381 lines
10 KiB
Text
381 lines
10 KiB
Text
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/// @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)
|
||
|
|
{
|
||
|
|
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs");
|
||
|
|
|
||
|
|
return vec<4, bool, Q>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w));
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename T, qualifier Q>
|
||
|
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThan(qua<T, Q> const& x, qua<T, Q> const& y)
|
||
|
|
{
|
||
|
|
vec<4, bool, Q> Result;
|
||
|
|
for(length_t i = 0; i < x.length(); ++i)
|
||
|
|
Result[i] = x[i] < y[i];
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename T, qualifier Q>
|
||
|
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThanEqual(qua<T, Q> const& x, qua<T, Q> const& y)
|
||
|
|
{
|
||
|
|
vec<4, bool, Q> Result;
|
||
|
|
for(length_t i = 0; i < x.length(); ++i)
|
||
|
|
Result[i] = x[i] <= y[i];
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename T, qualifier Q>
|
||
|
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThan(qua<T, Q> const& x, qua<T, Q> const& y)
|
||
|
|
{
|
||
|
|
vec<4, bool, Q> Result;
|
||
|
|
for(length_t i = 0; i < x.length(); ++i)
|
||
|
|
Result[i] = x[i] > y[i];
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename T, qualifier Q>
|
||
|
|
GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThanEqual(qua<T, Q> const& x, qua<T, Q> const& y)
|
||
|
|
{
|
||
|
|
vec<4, bool, Q> Result;
|
||
|
|
for(length_t i = 0; i < x.length(); ++i)
|
||
|
|
Result[i] = x[i] >= y[i];
|
||
|
|
return Result;
|
||
|
|
}
|
||
|
|
}//namespace glm
|
||
|
|
|
||
|
|
#if GLM_CONFIG_SIMD == GLM_ENABLE
|
||
|
|
# include "quaternion_simd.inl"
|
||
|
|
#endif
|
||
|
|
|