Struct nalgebra::geometry::Rotation [−][src]
#[repr(C)]pub struct Rotation<T, const D: usize> { /* fields omitted */ }
Expand description
A rotation matrix.
This is also known as an element of a Special Orthogonal (SO) group.
The Rotation
type can either represent a 2D or 3D rotation, represented as a matrix.
For a rotation based on quaternions, see UnitQuaternion
instead.
Note that instead of using the Rotation
type in your code directly, you should use one
of its aliases: Rotation2
, or Rotation3
. Though
keep in mind that all the documentation of all the methods of these aliases will also appears on
this page.
Construction
- Identity
identity
- From a 2D rotation angle
new
… - From an existing 2D matrix or rotations
from_matrix
,rotation_between
,powf
… - From a 3D axis and/or angles
new
,from_euler_angles
,from_axis_angle
… - From a 3D eye position and target point
look_at
,look_at_lh
,rotation_between
… - From an existing 3D matrix or rotations
from_matrix
,rotation_between
,powf
…
Transformation and composition
Note that transforming vectors and points can be done by multiplication, e.g., rotation * point
.
Composing an rotation with another transformation can also be done by multiplication or division.
- 3D axis and angle extraction
angle
,euler_angles
,scaled_axis
,angle_to
… - 2D angle extraction
angle
,angle_to
… - Transformation of a vector or a point
transform_vector
,inverse_transform_point
… - Transposition and inversion
transpose
,inverse
… - Interpolation
slerp
…
Conversion
Implementations
Creates a new rotation from the given square matrix.
The matrix orthonormality is not checked.
Example
let mat = Matrix3::new(0.8660254, -0.5, 0.0,
0.5, 0.8660254, 0.0,
0.0, 0.0, 1.0);
let rot = Rotation3::from_matrix_unchecked(mat);
assert_eq!(*rot.matrix(), mat);
let mat = Matrix2::new(0.8660254, -0.5,
0.5, 0.8660254);
let rot = Rotation2::from_matrix_unchecked(mat);
assert_eq!(*rot.matrix(), mat);
A reference to the underlying matrix representation of this rotation.
Example
let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
let expected = Matrix3::new(0.8660254, -0.5, 0.0,
0.5, 0.8660254, 0.0,
0.0, 0.0, 1.0);
assert_eq!(*rot.matrix(), expected);
let rot = Rotation2::new(f32::consts::FRAC_PI_6);
let expected = Matrix2::new(0.8660254, -0.5,
0.5, 0.8660254);
assert_eq!(*rot.matrix(), expected);
👎 Deprecated: Use .matrix_mut_unchecked()
instead.
Use .matrix_mut_unchecked()
instead.
A mutable reference to the underlying matrix representation of this rotation.
A mutable reference to the underlying matrix representation of this rotation.
This is suffixed by “_unchecked” because this allows the user to replace the matrix by another one that is non-inversible or non-orthonormal. If one of those properties is broken, subsequent method calls may return bogus results.
Unwraps the underlying matrix.
Example
let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
let mat = rot.into_inner();
let expected = Matrix3::new(0.8660254, -0.5, 0.0,
0.5, 0.8660254, 0.0,
0.0, 0.0, 1.0);
assert_eq!(mat, expected);
let rot = Rotation2::new(f32::consts::FRAC_PI_6);
let mat = rot.into_inner();
let expected = Matrix2::new(0.8660254, -0.5,
0.5, 0.8660254);
assert_eq!(mat, expected);
👎 Deprecated: use .into_inner()
instead
use .into_inner()
instead
Unwraps the underlying matrix.
Deprecated: Use Rotation::into_inner
instead.
pub fn to_homogeneous(
&self
) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> where
T: Zero + One,
Const<D>: DimNameAdd<U1>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
pub fn to_homogeneous(
&self
) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> where
T: Zero + One,
Const<D>: DimNameAdd<U1>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
Converts this rotation into its equivalent homogeneous transformation matrix.
This is the same as self.into()
.
Example
let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
let expected = Matrix4::new(0.8660254, -0.5, 0.0, 0.0,
0.5, 0.8660254, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0);
assert_eq!(rot.to_homogeneous(), expected);
let rot = Rotation2::new(f32::consts::FRAC_PI_6);
let expected = Matrix3::new(0.8660254, -0.5, 0.0,
0.5, 0.8660254, 0.0,
0.0, 0.0, 1.0);
assert_eq!(rot.to_homogeneous(), expected);
Transposes self
.
