return qua<T, Q>();
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vec<3, T, Q> const v(u / Angle);
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return qua<T, Q>(cos(Angle), sin(Angle) * v);
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> log(qua<T, Q> const& q)
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{
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vec<3, T, Q> u(q.x, q.y, q.z);
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T Vec3Len = length(u);
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if (Vec3Len < epsilon<T>())
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{
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if(q.w > static_cast<T>(0))
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return qua<T, Q>(log(q.w), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
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else if(q.w < static_cast<T>(0))
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return qua<T, Q>(log(-q.w), pi<T>(), static_cast<T>(0), static_cast<T>(0));
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else
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return qua<T, Q>(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 t = atan(Vec3Len, T(q.w)) / Vec3Len;
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T QuatLen2 = Vec3Len * Vec3Len + q.w * q.w;
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return qua<T, Q>(static_cast<T>(0.5) * log(QuatLen2), t * q.x, t * q.y, t * q.z);
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}
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> pow(qua<T, Q> const& x, T const& y)
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{
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//Raising to the power of 0 should yield 1
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//Needed to prevent a division by 0 error later on
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if(y > -epsilon<T>() && y < epsilon<T>())
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return qua<T, Q>(1,0,0,0);
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//To deal with non-unit quaternions
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T magnitude = sqrt(x.x * x.x + x.y * x.y + x.z * x.z + x.w *x.w);
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//Equivalent to raising a real number to a power
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//Needed to prevent a division by 0 error later on
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if(abs(x.w / magnitude) > static_cast<T>(1) - epsilon<T>() && abs(x.w / magnitude) < static_cast<T>(1) + epsilon<T>())
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return qua<T, Q>(pow(x.w, y),0,0,0);
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T Angle = acos(x.w / magnitude);
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T NewAngle = Angle * y;
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T Div = sin(NewAngle) / sin(Angle);
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T Mag = pow(magnitude, y - static_cast<T>(1));
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return qua<T, Q>(cos(NewAngle) * magnitude * Mag, x.x * Div * Mag, x.y * Div * Mag, x.z * Div * Mag);
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<3, T, Q> rotate(qua<T, Q> const& q, vec<3, T, Q> const& v)
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{
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return q * v;
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER vec<4, T, Q> rotate(qua<T, Q> const& q, vec<4, T, Q> const& v)
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{
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return q * v;
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER T extractRealComponent(qua<T, Q> const& q)
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{
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T w = static_cast<T>(1) - 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, qualifier Q>
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GLM_FUNC_QUALIFIER T length2(qua<T, Q> const& q)
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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, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> shortMix(qua<T, Q> const& x, qua<T, Q> const& y, T const& a)
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{
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if(a <= static_cast<T>(0)) return x;
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if(a >= static_cast<T>(1)) return y;
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T fCos = dot(x, y);
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qua<T, Q> y2(y); //BUG!!! qua<T> y2;
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if(fCos < static_cast<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 > (static_cast<T>(1) - epsilon<T>()))
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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((static_cast<T>(1) - a) * fAngle) * fOneOverSin;
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k1 = sin((static_cast<T>(0) + a) * fAngle) * fOneOverSin;
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}
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return qua<T, Q>(
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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, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> fastMix(qua<T, Q> const& x, qua<T, Q> const& y, T const& a)
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{
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return glm::normalize(x * (static_cast<T>(1) - a) + (y * a));
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> rotation(vec<3, T, Q> const& orig, vec<3, T, Q> const& dest)
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{
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T cosTheta = dot(orig, dest);
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vec<3, T, Q> rotationAxis;
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if(cosTheta >= static_cast<T>(1) - epsilon<T>()) {
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// orig and dest point in the same direction
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return quat_identity<T,Q>();
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}
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if(cosTheta < static_cast<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(vec<3, T, Q>(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(vec<3, T, Q>(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) * static_cast<T>(2));
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T invs = static_cast<T>(1) / s;
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return qua<T, Q>(
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s * static_cast<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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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> quatLookAt(vec<3, T, Q> const& direction, vec<3, T, Q> const& up)
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{
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# if GLM_CONFIG_CLIP_CONTROL & GLM_CLIP_CONTROL_LH_BIT
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return quatLookAtLH(direction, up);
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# else
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return quatLookAtRH(direction, up);
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# endif
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> quatLookAtRH(vec<3, T, Q> const& direction, vec<3, T, Q> const& up)
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{
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mat<3, 3, T, Q> Result;
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Result[2] = -direction;
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Result[0] = normalize(cross(up, Result[2]));
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Result[1] = cross(Result[2], Result[0]);
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return quat_cast(Result);
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}
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template<typename T, qualifier Q>
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GLM_FUNC_QUALIFIER qua<T, Q> quatLookAtLH(vec<3, T, Q> const& direction, vec<3, T, Q> const& up)
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{
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mat<3, 3, T, Q> Result;
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Result[2] = direction;
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Result[0] = normalize(cross(up, Result[2]));
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Result[1] = cross(Result[2], Result[0]);
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return quat_cast(Result);
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}
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}//namespace glm
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