Struct na::base::Unit

#[repr(transparent)]
pub struct Unit<T> { /* fields omitted */ }

A wrapper that ensures the underlying algebraic entity has a unit norm.

It is likely that the only piece of documentation that you need in this page are:

• The construction with normalization
• Data extraction and construction without normalization
• Interpolation between two unit vectors

All the other impl blocks you will see in this page are about UnitComplex and UnitQuaternion; both built on top of Unit. If you are interested in their documentation, read their dedicated pages directly.

Implementations

impl<T> Unit<T> where
    T: Normed, 

Construction with normalization

pub fn new_normalize(value: T) -> Unit<T>

Normalize the given vector and return it wrapped on a Unit structure.

pub fn try_new(value: T, min_norm: <T as Normed>::Norm) -> Option<Unit<T>> where
    <T as Normed>::Norm: RealField, 

Attempts to normalize the given vector and return it wrapped on a Unit structure.

Returns None if the norm was smaller or equal to min_norm.

pub fn new_and_get(value: T) -> (Unit<T>, <T as Normed>::Norm)

Normalize the given vector and return it wrapped on a Unit structure and its norm.

pub fn try_new_and_get(
    value: T,
    min_norm: <T as Normed>::Norm
) -> Option<(Unit<T>, <T as Normed>::Norm)> where
    <T as Normed>::Norm: RealField, 

Normalize the given vector and return it wrapped on a Unit structure and its norm.

Returns None if the norm was smaller or equal to min_norm.

pub fn renormalize(&mut self) -> <T as Normed>::Norm

Normalizes this vector again. This is useful when repeated computations might cause a drift in the norm because of float inaccuracies.

Returns the norm before re-normalization. See .renormalize_fast for a faster alternative that may be slightly less accurate if self drifted significantly from having a unit length.

pub fn renormalize_fast(&mut self)

Normalizes this vector again using a first-order Taylor approximation. This is useful when repeated computations might cause a drift in the norm because of float inaccuracies.

impl<T> Unit<T>

Data extraction and construction without normalization

pub fn new_unchecked(value: T) -> Unit<T>

Wraps the given value, assuming it is already normalized.

pub fn from_ref_unchecked(value: &'a T) -> &'a Unit<T>

Wraps the given reference, assuming it is already normalized.

pub fn into_inner(self) -> T

Retrieves the underlying value.

pub fn unwrap(self) -> T

👎 Deprecated:

use .into_inner() instead

Retrieves the underlying value. Deprecated: use Unit::into_inner instead.

pub fn as_mut_unchecked(&mut self) -> &mut T

Returns a mutable reference to the underlying value. This is _unchecked because modifying the underlying value in such a way that it no longer has unit length may lead to unexpected results.

impl<N, D, S> Unit<Matrix<N, D, U1, S>> where
    D: Dim,
    N: RealField,
    S: Storage<N, D, U1>, 

Interpolation between two unit vectors

pub fn slerp<S2>(
    &self,
    rhs: &Unit<Matrix<N, D, U1, S2>>,
    t: N
) -> Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> where
    S2: Storage<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>, 

Computes the spherical linear interpolation between two unit vectors.

Examples:

let v1 = Unit::new_normalize(Vector2::new(1.0, 2.0));
let v2 = Unit::new_normalize(Vector2::new(2.0, -3.0));

let v = v1.slerp(&v2, 1.0);

assert_eq!(v, v2);

pub fn try_slerp<S2>(
    &self,
    rhs: &Unit<Matrix<N, D, U1, S2>>,
    t: N,
    epsilon: N
) -> Option<Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> where
    S2: Storage<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>, 

Computes the spherical linear interpolation between two unit vectors.

Returns None if the two vectors are almost collinear and with opposite direction (in this case, there is an infinity of possible results).

impl<N> Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn angle(&self) -> N

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);

pub fn quaternion(&self) -> &Quaternion<N>

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));

#[must_use = "Did you mean to use conjugate_mut()?"]

pub fn conjugate(&self) -> Unit<Quaternion<N>>

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));

#[must_use = "Did you mean to use inverse_mut()?"]

pub fn inverse(&self) -> Unit<Quaternion<N>>

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());

pub fn angle_to(&self, other: &Unit<Quaternion<N>>) -> N

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);

pub fn rotation_to(&self, other: &Unit<Quaternion<N>>) -> Unit<Quaternion<N>>

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);

pub fn lerp(&self, other: &Unit<Quaternion<N>>, t: N) -> Quaternion<N>

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));

pub fn nlerp(&self, other: &Unit<Quaternion<N>>, t: N) -> Unit<Quaternion<N>>

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)));

pub fn slerp(&self, other: &Unit<Quaternion<N>>, t: N) -> Unit<Quaternion<N>> where
    N: RealField, 

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));

pub fn try_slerp(
    &self,
    other: &Unit<Quaternion<N>>,
    t: N,
    epsilon: N
) -> Option<Unit<Quaternion<N>>> where
    N: RealField, 

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 return None.

pub fn conjugate_mut(&mut self)

Compute the conjugate of this unit quaternion in-place.

pub fn inverse_mut(&mut self)

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());

pub fn axis(
    &self
) -> Option<Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>> where
    N: RealField, 

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());

pub fn scaled_axis(
    &self
) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> where
    N: RealField, 

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);

pub fn axis_angle(
    &self
) -> Option<(Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>, N)> where
    N: RealField, 

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());

pub fn exp(&self) -> Quaternion<N>

Compute the exponential of a quaternion.

