Struct nalgebra::geometry::Rotation

source · 
#[repr(C)]
pub struct Rotation<T, const D: usize> { /* private fields */ }
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

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.

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);

Conversion to a matrix

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.

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

Unwraps the underlying matrix. Deprecated: Use Rotation::into_inner instead.

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);

Transposition and inversion

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);

Transformation of a vector or a point

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);

Identity

Creates a new square identity rotation of the given dimension.

Example
let rot1 = Rotation2::identity();
let rot2 = Rotation2::new(std::f32::consts::FRAC_PI_2);

assert_eq!(rot1 * rot2, rot2);
assert_eq!(rot2 * rot1, rot2);

let rot1 = Rotation3::identity();
let rot2 = Rotation3::from_axis_angle(&Vector3::z_axis(), std::f32::consts::FRAC_PI_2);

assert_eq!(rot1 * rot2, rot2);
assert_eq!(rot2 * rot1, rot2);

Cast the components of self to another type.

Example
let rot = Rotation2::<f64>::identity();
let rot2 = rot.cast::<f32>();
assert_eq!(rot2, Rotation2::<f32>::identity());

Interpolation

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 return None.

Construction from a 2D rotation angle

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.

Construction from an existing 2D matrix or rotations

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.

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.

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.

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.

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);

2D angle extraction

The rotation angle.

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

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.

Construction from a 3D axis and/or angles

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);

Construction from a 3D eye position and target point

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());
👎Deprecated: 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());

Construction from an existing 3D matrix or rotations

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 rotation 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 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.

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.

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: a guess of the solution. Convergence will be significantly faster if an initial solution close to the actual solution is provided. Can be set to Rotation3::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.

3D axis and angle extraction

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 rotation matrix.

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().

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§

Used for specifying relative comparisons.
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.
The inverse of AbsDiffEq::abs_diff_eq.
Performs an operation.
Performs specific operation.
The rotation identity.
The rotation inverse.
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.
Type of the first rotation to be applied.
Type of the non-uniform scaling to be applied.
The type of the pure translation part of this affine transformation.
Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation.
Appends a translation to this similarity.
Prepends a translation to this similarity.
Appends a rotation to this similarity.
Prepends a rotation to this similarity.
Appends a scaling factor to this similarity.
Prepends a scaling factor to this similarity.
Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant. Read more
The archived representation of this type. Read more
The resolver for this type. It must contain all the additional information from serializing needed to make the archived type from the normal type.
Creates the archived version of this value at the given position and writes it to the given output. Read more
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impl<__C: ?Sized, T, const D: usize> CheckBytes<__C> for Rotation<T, D>where
    SMatrix<T, D, D>: CheckBytes<__C>,

The error that may result from checking the type.
Checks whether the given pointer points to a valid value within the given context. Read more
Returns a copy of the value. Read more
Performs copy-assignment from source. Read more
Formats the value using the given formatter. Read more
Returns the “default value” for a type. Read more
Deserialize this value from the given Serde deserializer. Read more
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impl<__D: Fallible + ?Sized, T, const D: usize> Deserialize<Rotation<T, D>, __D> for Archived<Rotation<T, D>>where
    T: Archive,
    SMatrix<T, D, D>: Archive<Archived = SMatrix<T::Archived, D, D>>,
    SMatrix<T, D, D>: Archive,
    Archived<SMatrix<T, D, D>>: Deserialize<SMatrix<T, D, D>, __D>,

Deserializes using the given deserializer
Formats the value using the given formatter. Read more

Generate a uniformly distributed random rotation.

Create an iterator that generates random values of T, using rng as the source of randomness. Read more
Create a distribution of values of ‘S’ by mapping the output of Self through the closure F Read more

Generate a uniformly distributed random rotation.

Create an iterator that generates random values of T, using rng as the source of randomness. Read more
Create a distribution of values of ‘S’ by mapping the output of Self through the closure F Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Feeds this value into the given Hasher. Read more
Feeds a slice of this type into the given Hasher. Read more
The identity element.
Specific identity.
The returned type after indexing.
Performs the indexing (container[index]) operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Returns the multiplicative identity element of Self, 1. Read more
Sets self to the multiplicative identity element of Self, 1.
Returns true if self is equal to the multiplicative identity. Read more
This method tests for self and other values to be equal, and is used by ==.
This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
Applies this group’s two_sided_inverse action on a point from the euclidean space.
Applies this group’s two_sided_inverse action on a vector from the euclidean space. Read more
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.

