Rotation2 in nalgebra::geometry - Rust
Description: A 2-dimensional rotation matrix.
Keywords: rust, rustlang, rust-lang, Rotation2

# Type Definition nalgebra::geometry::Rotation2

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    pub type Rotation2<T> = Rotation<T, 2>;

Expand description

A 2-dimensional rotation matrix.

Because this is an alias, not all its methods are listed here. See the `Rotation` type too.

## Implementations§

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### impl<T: SimdRealField> Rotation2<T>

#### Interpolation

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#### pub fn slerp(&self, other: &Self, t: T) -> Selfwhere
T::Element: SimdRealField,

Spherical linear interpolation between two rotation matrices.

##### Examples:

    let rot1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
    let rot2 = Rotation2::new(-std::f32::consts::PI);

    let rot = rot1.slerp(&rot2, 1.0 / 3.0);

    assert_relative_eq!(rot.angle(), std::f32::consts::FRAC_PI_2);

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### impl<T: SimdRealField> Rotation2<T>

#### Construction from a 2D rotation angle

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#### pub fn new(angle: T) -> Self

Builds a 2 dimensional rotation matrix from an angle in radian.

##### Example

    let rot = Rotation2::new(f32::consts::FRAC_PI_2);

    assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));

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#### pub fn from_scaled_axis<SB: Storage<T, U1>>(
axisangle: Vector<T, U1, SB>
) -> Self

Builds a 2 dimensional rotation matrix from an angle in radian wrapped in a 1-dimensional vector.

This is generally used in the context of generic programming. Using the `::new(angle)` method instead is more common.

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### impl<T: SimdRealField> Rotation2<T>

#### Construction from an existing 2D matrix or rotations

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#### pub fn from_basis_unchecked(basis: &[Vector2<T>; 2]) -> Self

Builds a rotation from a basis assumed to be orthonormal.

In order to get a valid rotation matrix, the input must be an orthonormal basis, i.e., all vectors are normalized, and the are all orthogonal to each other. These invariants are not checked by this method.

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#### pub fn from_matrix(m: &Matrix2<T>) -> Selfwhere
T: RealField,

Builds a rotation matrix by extracting the rotation part of the given transformation `m`.

This is an iterative method. See `.from_matrix_eps` to provide mover convergence parameters and starting solution. This implements “A Robust Method to Extract the Rotational Part of Deformations” by Müller et al.

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#### pub fn from_matrix_eps(
m: &Matrix2<T>,
eps: T,
max_iter: usize,
guess: Self
) -> Selfwhere
T: RealField,

Builds a rotation matrix by extracting the rotation part of the given transformation `m`.

This implements “A Robust Method to Extract the Rotational Part of Deformations” by Müller et al.

##### Parameters

- `m`: the matrix from which the rotational part is to be extracted.
- `eps`: the angular errors tolerated between the current rotation and the optimal one.
- `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
- `guess`: an estimate of the solution. Convergence will be significantly faster if an initial solution close to the actual solution is provided. Can be set to `Rotation2::identity()` if no other guesses come to mind.

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#### pub fn rotation_between<SB, SC>(
a: &Vector<T, U2, SB>,
b: &Vector<T, U2, SC>
) -> Selfwhere
T: RealField,
SB: Storage<T, U2>,
SC: Storage<T, U2>,

The rotation matrix required to align `a` and `b` but with its angle.

This is the rotation `R` such that `(R * a).angle(b) == 0 && (R * a).dot(b).is_positive()`.

##### Example

    let a = Vector2::new(1.0, 2.0);
    let b = Vector2::new(2.0, 1.0);
    let rot = Rotation2::rotation_between(&a, &b);
    assert_relative_eq!(rot * a, b);
    assert_relative_eq!(rot.inverse() * b, a);

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#### pub fn scaled_rotation_between<SB, SC>(
a: &Vector<T, U2, SB>,
b: &Vector<T, U2, SC>,
s: T
) -> Selfwhere
T: RealField,
SB: Storage<T, U2>,
SC: Storage<T, U2>,

The smallest rotation needed to make `a` and `b` collinear and point toward the same direction, raised to the power `s`.

##### Example

    let a = Vector2::new(1.0, 2.0);
    let b = Vector2::new(2.0, 1.0);
    let rot2 = Rotation2::scaled_rotation_between(&a, &b, 0.2);
    let rot5 = Rotation2::scaled_rotation_between(&a, &b, 0.5);
    assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
    assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);

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#### pub fn rotation_to(&self, other: &Self) -> Self

The rotation matrix needed to make `self` and `other` coincide.

The result is such that: `self.rotation_to(other) * self == other`.

##### Example

    let rot1 = Rotation2::new(0.1);
    let rot2 = Rotation2::new(1.7);
    let rot_to = rot1.rotation_to(&rot2);

    assert_relative_eq!(rot_to * rot1, rot2);
    assert_relative_eq!(rot_to.inverse() * rot2, rot1);

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#### pub fn renormalize(&mut self)where
T: RealField,

Ensure this rotation is an orthonormal rotation matrix. This is useful when repeated computations might cause the matrix from progressively not being orthonormal anymore.

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#### pub fn powf(&self, n: T) -> Self

Raise the rotation to a given floating power, i.e., returns the rotation with the angle of `self` multiplied by `n`.

##### Example

    let rot = Rotation2::new(0.78);
    let pow = rot.powf(2.0);
    assert_relative_eq!(pow.angle(), 2.0 * 0.78);

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### impl<T: SimdRealField> Rotation2<T>

#### 2D angle extraction

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#### pub fn angle(&self) -> T

The rotation angle.

##### Example

    let rot = Rotation2::new(1.78);
    assert_relative_eq!(rot.angle(), 1.78);

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#### pub fn angle_to(&self, other: &Self) -> T

The rotation angle needed to make `self` and `other` coincide.

##### Example

    let rot1 = Rotation2::new(0.1);
    let rot2 = Rotation2::new(1.7);
    assert_relative_eq!(rot1.angle_to(&rot2), 1.6);

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#### pub fn scaled_axis(&self) -> SVector<T, 1>

The rotation angle returned as a 1-dimensional vector.

This is generally used in the context of generic programming. Using the `.angle()` method instead is more common.

## Trait Implementations§

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### impl<T: SimdRealField> From<Unit<Complex<T>>> for Rotation2<T>where
T::Element: SimdRealField,

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#### fn from(q: UnitComplex<T>) -> Self

Converts to this type from the input type.
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### impl<T1, T2> SubsetOf<Unit<Complex<T2>>> for Rotation2<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitComplex<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(q: &UnitComplex<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(q: &UnitComplex<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more