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380 lines
10 KiB
380 lines
10 KiB
/// @ref gtc_quaternion |
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#include "../trigonometric.hpp" |
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#include "../geometric.hpp" |
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#include "../exponential.hpp" |
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#include "epsilon.hpp" |
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#include <limits> |
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namespace glm |
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{ |
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// -- Operations -- |
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/* |
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// (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle)) |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER qua<T, Q> mix(qua<T, Q> const& x, qua<T, Q> const& y, T const& a) |
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{ |
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if(a <= T(0)) return x; |
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if(a >= T(1)) return y; |
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float fCos = dot(x, y); |
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qua<T, Q> y2(y); //BUG!!! qua<T, Q> y2; |
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if(fCos < 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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float k0, k1; |
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if(fCos > T(0.9999)) |
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{ |
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k0 = T(1) - a; |
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k1 = 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((T(1) - a) * fAngle) * fOneOverSin; |
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k1 = sin((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> mix2 |
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( |
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qua<T, Q> const& x, |
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qua<T, Q> const& y, |
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T const& a |
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) |
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{ |
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bool flip = false; |
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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 cos_t = dot(x, y); |
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if(cos_t < T(0)) |
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{ |
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cos_t = -cos_t; |
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flip = true; |
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} |
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T alpha(0), beta(0); |
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if(T(1) - cos_t < 1e-7) |
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beta = static_cast<T>(1) - alpha; |
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else |
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{ |
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T theta = acos(cos_t); |
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T sin_t = sin(theta); |
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beta = sin(theta * (T(1) - alpha)) / sin_t; |
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alpha = sin(alpha * theta) / sin_t; |
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} |
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if(flip) |
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alpha = -alpha; |
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return normalize(beta * x + alpha * y); |
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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> mix(qua<T, Q> const& x, qua<T, Q> const& y, T a) |
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{ |
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T cosTheta = dot(x, y); |
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// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator |
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if(cosTheta > T(1) - epsilon<T>()) |
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{ |
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// Linear interpolation |
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return qua<T, Q>( |
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mix(x.w, y.w, a), |
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mix(x.x, y.x, a), |
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mix(x.y, y.y, a), |
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mix(x.z, y.z, a)); |
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} |
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else |
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{ |
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// Essential Mathematics, page 467 |
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T angle = acos(cosTheta); |
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return (sin((T(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle); |
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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> lerp(qua<T, Q> const& x, qua<T, Q> const& y, T a) |
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{ |
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// Lerp is only defined in [0, 1] |
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assert(a >= static_cast<T>(0)); |
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assert(a <= static_cast<T>(1)); |
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return x * (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> slerp(qua<T, Q> const& x, qua<T, Q> const& y, T a) |
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{ |
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qua<T, Q> z = y; |
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T cosTheta = dot(x, y); |
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// If cosTheta < 0, the interpolation will take the long way around the sphere. |
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// To fix this, one quat must be negated. |
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if (cosTheta < T(0)) |
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{ |
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z = -y; |
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cosTheta = -cosTheta; |
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} |
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// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator |
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if(cosTheta > T(1) - epsilon<T>()) |
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{ |
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// Linear interpolation |
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return qua<T, Q>( |
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mix(x.w, z.w, a), |
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mix(x.x, z.x, a), |