Subgroups of the n-dimensional rotation group SO(n).

Raises this rotation to a power. If this is a simple rotation, the result must be equivalent to multiplying the rotation angle by n.
Computes a simple rotation that makes the angle between a and b equal to zero, i.e., b.angle(a * delta_rotation(a, b)) = 0. If a and b are collinear, the computed rotation may not be unique. Returns None if no such simple rotation exists in the subgroup represented by Self.
Computes the rotation between a and b and raises it to the power n. Read more
source§

impl<__S: Fallible + ?Sized, T, const D: usize> Serialize<__S> for Rotation<T, D>where
    T: Archive,
    SMatrix<T, D, D>: Archive<Archived = SMatrix<T::Archived, D, D>>,
    SMatrix<T, D, D>: Serialize<__S>,

Writes the dependencies for the object and returns a resolver that can create the archived type.
Serialize this value into the given Serde serializer. Read more
The type of the elements of each lane of this SIMD value.
Type of the result of comparing two SIMD values like self.
The number of lanes of this SIMD value.
Initializes an SIMD value with each lanes set to val.
Extracts the i-th lane of self. Read more
Extracts the i-th lane of self without bound-checking.
Replaces the i-th lane of self by val. Read more
Replaces the i-th lane of self by val without bound-checking.
Merges self and other depending on the lanes of cond. Read more
Applies a function to each lane of self. Read more
Applies a function to each lane of self paired with the corresponding lane of b. Read more
The type of the pure (uniform) scaling part of this similarity transformation.
The pure translational component of this similarity transformation.
The pure rotational component of this similarity transformation.
The pure scaling component of this similarity transformation.
Applies this transformation’s pure translational part to a point.
Applies this transformation’s pure rotational part to a point.
Applies this transformation’s pure scaling part to a point.
Applies this transformation’s pure rotational part to a vector.
Applies this transformation’s pure scaling part to a vector.
Applies this transformation inverse’s pure translational part to a point.
Applies this transformation inverse’s pure rotational part to a point.
Applies this transformation inverse’s pure scaling part to a point.
Applies this transformation inverse’s pure rotational part to a vector.
Applies this transformation inverse’s pure scaling part to a vector.
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
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
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
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
Applies this group’s action on a point from the euclidean space.
Applies this group’s action on a vector from the euclidean space. Read more
Returns the two_sided_inverse of self, relative to the operator O. Read more
In-place inversion of self, relative to the operator O. 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.
The inverse of UlpsEq::ulps_eq.
Calls zeroed. Read more

Auto Trait Implementations§

Blanket Implementations§

Gets the TypeId of self. Read more
The archived version of the pointer metadata for this type.
Converts some archived metadata to the pointer metadata for itself.
The archived counterpart of this type. Unlike Archive, it may be unsized. Read more
The resolver for the metadata of this type. Read more
Creates the archived version of the metadata for this value at the given position and writes it to the given output. Read more
Resolves a relative pointer to this value with the given from and to and writes it to the given output. Read more
Immutably borrows from an owned value. Read more
Mutably borrows from an owned value. Read more
Self must have the same layout as the specified Bits except for the possible invalid bit patterns being checked during is_valid_bit_pattern.
If this function returns true, then it must be valid to reinterpret bits as &Self.
Deserializes using the given deserializer

Returns the argument unchanged.

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

Gets the layout of the type.
The alignment of pointer.
The type for initializers.
Initializes a with the given initializer. Read more
Dereferences the given pointer. Read more
Mutably dereferences the given pointer. Read more
Drops the object pointed to by the given pointer. Read more
The type for metadata in pointers and references to Self.
Should always be Self
Writes the object and returns the position of the archived type.
Serializes the metadata for the given type.
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.
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.
The resulting type after obtaining ownership.
Creates owned data from borrowed data, usually by cloning. Read more
Uses borrowed data to replace owned data, usually by cloning. Read more
Converts the given value to a String. Read more
The type returned in the event of a conversion error.
Performs the conversion.
The type returned in the event of a conversion error.
Performs the conversion.