Same as .inverse()
because the inverse of a rotation matrix is its transform.
Example
let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
let tr_rot = rot.transpose();
assert_relative_eq!(rot * tr_rot, Rotation3::identity(), epsilon = 1.0e-6);
assert_relative_eq!(tr_rot * rot, Rotation3::identity(), epsilon = 1.0e-6);
let rot = Rotation2::new(1.2);
let tr_rot = rot.transpose();
assert_relative_eq!(rot * tr_rot, Rotation2::identity(), epsilon = 1.0e-6);
assert_relative_eq!(tr_rot * rot, Rotation2::identity(), epsilon = 1.0e-6);
Inverts self
.
Same as .transpose()
because the inverse of a rotation matrix is its transform.
Example
let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
let inv = rot.inverse();
assert_relative_eq!(rot * inv, Rotation3::identity(), epsilon = 1.0e-6);
assert_relative_eq!(inv * rot, Rotation3::identity(), epsilon = 1.0e-6);
let rot = Rotation2::new(1.2);
let inv = rot.inverse();
assert_relative_eq!(rot * inv, Rotation2::identity(), epsilon = 1.0e-6);
assert_relative_eq!(inv * rot, Rotation2::identity(), epsilon = 1.0e-6);
Transposes self
in-place.
Same as .inverse_mut()
because the inverse of a rotation matrix is its transform.
Example
let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
let mut tr_rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
tr_rot.transpose_mut();
assert_relative_eq!(rot * tr_rot, Rotation3::identity(), epsilon = 1.0e-6);
assert_relative_eq!(tr_rot * rot, Rotation3::identity(), epsilon = 1.0e-6);
let rot = Rotation2::new(1.2);
let mut tr_rot = Rotation2::new(1.2);
tr_rot.transpose_mut();
assert_relative_eq!(rot * tr_rot, Rotation2::identity(), epsilon = 1.0e-6);
assert_relative_eq!(tr_rot * rot, Rotation2::identity(), epsilon = 1.0e-6);
Inverts self
in-place.
Same as .transpose_mut()
because the inverse of a rotation matrix is its transform.
Example
let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
let mut inv = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
inv.inverse_mut();
assert_relative_eq!(rot * inv, Rotation3::identity(), epsilon = 1.0e-6);
assert_relative_eq!(inv * rot, Rotation3::identity(), epsilon = 1.0e-6);
let rot = Rotation2::new(1.2);
let mut inv = Rotation2::new(1.2);
inv.inverse_mut();
assert_relative_eq!(rot * inv, Rotation2::identity(), epsilon = 1.0e-6);
assert_relative_eq!(inv * rot, Rotation2::identity(), epsilon = 1.0e-6);
Rotate the given point.
This is the same as the multiplication self * pt
.
Example
let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
let transformed_point = rot.transform_point(&Point3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_point, Point3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
Rotate the given vector.
This is the same as the multiplication self * v
.
Example
let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
let transformed_vector = rot.transform_vector(&Vector3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_vector, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
Rotate the given point by the inverse of this rotation. This may be cheaper than inverting the rotation and then transforming the given point.
Example
let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
let transformed_point = rot.inverse_transform_point(&Point3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_point, Point3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
Rotate the given vector by the inverse of this rotation. This may be cheaper than inverting the rotation and then transforming the given vector.
Example
let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
let transformed_vector = rot.inverse_transform_vector(&Vector3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_vector, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
Rotate the given vector by the inverse of this rotation. This may be cheaper than inverting the rotation and then transforming the given vector.
Example
let rot = Rotation3::new(Vector3::z() * f32::consts::FRAC_PI_2);
let transformed_vector = rot.inverse_transform_unit_vector(&Vector3::x_axis());
assert_relative_eq!(transformed_vector, -Vector3::y_axis(), epsilon = 1.0e-6);
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);
Spherical linear interpolation between two rotation matrices.
Panics if the angle between both rotations is 180 degrees (in which case the interpolation
is not well-defined). Use .try_slerp
instead to avoid the panic.
Examples:
let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
let q = q1.slerp(&q2, 1.0 / 3.0);
assert_eq!(q.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
Computes the spherical linear interpolation between two rotation matrices or returns None
if both rotations are approximately 180 degrees apart (in which case the interpolation is
not well-defined).
