5 #ifndef __pinocchio_math_quaternion_hpp__
6 #define __pinocchio_math_quaternion_hpp__
8 #ifndef PINOCCHIO_DEFAULT_QUATERNION_NORM_TOLERANCE_VALUE
9 #define PINOCCHIO_DEFAULT_QUATERNION_NORM_TOLERANCE_VALUE 1e-8
12 #include "pinocchio/math/fwd.hpp"
13 #include "pinocchio/math/comparison-operators.hpp"
14 #include "pinocchio/math/matrix.hpp"
15 #include "pinocchio/math/sincos.hpp"
16 #include "pinocchio/utils/static-if.hpp"
18 #include <boost/type_traits.hpp>
19 #include <Eigen/Geometry>
33 template<
typename D1,
typename D2>
35 const Eigen::QuaternionBase<D1> & q1,
const Eigen::QuaternionBase<D2> & q2)
37 typedef typename D1::Scalar Scalar;
38 const Scalar innerprod = q1.dot(q2);
39 Scalar theta = math::acos(innerprod);
40 static const Scalar PI_value = PI<Scalar>();
42 theta = internal::if_then_else(
43 internal::LT, innerprod, Scalar(0),
static_cast<Scalar
>(PI_value - theta), theta);
56 template<
typename D1,
typename D2>
58 const Eigen::QuaternionBase<D1> & q1,
59 const Eigen::QuaternionBase<D2> & q2,
60 const typename D1::RealScalar & prec =
61 Eigen::NumTraits<typename D1::Scalar>::dummy_precision())
63 return (q1.coeffs().isApprox(q2.coeffs(), prec) || q1.coeffs().isApprox(-q2.coeffs(), prec));
91 typedef typename D::Scalar Scalar;
92 const Scalar N2 = q.squaredNorm();
94 const Scalar epsilon = sqrt(sqrt(Eigen::NumTraits<Scalar>::epsilon()));
97 assert(static_leq::op(math::fabs(
static_cast<Scalar
>(N2 - Scalar(1))), epsilon));
99 const Scalar alpha = ((Scalar)3 - N2) / Scalar(2);
100 PINOCCHIO_EIGEN_CONST_CAST(D, q).coeffs() *= alpha;
103 Scalar(3) * math::pow(Scalar(1) - epsilon, ((Scalar)-Scalar(5)) / Scalar(2)) / Scalar(4);
104 assert(static_leq::op(
105 math::fabs(
static_cast<Scalar
>(q.norm() - Scalar(1))),
107 M * sqrt(N2) * (N2 - Scalar(1)) * (N2 - Scalar(1)) / Scalar(2),
108 Eigen::NumTraits<Scalar>::dummy_precision())));
113 template<
typename Derived>
116 typedef typename Derived::Scalar Scalar;
119 const Scalar u1 = (Scalar)rand() / RAND_MAX;
120 const Scalar u2 = (Scalar)rand() / RAND_MAX;
121 const Scalar u3 = (Scalar)rand() / RAND_MAX;
123 const Scalar mult1 = sqrt(Scalar(1) - u1);
124 const Scalar mult2 = sqrt(u1);
126 static const Scalar PI_value = PI<Scalar>();
128 SINCOS(Scalar(2) * PI_value * u2, &s2, &c2);
130 SINCOS(Scalar(2) * PI_value * u3, &s3, &c3);
141 template<typename Scalar, bool value = is_floating_point<Scalar>::value>
142 struct quaternionbase_assign_impl;
144 template<Eigen::DenseIndex i>
145 struct quaternionbase_assign_impl_if_t_negative
147 template<
typename Scalar,
typename Matrix3,
typename QuaternionDerived>
149 run(Scalar t, Eigen::QuaternionBase<QuaternionDerived> & q,
const Matrix3 & mat)
151 using pinocchio::math::sqrt;
153 Eigen::DenseIndex j = (i + 1) % 3;
154 Eigen::DenseIndex k = (j + 1) % 3;
156 t = sqrt(mat.coeff(i, i) - mat.coeff(j, j) - mat.coeff(k, k) + Scalar(1.0));
157 q.coeffs().coeffRef(i) = Scalar(0.5) * t;
159 q.w() = (mat.coeff(k, j) - mat.coeff(j, k)) * t;
160 q.coeffs().coeffRef(j) = (mat.coeff(j, i) + mat.coeff(i, j)) * t;
161 q.coeffs().coeffRef(k) = (mat.coeff(k, i) + mat.coeff(i, k)) * t;
165 struct quaternionbase_assign_impl_if_t_positive
167 template<
typename Scalar,
typename Matrix3,
typename QuaternionDerived>
169 run(Scalar t, Eigen::QuaternionBase<QuaternionDerived> & q,
const Matrix3 & mat)
171 using pinocchio::math::sqrt;
173 t = sqrt(t + Scalar(1.0));
174 q.w() = Scalar(0.5) * t;
176 q.x() = (mat.coeff(2, 1) - mat.coeff(1, 2)) * t;
177 q.y() = (mat.coeff(0, 2) - mat.coeff(2, 0)) * t;
178 q.z() = (mat.coeff(1, 0) - mat.coeff(0, 1)) * t;
182 template<
typename Scalar>
183 struct quaternionbase_assign_impl<Scalar, true>
185 template<
typename Matrix3,
typename QuaternionDerived>
186 static inline void run(Eigen::QuaternionBase<QuaternionDerived> & q,
