Template Struct Pose2

Class representing 2D transformations (rigid body motion in 2D).

This class represents elements of the SE(2) group, which combines 2D rotations and translations. Each pose consists of a rotation component (SO2) and a translation vector in 2D space.

Template Parameters

K – Scalar type (typically float or double).

Public Types

using Scalar = K

Public Functions

inline Pose2 inverse() const

Get the inverse transformation.

Returns

Inverse transformation.

inline Matrix3<K> matrix() const

Get the 3×3 homogeneous transformation matrix representation.

Returns

3×3 transformation matrix.

template<typename S, typename std::enable_if_t<!std::is_same<S, K>::value, int> = 0>
inline Pose2<S> cast() const

Cast to a different scalar type.

Template Parameters

S – Target scalar type.

Returns

Pose cast to the target type.

template<typename S, typename std::enable_if_t<std::is_same<S, K>::value, int> = 0>
inline const Pose2 &cast() const

Cast to the same scalar type (no-op).

Template Parameters

S – Target scalar type (same as K).

Returns

Reference to this pose.

inline Pose2 pow(K exponent) const

Compute the power of the transformation.

This computes the transformation raised to the given exponent using exponential coordinates and matrix exponentiation.

Parameters

exponent – Power to raise the transformation to.

Returns

Transformation raised to the given power.

Public Members

SO2<K> rotation

Rotation component.

Vector2<K> translation

Translation component.

Public Static Functions

static inline Pose2 identity()

Create the identity transformation.

Returns

Identity transformation (no rotation or translation).

static inline Pose2 from_translation(const Vector2<K> &translation)

Create a pure translation transformation.

Parameters

translation – Translation vector.

Returns

Translation-only transformation.

static inline Pose2 from_translation(K x, K y)

Create a pure translation transformation from components.

Parameters

• x – X component of translation.

• y – Y component of translation.

Returns

Translation-only transformation.

static inline Pose2 from_rotation(const K angle)

Create a pure rotation transformation.

Parameters

angle – Rotation angle in radians.

Returns

Rotation-only transformation.

static inline Pose2 from_xy_a(K px, K py, K angle)

Create a pose from position and angle components.

Parameters

• px – X component of translation.

• py – Y component of translation.

• angle – Rotation angle in radians.

Returns

Pose with specified translation and rotation.

static inline Pose2 from_matrix(const Matrix3<K> &matrix)

Create a pose from a 3×3 transformation matrix.

Parameters

matrix – 3×3 homogeneous transformation matrix.

Returns

Pose represented by the matrix.

Public Static Attributes

static constexpr int kDimension = 2

Friends

inline friend Pose2 operator*(const Pose2 &lhs, const Pose2 &rhs)

Compose two poses.

Parameters

• lhs – Left pose.

• rhs – Right pose.

Returns

Composed pose lhs * rhs.

inline friend Vector2<K> operator*(const Pose2 &pose, const Vector2<K> &vec)

Transform a 2D vector with the given transformation.

Parameters

• pose – Transformation to apply.

• vec – Vector to transform.

Returns

Transformed vector.