Type Definition nalgebra::geometry::UnitQuaternion [−][src]
pub type UnitQuaternion<T> = Unit<Quaternion<T>>;
Expand description
A unit quaternions. May be used to represent a rotation.
Implementations
The rotation angle in [0; pi] of this unit quaternion.
Example
let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let rot = UnitQuaternion::from_axis_angle(&axis, 1.78);
assert_eq!(rot.angle(), 1.78);
The underlying quaternion.
Same as self.as_ref()
.
Example
let axis = UnitQuaternion::identity();
assert_eq!(*axis.quaternion(), Quaternion::new(1.0, 0.0, 0.0, 0.0));
Compute the conjugate of this unit quaternion.
Example
let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let rot = UnitQuaternion::from_axis_angle(&axis, 1.78);
let conj = rot.conjugate();
assert_eq!(conj, UnitQuaternion::from_axis_angle(&-axis, 1.78));
Inverts this quaternion if it is not zero.
Example
let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let rot = UnitQuaternion::from_axis_angle(&axis, 1.78);
let inv = rot.inverse();
assert_eq!(rot * inv, UnitQuaternion::identity());
assert_eq!(inv * rot, UnitQuaternion::identity());
The rotation angle needed to make self
and other
coincide.
Example
let rot1 = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 1.0);
let rot2 = UnitQuaternion::from_axis_angle(&Vector3::x_axis(), 0.1);
assert_relative_eq!(rot1.angle_to(&rot2), 1.0045657, epsilon = 1.0e-6);
The unit quaternion needed to make self
and other
coincide.
The result is such that: self.rotation_to(other) * self == other
.
Example
let rot1 = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 1.0);
let rot2 = UnitQuaternion::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);
Linear interpolation between two unit quaternions.
The result is not normalized.
Example
let q1 = UnitQuaternion::new_normalize(Quaternion::new(1.0, 0.0, 0.0, 0.0));
let q2 = UnitQuaternion::new_normalize(Quaternion::new(0.0, 1.0, 0.0, 0.0));
assert_eq!(q1.lerp(&q2, 0.1), Quaternion::new(0.9, 0.1, 0.0, 0.0));
Normalized linear interpolation between two unit quaternions.
This is the same as self.lerp
except that the result is normalized.
Example
let q1 = UnitQuaternion::new_normalize(Quaternion::new(1.0, 0.0, 0.0, 0.0));
let q2 = UnitQuaternion::new_normalize(Quaternion::new(0.0, 1.0, 0.0, 0.0));
assert_eq!(q1.nlerp(&q2, 0.1), UnitQuaternion::new_normalize(Quaternion::new(0.9, 0.1, 0.0, 0.0)));
Spherical linear interpolation between two unit quaternions.
Panics if the angle between both quaternion is 180 degrees (in which case the interpolation
is not well-defined). Use .try_slerp
instead to avoid the panic.
Examples:
let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = UnitQuaternion::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 unit quaternions or returns None
if both quaternions are approximately 180 degrees apart (in which case the interpolation is
not well-defined).
Arguments
self
: the first quaternion to interpolate from.other
: the second quaternion 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 quaternion must be to returnNone
.
Compute the conjugate of this unit quaternion in-place.
Inverts this quaternion if it is not zero.
Example
let axisangle = Vector3::new(0.1, 0.2, 0.3);
let mut rot = UnitQuaternion::new(axisangle);
rot.inverse_mut();
assert_relative_eq!(rot * UnitQuaternion::new(axisangle), UnitQuaternion::identity());
assert_relative_eq!(UnitQuaternion::new(axisangle) * rot, UnitQuaternion::identity());
The rotation axis of this unit quaternion or None
if the rotation is zero.
Example
let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let angle = 1.2;
let rot = UnitQuaternion::from_axis_angle(&axis, angle);
assert_eq!(rot.axis(), Some(axis));
// Case with a zero angle.
let rot = UnitQuaternion::from_axis_angle(&axis, 0.0);
assert!(rot.axis().is_none());
The rotation axis of this unit quaternion multiplied by the rotation angle.