const Matrix3 & mat)
188 using pinocchio::math::sqrt;
190 Scalar t = mat.trace();
192 quaternionbase_assign_impl_if_t_positive::run(t, q, mat);
195 Eigen::DenseIndex i = 0;
196 if (mat.coeff(1, 1) > mat.coeff(0, 0))
198 if (mat.coeff(2, 2) > mat.coeff(i, i))
202 quaternionbase_assign_impl_if_t_negative<0>::run(t, q, mat);
204 quaternionbase_assign_impl_if_t_negative<1>::run(t, q, mat);
206 quaternionbase_assign_impl_if_t_negative<2>::run(t, q, mat);
213 template<
typename D,
typename Matrix3>
214 void assignQuaternion(Eigen::QuaternionBase<D> & quat,
const Eigen::MatrixBase<Matrix3> & R)
216 internal::quaternionbase_assign_impl<typename Matrix3::Scalar>::run(
217 quat.derived(), R.derived());
228 template<
typename Quaternion>
230 const Eigen::QuaternionBase<Quaternion> & quat,
231 const typename Quaternion::Coefficients::RealScalar & prec =
232 Eigen::NumTraits<typename Quaternion::Coefficients::RealScalar>::dummy_precision())
242 template<
typename Quaternion>
243 inline void normalize(
const Eigen::QuaternionBase<Quaternion> & quat)
256 typename QuaternionIn1,
257 typename QuaternionIn2,
258 typename QuaternionOut>
261 const Eigen::QuaternionBase<QuaternionIn1> & quat0,
262 const Eigen::QuaternionBase<QuaternionIn2> & quat1,
263 const Eigen::QuaternionBase<QuaternionOut> & res)
265 const Scalar one = Scalar(1) - Eigen::NumTraits<Scalar>::epsilon();
266 const Scalar d = quat0.dot(quat1);
267 const Scalar absD = fabs(d);
269 const Scalar theta = acos(absD);
270 const Scalar sinTheta = sin(theta);
274 const Scalar scale0 = if_then_else(
275 pinocchio::internal::GE, absD, one,
276 static_cast<Scalar
>(Scalar(1) - u),
277 static_cast<Scalar
>(sin((Scalar(1) - u) * theta) / sinTheta)
280 const Scalar scale1_factor =
281 if_then_else(pinocchio::internal::LT, d, Scalar(0), Scalar(-1), Scalar(1));
282 const Scalar scale1 = if_then_else(
283 pinocchio::internal::GE, absD, one,
285 static_cast<Scalar
>(sin((u * theta)) / sinTheta)
289 PINOCCHIO_EIGEN_CONST_CAST(QuaternionOut, res.derived()).coeffs() =
290 scale0 * quat0.coeffs() + scale1 * quat1.coeffs();
void slerp(const Scalar &u, const Eigen::QuaternionBase< QuaternionIn1 > &quat0, const Eigen::QuaternionBase< QuaternionIn2 > &quat1, const Eigen::QuaternionBase< QuaternionOut > &res)
void firstOrderNormalize(const Eigen::QuaternionBase< D > &q)
D1::Scalar angleBetweenQuaternions(const Eigen::QuaternionBase< D1 > &q1, const Eigen::QuaternionBase< D2 > &q2)
Compute the minimal angle between q1 and q2.
bool defineSameRotation(const Eigen::QuaternionBase< D1 > &q1, const Eigen::QuaternionBase< D2 > &q2, const typename D1::RealScalar &prec=Eigen::NumTraits< typename D1::Scalar >::dummy_precision())
Check if two quaternions define the same rotations.
bool isNormalized(const Eigen::QuaternionBase< Quaternion > &quat, const typename Quaternion::Coefficients::RealScalar &prec=Eigen::NumTraits< typename Quaternion::Coefficients::RealScalar >::dummy_precision())
Check whether the input quaternion is Normalized within the given precision.
void normalize(const Eigen::QuaternionBase< Quaternion > &quat)
Normalize the input quaternion.
void uniformRandom(Eigen::QuaternionBase< Derived > &q)
Uniformly random quaternion sphere.
Main pinocchio namespace.
bool isNormalized(const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const Eigen::MatrixBase< ConfigVectorType > &q, const Scalar &prec=Eigen::NumTraits< Scalar >::dummy_precision())
Check whether a configuration vector is normalized within the given precision provided by prec.
void normalize(const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const Eigen::MatrixBase< ConfigVectorType > &qout)
Normalize a configuration vector.
void SINCOS(const S1 &a, S2 *sa, S3 *ca)
Computes sin/cos values of a given input scalar.