Note that this function yields a Quaternion<N> because it loses the unit property.

pub fn ln(&self) -> Quaternion<N> where
    N: RealField, 

Compute the natural logarithm of a quaternion.

Note that this function yields a Quaternion<N> 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);

pub fn powf(&self, n: N) -> Unit<Quaternion<N>> where
    N: RealField, 

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);

pub fn to_rotation_matrix(&self) -> Rotation<N, U3>

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);

pub fn to_euler_angles(&self) -> (N, N, N) where
    N: RealField, 

👎 Deprecated:

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).

pub fn euler_angles(&self) -> (N, N, N) where
    N: RealField, 

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);

pub fn to_homogeneous(
    &self
) -> Matrix<N, U4, U4, <DefaultAllocator as Allocator<N, U4, U4>>::Buffer>

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);

pub fn transform_point(&self, pt: &Point<N, U3>) -> Point<N, U3>

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);

pub fn transform_vector(
    &self,
    v: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>

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);

pub fn inverse_transform_point(&self, pt: &Point<N, U3>) -> Point<N, U3>

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);

pub fn inverse_transform_vector(
    &self,
    v: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>

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);

pub fn inverse_transform_unit_vector(
    &self,
    v: &Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>
) -> Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>

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);

impl<N> Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn identity() -> Unit<Quaternion<N>>

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);

pub fn from_axis_angle<SB>(
    axis: &Unit<Matrix<N, U3, U1, SB>>,
    angle: N
) -> Unit<Quaternion<N>> where
    SB: Storage<N, U3, U1>, 

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());

pub fn from_quaternion(q: Quaternion<N>) -> Unit<Quaternion<N>>

Creates a new unit quaternion from a quaternion.

The input quaternion will be normalized.

pub fn from_euler_angles(roll: N, pitch: N, yaw: N) -> Unit<Quaternion<N>>

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);

pub fn from_rotation_matrix(rotmat: &Rotation<N, U3>) -> Unit<Quaternion<N>>

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);

pub fn from_matrix(
    m: &Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer>
) -> Unit<Quaternion<N>> where
    N: RealField, 

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: &Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer>,
    eps: N,
    max_iter: usize,
    guess: Unit<Quaternion<N>>
) -> Unit<Quaternion<N>> where
    N: 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 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 UnitQuaternion::identity() if no other guesses come to mind.

pub fn rotation_between<SB, SC>(
    a: &Matrix<N, U3, U1, SB>,
    b: &Matrix<N, U3, U1, SC>
) -> Option<Unit<Quaternion<N>>> where
    N: RealField,
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 

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);

pub fn scaled_rotation_between<SB, SC>(
    a: &Matrix<N, U3, U1, SB>,
    b: &Matrix<N, U3, U1, SC>,
    s: N
) -> Option<Unit<Quaternion<N>>> where
    N: RealField,
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 

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);

pub fn rotation_between_axis<SB, SC>(
    a: &Unit<Matrix<N, U3, U1, SB>>,
    b: &Unit<Matrix<N, U3, U1, SC>>
) -> Option<Unit<Quaternion<N>>> where
    N: RealField,
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 

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);

pub fn scaled_rotation_between_axis<SB, SC>(
    na: &Unit<Matrix<N, U3, U1, SB>>,
    nb: &Unit<Matrix<N, U3, U1, SC>>,
    s: N
) -> Option<Unit<Quaternion<N>>> where
    N: RealField,
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 

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);

pub fn face_towards<SB, SC>(
    dir: &Matrix<N, U3, U1, SB>,
    up: &Matrix<N, U3, U1, SC>
) -> Unit<Quaternion<N>> where
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 

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: &Matrix<N, U3, U1, SB>,
    up: &Matrix<N, U3, U1, SC>
) -> Unit<Quaternion<N>> where
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 

👎 Deprecated:

renamed to face_towards

Deprecated: Use [UnitQuaternion::face_towards] instead.

pub fn look_at_rh<SB, SC>(
    dir: &Matrix<N, U3, U1, SB>,
    up: &Matrix<N, U3, U1, SC>
) -> Unit<Quaternion<N>> where
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 

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());

pub fn look_at_lh<SB, SC>(
    dir: &Matrix<N, U3, U1, SB>,
    up: &Matrix<N, U3, U1, SC>
) -> Unit<Quaternion<N>> where
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 

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());

pub fn new<SB>(axisangle: Matrix<N, U3, U1, SB>) -> Unit<Quaternion<N>> where
    SB: Storage<N, U3, U1>, 

Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.