Example
let axisangle = Vector3::new(0.1, 0.2, 0.3);
let rot = UnitQuaternion::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 = UnitQuaternion::from_axis_angle(&axis, angle);
assert_eq!(rot.axis_angle(), Some((axis, angle)));
// Case with a zero angle.
let rot = UnitQuaternion::from_axis_angle(&axis, 0.0);
assert!(rot.axis_angle().is_none());
Compute the exponential of a quaternion.
Note that this function yields a Quaternion<T>
because it loses the unit property.
Compute the natural logarithm of a quaternion.
Note that this function yields a Quaternion<T>
because it loses the unit property.
The vector part of the return value corresponds to the axis-angle representation (divided
by 2.0) of this unit quaternion.
Example
let axisangle = Vector3::new(0.1, 0.2, 0.3);
let q = UnitQuaternion::new(axisangle);
assert_relative_eq!(q.ln().vector().into_owned(), axisangle, epsilon = 1.0e-6);
Raise the quaternion to a given floating power.
This returns the unit quaternion that identifies a rotation with axis self.axis()
and
angle self.angle() × n
.
Example
let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let angle = 1.2;
let rot = UnitQuaternion::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 matrix from this unit quaternion.
Example
let q = UnitQuaternion::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
let rot = q.to_rotation_matrix();
let expected = Matrix3::new(0.8660254, -0.5, 0.0,
0.5, 0.8660254, 0.0,
0.0, 0.0, 1.0);
assert_relative_eq!(*rot.matrix(), expected, epsilon = 1.0e-6);
👎 Deprecated: This is renamed to use .euler_angles()
.
This is renamed to use .euler_angles()
.
Converts this unit quaternion into its equivalent Euler angles.
The angles are produced in the form (roll, pitch, yaw).
Retrieves the euler angles corresponding to this unit quaternion.
The angles are produced in the form (roll, pitch, yaw).
Example
let rot = UnitQuaternion::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);
Converts this unit quaternion into its equivalent homogeneous transformation matrix.
Example
let rot = UnitQuaternion::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_relative_eq!(rot.to_homogeneous(), expected, epsilon = 1.0e-6);
Rotate a point by this unit quaternion.
This is the same as the multiplication self * pt
.
Example
let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 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 a vector by this unit quaternion.
This is the same as the multiplication self * v
.
Example
let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 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 a point by the inverse of this unit quaternion. This may be cheaper than inverting the unit quaternion and transforming the point.
Example
let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 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 a vector by the inverse of this unit quaternion. This may be cheaper than inverting the unit quaternion and transforming the vector.
Example
let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 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 a vector by the inverse of this unit quaternion. This may be cheaper than inverting the unit quaternion and transforming the vector.
Example
let rot = UnitQuaternion::from_axis_angle(&Vector3::z_axis(), 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);
Appends to self
a rotation given in the axis-angle form, using a linearized formulation.
This is faster, but approximate, way to compute UnitQuaternion::new(axisangle) * self
.
The rotation identity.
Example
let q = UnitQuaternion::identity();
let q2 = UnitQuaternion::new(Vector3::new(1.0, 2.0, 3.0));
let v = Vector3::new_random();
let p = Point3::from(v);
assert_eq!(q * q2, q2);
assert_eq!(q2 * q, q2);
assert_eq!(q * v, v);
assert_eq!(q * p, p);
Cast the components of self
to another type.
Example
let q = UnitQuaternion::from_euler_angles(1.0f64, 2.0, 3.0);
let q2 = q.cast::<f32>();
assert_relative_eq!(q2, UnitQuaternion::from_euler_angles(1.0f32, 2.0, 3.0), epsilon = 1.0e-6);
Creates a new quaternion from a unit vector (the rotation axis) and an angle (the 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 q = UnitQuaternion::from_axis_angle(&axis, angle);
assert_eq!(q.axis().unwrap(), axis);
assert_eq!(q.angle(), angle);
assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
// A zero vector yields an identity.
assert_eq!(UnitQuaternion::from_scaled_axis(Vector3::<f32>::zeros()), UnitQuaternion::identity());
Creates a new unit quaternion from a quaternion.
The input quaternion will be normalized.
Creates a new unit quaternion from Euler angles.
The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
Example
let rot = UnitQuaternion::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);
Builds an unit quaternion 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 an unit quaternion from a rotation matrix.