Arguments
self
: the first rotation to interpolate from.other
: the second rotation to interpolate toward.t
: the interpolation parameter. Should be between 0 and 1.epsilon
: the value below which the sinus of the angle separating both rotations must be to returnNone
.
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));
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.
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.
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<T>,
eps: T,
max_iter: usize,
guess: Self
) -> Self where
T: RealField,
pub fn from_matrix_eps(
m: &Matrix2<T>,
eps: T,
max_iter: usize,
guess: Self
) -> Self where
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.
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);
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);
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);
Ensure this rotation is an orthonormal rotation matrix. This is useful when repeated computations might cause the matrix from progressively not being orthonormal anymore.
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);
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.
Builds a 3 dimensional rotation matrix from an axis and an angle.
Arguments
axisangle
- A vector representing the rotation. Its magnitude is the amount of rotation in radian. Its direction is the axis of rotation.
Example
let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);
let rot = Rotation3::new(axisangle);
assert_relative_eq!(rot * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(rot * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
// A zero vector yields an identity.
assert_eq!(Rotation3::new(Vector3::<f32>::zeros()), Rotation3::identity());
Builds a 3D rotation matrix from an axis scaled by the rotation angle.
This is the same as Self::new(axisangle)
.
Example
let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);
let rot = Rotation3::new(axisangle);
assert_relative_eq!(rot * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(rot * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
// A zero vector yields an identity.
assert_eq!(Rotation3::from_scaled_axis(Vector3::<f32>::zeros()), Rotation3::identity());
Builds a 3D rotation matrix from an axis and a rotation angle.
Example
let axis = Vector3::y_axis();
let angle = f32::consts::FRAC_PI_2;
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);
let rot = Rotation3::from_axis_angle(&axis, angle);
assert_eq!(rot.axis().unwrap(), axis);
assert_eq!(rot.angle(), angle);
assert_relative_eq!(rot * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(rot * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
// A zero vector yields an identity.
assert_eq!(Rotation3::from_scaled_axis(Vector3::<f32>::zeros()), Rotation3::identity());
Creates a new rotation from Euler angles.
The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
Example
let rot = Rotation3::from_euler_angles(0.1, 0.2, 0.3);
let euler = rot.euler_angles();
assert_relative_eq!(euler.0, 0.1, epsilon = 1.0e-6);
assert_relative_eq!(euler.1, 0.2, epsilon = 1.0e-6);
assert_relative_eq!(euler.2, 0.3, epsilon = 1.0e-6);
Creates a rotation that corresponds to the local frame of an observer standing at the
origin and looking toward dir
.
It maps the z
axis to the direction dir
.
Arguments
- dir - The look direction, that is, direction the matrix
z
axis will be aligned with. - up - The vertical direction. The only requirement of this parameter is to not be
collinear to
dir
. Non-collinearity is not checked.
Example
let dir = Vector3::new(1.0, 2.0, 3.0);
let up = Vector3::y();
let rot = Rotation3::face_towards(&dir, &up);
assert_relative_eq!(rot * Vector3::z(), dir.normalize());
pub fn new_observer_frames<SB, SC>(
dir: &Vector<T, U3, SB>,
up: &Vector<T, U3, SC>
) -> Self where
SB: Storage<T, U3>,
SC: Storage<T, U3>,
👎 Deprecated: renamed to face_towards
pub fn new_observer_frames<SB, SC>(
dir: &Vector<T, U3, SB>,
up: &Vector<T, U3, SC>
) -> Self where
SB: Storage<T, U3>,
SC: Storage<T, U3>,
renamed to face_towards
Deprecated: Use Rotation3::face_towards
instead.
Builds a right-handed look-at view matrix without translation.
It maps the view direction dir
to the negative z
axis.
This conforms to the common notion of right handed look-at matrix from the computer
graphics community.
Arguments
- dir - The direction toward which the camera looks.
- up - A vector approximately aligned with required the vertical axis. The only
requirement of this parameter is to not be collinear to
dir
.
Example
let dir = Vector3::new(1.0, 2.0, 3.0);
let up = Vector3::y();
let rot = Rotation3::look_at_rh(&dir, &up);
assert_relative_eq!(rot * dir.normalize(), -Vector3::z());
Builds a left-handed look-at view matrix without translation.
