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| SOPHUS_FUNC Adjoint | Adj () const |
| | Adjoint transformation. More...
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| template<class S = Scalar> |
| SOPHUS_FUNC enable_if_t< std::is_floating_point< S >::value, S > | angleX () const |
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| template<class S = Scalar> |
| SOPHUS_FUNC enable_if_t< std::is_floating_point< S >::value, S > | angleY () const |
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| template<class S = Scalar> |
| SOPHUS_FUNC enable_if_t< std::is_floating_point< S >::value, S > | angleZ () const |
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| template<class NewScalarType > |
| SOPHUS_FUNC SO3< NewScalarType > | cast () const |
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| SOPHUS_FUNC Scalar * | data () |
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| SOPHUS_FUNC Scalar const * | data () const |
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| SOPHUS_FUNC Matrix< Scalar, num_parameters, DoF > | Dx_this_mul_exp_x_at_0 () const |
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| SOPHUS_FUNC SO3< Scalar > | inverse () const |
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| SOPHUS_FUNC Tangent | log () const |
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| SOPHUS_FUNC TangentAndTheta | logAndTheta () const |
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| SOPHUS_FUNC Transformation | matrix () const |
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| SOPHUS_FUNC void | normalize () |
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| template<typename HPointDerived , typename = typename std::enable_if< IsFixedSizeVector<HPointDerived, 4>::value>::type> |
| SOPHUS_FUNC HomogeneousPointProduct< HPointDerived > | operator* (Eigen::MatrixBase< HPointDerived > const &p) const |
| | Group action on homogeneous 3-points. See above for more details. More...
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| template<typename PointDerived , typename = typename std::enable_if< IsFixedSizeVector<PointDerived, 3>::value>::type> |
| SOPHUS_FUNC PointProduct< PointDerived > | operator* (Eigen::MatrixBase< PointDerived > const &p) const |
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| SOPHUS_FUNC Line | operator* (Line const &l) const |
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| template<typename OtherDerived > |
| SOPHUS_FUNC SO3Product< OtherDerived > | operator* (SO3Base< OtherDerived > const &other) const |
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| template<typename OtherDerived , typename = typename std::enable_if< std::is_same<Scalar, ReturnScalar<OtherDerived>>::value>::type> |
| SOPHUS_FUNC SO3Base< Derived > & | operator*= (SO3Base< OtherDerived > const &other) |
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| SOPHUS_FUNC SO3Base & | operator= (SO3Base const &other)=default |
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| template<class OtherDerived > |
| SOPHUS_FUNC SO3Base< Derived > & | operator= (SO3Base< OtherDerived > const &other) |
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| SOPHUS_FUNC Sophus::Vector< Scalar, num_parameters > | params () const |
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| SOPHUS_FUNC void | setQuaternion (Eigen::Quaternion< Scalar > const &quaternion) |
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| SOPHUS_FUNC QuaternionType const & | unit_quaternion () const |
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template<class Derived>
class Sophus::SO3Base< Derived >
SO3 base type - implements SO3 class but is storage agnostic.
SO(3) is the group of rotations in 3d. As a matrix group, it is the set of matrices which are orthogonal such that R * R' = I (with R' being the transpose of R) and have a positive determinant. In particular, the determinant is 1. Internally, the group is represented as a unit quaternion. Unit quaternion can be seen as members of the special unitary group SU(2). SU(2) is a double cover of SO(3). Hence, for every rotation matrix R, there exist two unit quaternions: (r, v) and (-r, -v), with r the real part and v being the imaginary 3-vector part of the quaternion.
SO(3) is a compact, but non-commutative group. First it is compact since the set of rotation matrices is a closed and bounded set. Second it is non-commutative since the equation R_1 * R_2 = R_2 * R_1 does not hold in general. For example rotating an object by some degrees about its x-axis and then by some degrees about its y axis, does not lead to the same orientation when rotation first about y and then about x.
Class invariant: The 2-norm of unit_quaternion must be close to 1. Technically speaking, it must hold that:
|unit_quaternion().squaredNorm() - 1| <= Constants::epsilon().
Definition at line 74 of file so3.hpp.
template<class Derived >
template<typename PointDerived , typename = typename std::enable_if< IsFixedSizeVector<PointDerived, 3>::value>::type>
Group action on 3-points.
This function rotates a 3 dimensional point p by the SO3 element bar_R_foo (= rotation matrix): p_bar = bar_R_foo * p_foo.
Since SO3 is internally represented by a unit quaternion q, it is implemented as p_bar = q * p_foo * q^{*} with q^{*} being the quaternion conjugate of q.
Geometrically, p is rotated by angle |omega| around the axis omega/|omega| with omega := vee(log(bar_R_foo)).
For vee-operator, see below.
NOTE: We cannot use Eigen's Quaternion transformVector because it always returns a Vector3 of the same Scalar as this quaternion, so it is not able to be applied to Jets and doubles correctly.
Definition at line 357 of file so3.hpp.
