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246 lines
6.8 KiB
246 lines
6.8 KiB
/// @ref gtx_quaternion |
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/// @file glm/gtx/quaternion.inl |
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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, precision P> |
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GLM_FUNC_QUALIFIER vec<3, T, P> cross(vec<3, T, P> const& v, tquat<T, P> 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, precision P> |
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GLM_FUNC_QUALIFIER vec<3, T, P> cross(tquat<T, P> const& q, vec<3, T, P> const& v) |
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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 tquat<T, P> squad |
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( |
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tquat<T, P> const & q1, |
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tquat<T, P> const & q2, |
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tquat<T, P> const & s1, |
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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), static_cast<T>(2) * (static_cast<T>(1) - h) * h); |
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} |
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template<typename T, precision P> |
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GLM_FUNC_QUALIFIER tquat<T, P> intermediate |
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( |
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tquat<T, P> const & prev, |
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tquat<T, P> const & curr, |
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tquat<T, P> const & next |
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) |
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{ |
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tquat<T, P> 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, precision P> |
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GLM_FUNC_QUALIFIER tquat<T, P> exp(tquat<T, P> const& q) |
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{ |
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vec<3, T, P> 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 tquat<T, P>(); |
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vec<3, T, P> const v(u / Angle); |
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return 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 tquat<T, P> log(tquat<T, P> const& q) |
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{ |
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vec<3, T, P> 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 tquat<T, P>(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 tquat<T, P>(log(-q.w), pi<T>(), static_cast<T>(0), static_cast<T>(0)); |
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else |
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return 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 t = atan(Vec3Len, T(q.w)) / Vec3Len; |
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T QuatLen2 = Vec3Len * Vec3Len + q.w * q.w; |
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return tquat<T, P>(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, precision P> |
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GLM_FUNC_QUALIFIER tquat<T, P> pow(tquat<T, P> 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 tquat<T, P>(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 tquat<T, P>(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 tquat<T, P>(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, precision P> |
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GLM_FUNC_QUALIFIER vec<3, T, P> rotate(tquat<T, P> const& q, vec<3, T, P> const& v) |
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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 vec<4, T, P> rotate(tquat<T, P> const& q, vec<4, T, P> const& v) |
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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(tquat<T, P> 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, precision P> |
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GLM_FUNC_QUALIFIER T length2(tquat<T, P> 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, precision P> |
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GLM_FUNC_QUALIFIER tquat<T, P> shortMix(tquat<T, P> const& x, tquat<T, P> 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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tquat<T, P> y2(y); //BUG!!! tquat<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 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 tquat<T, P> fastMix(tquat<T, P> const& x, tquat<T, P> 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, precision P> |
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GLM_FUNC_QUALIFIER tquat<T, P> rotation(vec<3, T, P> const& orig, vec<3, T, P> const& dest) |
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{ |
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T cosTheta = dot(orig, dest); |
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vec<3, T, P> rotationAxis; |
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if(cosTheta >= static_cast<T>(1) - epsilon<T>()) |
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return quat(); |
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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, 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(vec<3, 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) * static_cast<T>(2)); |
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T invs = static_cast<T>(1) / s; |
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return tquat<T, P>( |
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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, precision P> |
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GLM_FUNC_QUALIFIER tquat<T, P> quatLookAt(tvec3<T, P> const& direction, tvec3<T, P> const& up) |
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{ |
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# if GLM_COORDINATE_SYSTEM == GLM_LEFT_HANDED |
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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, precision P> |
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GLM_FUNC_QUALIFIER tquat<T, P> quatLookAtRH(tvec3<T, P> const& direction, tvec3<T, P> const& up) |
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{ |
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tmat3x3<T, P> Result(uninitialize); |
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Result[2] = -normalize(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, precision P> |
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GLM_FUNC_QUALIFIER tquat<T, P> quatLookAtLH(tvec3<T, P> const& direction, tvec3<T, P> const& up) |
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{ |
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tmat3x3<T, P> Result(uninitialize); |
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Result[2] = normalize(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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