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gtsam::traits< Rot3 > Struct Reference
Inheritance diagram for gtsam::traits< Rot3 >:
Static Public Member Functions | |
| template<int D = 1> | |
| static Matrix | QcqpValue (const Rot3 &value) |
| Return a matrix-valued QCQP variable for Rot3. | |
| template<int D = 1> | |
| static std::vector< std::pair< Matrix, double > > | QcqpConstraints () |
| Return row-space QCQP equality constraints A, b such that trace(X' A X) = b. | |
| template<int D> | |
| static Rot3 | FromQcqpValue (const Matrix &X) |
| Project a D=1 vector or canonical 3-by-D lift back to Rot3. | |
| Static Public Member Functions inherited from gtsam::internal::MatrixLieGroupTraits< Rot3, N > | |
| static LieAlgebra | Hat (const TangentVector &v) |
| static TangentVector | Vee (const LieAlgebra &X) |
| static Eigen::Matrix< double, product(N, N), 1 > | Vec (const Rot3 &m, OptionalJacobian< product(N, N), LieGroupTraits< Rot3 >::dimension > H={}) |
| Vectorize the matrix representation of a Lie group element. | |
| static TangentVector | AdjointTranspose (const Rot3 &m, const TangentVector &x, ChartJacobian Hm={}, ChartJacobian Hx={}) |
| static TangentVector | Adjoint (const Rot3 &m, const TangentVector &x, ChartJacobian Hm={}, ChartJacobian Hx={}) |
| static Jacobian | adjointMap (const TangentVector &xi) |
| static TangentVector | adjoint (const TangentVector &xi, const TangentVector &y, ChartJacobian Hxi={}, ChartJacobian H_y={}) |
| static TangentVector | adjointTranspose (const TangentVector &xi, const TangentVector &y, ChartJacobian Hxi={}, ChartJacobian H_y={}) |
| Static Public Member Functions inherited from gtsam::internal::LieGroupTraits< Rot3 > | |
| static TangentVector | Logmap (const Rot3 &m) |
| static Rot3 | Expmap (const TangentVector &v) |
| static Rot3 | Compose (const Rot3 &m1, const Rot3 &m2, ChartJacobian H1={}, ChartJacobian H2={}) |
| static Rot3 | Between (const Rot3 &m1, const Rot3 &m2, ChartJacobian H1={}, ChartJacobian H2={}) |
| static Rot3 | Inverse (const Rot3 &m, ChartJacobian H={}) |
| static Eigen::Matrix< double, dimension, dimension > | AdjointMap (const Rot3 &m) |
| static Rot3 | Identity () |
| Static Public Member Functions inherited from gtsam::internal::ManifoldTraits< Rot3 > | |
| static TangentVector | Local (const Rot3 &origin, const Rot3 &other) |
| static Rot3 | Retract (const Rot3 &origin, const TangentVector &v) |
| Static Public Member Functions inherited from gtsam::internal::GetDimensionImpl< Rot3, Rot3::dimension > | |
| static size_t | GetDimension (const Rot3 &m) |
| Static Public Member Functions inherited from gtsam::Testable< Rot3 > | |
| static void | Print (const Rot3 &m, const std::string &str="") |
| static bool | Equals (const Rot3 &m1, const Rot3 &m2, double tol=1e-8) |
Static Public Attributes | |
| static constexpr int | QcqpVectorDim = 10 |
| Dimension of the D=1 homogenized QCQP vector. | |
| static constexpr auto | dimension |
| Static Public Attributes inherited from gtsam::internal::ManifoldTraits< Rot3 > | |
| static constexpr auto | dimension |
Additional Inherited Members | |
| Public Member Functions inherited from gtsam::internal::ManifoldTraits< Rot3 > | |
| GTSAM_CONCEPT_ASSERT (HasManifoldPrereqs< Rot3 >) | |
| Public Member Functions inherited from gtsam::Testable< Rot3 > | |
| GTSAM_CONCEPT_ASSERT (HasTestablePrereqs< Rot3 >) | |
| Public Types inherited from gtsam::internal::MatrixLieGroupTraits< Rot3, N > | |
| using | LieAlgebra |
| using | TangentVector |
| using | Jacobian |
| using | ChartJacobian |
| Public Types inherited from gtsam::internal::LieGroupTraits< Rot3 > | |
| typedef OptionalJacobian< dimension, dimension > | ChartJacobian |
| typedef Rot3 | ManifoldType |
| typedef Eigen::Matrix< double, dimension, 1 > | TangentVector |
| using | Manifold |
| using | structure_category |
| using | group_flavor |
| using | Jacobian |
| Public Types inherited from gtsam::internal::ManifoldTraits< Rot3 > | |
| typedef Rot3 | ManifoldType |
| typedef manifold_tag | structure_category |
| typedef Eigen::Matrix< double, dimension, 1 > | TangentVector |
| typedef OptionalJacobian< dimension, dimension > | ChartJacobian |
Member Function Documentation
◆ FromQcqpValue()
template<int D>
|
inlinestatic |
Project a D=1 vector or canonical 3-by-D lift back to Rot3.
Matrix-form QCQP solutions have a right-O(D) gauge, making this leading-block projection gauge-dependent unless the caller has first chosen a gauge. Matrix-form X must be exactly 3-by-D.
◆ QcqpConstraints()
template<int D = 1>
|
inlinestatic |
Return row-space QCQP equality constraints A, b such that trace(X' A X) = b.
For D=1 these are the lifted SO(3) constraints in column-major coordinates. For D>=3 the same 3-by-3 constraints enforce XX'=I. The D=1 right-handedness constraints distinguish SO(3) from the reflected component of O(3).
◆ QcqpValue()
template<int D = 1>
|
inlinestatic |
Return a matrix-valued QCQP variable for Rot3.
D=1 prepends a fixed homogenization coordinate to the existing column-major SO(3) vectorization, yielding a 10-by-1 matrix. D>=3 returns [R', 0] as a 3-by-D row-orthonormal matrix. These variables form a Stiefel relaxation with a common right-O(D) gauge.
The documentation for this struct was generated from the following file:
- /tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/geometry/Rot3.h