It maps the view direction dir
to the positive z
axis.
This conforms to the common notion of left handed look-at matrix from the computer
graphics community.
Arguments
- dir - The direction toward which the camera looks.
- up - A vector approximately aligned with required the vertical axis. The only
requirement of this parameter is to not be collinear to
dir
.
Example
let dir = Vector3::new(1.0, 2.0, 3.0);
let up = Vector3::y();
let rot = Rotation3::look_at_lh(&dir, &up);
assert_relative_eq!(rot * dir.normalize(), Vector3::z());
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 = Vector3::new(1.0, 2.0, 3.0);
let b = Vector3::new(3.0, 1.0, 2.0);
let rot = Rotation3::rotation_between(&a, &b).unwrap();
assert_relative_eq!(rot * a, b, epsilon = 1.0e-6);
assert_relative_eq!(rot.inverse() * b, a, epsilon = 1.0e-6);
The smallest rotation needed to make a
and b
collinear and point toward the same
direction, raised to the power s
.
Example
let a = Vector3::new(1.0, 2.0, 3.0);
let b = Vector3::new(3.0, 1.0, 2.0);
let rot2 = Rotation3::scaled_rotation_between(&a, &b, 0.2).unwrap();
let rot5 = Rotation3::scaled_rotation_between(&a, &b, 0.5).unwrap();
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);
The rotation matrix needed to make self
and other
coincide.
The result is such that: self.rotation_to(other) * self == other
.
Example
let rot1 = Rotation3::from_axis_angle(&Vector3::y_axis(), 1.0);
let rot2 = Rotation3::from_axis_angle(&Vector3::x_axis(), 0.1);
let rot_to = rot1.rotation_to(&rot2);
assert_relative_eq!(rot_to * rot1, rot2, epsilon = 1.0e-6);
Raise the quaternion to a given floating power, i.e., returns the rotation with the same
axis as self
and an angle equal to self.angle()
multiplied by n
.
Example
let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let angle = 1.2;
let rot = Rotation3::from_axis_angle(&axis, angle);
let pow = rot.powf(2.0);
assert_relative_eq!(pow.axis().unwrap(), axis, epsilon = 1.0e-6);
assert_eq!(pow.angle(), 2.4);
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.
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: &Matrix3<T>,
eps: T,
max_iter: usize,
guess: Self
) -> Self where
T: RealField,
pub fn from_matrix_eps(
m: &Matrix3<T>,
eps: T,
max_iter: usize,
guess: Self
) -> Self where
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
: a guess of the solution. Convergence will be significantly faster if an initial solution close to the actual solution is provided. Can be set toRotation3::identity()
if no other guesses come to mind.
Ensure this rotation is an orthonormal rotation matrix. This is useful when repeated computations might cause the matrix from progressively not being orthonormal anymore.
The rotation angle in [0; pi].
Example
let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let rot = Rotation3::from_axis_angle(&axis, 1.78);
assert_relative_eq!(rot.angle(), 1.78);
The rotation axis. Returns None
if the rotation angle is zero or PI.
Example
let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let angle = 1.2;
let rot = Rotation3::from_axis_angle(&axis, angle);
assert_relative_eq!(rot.axis().unwrap(), axis);
// Case with a zero angle.
let rot = Rotation3::from_axis_angle(&axis, 0.0);
assert!(rot.axis().is_none());
The rotation axis multiplied by the rotation angle.
Example
let axisangle = Vector3::new(0.1, 0.2, 0.3);
let rot = Rotation3::new(axisangle);
assert_relative_eq!(rot.scaled_axis(), axisangle, epsilon = 1.0e-6);
The rotation axis and angle in ]0, pi] of this unit quaternion.
Returns None
if the angle is zero.
Example
let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let angle = 1.2;
let rot = Rotation3::from_axis_angle(&axis, angle);
let axis_angle = rot.axis_angle().unwrap();
assert_relative_eq!(axis_angle.0, axis);
assert_relative_eq!(axis_angle.1, angle);
// Case with a zero angle.
let rot = Rotation3::from_axis_angle(&axis, 0.0);
assert!(rot.axis_angle().is_none());
The rotation angle needed to make self
and other
coincide.