Example
let axis = Vector3::y_axis();
let angle = 0.1;
let rot = Rotation3::from_axis_angle(&axis, angle);
let q = UnitQuaternion::from_rotation_matrix(&rot);
assert_relative_eq!(q.to_rotation_matrix(), rot, epsilon = 1.0e-6);
assert_relative_eq!(q.axis().unwrap(), rot.axis().unwrap(), epsilon = 1.0e-6);
assert_relative_eq!(q.angle(), rot.angle(), epsilon = 1.0e-6);
Builds an unit quaternion 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 an unit quaternion 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 toUnitQuaternion::identity()
if no other guesses come to mind.
The unit quaternion needed to make a
and b
be collinear and point toward the same
direction. Returns None
if both a
and b
are collinear and point to opposite directions, as then the
rotation desired is not unique.
Example
let a = Vector3::new(1.0, 2.0, 3.0);
let b = Vector3::new(3.0, 1.0, 2.0);
let q = UnitQuaternion::rotation_between(&a, &b).unwrap();
assert_relative_eq!(q * a, b);
assert_relative_eq!(q.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 = Vector3::new(1.0, 2.0, 3.0);
let b = Vector3::new(3.0, 1.0, 2.0);
let q2 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.2).unwrap();
let q5 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.5).unwrap();
assert_relative_eq!(q2 * q2 * q2 * q2 * q2 * a, b, epsilon = 1.0e-6);
assert_relative_eq!(q5 * q5 * a, b, epsilon = 1.0e-6);
The unit quaternion needed to make a
and b
be collinear and point toward the same
direction.
Example
let a = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let b = Unit::new_normalize(Vector3::new(3.0, 1.0, 2.0));
let q = UnitQuaternion::rotation_between(&a, &b).unwrap();
assert_relative_eq!(q * a, b);
assert_relative_eq!(q.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 = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let b = Unit::new_normalize(Vector3::new(3.0, 1.0, 2.0));
let q2 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.2).unwrap();
let q5 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.5).unwrap();
assert_relative_eq!(q2 * q2 * q2 * q2 * q2 * a, b, epsilon = 1.0e-6);
assert_relative_eq!(q5 * q5 * a, b, epsilon = 1.0e-6);
Creates an unit quaternion 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. It does not need to be normalized.
- up - The vertical direction. It does not need to be normalized.
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 q = UnitQuaternion::face_towards(&dir, &up);
assert_relative_eq!(q * 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 UnitQuaternion::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 view direction. It does not need to be normalized.
- up - A vector approximately aligned with required the vertical axis. It does not need
to be normalized. 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 q = UnitQuaternion::look_at_rh(&dir, &up);
assert_relative_eq!(q * 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 view direction. It does not need to be normalized.
- 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 q = UnitQuaternion::look_at_lh(&dir, &up);
assert_relative_eq!(q * dir.normalize(), Vector3::z());
Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.
If axisangle
has a magnitude smaller than T::default_epsilon()
, this returns the identity 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 q = UnitQuaternion::new(axisangle);
assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
// A zero vector yields an identity.
assert_eq!(UnitQuaternion::new(Vector3::<f32>::zeros()), UnitQuaternion::identity());
Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.
If axisangle
has a magnitude smaller than eps
, this returns the identity 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 q = UnitQuaternion::new_eps(axisangle, 1.0e-6);
assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
// An almost zero vector yields an identity.
assert_eq!(UnitQuaternion::new_eps(Vector3::new(1.0e-8, 1.0e-9, 1.0e-7), 1.0e-6), UnitQuaternion::identity());
Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.
If axisangle
has a magnitude smaller than T::default_epsilon()
, this returns the identity rotation.
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 q = UnitQuaternion::from_scaled_axis(axisangle);
assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
// A zero vector yields an identity.
assert_eq!(UnitQuaternion::from_scaled_axis(Vector3::<f32>::zeros()), UnitQuaternion::identity());
Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.
If axisangle
has a magnitude smaller than eps
, this returns the identity rotation.
Same as Self::new_eps(axisangle, eps)
.
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 q = UnitQuaternion::from_scaled_axis_eps(axisangle, 1.0e-6);
assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
// An almost zero vector yields an identity.
assert_eq!(UnitQuaternion::from_scaled_axis_eps(Vector3::new(1.0e-8, 1.0e-9, 1.0e-7), 1.0e-6), UnitQuaternion::identity());
Create the mean unit quaternion from a data structure implementing IntoIterator
returning unit quaternions.
