90 lines
2.8 KiB
Plaintext
90 lines
2.8 KiB
Plaintext
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#include "scalar_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> 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>::wxyz(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>::wxyz(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>::wxyz(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>::wxyz(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 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>::wxyz(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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T Angle;
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if(abs(x.w / magnitude) > cos_one_over_two<T>())
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{
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//Scalar component is close to 1; using it to recover angle would lose precision
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//Instead, we use the non-scalar components since sin() is accurate around 0
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//Prevent a division by 0 error later on
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T VectorMagnitude = x.x * x.x + x.y * x.y + x.z * x.z;
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//Despite the compiler might say, we actually want to compare
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//VectorMagnitude to 0. here; we could use denorm_int() compiling a
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//project with unsafe maths optimizations might make the comparison
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//always false, even when VectorMagnitude is 0.
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if (VectorMagnitude < std::numeric_limits<T>::min()) {
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//Equivalent to raising a real number to a power
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return qua<T, Q>::wxyz(pow(x.w, y), 0, 0, 0);
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}
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Angle = asin(sqrt(VectorMagnitude) / magnitude);
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}
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else
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{
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//Scalar component is small, shouldn't cause loss of precision
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Angle = acos(x.w / magnitude);
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}
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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>::wxyz(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 qua<T, Q> sqrt(qua<T, Q> const& x)
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{
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return pow(x, static_cast<T>(0.5));
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}
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}//namespace glm
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