If axisangle has a magnitude smaller than N::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());

pub fn new_eps<SB>(
    axisangle: Matrix<N, U3, U1, SB>,
    eps: N
) -> Unit<Quaternion<N>> where
    SB: Storage<N, U3, U1>, 

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());

pub fn from_scaled_axis<SB>(
    axisangle: Matrix<N, U3, U1, SB>
) -> Unit<Quaternion<N>> where
    SB: Storage<N, U3, U1>, 

Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.

If axisangle has a magnitude smaller than N::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());

pub fn from_scaled_axis_eps<SB>(
    axisangle: Matrix<N, U3, U1, SB>,
    eps: N
) -> Unit<Quaternion<N>> where
    SB: Storage<N, U3, U1>, 

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());

pub fn mean_of(
    unit_quaternions: impl IntoIterator<Item = Unit<Quaternion<N>>>
) -> Unit<Quaternion<N>> where
    N: RealField, 

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)

impl<N> Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

Angle extraction

pub fn angle(&self) -> N

The rotation angle in ]-pi; pi] of this unit complex number.

Example

let rot = UnitComplex::new(1.78);
assert_eq!(rot.angle(), 1.78);

pub fn sin_angle(&self) -> N

The sine of the rotation angle.

Example

let angle = 1.78f32;
let rot = UnitComplex::new(angle);
assert_eq!(rot.sin_angle(), angle.sin());

pub fn cos_angle(&self) -> N

The cosine of the rotation angle.

Example

let angle = 1.78f32;
let rot = UnitComplex::new(angle);
assert_eq!(rot.cos_angle(),angle.cos());

pub fn scaled_axis(
    &self
) -> Matrix<N, U1, U1, <DefaultAllocator as Allocator<N, U1, U1>>::Buffer>

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.

pub fn axis_angle(
    &self
) -> Option<(Unit<Matrix<N, U1, U1, <DefaultAllocator as Allocator<N, U1, U1>>::Buffer>>, N)> where
    N: RealField, 

The rotation axis and angle in ]0, pi] of this complex number.

This is generally used in the context of generic programming. Using the .angle() method instead is more common. Returns None if the angle is zero.

pub fn angle_to(&self, other: &Unit<Complex<N>>) -> N

The rotation angle needed to make self and other coincide.

Example

let rot1 = UnitComplex::new(0.1);
let rot2 = UnitComplex::new(1.7);
assert_relative_eq!(rot1.angle_to(&rot2), 1.6);

impl<N> Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

Conjugation and inversion

#[must_use = "Did you mean to use conjugate_mut()?"]

pub fn conjugate(&self) -> Unit<Complex<N>>

Compute the conjugate of this unit complex number.

Example

let rot = UnitComplex::new(1.78);
let conj = rot.conjugate();
assert_eq!(rot.complex().im, -conj.complex().im);
assert_eq!(rot.complex().re, conj.complex().re);

#[must_use = "Did you mean to use inverse_mut()?"]

pub fn inverse(&self) -> Unit<Complex<N>>

Inverts this complex number if it is not zero.

Example

let rot = UnitComplex::new(1.2);
let inv = rot.inverse();
assert_relative_eq!(rot * inv, UnitComplex::identity(), epsilon = 1.0e-6);
assert_relative_eq!(inv * rot, UnitComplex::identity(), epsilon = 1.0e-6);

pub fn conjugate_mut(&mut self)

Compute in-place the conjugate of this unit complex number.

Example

let angle = 1.7;
let rot = UnitComplex::new(angle);
let mut conj = UnitComplex::new(angle);
conj.conjugate_mut();
assert_eq!(rot.complex().im, -conj.complex().im);
assert_eq!(rot.complex().re, conj.complex().re);

pub fn inverse_mut(&mut self)

Inverts in-place this unit complex number.

Example

let angle = 1.7;
let mut rot = UnitComplex::new(angle);
rot.inverse_mut();
assert_relative_eq!(rot * UnitComplex::new(angle), UnitComplex::identity());
assert_relative_eq!(UnitComplex::new(angle) * rot, UnitComplex::identity());

impl<N> Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

Conversion to a matrix

pub fn to_rotation_matrix(&self) -> Rotation<N, U2>

Builds the rotation matrix corresponding to this unit complex number.

Example

let rot = UnitComplex::new(f32::consts::FRAC_PI_6);
let expected = Rotation2::new(f32::consts::FRAC_PI_6);
assert_eq!(rot.to_rotation_matrix(), expected);

pub fn to_homogeneous(
    &self
) -> Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer>

Converts this unit complex number into its equivalent homogeneous transformation matrix.

Example

let rot = UnitComplex::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);

impl<N> Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

Transformation of a vector or a point

pub fn transform_point(&self, pt: &Point<N, U2>) -> Point<N, U2>

Rotate the given point by this unit complex number.

This is the same as the multiplication self * pt.

Example

let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
let transformed_point = rot.transform_point(&Point2::new(1.0, 2.0));
assert_relative_eq!(transformed_point, Point2::new(-2.0, 1.0), epsilon = 1.0e-6);

pub fn transform_vector(
    &self,
    v: &Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>
) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>

Rotate the given vector by this unit complex number.