Example
let rot1 = Rotation3::from_axis_angle(&Vector3::y_axis(), 1.0);
let rot2 = Rotation3::from_axis_angle(&Vector3::x_axis(), 0.1);
assert_relative_eq!(rot1.angle_to(&rot2), 1.0045657, epsilon = 1.0e-6);
👎 Deprecated: This is renamed to use .euler_angles()
.
This is renamed to use .euler_angles()
.
Creates Euler angles from a rotation.
The angles are produced in the form (roll, pitch, yaw).
Euler angles corresponding to this rotation from a rotation.
The angles are produced in the form (roll, pitch, yaw).
Example
let rot = Rotation3::from_euler_angles(0.1, 0.2, 0.3);
let euler = rot.euler_angles();
assert_relative_eq!(euler.0, 0.1, epsilon = 1.0e-6);
assert_relative_eq!(euler.1, 0.2, epsilon = 1.0e-6);
assert_relative_eq!(euler.2, 0.3, epsilon = 1.0e-6);
Trait Implementations
The default tolerance to use when testing values that are close together. Read more
A test for equality that uses the absolute difference to compute the approximate equality of two numbers. Read more
The inverse of AbsDiffEq::abs_diff_eq
.
impl<T: SimdRealField, const D: usize> AbstractRotation<T, D> for Rotation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> AbstractRotation<T, D> for Rotation<T, D> where
T::Element: SimdRealField,
Change self
to its inverse.
Apply the rotation to the given vector.
Apply the rotation to the given point.
Apply the inverse rotation to the given vector.
Apply the inverse rotation to the given unit vector.
Apply the inverse rotation to the given point.
impl<'a, T: Scalar, const D: usize> Deserialize<'a> for Rotation<T, D> where
Owned<T, Const<D>, Const<D>>: Deserialize<'a>,
impl<'a, T: Scalar, const D: usize> Deserialize<'a> for Rotation<T, D> where
Owned<T, Const<D>, Const<D>>: Deserialize<'a>,
fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error> where
Des: Deserializer<'a>,
fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error> where
Des: Deserializer<'a>,
Deserialize this value from the given Serde deserializer. Read more
impl<'b, T: SimdRealField, const D: usize> Div<&'b Isometry<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Div<&'b Isometry<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Rotation<T, 2_usize>> for &'a UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Rotation<T, 2_usize>> for &'a UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Rotation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Rotation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'b, T, C, const D: usize> Div<&'b Rotation<T, D>> for Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'b, T, C, const D: usize> Div<&'b Rotation<T, D>> for Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, 'b, T, C, const D: usize> Div<&'b Rotation<T, D>> for &'a Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, 'b, T, C, const D: usize> Div<&'b Rotation<T, D>> for &'a Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, 'b, T, R1, C1, SA, const D2: usize> Div<&'b Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,
impl<'a, 'b, T, R1, C1, SA, const D2: usize> Div<&'b Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,
impl<'b, T: SimdRealField, const D: usize> Div<&'b Similarity<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Div<&'b Similarity<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
type Output = Similarity<T, Rotation<T, D>, D>
type Output = Similarity<T, Rotation<T, D>, D>
The resulting type after applying the /
operator.
impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
type Output = Similarity<T, Rotation<T, D>, D>
type Output = Similarity<T, Rotation<T, D>, D>
The resulting type after applying the /
operator.
impl<'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, 'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for &'a Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, 'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for &'a Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
type Output = UnitComplex<T>
type Output = UnitComplex<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Rotation<T, 2> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Rotation<T, 2> where
T::Element: SimdRealField,
type Output = UnitComplex<T>
type Output = UnitComplex<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Rotation<T, 3> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Rotation<T, 3> where
T::Element: SimdRealField,
type Output = UnitQuaternion<T>
type Output = UnitQuaternion<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Rotation<T, 3> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Rotation<T, 3> where
T::Element: SimdRealField,
type Output = UnitQuaternion<T>
type Output = UnitQuaternion<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<T: SimdRealField, const D: usize> Div<Isometry<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Div<Isometry<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Div<Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Div<Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Rotation<T, 2_usize>> for &'a UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Rotation<T, 2_usize>> for &'a UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Rotation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Rotation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Div<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Div<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Div<Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Div<Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Div<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Div<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Div<Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Div<Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<T, C, const D: usize> Div<Rotation<T, D>> for Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<T, C, const D: usize> Div<Rotation<T, D>> for Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, T, C, const D: usize> Div<Rotation<T, D>> for &'a Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, T, C, const D: usize> Div<Rotation<T, D>> for &'a Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<T: SimdRealField, const D: usize> Div<Similarity<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Div<Similarity<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
type Output = Similarity<T, Rotation<T, D>, D>
type Output = Similarity<T, Rotation<T, D>, D>
The resulting type after applying the /
operator.