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mix(x.y, z.y, a), |
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mix(x.z, z.z, a)); |
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} |
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else |
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{ |
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// Essential Mathematics, page 467 |
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T angle = acos(cosTheta); |
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return (sin((T(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle); |
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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> rotate(qua<T, Q> const& q, T const& angle, vec<3, T, Q> const& v) |
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{ |
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vec<3, T, Q> Tmp = v; |
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// Axis of rotation must be normalised |
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T len = glm::length(Tmp); |
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if(abs(len - T(1)) > T(0.001)) |
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{ |
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T oneOverLen = static_cast<T>(1) / len; |
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Tmp.x *= oneOverLen; |
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Tmp.y *= oneOverLen; |
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Tmp.z *= oneOverLen; |
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} |
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T const AngleRad(angle); |
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T const Sin = sin(AngleRad * T(0.5)); |
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return q * qua<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin); |
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//return gtc::quaternion::cross(q, qua<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin)); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<3, T, Q> eulerAngles(qua<T, Q> const& x) |
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{ |
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return vec<3, T, Q>(pitch(x), yaw(x), roll(x)); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER T roll(qua<T, Q> const& q) |
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{ |
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return static_cast<T>(atan(static_cast<T>(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z)); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER T pitch(qua<T, Q> const& q) |
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{ |
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//return T(atan(T(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z)); |
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T const y = static_cast<T>(2) * (q.y * q.z + q.w * q.x); |
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T const x = q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z; |
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if(all(equal(vec<2, T, Q>(x, y), vec<2, T, Q>(0), epsilon<T>()))) //avoid atan2(0,0) - handle singularity - Matiis |
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return static_cast<T>(static_cast<T>(2) * atan(q.x, q.w)); |
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return static_cast<T>(atan(y, x)); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER T yaw(qua<T, Q> const& q) |
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{ |
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return asin(clamp(static_cast<T>(-2) * (q.x * q.z - q.w * q.y), static_cast<T>(-1), static_cast<T>(1))); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER mat<3, 3, T, Q> mat3_cast(qua<T, Q> const& q) |
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{ |
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mat<3, 3, T, Q> Result(T(1)); |
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T qxx(q.x * q.x); |
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T qyy(q.y * q.y); |
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T qzz(q.z * q.z); |
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T qxz(q.x * q.z); |
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T qxy(q.x * q.y); |
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T qyz(q.y * q.z); |
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T qwx(q.w * q.x); |
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T qwy(q.w * q.y); |
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T qwz(q.w * q.z); |
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Result[0][0] = T(1) - T(2) * (qyy + qzz); |
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Result[0][1] = T(2) * (qxy + qwz); |
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Result[0][2] = T(2) * (qxz - qwy); |
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Result[1][0] = T(2) * (qxy - qwz); |
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Result[1][1] = T(1) - T(2) * (qxx + qzz); |
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Result[1][2] = T(2) * (qyz + qwx); |
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Result[2][0] = T(2) * (qxz + qwy); |
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Result[2][1] = T(2) * (qyz - qwx); |
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Result[2][2] = T(1) - T(2) * (qxx + qyy); |
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return Result; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER mat<4, 4, T, Q> mat4_cast(qua<T, Q> const& q) |
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{ |
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return mat<4, 4, T, Q>(mat3_cast(q)); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER qua<T, Q> quat_cast(mat<3, 3, T, Q> const& m) |
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{ |
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T fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2]; |
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T fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2]; |
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T fourZSquaredMinus1 = m[2][2] - m[0][0] - m[1][1]; |
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T fourWSquaredMinus1 = m[0][0] + m[1][1] + m[2][2]; |
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int biggestIndex = 0; |
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T fourBiggestSquaredMinus1 = fourWSquaredMinus1; |
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if(fourXSquaredMinus1 > fourBiggestSquaredMinus1) |
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{ |
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fourBiggestSquaredMinus1 = fourXSquaredMinus1; |
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biggestIndex = 1; |
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} |
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if(fourYSquaredMinus1 > fourBiggestSquaredMinus1) |
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{ |
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fourBiggestSquaredMinus1 = fourYSquaredMinus1; |
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biggestIndex = 2; |