This is the same as the multiplication self * v.

Example

let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
let transformed_vector = rot.transform_vector(&Vector2::new(1.0, 2.0));
assert_relative_eq!(transformed_vector, Vector2::new(-2.0, 1.0), epsilon = 1.0e-6);

pub fn inverse_transform_point(&self, pt: &Point<N, U2>) -> Point<N, U2>

Rotate the given point by the inverse of this unit complex number.

Example

let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
let transformed_point = rot.inverse_transform_point(&Point2::new(1.0, 2.0));
assert_relative_eq!(transformed_point, Point2::new(2.0, -1.0), epsilon = 1.0e-6);

pub fn inverse_transform_vector(
    &self,
    v: &Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>
) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>

Rotate the given vector by the inverse of this unit complex number.

Example

let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
let transformed_vector = rot.inverse_transform_vector(&Vector2::new(1.0, 2.0));
assert_relative_eq!(transformed_vector, Vector2::new(2.0, -1.0), epsilon = 1.0e-6);

pub fn inverse_transform_unit_vector(
    &self,
    v: &Unit<Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>>
) -> Unit<Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>>

Rotate the given vector by the inverse of this unit complex number.

Example

let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
let transformed_vector = rot.inverse_transform_unit_vector(&Vector2::x_axis());
assert_relative_eq!(transformed_vector, -Vector2::y_axis(), epsilon = 1.0e-6);

impl<N> Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

Interpolation

pub fn slerp(&self, other: &Unit<Complex<N>>, t: N) -> Unit<Complex<N>>

Spherical linear interpolation between two rotations represented as unit complex numbers.

Examples:

let rot1 = UnitComplex::new(std::f32::consts::FRAC_PI_4);
let rot2 = UnitComplex::new(-std::f32::consts::PI);

let rot = rot1.slerp(&rot2, 1.0 / 3.0);

assert_relative_eq!(rot.angle(), std::f32::consts::FRAC_PI_2);

impl<N> Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

Identity

pub fn identity() -> Unit<Complex<N>>

The unit complex number multiplicative identity.

Example

let rot1 = UnitComplex::identity();
let rot2 = UnitComplex::new(1.7);

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

impl<N> Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

Construction from a 2D rotation angle

pub fn new(angle: N) -> Unit<Complex<N>>

Builds the unit complex number corresponding to the rotation with the given angle.

Example

let rot = UnitComplex::new(f32::consts::FRAC_PI_2);

assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));

pub fn from_angle(angle: N) -> Unit<Complex<N>>

Builds the unit complex number corresponding to the rotation with the angle.

Same as Self::new(angle).

Example

let rot = UnitComplex::from_angle(f32::consts::FRAC_PI_2);

assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));

pub fn from_cos_sin_unchecked(cos: N, sin: N) -> Unit<Complex<N>>

Builds the unit complex number from the sinus and cosinus of the rotation angle.

The input values are not checked to actually be cosines and sine of the same value. Is is generally preferable to use the ::new(angle) constructor instead.

Example

let angle = f32::consts::FRAC_PI_2;
let rot = UnitComplex::from_cos_sin_unchecked(angle.cos(), angle.sin());

assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));

pub fn from_scaled_axis<SB>(
    axisangle: Matrix<N, U1, U1, SB>
) -> Unit<Complex<N>> where
    SB: Storage<N, U1, U1>, 

Builds a unit complex rotation from an angle in radian wrapped in a 1-dimensional vector.

This is generally used in the context of generic programming. Using the ::new(angle) method instead is more common.

impl<N> Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

Construction from an existing 2D matrix or complex number

pub fn complex(&self) -> &Complex<N>

The underlying complex number.

Same as self.as_ref().

Example

let angle = 1.78f32;
let rot = UnitComplex::new(angle);
assert_eq!(*rot.complex(), Complex::new(angle.cos(), angle.sin()));

pub fn from_complex(q: Complex<N>) -> Unit<Complex<N>>

Creates a new unit complex number from a complex number.

The input complex number will be normalized.

pub fn from_complex_and_get(q: Complex<N>) -> (Unit<Complex<N>>, N)

Creates a new unit complex number from a complex number.

The input complex number will be normalized. Returns the norm of the complex number as well.

pub fn from_rotation_matrix(rotmat: &Rotation<N, U2>) -> Unit<Complex<N>>

Builds the unit complex number from the corresponding 2D rotation matrix.

Example

let rot = Rotation2::new(1.7);
let complex = UnitComplex::from_rotation_matrix(&rot);
assert_eq!(complex, UnitComplex::new(1.7));

pub fn from_matrix(
    m: &Matrix<N, U2, U2, <DefaultAllocator as Allocator<N, U2, U2>>::Buffer>
) -> Unit<Complex<N>> where
    N: RealField, 

Builds an unit complex 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: &Matrix<N, U2, U2, <DefaultAllocator as Allocator<N, U2, U2>>::Buffer>,
    eps: N,
    max_iter: usize,
    guess: Unit<Complex<N>>
) -> Unit<Complex<N>> where
    N: RealField, 

Builds an unit complex 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 UnitQuaternion::identity() if no other guesses come to mind.

pub fn rotation_to(&self, other: &Unit<Complex<N>>) -> Unit<Complex<N>>

The unit complex number needed to make self and other coincide.