impl<'a, T: SimdRealField, const D: usize> Div<Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Div<Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
type Output = Similarity<T, Rotation<T, D>, D>
type Output = Similarity<T, Rotation<T, D>, D>
The resulting type after applying the /
operator.
impl<T, C, const D: usize> Div<Transform<T, C, D>> for Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<T, C, const D: usize> Div<Transform<T, C, D>> for Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, T, C, const D: usize> Div<Transform<T, C, D>> for &'a Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, T, C, const D: usize> Div<Transform<T, C, D>> for &'a Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<T: SimdRealField> Div<Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
type Output = UnitComplex<T>
type Output = UnitComplex<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Rotation<T, 2> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Rotation<T, 2> where
T::Element: SimdRealField,
type Output = UnitComplex<T>
type Output = UnitComplex<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Rotation<T, 3> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Rotation<T, 3> where
T::Element: SimdRealField,
type Output = UnitQuaternion<T>
type Output = UnitQuaternion<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Rotation<T, 3> where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Rotation<T, 3> where
T::Element: SimdRealField,
type Output = UnitQuaternion<T>
type Output = UnitQuaternion<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'b, T: SimdRealField> DivAssign<&'b Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> DivAssign<&'b Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
Performs the /=
operation. Read more
impl<'b, T: SimdRealField> DivAssign<&'b Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> DivAssign<&'b Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
impl<'b, T, const D: usize> DivAssign<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,
impl<'b, T, const D: usize> DivAssign<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,
Performs the /=
operation. Read more
Performs the /=
operation. Read more
impl<'b, T: SimdRealField> DivAssign<&'b Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> DivAssign<&'b Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
Performs the /=
operation. Read more
impl<T: SimdRealField> DivAssign<Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> DivAssign<Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
Performs the /=
operation. Read more
impl<T: SimdRealField> DivAssign<Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> DivAssign<Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
impl<T, const D: usize> DivAssign<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,
impl<T, const D: usize> DivAssign<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,
Performs the /=
operation. Read more
Performs the /=
operation. Read more
impl<T: SimdRealField> DivAssign<Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
impl<T: SimdRealField> DivAssign<Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
Performs the /=
operation. Read more
impl<T: SimdRealField> From<Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> From<Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> From<Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> From<Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Isometry<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Isometry<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T, R2, C2, SB, const D1: usize> Mul<&'b Matrix<T, R2, C2, SB>> for &'a Rotation<T, D1> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R2: Dim,
C2: Dim,
SB: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, Const<D1>, C2>,
ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>,
impl<'a, 'b, T, R2, C2, SB, const D1: usize> Mul<&'b Matrix<T, R2, C2, SB>> for &'a Rotation<T, D1> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R2: Dim,
C2: Dim,
SB: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, Const<D1>, C2>,
ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>,
impl<'b, T: SimdRealField> Mul<&'b Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Rotation<T, 2_usize>> for &'a UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Rotation<T, 2_usize>> for &'a UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Rotation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Rotation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Translation<T, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Translation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Translation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Translation<T, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'b, T, C, const D: usize> Mul<&'b Rotation<T, D>> for Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'b, T, C, const D: usize> Mul<&'b Rotation<T, D>> for Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, 'b, T, C, const D: usize> Mul<&'b Rotation<T, D>> for &'a Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, 'b, T, C, const D: usize> Mul<&'b Rotation<T, D>> for &'a Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, 'b, T, R1, C1, SA, const D2: usize> Mul<&'b Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,
impl<'a, 'b, T, R1, C1, SA, const D2: usize> Mul<&'b Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Similarity<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Similarity<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
type Output = Similarity<T, Rotation<T, D>, D>
type Output = Similarity<T, Rotation<T, D>, D>
The resulting type after applying the *
operator.