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} |
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if(fourZSquaredMinus1 > fourBiggestSquaredMinus1) |
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{ |
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fourBiggestSquaredMinus1 = fourZSquaredMinus1; |
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biggestIndex = 3; |
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} |
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T biggestVal = sqrt(fourBiggestSquaredMinus1 + static_cast<T>(1)) * static_cast<T>(0.5); |
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T mult = static_cast<T>(0.25) / biggestVal; |
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switch(biggestIndex) |
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{ |
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case 0: |
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return qua<T, Q>(biggestVal, (m[1][2] - m[2][1]) * mult, (m[2][0] - m[0][2]) * mult, (m[0][1] - m[1][0]) * mult); |
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case 1: |
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return qua<T, Q>((m[1][2] - m[2][1]) * mult, biggestVal, (m[0][1] + m[1][0]) * mult, (m[2][0] + m[0][2]) * mult); |
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case 2: |
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return qua<T, Q>((m[2][0] - m[0][2]) * mult, (m[0][1] + m[1][0]) * mult, biggestVal, (m[1][2] + m[2][1]) * mult); |
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case 3: |
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return qua<T, Q>((m[0][1] - m[1][0]) * mult, (m[2][0] + m[0][2]) * mult, (m[1][2] + m[2][1]) * mult, biggestVal); |
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default: // Silence a -Wswitch-default warning in GCC. Should never actually get here. Assert is just for sanity. |
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assert(false); |
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return qua<T, Q>(1, 0, 0, 0); |
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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> quat_cast(mat<4, 4, T, Q> const& m4) |
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{ |
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return quat_cast(mat<3, 3, T, Q>(m4)); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER T angle(qua<T, Q> const& x) |
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{ |
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return acos(x.w) * static_cast<T>(2); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<3, T, Q> axis(qua<T, Q> const& x) |
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{ |
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T tmp1 = static_cast<T>(1) - x.w * x.w; |
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if(tmp1 <= static_cast<T>(0)) |
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return vec<3, T, Q>(0, 0, 1); |
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T tmp2 = static_cast<T>(1) / sqrt(tmp1); |
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return vec<3, T, Q>(x.x * tmp2, x.y * tmp2, x.z * tmp2); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER qua<T, Q> angleAxis(T const& angle, vec<3, T, Q> const& v) |
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{ |
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qua<T, Q> Result; |
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T const a(angle); |
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T const s = glm::sin(a * static_cast<T>(0.5)); |
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Result.w = glm::cos(a * static_cast<T>(0.5)); |
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Result.x = v.x * s; |
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Result.y = v.y * s; |
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Result.z = v.z * s; |
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return Result; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<4, bool, Q> isnan(qua<T, Q> const& q) |
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{ |
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GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isnan' only accept floating-point inputs"); |
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return vec<4, bool, Q>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w)); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<4, bool, Q> isinf(qua<T, Q> const& q) |
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{ |
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GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs"); |
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return vec<4, bool, Q>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w)); |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThan(qua<T, Q> const& A, qua<T, Q> const& B) |
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{ |
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vec<4, bool, Q> Result; |
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for(length_t i = 0; i < x.length(); ++i) |
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Result[i] = x[i] < y[i]; |
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return Result; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThanEqual(qua<T, Q> const& x, qua<T, Q> const& y) |
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{ |
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vec<4, bool, Q> Result; |
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for(length_t i = 0; i < x.length(); ++i) |
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Result[i] = x[i] <= y[i]; |
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return Result; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThan(qua<T, Q> const& x, qua<T, Q> const& y) |
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{ |
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vec<4, bool, Q> Result; |
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for(length_t i = 0; i < x.length(); ++i) |
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Result[i] = x[i] > y[i]; |
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return Result; |
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} |
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template<typename T, qualifier Q> |
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GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThanEqual(qua<T, Q> const& x, qua<T, Q> const& y) |
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{ |
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vec<4, bool, Q> Result; |
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for(length_t i = 0; i < x.length(); ++i) |
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Result[i] = x[i] >= y[i]; |
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return Result; |
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} |
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}//namespace glm |
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#if GLM_CONFIG_SIMD == GLM_ENABLE |
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# include "quaternion_simd.inl" |
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#endif |
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