template<class Scalar_, int Options>
class Sophus::Sim3< Scalar_, Options >
Sim3 using default storage; derived from Sim3Base.
Definition at line 12 of file sim3.hpp.
template<class Scalar_ , int Options>
template<class D1 , class D2 >
| SOPHUS_FUNC Sophus::Sim3< Scalar_, Options >::Sim3 |
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Eigen::QuaternionBase< D1 > const & |
quaternion, |
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Eigen::MatrixBase< D2 > const & |
translation |
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) |
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inline |
Constructor from quaternion and translation vector.
Precondition: quaternion must not be close to zero.
Definition at line 404 of file sim3.hpp.
template<class Scalar_ , int Options>
Constructor from 4x4 matrix
Precondition: Top-left 3x3 matrix needs to be "scaled-orthogonal" with positive determinant. The last row must be (0, 0, 0, 1).
Definition at line 418 of file sim3.hpp.
template<class Scalar_ , int Options>
Group exponential
This functions takes in an element of tangent space and returns the corresponding element of the group Sim(3).
The first three components of a represent the translational part upsilon in the tangent space of Sim(3), the following three components of a represents the rotation vector omega and the final component represents the logarithm of the scaling factor sigma. To be more specific, this function computes expmat(hat(a)) with expmat(.) being the matrix exponential and hat(.) the hat-operator of Sim(3), see below.
Definition at line 476 of file sim3.hpp.
template<class Scalar_ , int Options>
Returns the ith infinitesimal generators of Sim(3).
The infinitesimal generators of Sim(3) are:
| 0 0 0 1 |
G_0 = | 0 0 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
G_1 = | 0 0 0 1 |
| 0 0 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
G_2 = | 0 0 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
| 0 0 0 0 |
G_3 = | 0 0 -1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 1 0 |
G_4 = | 0 0 0 0 |
| -1 0 0 0 |
| 0 0 0 0 |
| 0 -1 0 0 |
G_5 = | 1 0 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
| 1 0 0 0 |
G_6 = | 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 0 |
Precondition: i must be in [0, 6].
Definition at line 536 of file sim3.hpp.
template<class Scalar_ , int Options>
hat-operator
It takes in the 7-vector representation and returns the corresponding matrix representation of Lie algebra element.
Formally, the hat()-operator of Sim(3) is defined as
hat(.): R^7 -> R^{4x4}, hat(a) = sum_i a_i * G_i (for i=0,...,6)
with G_i being the ith infinitesimal generator of Sim(3).
The corresponding inverse is the vee()-operator, see below.
Definition at line 557 of file sim3.hpp.
template<class Scalar_ , int Options>
Lie bracket
It computes the Lie bracket of Sim(3). To be more specific, it computes
[omega_1, omega_2]_sim3 := vee([hat(omega_1), hat(omega_2)])
with [A,B] := AB-BA being the matrix commutator, hat(.) the hat()-operator and vee(.) the vee()-operator of Sim(3).
Definition at line 575 of file sim3.hpp.
template<class Scalar_ , int Options>
template<class UniformRandomBitGenerator >
| static Sim3 Sophus::Sim3< Scalar_, Options >::sampleUniform |
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UniformRandomBitGenerator & |
generator | ) |
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inlinestatic |
Draw uniform sample from Sim(3) manifold.
Translations are drawn component-wise from the range [-1, 1]. The scale factor is drawn uniformly in log2-space from [-1, 1], hence the scale is in [0.5, 2].
Definition at line 600 of file sim3.hpp.
template<class Scalar_ , int Options>
vee-operator
It takes the 4x4-matrix representation Omega and maps it to the corresponding 7-vector representation of Lie algebra.
This is the inverse of the hat()-operator, see above.
Precondition: Omega must have the following structure:
| g -f e a |
| f g -d b |
| -e d g c |
| 0 0 0 0 |
Definition at line 621 of file sim3.hpp.