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
type Output = Similarity<T, Rotation<T, D>, D>
type Output = Similarity<T, Rotation<T, D>, D>
The resulting type after applying the *
operator.
impl<'b, T, C, const D: usize> Mul<&'b Transform<T, C, D>> for Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'b, T, C, const D: usize> Mul<&'b Transform<T, C, D>> for Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, 'b, T, C, const D: usize> Mul<&'b Transform<T, C, D>> for &'a Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, 'b, T, C, const D: usize> Mul<&'b Transform<T, C, D>> for &'a Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Translation<T, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, const D: usize> Mul<&'b Translation<T, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Translation<T, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Translation<T, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
type Output = UnitComplex<T>
type Output = UnitComplex<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Rotation<T, 2> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Rotation<T, 2> where
T::Element: SimdRealField,
type Output = UnitComplex<T>
type Output = UnitComplex<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Rotation<T, 3> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Rotation<T, 3> where
T::Element: SimdRealField,
type Output = UnitQuaternion<T>
type Output = UnitQuaternion<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Rotation<T, 3> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Rotation<T, 3> where
T::Element: SimdRealField,
type Output = UnitQuaternion<T>
type Output = UnitQuaternion<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<T: SimdRealField, const D: usize> Mul<Isometry<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Mul<Isometry<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Rotation<T, 2_usize>> for &'a UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Rotation<T, 2_usize>> for &'a UnitComplex<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Rotation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Rotation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Translation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Translation<T, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Translation<T, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Translation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D> where
T::Element: SimdRealField,
impl<T, C, const D: usize> Mul<Rotation<T, D>> for Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<T, C, const D: usize> Mul<Rotation<T, D>> for Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, T, C, const D: usize> Mul<Rotation<T, D>> for &'a Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, T, C, const D: usize> Mul<Rotation<T, D>> for &'a Transform<T, C, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<T: SimdRealField, const D: usize> Mul<Similarity<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Mul<Similarity<T, Rotation<T, D>, D>> for Rotation<T, D> where
T::Element: SimdRealField,
type Output = Similarity<T, Rotation<T, D>, D>
type Output = Similarity<T, Rotation<T, D>, D>
The resulting type after applying the *
operator.
impl<'a, T: SimdRealField, const D: usize> Mul<Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
type Output = Similarity<T, Rotation<T, D>, D>
type Output = Similarity<T, Rotation<T, D>, D>
The resulting type after applying the *
operator.
impl<T, C, const D: usize> Mul<Transform<T, C, D>> for Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<T, C, const D: usize> Mul<Transform<T, C, D>> for Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, T, C, const D: usize> Mul<Transform<T, C, D>> for &'a Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<'a, T, C, const D: usize> Mul<Transform<T, C, D>> for &'a Rotation<T, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<T: SimdRealField, const D: usize> Mul<Translation<T, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField, const D: usize> Mul<Translation<T, D>> for Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Translation<T, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, const D: usize> Mul<Translation<T, D>> for &'a Rotation<T, D> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
type Output = UnitComplex<T>
type Output = UnitComplex<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Rotation<T, 2> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Rotation<T, 2> where
T::Element: SimdRealField,
type Output = UnitComplex<T>
type Output = UnitComplex<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Rotation<T, 3> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Rotation<T, 3> where
T::Element: SimdRealField,
type Output = UnitQuaternion<T>
type Output = UnitQuaternion<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Rotation<T, 3> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Rotation<T, 3> where
T::Element: SimdRealField,
type Output = UnitQuaternion<T>
type Output = UnitQuaternion<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'b, T: SimdRealField> MulAssign<&'b Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> MulAssign<&'b Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
Performs the *=
operation. Read more
impl<'b, T: SimdRealField> MulAssign<&'b Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> MulAssign<&'b Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
impl<'b, T, const D: usize> MulAssign<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,
impl<'b, T, const D: usize> MulAssign<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,
Performs the *=
operation. Read more
Performs the *=
operation. Read more
impl<'b, T: SimdRealField> MulAssign<&'b Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> MulAssign<&'b Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
Performs the *=
operation. Read more
impl<T: SimdRealField> MulAssign<Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> MulAssign<Rotation<T, 2_usize>> for UnitComplex<T> where
T::Element: SimdRealField,
Performs the *=
operation. Read more
impl<T: SimdRealField> MulAssign<Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> MulAssign<Rotation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
impl<T, const D: usize> MulAssign<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,
impl<T, const D: usize> MulAssign<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D> where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,
Performs the *=
operation. Read more
Performs the *=
operation. Read more
impl<T: SimdRealField> MulAssign<Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
impl<T: SimdRealField> MulAssign<Unit<Complex<T>>> for Rotation<T, 2> where
T::Element: SimdRealField,
Performs the *=
operation. Read more
impl<T, const D: usize> RelativeEq<Rotation<T, D>> for Rotation<T, D> where
T: Scalar + RelativeEq,
T::Epsilon: Clone,
impl<T, const D: usize> RelativeEq<Rotation<T, D>> for Rotation<T, D> where
T: Scalar + RelativeEq,
T::Epsilon: Clone,
The default relative tolerance for testing values that are far-apart. Read more
A test for equality that uses a relative comparison if the values are far apart.