The result is such that: self.rotation_to(other) * self == other.

Example

let rot1 = UnitComplex::new(0.1);
let rot2 = UnitComplex::new(1.7);
let rot_to = rot1.rotation_to(&rot2);

assert_relative_eq!(rot_to * rot1, rot2);
assert_relative_eq!(rot_to.inverse() * rot2, rot1);

pub fn powf(&self, n: N) -> Unit<Complex<N>>

Raise this unit complex number to a given floating power.

This returns the unit complex number that identifies a rotation angle equal to self.angle() × n.

Example

let rot = UnitComplex::new(0.78);
let pow = rot.powf(2.0);
assert_relative_eq!(pow.angle(), 2.0 * 0.78);

impl<N> Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

Construction from two vectors

pub fn rotation_between<SB, SC>(
    a: &Matrix<N, U2, U1, SB>,
    b: &Matrix<N, U2, U1, SC>
) -> Unit<Complex<N>> where
    N: RealField,
    SB: Storage<N, U2, U1>,
    SC: Storage<N, U2, U1>, 

The unit complex needed to make a and b be collinear and point toward the same direction.

Example

let a = Vector2::new(1.0, 2.0);
let b = Vector2::new(2.0, 1.0);
let rot = UnitComplex::rotation_between(&a, &b);
assert_relative_eq!(rot * a, b);
assert_relative_eq!(rot.inverse() * b, a);

pub fn scaled_rotation_between<SB, SC>(
    a: &Matrix<N, U2, U1, SB>,
    b: &Matrix<N, U2, U1, SC>,
    s: N
) -> Unit<Complex<N>> where
    N: RealField,
    SB: Storage<N, U2, U1>,
    SC: Storage<N, U2, U1>, 

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 = UnitComplex::scaled_rotation_between(&a, &b, 0.2);
let rot5 = UnitComplex::scaled_rotation_between(&a, &b, 0.5);
assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);

pub fn rotation_between_axis<SB, SC>(
    a: &Unit<Matrix<N, U2, U1, SB>>,
    b: &Unit<Matrix<N, U2, U1, SC>>
) -> Unit<Complex<N>> where
    SB: Storage<N, U2, U1>,
    SC: Storage<N, U2, U1>, 

The unit complex needed to make a and b be collinear and point toward the same direction.

Example

let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
let rot = UnitComplex::rotation_between_axis(&a, &b);
assert_relative_eq!(rot * a, b);
assert_relative_eq!(rot.inverse() * b, a);

pub fn scaled_rotation_between_axis<SB, SC>(
    na: &Unit<Matrix<N, U2, U1, SB>>,
    nb: &Unit<Matrix<N, U2, U1, SC>>,
    s: N
) -> Unit<Complex<N>> where
    SB: Storage<N, U2, U1>,
    SC: Storage<N, U2, U1>, 

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(Vector2::new(1.0, 2.0));
let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
let rot2 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.2);
let rot5 = UnitComplex::scaled_rotation_between_axis(&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);

Trait Implementations

impl<N> AbsDiffEq<Unit<Complex<N>>> for Unit<Complex<N>> where
    N: RealField, 

type Epsilon = N

Used for specifying relative comparisons.

pub fn default_epsilon(
) -> <Unit<Complex<N>> as AbsDiffEq<Unit<Complex<N>>>>::Epsilon

The default tolerance to use when testing values that are close together.

pub fn abs_diff_eq(
    &self,
    other: &Unit<Complex<N>>,
    epsilon: <Unit<Complex<N>> as AbsDiffEq<Unit<Complex<N>>>>::Epsilon
) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

pub fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<N, R, C, S> AbsDiffEq<Unit<Matrix<N, R, C, S>>> for Unit<Matrix<N, R, C, S>> where
    C: Dim,
    N: Scalar + AbsDiffEq<N>,
    S: Storage<N, R, C>,
    R: Dim,
    <N as AbsDiffEq<N>>::Epsilon: Copy, 

type Epsilon = <N as AbsDiffEq<N>>::Epsilon

Used for specifying relative comparisons.

pub fn default_epsilon(
) -> <Unit<Matrix<N, R, C, S>> as AbsDiffEq<Unit<Matrix<N, R, C, S>>>>::Epsilon

The default tolerance to use when testing values that are close together.

pub fn abs_diff_eq(
    &self,
    other: &Unit<Matrix<N, R, C, S>>,
    epsilon: <Unit<Matrix<N, R, C, S>> as AbsDiffEq<Unit<Matrix<N, R, C, S>>>>::Epsilon
) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

pub fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<N> AbsDiffEq<Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: RealField<Epsilon = N> + AbsDiffEq<N>, 

type Epsilon = N

Used for specifying relative comparisons.

