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.
Aliased Type§
struct Rotation2<T> { /* private fields */ }
Implementations§
source§impl<T: SimdRealField> Rotation2<T>
impl<T: SimdRealField> Rotation2<T>
§Interpolation
sourcepub fn slerp(&self, other: &Self, t: T) -> Selfwhere
T::Element: SimdRealField,
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);
source§impl<T: SimdRealField> Rotation2<T>
impl<T: SimdRealField> Rotation2<T>
§Construction from a 2D rotation angle
sourcepub fn new(angle: T) -> Self
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));
sourcepub fn from_scaled_axis<SB: Storage<T, U1>>(
axisangle: Vector<T, U1, SB>
) -> Self
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.
source§impl<T: SimdRealField> Rotation2<T>
impl<T: SimdRealField> Rotation2<T>
§Construction from an existing 2D matrix or rotations
sourcepub fn from_basis_unchecked(basis: &[Vector2<T>; 2]) -> Self
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.
sourcepub fn from_matrix(m: &Matrix2<T>) -> Selfwhere
T: RealField,
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.
sourcepub fn from_matrix_eps(
m: &Matrix2<T>,
eps: T,
max_iter: usize,
guess: Self
) -> Selfwhere
T: RealField,
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 to0
.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 toRotation2::identity()
if no other guesses come to mind.
sourcepub fn rotation_between<SB, SC>(
a: &Vector<T, U2, SB>,
b: &Vector<T, U2, SC>
) -> Self
pub fn rotation_between<SB, SC>( a: &Vector<T, U2, SB>, b: &Vector<T, U2, SC> ) -> Self
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);
sourcepub fn scaled_rotation_between<SB, SC>(
a: &Vector<T, U2, SB>,
b: &Vector<T, U2, SC>,
s: T
) -> Self
pub fn scaled_rotation_between<SB, SC>( a: &Vector<T, U2, SB>, b: &Vector<T, U2, SC>, s: T ) -> Self
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);
sourcepub fn rotation_to(&self, other: &Self) -> Self
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);
sourcepub fn renormalize(&mut self)where
T: RealField,
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.
source§impl<T: SimdRealField> Rotation2<T>
impl<T: SimdRealField> Rotation2<T>
§2D angle extraction
sourcepub fn angle(&self) -> T
pub fn angle(&self) -> T
The rotation angle.
§Example
let rot = Rotation2::new(1.78);
assert_relative_eq!(rot.angle(), 1.78);
sourcepub fn angle_to(&self, other: &Self) -> T
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);
sourcepub fn scaled_axis(&self) -> SVector<T, 1>
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§
source§impl<T: SimdRealField> From<Unit<Complex<T>>> for Rotation2<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> From<Unit<Complex<T>>> for Rotation2<T>where
T::Element: SimdRealField,
source§fn from(q: UnitComplex<T>) -> Self
fn from(q: UnitComplex<T>) -> Self
source§impl<T1, T2> SubsetOf<Unit<Complex<T2>>> for Rotation2<T1>
impl<T1, T2> SubsetOf<Unit<Complex<T2>>> for Rotation2<T1>
source§fn to_superset(&self) -> UnitComplex<T2>
fn to_superset(&self) -> UnitComplex<T2>
self
to the equivalent element of its superset.source§fn is_in_subset(q: &UnitComplex<T2>) -> bool
fn is_in_subset(q: &UnitComplex<T2>) -> bool
element
is actually part of the subset Self
(and can be converted to it).source§fn from_superset_unchecked(q: &UnitComplex<T2>) -> Self
fn from_superset_unchecked(q: &UnitComplex<T2>) -> Self
self.to_superset
but without any property checks. Always succeeds.