The inverse of RelativeEq::relative_eq
.
impl<T1, T2, R, const D: usize> SubsetOf<Isometry<T2, R, D>> for Rotation<T1, D> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, D> + SupersetOf<Self>,
impl<T1, T2, R, const D: usize> SubsetOf<Isometry<T2, R, D>> for Rotation<T1, D> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, D> + SupersetOf<Self>,
The inclusion map: converts self
to the equivalent element of its superset.
Checks if element
is actually part of the subset Self
(and can be converted to it).
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
impl<T1, T2, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1_usize>>>::Output, <Const<D> as DimNameAdd<Const<1_usize>>>::Output, <DefaultAllocator as Allocator<T2, <Const<D> as DimNameAdd<Const<1_usize>>>::Output, <Const<D> as DimNameAdd<Const<1_usize>>>::Output>>::Buffer>> for Rotation<T1, D> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>,
DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<T1, T2, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1_usize>>>::Output, <Const<D> as DimNameAdd<Const<1_usize>>>::Output, <DefaultAllocator as Allocator<T2, <Const<D> as DimNameAdd<Const<1_usize>>>::Output, <Const<D> as DimNameAdd<Const<1_usize>>>::Output>>::Buffer>> for Rotation<T1, D> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>,
DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
The inclusion map: converts self
to the equivalent element of its superset.
Checks if element
is actually part of the subset Self
(and can be converted to it).
fn from_superset_unchecked(
m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> Self
fn from_superset_unchecked(
m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> Self
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
impl<T1, T2> SubsetOf<Rotation<T2, 2_usize>> for UnitComplex<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
impl<T1, T2> SubsetOf<Rotation<T2, 2_usize>> for UnitComplex<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
The inclusion map: converts self
to the equivalent element of its superset.
Checks if element
is actually part of the subset Self
(and can be converted to it).
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
impl<T1, T2> SubsetOf<Rotation<T2, 3_usize>> for UnitQuaternion<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
impl<T1, T2> SubsetOf<Rotation<T2, 3_usize>> for UnitQuaternion<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
The inclusion map: converts self
to the equivalent element of its superset.
Checks if element
is actually part of the subset Self
(and can be converted to it).
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
The inclusion map: converts self
to the equivalent element of its superset.
Checks if element
is actually part of the subset Self
(and can be converted to it).
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
impl<T1, T2, R, const D: usize> SubsetOf<Similarity<T2, R, D>> for Rotation<T1, D> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, D> + SupersetOf<Self>,
impl<T1, T2, R, const D: usize> SubsetOf<Similarity<T2, R, D>> for Rotation<T1, D> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, D> + SupersetOf<Self>,
The inclusion map: converts self
to the equivalent element of its superset.
Checks if element
is actually part of the subset Self
(and can be converted to it).
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
impl<T1, T2, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Rotation<T1, D> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
C: SuperTCategoryOf<TAffine>,
Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>,
DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
impl<T1, T2, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Rotation<T1, D> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
C: SuperTCategoryOf<TAffine>,
Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>,
DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
The inclusion map: converts self
to the equivalent element of its superset.
Checks if element
is actually part of the subset Self
(and can be converted to it).
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
The default ULPs to tolerate when testing values that are far-apart. Read more
A test for equality that uses units in the last place (ULP) if the values are far apart.
Auto Trait Implementations
impl<T, const D: usize> RefUnwindSafe for Rotation<T, D> where
T: RefUnwindSafe,
impl<T, const D: usize> UnwindSafe for Rotation<T, D> where
T: UnwindSafe,
Blanket Implementations
Mutably borrows from an owned value. Read more
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
Checks if self
is actually part of its subset T
(and can be converted to it).
Use with care! Same as self.to_subset
but without any property checks. Always succeeds.
The inclusion map: converts self
to the equivalent element of its superset.