The method will panic if the iterator does not return any quaternions.
Algorithm from: Oshman, Yaakov, and Avishy Carmi. “Attitude estimation from vector observations using a genetic-algorithm-embedded quaternion particle filter.” Journal of Guidance, Control, and Dynamics 29.4 (2006): 879-891.
Example
let q1 = UnitQuaternion::from_euler_angles(0.0, 0.0, 0.0);
let q2 = UnitQuaternion::from_euler_angles(-0.1, 0.0, 0.0);
let q3 = UnitQuaternion::from_euler_angles(0.1, 0.0, 0.0);
let quat_vec = vec![q1, q2, q3];
let q_mean = UnitQuaternion::mean_of(quat_vec);
let euler_angles_mean = q_mean.euler_angles();
assert_relative_eq!(euler_angles_mean.0, 0.0, epsilon = 1.0e-7)
Trait Implementations
impl<T: RealField + AbsDiffEq<Epsilon = T>> AbsDiffEq<Unit<Quaternion<T>>> for UnitQuaternion<T>
impl<T: RealField + AbsDiffEq<Epsilon = T>> AbsDiffEq<Unit<Quaternion<T>>> for UnitQuaternion<T>
type Epsilon = T
type Epsilon = T
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. Read more
The inverse of AbsDiffEq::abs_diff_eq
.
impl<T: SimdRealField> AbstractRotation<T, 3_usize> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> AbstractRotation<T, 3_usize> for UnitQuaternion<T> 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 point.
impl<'b, T: SimdRealField> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the /
operator.
impl<'a, 'b, T: SimdRealField> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the /
operator.
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> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Similarity<T, UnitQuaternion<T>, 3>
type Output = Similarity<T, UnitQuaternion<T>, 3>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'a, 'b, T: SimdRealField> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Similarity<T, UnitQuaternion<T>, 3>
type Output = Similarity<T, UnitQuaternion<T>, 3>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = UnitDualQuaternion<T>
type Output = UnitDualQuaternion<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = UnitDualQuaternion<T>
type Output = UnitDualQuaternion<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 UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a UnitQuaternion<T> 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 UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for UnitQuaternion<T> 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<Isometry<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Isometry<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the /
operator.
impl<'a, T: SimdRealField> Div<Isometry<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Isometry<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the /
operator.
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> Div<Similarity<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Similarity<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Similarity<T, UnitQuaternion<T>, 3>
type Output = Similarity<T, UnitQuaternion<T>, 3>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'a, T: SimdRealField> Div<Similarity<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Similarity<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Similarity<T, UnitQuaternion<T>, 3>
type Output = Similarity<T, UnitQuaternion<T>, 3>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = UnitDualQuaternion<T>
type Output = UnitDualQuaternion<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = UnitDualQuaternion<T>
type Output = UnitDualQuaternion<T>
The resulting type after applying the /
operator.
Performs the /
operation. Read more
impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a UnitQuaternion<T> 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 UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for UnitQuaternion<T> 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, 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
impl<'b, T: SimdRealField> DivAssign<&'b Unit<Quaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> DivAssign<&'b Unit<Quaternion<T>>> for UnitQuaternion<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
impl<T: SimdRealField> DivAssign<Unit<Quaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> DivAssign<Unit<Quaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
Performs the /=
operation. Read more
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> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
impl<'a, 'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
impl<'a, 'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Matrix<T, Const<3_usize>, Const<1_usize>, SB>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Matrix<T, Const<3_usize>, Const<1_usize>, SB>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b OPoint<T, Const<3_usize>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b OPoint<T, Const<3_usize>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b OPoint<T, Const<3_usize>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b OPoint<T, Const<3_usize>>> for 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<'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> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Similarity<T, UnitQuaternion<T>, 3>
type Output = Similarity<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, 'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Similarity<T, UnitQuaternion<T>, 3>
type Output = Similarity<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'b, T: SimdRealField> Mul<&'b Translation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Translation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, 'b, T: SimdRealField> Mul<&'b Translation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Translation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = UnitDualQuaternion<T>
type Output = UnitDualQuaternion<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = UnitDualQuaternion<T>
type Output = UnitDualQuaternion<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, 'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Unit<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Unit<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Unit<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Unit<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a UnitQuaternion<T> 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 UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for UnitQuaternion<T> 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<Isometry<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Isometry<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
impl<'a, T: SimdRealField> Mul<Isometry<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Isometry<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
impl<'a, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<OPoint<T, Const<3_usize>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<OPoint<T, Const<3_usize>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<OPoint<T, Const<3_usize>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<OPoint<T, Const<3_usize>>> for UnitQuaternion<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> Mul<Similarity<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Similarity<T, Unit<Quaternion<T>>, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Similarity<T, UnitQuaternion<T>, 3>
type Output = Similarity<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, T: SimdRealField> Mul<Similarity<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Similarity<T, Unit<Quaternion<T>>, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Similarity<T, UnitQuaternion<T>, 3>
type Output = Similarity<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<T: SimdRealField> Mul<Translation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Translation<T, 3_usize>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, T: SimdRealField> Mul<Translation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Translation<T, 3_usize>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = Isometry<T, UnitQuaternion<T>, 3>
type Output = Isometry<T, UnitQuaternion<T>, 3>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = UnitDualQuaternion<T>
type Output = UnitDualQuaternion<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
type Output = UnitDualQuaternion<T>
type Output = UnitDualQuaternion<T>
The resulting type after applying the *
operator.