pub fn default_epsilon(
) -> <Unit<Quaternion<N>> as AbsDiffEq<Unit<Quaternion<N>>>>::Epsilon

The default tolerance to use when testing values that are close together.

pub fn abs_diff_eq(
    &self,
    other: &Unit<Quaternion<N>>,
    epsilon: <Unit<Quaternion<N>> as AbsDiffEq<Unit<Quaternion<N>>>>::Epsilon
) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

pub fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<N> AbstractRotation<N, U2> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn identity() -> Unit<Complex<N>>

The rotation identity.

pub fn inverse(&self) -> Unit<Complex<N>>

The rotation inverse.

pub fn inverse_mut(&mut self)

Change self to its inverse.

pub fn transform_vector(
    &self,
    v: &Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>
) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>

Apply the rotation to the given vector.

pub fn transform_point(&self, p: &Point<N, U2>) -> Point<N, U2>

Apply the rotation to the given point.

pub fn inverse_transform_vector(
    &self,
    v: &Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>
) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>

Apply the inverse rotation to the given vector.

pub fn inverse_transform_point(&self, p: &Point<N, U2>) -> Point<N, U2>

Apply the inverse rotation to the given point.

pub fn inverse_transform_unit_vector(
    &self,
    v: &Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>
) -> Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> where
    DefaultAllocator: Allocator<N, D, U1>, 

Apply the inverse rotation to the given unit vector.

impl<N> AbstractRotation<N, U3> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn identity() -> Unit<Quaternion<N>>

The rotation identity.

pub fn inverse(&self) -> Unit<Quaternion<N>>

The rotation inverse.

pub fn inverse_mut(&mut self)

Change self to its inverse.

pub fn transform_vector(
    &self,
    v: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>

Apply the rotation to the given vector.

pub fn transform_point(&self, p: &Point<N, U3>) -> Point<N, U3>

Apply the rotation to the given point.

pub fn inverse_transform_vector(
    &self,
    v: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>

Apply the inverse rotation to the given vector.

pub fn inverse_transform_point(&self, p: &Point<N, U3>) -> Point<N, U3>

Apply the inverse rotation to the given point.

pub fn inverse_transform_unit_vector(
    &self,
    v: &Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>
) -> Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> where
    DefaultAllocator: Allocator<N, D, U1>, 

Apply the inverse rotation to the given unit vector.

impl<T> AsRef<T> for Unit<T>

pub fn as_ref(&self) -> &T

Performs the conversion.

impl<T> Clone for Unit<T> where
    T: Clone, 

pub fn clone(&self) -> Unit<T>

Returns a copy of the value.

pub fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T> Debug for Unit<T> where
    T: Debug, 

pub fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<N> Default for Unit<Quaternion<N>> where
    N: RealField, 

pub fn default() -> Unit<Quaternion<N>>

Returns the “default value” for a type.

impl<T> Deref for Unit<T>

type Target = T

The resulting type after dereferencing.

pub fn deref(&self) -> &T

Dereferences the value.

impl<'de, T> Deserialize<'de> for Unit<T> where
    T: Deserialize<'de>, 

pub fn deserialize<D>(
    deserializer: D
) -> Result<Unit<T>, <D as Deserializer<'de>>::Error> where
    D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<N> Display for Unit<Complex<N>> where
    N: RealField + Display, 

pub fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<N> Display for Unit<Quaternion<N>> where
    N: RealField + Display, 

pub fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<'b, N> Div<&'b Isometry<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    right: &'b Isometry<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Div<&'b Isometry<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Isometry<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    right: &'b Isometry<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Div<&'b Isometry<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Rotation<N, U2>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Rotation<N, U2>
) -> <&'a Unit<Complex<N>> as Div<&'b Rotation<N, U2>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Rotation<N, U2>
) -> <Unit<Complex<N>> as Div<&'b Rotation<N, U2>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Rotation<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Rotation<N, U3>
) -> <&'a Unit<Quaternion<N>> as Div<&'b Rotation<N, U3>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Rotation<N, U3>
) -> <Unit<Quaternion<N>> as Div<&'b Rotation<N, U3>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Similarity<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    right: &'b Similarity<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Div<&'b Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Similarity<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    right: &'b Similarity<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Div<&'b Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<'a, 'b, N, C> Div<&'b Transform<N, U3, C>> for &'a Unit<Quaternion<N>> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U4>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Transform<N, U3, C>
) -> <&'a Unit<Quaternion<N>> as Div<&'b Transform<N, U3, C>>>::Output

Performs the / operation.

