File unit3.h¶
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namespace sym
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template<typename ScalarType>
class Unit3 - #include <unit3.h>
Autogenerated C++ implementation of
symforce.geo.unit3.Unit3
.Direction in R^3 represented as a unit vector on the S^2 sphere manifold.
Storage is three dimensional, and tangent space is two dimensional. Due to the nature of the manifold, the unit X vector is handled as a singularity.
The implementation of the retract and local_coordinates functions are based on Appendix B.2 :
[Hertzberg 2013] Integrating Generic Sensor Fusion Algorithms with Sound State Representations through Encapsulation of Manifolds
The retract operation performs a perturbation to the desired unit X vector, which is then rotated to desired position along the actual stored unit vector through a Householder-reflection + relection across the XZ plane.
See:x.retract(delta) = x [+] delta = Rx * Exp(delta), where Exp(delta) = [cos(||delta||), sinc(||delta||) * delta], and Rx = (I - 2 vv^T / (v^Tv))X, v = x - e_x != 0, X is a matrix negating 2nd vector component = diag(1, -1, -1) , x = e_x
unit3_visualization.ipynb
for a visualization of the Unit3 manifold.Public Types
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using Scalar = ScalarType
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using DataVec = Eigen::Matrix<Scalar, 3, 1, Eigen::DontAlign>
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using TangentVec = Eigen::Matrix<Scalar, 2, 1>
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using SelfJacobian = Eigen::Matrix<Scalar, 2, 2>
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using Vector3 = Eigen::Matrix<Scalar, 3, 1>
Public Functions
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inline explicit Unit3(const DataVec &data, const bool normalize = true)
Construct from data vec
- Parameters:
normalize – Project to the manifold on construction. This ensures numerical stability as this constructor is called after each codegen operation. Constructing from a normalized vector may be faster, e.g. with
FromStorage
.
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inline const DataVec &Data() const
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const Eigen::Matrix<Scalar, 3, 2> Basis(const Scalar epsilon) const
Returns a :class:
Matrix32
with the basis vectors of the tangent space (in R^3) at the current Unit3 direction.
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const Vector3 ToUnitVector() const
Returns a :class:
Vector3
version of the unit direction.
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inline void ToStorage(Scalar *const vec) const
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inline Self Retract(const TangentVec &vec, const Scalar epsilon = kDefaultEpsilon<Scalar>) const
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inline TangentVec LocalCoordinates(const Self &b, const Scalar epsilon = kDefaultEpsilon<Scalar>) const
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inline Self Interpolate(const Self b, const Scalar alpha, const Scalar epsilon = kDefaultEpsilon<Scalar>) const
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inline bool operator==(const Unit3 &rhs) const
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inline bool operator!=(const Unit3 &rhs) const
Public Static Functions
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template<typename Generator>
static inline Unit3 Random(Generator &gen, Scalar epsilon = kDefaultEpsilon<Scalar>)
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static inline const sym::Unit3<Scalar> FromVector(const Vector3 &a)
Return a :class:
Unit3
that points along the direction of vectora
a
will be normalized.
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static inline const sym::Unit3<Scalar> FromUnitVector(const Vector3 &a)
Return a :class:
Unit3
that points along the direction of vectora
a
is expected to be a unit vector.
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static const sym::Unit3<Scalar> RandomFromUniformSamples(const Scalar u1, const Scalar u2, const Scalar epsilon)
Generate a random :class:
Unit3
direction from two variables uniformly sampled in [0, 1].
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static inline constexpr int32_t StorageDim()
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static inline constexpr int32_t TangentDim()
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using Scalar = ScalarType
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template<typename ScalarType>