Template Class SO2

Class representing 2D rotations using the SO(2) group.

This class represents rotations in 2D space as elements of the special orthogonal group SO(2). Internally, rotations are stored as normalized direction vectors (cos, sin) to avoid trigonometric function calls during composition and transformation operations.

Template Parameters

K – Scalar type (typically float or double).

Public Types

using Scalar = K

Public Functions

inline SO2()

Default constructor creates an undefined rotation.

Note

Use identity() to create the identity rotation.

inline K cos() const

Get the cosine of the rotation angle.

Note

This is a simple getter and does not call trigonometric functions.

Returns

Cosine of the rotation angle.

inline K sin() const

Get the sine of the rotation angle.

Note

This is a simple getter and does not call trigonometric functions.

Returns

Sine of the rotation angle.

inline const Vector2<K> &as_direction() const

Get the cos and sin of the rotation angle as a direction vector.

Returns

Direction vector (cos, sin).

inline K angle() const

Get the rotation angle in range [-π, π].

Note

This uses a call to a trigonometric function.

Returns

Rotation angle in radians.

inline Matrix2<K> matrix() const

Get the 2×2 rotation matrix representation.

Returns

2×2 rotation matrix.

inline SO2 inverse() const

Get the inverse rotation.

Returns

Inverse rotation.

template<typename S, typename std::enable_if_t<!std::is_same<S, K>::value, int> = 0>
inline SO2<S> cast() const

Cast to a different scalar type.

Template Parameters

S – Target scalar type.

Returns

Rotation cast to the target type.

template<typename S, typename std::enable_if_t<std::is_same<S, K>::value, int> = 0>
inline const SO2 &cast() const

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

Template Parameters

S – Target scalar type (same as K).

Returns

Reference to this rotation.

Public Static Functions

static inline SO2 identity()

Create the identity rotation.

Returns

Identity rotation (no rotation).

static inline SO2 from_angle(K angle)

Create rotation from an angle.

Note

This uses calls to trigonometric functions.

Parameters

angle – Rotation angle in radians.

Returns

Rotation representing the given angle.

static inline SO2 from_direction(const Vector2<K> &direction)

Create rotation from a not necessarily normalized direction vector.

Parameters

direction – Direction vector (will be normalized internally).

Returns

Rotation aligned with the given direction.

static inline SO2 from_direction(K dx, K dy)

Create rotation from direction components.

Parameters

• dx – X component of direction vector.

• dy – Y component of direction vector.

Returns

Rotation aligned with the given direction.

static inline SO2 from_normalized(const Vector2<K> &cos_sin)

Create rotation from a normalized cos/sin direction vector.

Parameters

cos_sin – Normalized direction vector (cos, sin).

Returns

Rotation represented by the given cos/sin values.

static inline SO2 from_normalized(K cos_angle, K sin_angle)

Create rotation from normalized cos and sin values.

Parameters

• cos_angle – Cosine of the rotation angle.

• sin_angle – Sine of the rotation angle.

Returns

Rotation represented by the given cos/sin values.

Public Static Attributes

static constexpr int kDimension = 2

Friends

inline friend SO2 operator*(const SO2 &lhs, const SO2 &rhs)

Compose two rotations.

Parameters

• lhs – Left rotation.

• rhs – Right rotation.

Returns

Composed rotation lhs * rhs.

inline friend Vector2<K> operator*(const SO2 &lhs, const Vector2<K> &vec)

Rotate a 2D vector.

Parameters

• lhs – Rotation to apply.

• vec – Vector to rotate.

Returns

Rotated vector.