impl<'b, N, C> Div<&'b Transform<N, U3, C>> for Unit<Quaternion<N>> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U4>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Transform<N, U3, C>
) -> <Unit<Quaternion<N>> as Div<&'b Transform<N, U3, C>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <Rotation<N, U2> as Div<&'b Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <Isometry<N, U2, Unit<Complex<N>>> as Div<&'b Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Unit<Complex<N>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <Unit<Complex<N>> as Div<&'b Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Unit<Complex<N>>> for Similarity<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <Similarity<N, U2, Unit<Complex<N>>> as Div<&'b Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Unit<Complex<N>>> for &'a Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <&'a Isometry<N, U2, Unit<Complex<N>>> as Div<&'b Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Unit<Complex<N>>> for &'a Similarity<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <&'a Similarity<N, U2, Unit<Complex<N>>> as Div<&'b Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Unit<Complex<N>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <&'a Unit<Complex<N>> as Div<&'b Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Unit<Complex<N>>> for &'a Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <&'a Rotation<N, U2> as Div<&'b Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Isometry<N, U3, Unit<Quaternion<N>>> as Div<&'b Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'b, N, C> Div<&'b Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Transform<N, U3, C> as Div<&'b Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'a, 'b, N, C> Div<&'b Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Transform<N, U3, C> as Div<&'b Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Unit<Quaternion<N>> as Div<&'b Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Unit<Quaternion<N>>> for &'a Similarity<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Similarity<N, U3, Unit<Quaternion<N>>> as Div<&'b Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Unit<Quaternion<N>>> for &'a Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Isometry<N, U3, Unit<Quaternion<N>>> as Div<&'b Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Unit<Quaternion<N>>> for Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Rotation<N, U3> as Div<&'b Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Rotation<N, U3> as Div<&'b Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Unit<Quaternion<N>>> for Similarity<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Similarity<N, U3, Unit<Quaternion<N>>> as Div<&'b Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'a, 'b, N> Div<&'b Unit<Quaternion<N>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Unit<Quaternion<N>> as Div<&'b Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<N> Div<Isometry<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    right: Isometry<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Div<Isometry<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<'a, N> Div<Isometry<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    right: Isometry<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Div<Isometry<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<N> Div<Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Rotation<N, U2>
) -> <Unit<Complex<N>> as Div<Rotation<N, U2>>>::Output

Performs the / operation.

impl<'a, N> Div<Rotation<N, U2>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Rotation<N, U2>
) -> <&'a Unit<Complex<N>> as Div<Rotation<N, U2>>>::Output

Performs the / operation.

impl<'a, N> Div<Rotation<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Rotation<N, U3>
) -> <&'a Unit<Quaternion<N>> as Div<Rotation<N, U3>>>::Output

Performs the / operation.

impl<N> Div<Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Rotation<N, U3>
) -> <Unit<Quaternion<N>> as Div<Rotation<N, U3>>>::Output

Performs the / operation.

impl<'a, N> Div<Similarity<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    right: Similarity<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Div<Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<N> Div<Similarity<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    right: Similarity<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Div<Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<'a, N, C> Div<Transform<N, U3, C>> for &'a Unit<Quaternion<N>> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U4>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Transform<N, U3, C>
) -> <&'a Unit<Quaternion<N>> as Div<Transform<N, U3, C>>>::Output

Performs the / operation.

impl<N, C> Div<Transform<N, U3, C>> for Unit<Quaternion<N>> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U4>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Transform<N, U3, C>
) -> <Unit<Quaternion<N>> as Div<Transform<N, U3, C>>>::Output

Performs the / operation.

impl<'a, N> Div<Unit<Complex<N>>> for &'a Similarity<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <&'a Similarity<N, U2, Unit<Complex<N>>> as Div<Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'a, N> Div<Unit<Complex<N>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <&'a Unit<Complex<N>> as Div<Unit<Complex<N>>>>::Output

Performs the / operation.

impl<N> Div<Unit<Complex<N>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <Unit<Complex<N>> as Div<Unit<Complex<N>>>>::Output

Performs the / operation.

impl<N> Div<Unit<Complex<N>>> for Similarity<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <Similarity<N, U2, Unit<Complex<N>>> as Div<Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'a, N> Div<Unit<Complex<N>>> for &'a Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <&'a Isometry<N, U2, Unit<Complex<N>>> as Div<Unit<Complex<N>>>>::Output

Performs the / operation.

impl<'a, N> Div<Unit<Complex<N>>> for &'a Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <&'a Rotation<N, U2> as Div<Unit<Complex<N>>>>::Output

Performs the / operation.

impl<N> Div<Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <Rotation<N, U2> as Div<Unit<Complex<N>>>>::Output

Performs the / operation.

impl<N> Div<Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <Isometry<N, U2, Unit<Complex<N>>> as Div<Unit<Complex<N>>>>::Output

Performs the / operation.

impl<N, C> Div<Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Transform<N, U3, C> as Div<Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'a, N> Div<Unit<Quaternion<N>>> for &'a Similarity<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Similarity<N, U3, Unit<Quaternion<N>>> as Div<Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<N> Div<Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Unit<Quaternion<N>> as Div<Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<N> Div<Unit<Quaternion<N>>> for Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Rotation<N, U3> as Div<Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<N> Div<Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Isometry<N, U3, Unit<Quaternion<N>>> as Div<Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'a, N> Div<Unit<Quaternion<N>>> for &'a Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Isometry<N, U3, Unit<Quaternion<N>>> as Div<Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'a, N> Div<Unit<Quaternion<N>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Unit<Quaternion<N>> as Div<Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'a, N, C> Div<Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Transform<N, U3, C> as Div<Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'a, N> Div<Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Rotation<N, U3> as Div<Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<N> Div<Unit<Quaternion<N>>> for Similarity<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Similarity<N, U3, Unit<Quaternion<N>>> as Div<Unit<Quaternion<N>>>>::Output

