Class sym::Rot2

template<typename ScalarType>
class Rot2

Autogenerated C++ implementation of symforce.geo.rot2.Rot2.

Group of two-dimensional orthogonal matrices with determinant +1, representing rotations in 2D space. Backed by a complex number.

Public Types

using Scalar = ScalarType

using Self = Rot2<Scalar>

using DataVec = Eigen::Matrix<Scalar, 2, 1, Eigen::DontAlign>

using TangentVec = Eigen::Matrix<Scalar, 1, 1>

using SelfJacobian = Eigen::Matrix<Scalar, 1, 1>

using Vector2 = Eigen::Matrix<Scalar, 2, 1>

Public Functions

inline explicit Rot2(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.

inline Rot2()

inline const DataVec &Data() const

inline explicit Rot2(const Scalar angle)

const Vector2 ComposeWithPoint(const Vector2 &right) const

Left-multiplication. Either rotation concatenation or point transform.

const Eigen::Matrix<Scalar, 2, 2> ToRotationMatrix() const

A matrix representation of this element in the Euclidean space that contains it.

inline void ToStorage(Scalar *const vec) const

inline Vector2 Compose(const Vector2 &point) const

inline Self Inverse() const

inline Self Compose(const Self &b) const

inline Self Between(const Self &b) const

inline Self InverseWithJacobian(SelfJacobian *const res_D_a = nullptr) const

inline Self ComposeWithJacobians(const Self &b, SelfJacobian *const res_D_a = nullptr, SelfJacobian *const res_D_b = nullptr) const

inline Self BetweenWithJacobians(const Self &b, SelfJacobian *const res_D_a = nullptr, SelfJacobian *const res_D_b = nullptr) const

template<typename Other>
inline auto operator*(const Other &b) const -> decltype(Compose(b))

inline TangentVec ToTangent(const Scalar epsilon = kDefaultEpsilon<Scalar>) const

inline Self Retract(const TangentVec &vec, const Scalar epsilon = kDefaultEpsilon<Scalar>) const

inline TangentVec LocalCoordinates(const Self &b, const Scalar epsilon = kDefaultEpsilon<Scalar>) const

inline Self Interpolate(const Self b, const Scalar alpha, const Scalar epsilon = kDefaultEpsilon<Scalar>) const

inline bool IsApprox(const Self &b, const Scalar tol) const

template<typename ToScalar>
inline Rot2<ToScalar> Cast() const

inline bool operator==(const Rot2 &rhs) const

inline bool operator!=(const Rot2 &rhs) const

Public Static Functions

static inline Rot2 RandomFromUniformSamples(const Scalar u1)

template<typename Generator>
static inline Rot2 Random(Generator &gen)

static const sym::Rot2<Scalar> FromAngle(const Scalar theta)

Create a Rot2 from an angle theta in radians

This is equivalent to from_tangent([theta])

static const sym::Rot2<Scalar> FromRotationMatrix(const Eigen::Matrix<Scalar, 2, 2> &r)

Create a Rot2 from a 2x2 rotation matrix.

Returns the closest Rot2 to the input matrix, by the Frobenius norm. Will be singular when r[0, 0] == -r[1, 1] and r[0, 1] == r[1, 0] are both true.

See notebooks/rot2_from_rotation_matrix_derivation.ipynb for the derivation.

static const sym::Rot2<Scalar> RandomFromUniformSample(const Scalar u1)

Generate a random element of SO2 from a variable uniformly sampled on [0, 1].

static inline constexpr int32_t StorageDim()

static inline Rot2 FromStorage(const Scalar *const vec)

static inline Self Identity()

static inline constexpr int32_t TangentDim()

static inline Self FromTangent(const TangentVec &vec, const Scalar epsilon = kDefaultEpsilon<Scalar>)