Type Definition nalgebra::geometry::Rotation2 [−][src]
type Rotation2<N> = Rotation<N, U2>;
A 2-dimensional rotation matrix.
Because this is an alias, not all its methods are listed here. See the Rotation
type too.
Implementations
impl<N: SimdRealField> Rotation2<N>
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pub fn slerp(&self, other: &Self, t: N) -> Self where
N::Element: SimdRealField,
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N::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);
impl<N: SimdRealField> Rotation2<N>
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pub fn new(angle: N) -> Self
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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));
pub fn from_scaled_axis<SB: Storage<N, U1>>(
axisangle: Vector<N, U1, SB>
) -> Self
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axisangle: Vector<N, 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.
impl<N: SimdRealField> Rotation2<N>
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pub fn from_basis_unchecked(basis: &[Vector2<N>; 2]) -> Self
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Builds a rotation from a basis assumed to be orthonormal.
In order to get a valid unit-quaternion, 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.
pub fn from_matrix(m: &Matrix2<N>) -> Self where
N: RealField,
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N: 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.
pub fn from_matrix_eps(
m: &Matrix2<N>,
eps: N,
max_iter: usize,
guess: Self
) -> Self where
N: RealField,
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m: &Matrix2<N>,
eps: N,
max_iter: usize,
guess: Self
) -> Self where
N: 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.
pub fn rotation_between<SB, SC>(
a: &Vector<N, U2, SB>,
b: &Vector<N, U2, SC>
) -> Self where
N: RealField,
SB: Storage<N, U2>,
SC: Storage<N, U2>,
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a: &Vector<N, U2, SB>,
b: &Vector<N, U2, SC>
) -> Self where
N: RealField,
SB: Storage<N, U2>,
SC: Storage<N, 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);
pub fn scaled_rotation_between<SB, SC>(
a: &Vector<N, U2, SB>,
b: &Vector<N, U2, SC>,
s: N
) -> Self where
N: RealField,
SB: Storage<N, U2>,
SC: Storage<N, U2>,
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a: &Vector<N, U2, SB>,
b: &Vector<N, U2, SC>,
s: N
) -> Self where
N: RealField,
SB: Storage<N, U2>,
SC: Storage<N, 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);
pub fn rotation_to(&self, other: &Self) -> Self
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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);
pub fn renormalize(&mut self) where
N: RealField,
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N: 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.
pub fn powf(&self, n: N) -> Self
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Raise the quaternion 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);
impl<N: SimdRealField> Rotation2<N>
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pub fn angle(&self) -> N
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pub fn angle_to(&self, other: &Self) -> N
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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);
pub fn scaled_axis(&self) -> VectorN<N, U1>
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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
impl<N: SimdRealField> From<Unit<Complex<N>>> for Rotation2<N> where
N::Element: SimdRealField,
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N::Element: SimdRealField,
fn from(q: UnitComplex<N>) -> Self
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impl<N1, N2> SubsetOf<Unit<Complex<N2>>> for Rotation2<N1> where
N1: RealField,
N2: RealField + SupersetOf<N1>,
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N1: RealField,
N2: RealField + SupersetOf<N1>,