Performs the *
operation. Read more
impl<'a, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Unit<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Unit<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Unit<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Unit<Matrix<T, Const<{ typenum::$D::USIZE }>, Const<1_usize>, SB>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a UnitQuaternion<T> 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 UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for UnitQuaternion<T> 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, 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
impl<'b, T: SimdRealField> MulAssign<&'b Unit<Quaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> MulAssign<&'b Unit<Quaternion<T>>> for UnitQuaternion<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
impl<T: SimdRealField> MulAssign<Unit<Quaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
impl<T: SimdRealField> MulAssign<Unit<Quaternion<T>>> for UnitQuaternion<T> where
T::Element: SimdRealField,
Performs the *=
operation. Read more
impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq<Unit<Quaternion<T>>> for UnitQuaternion<T>
impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq<Unit<Quaternion<T>>> for UnitQuaternion<T>
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
.
type Element = UnitQuaternion<T::Element>
type Element = UnitQuaternion<T::Element>
The type of the elements of each lane of this SIMD value.
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
impl<T1, T2, R> SubsetOf<Isometry<T2, R, 3_usize>> for UnitQuaternion<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, 3> + SupersetOf<Self>,
impl<T1, T2, R> SubsetOf<Isometry<T2, R, 3_usize>> for UnitQuaternion<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, 3> + 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: RealField, T2: RealField + SupersetOf<T1>> SubsetOf<Matrix<T2, Const<{ typenum::$D::USIZE }>, Const<{ typenum::$D::USIZE }>, ArrayStorage<T2, 4_usize, 4_usize>>> for UnitQuaternion<T1>
impl<T1: RealField, T2: RealField + SupersetOf<T1>> SubsetOf<Matrix<T2, Const<{ typenum::$D::USIZE }>, Const<{ typenum::$D::USIZE }>, ArrayStorage<T2, 4_usize, 4_usize>>> for UnitQuaternion<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
impl<T1, T2, R> SubsetOf<Similarity<T2, R, 3_usize>> for UnitQuaternion<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, 3> + SupersetOf<Self>,
impl<T1, T2, R> SubsetOf<Similarity<T2, R, 3_usize>> for UnitQuaternion<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, 3> + 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> SubsetOf<Transform<T2, C, 3_usize>> for UnitQuaternion<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
C: SuperTCategoryOf<TAffine>,
impl<T1, T2, C> SubsetOf<Transform<T2, C, 3_usize>> for UnitQuaternion<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
C: SuperTCategoryOf<TAffine>,
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<Unit<DualQuaternion<T2>>> for UnitQuaternion<T1> where
T1: RealField,
T2: RealField + SupersetOf<T1>,
impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> 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
impl<T1, T2> SubsetOf<Unit<Quaternion<T2>>> for UnitQuaternion<T1> where
T1: Scalar,
T2: Scalar + SupersetOf<T1>,
impl<T1, T2> SubsetOf<Unit<Quaternion<T2>>> for UnitQuaternion<T1> where
T1: Scalar,
T2: Scalar + 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 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.