Performs the / operation.

impl<'b, N> DivAssign<&'b Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn div_assign(&mut self, rhs: &'b Rotation<N, U2>)

Performs the /= operation.

impl<'b, N> DivAssign<&'b Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn div_assign(&mut self, rhs: &'b Rotation<N, U3>)

Performs the /= operation.

impl<'b, N> DivAssign<&'b Unit<Complex<N>>> for Similarity<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn div_assign(&mut self, rhs: &'b Unit<Complex<N>>)

Performs the /= operation.

impl<'b, N> DivAssign<&'b Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn div_assign(&mut self, rhs: &'b Unit<Complex<N>>)

Performs the /= operation.

impl<'b, N> DivAssign<&'b Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn div_assign(&mut self, rhs: &'b Unit<Complex<N>>)

Performs the /= operation.

impl<'b, N> DivAssign<&'b Unit<Complex<N>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn div_assign(&mut self, rhs: &'b Unit<Complex<N>>)

Performs the /= operation.

impl<'b, N> DivAssign<&'b Unit<Quaternion<N>>> for Similarity<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn div_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)

Performs the /= operation.

impl<'b, N, C> DivAssign<&'b Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategory,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>, 

pub fn div_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)

Performs the /= operation.

impl<'b, N> DivAssign<&'b Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

pub fn div_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)

Performs the /= operation.

impl<'b, N> DivAssign<&'b Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn div_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)

Performs the /= operation.

impl<N> DivAssign<Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn div_assign(&mut self, rhs: Rotation<N, U2>)

Performs the /= operation.

impl<N> DivAssign<Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn div_assign(&mut self, rhs: Rotation<N, U3>)

Performs the /= operation.

impl<N> DivAssign<Unit<Complex<N>>> for Similarity<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn div_assign(&mut self, rhs: Unit<Complex<N>>)

Performs the /= operation.

impl<N> DivAssign<Unit<Complex<N>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn div_assign(&mut self, rhs: Unit<Complex<N>>)

Performs the /= operation.

impl<N> DivAssign<Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn div_assign(&mut self, rhs: Unit<Complex<N>>)

Performs the /= operation.

impl<N> DivAssign<Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn div_assign(&mut self, rhs: Unit<Complex<N>>)

Performs the /= operation.

impl<N, C> DivAssign<Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategory,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>, 

pub fn div_assign(&mut self, rhs: Unit<Quaternion<N>>)

Performs the /= operation.

impl<N> DivAssign<Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn div_assign(&mut self, rhs: Unit<Quaternion<N>>)

Performs the /= operation.

impl<N> DivAssign<Unit<Quaternion<N>>> for Similarity<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn div_assign(&mut self, rhs: Unit<Quaternion<N>>)

Performs the /= operation.

impl<N> DivAssign<Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

pub fn div_assign(&mut self, rhs: Unit<Quaternion<N>>)

Performs the /= operation.

impl<N> From<[Unit<Complex<<N as SimdValue>::Element>>; 16]> for Unit<Complex<N>> where
    N: Scalar + Copy + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 16]>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy, 

pub fn from(
    arr: [Unit<Complex<<N as SimdValue>::Element>>; 16]
) -> Unit<Complex<N>>

Performs the conversion.

impl<N> From<[Unit<Complex<<N as SimdValue>::Element>>; 2]> for Unit<Complex<N>> where
    N: Scalar + Copy + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 2]>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy, 

pub fn from(
    arr: [Unit<Complex<<N as SimdValue>::Element>>; 2]
) -> Unit<Complex<N>>

Performs the conversion.

impl<N> From<[Unit<Complex<<N as SimdValue>::Element>>; 4]> for Unit<Complex<N>> where
    N: Scalar + Copy + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 4]>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy, 

pub fn from(
    arr: [Unit<Complex<<N as SimdValue>::Element>>; 4]
) -> Unit<Complex<N>>

Performs the conversion.

impl<N> From<[Unit<Complex<<N as SimdValue>::Element>>; 8]> for Unit<Complex<N>> where
    N: Scalar + Copy + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 8]>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy, 

pub fn from(
    arr: [Unit<Complex<<N as SimdValue>::Element>>; 8]
) -> Unit<Complex<N>>

Performs the conversion.

impl<N, R, C> From<[Unit<Matrix<<N as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<N as SimdValue>::Element, R, C>>::Buffer>>; 16]> for Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>> where
    C: Dim,
    N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 16]>,
    R: Dim,
    <N as SimdValue>::Element: Scalar,
    DefaultAllocator: Allocator<N, R, C>,
    DefaultAllocator: Allocator<<N as SimdValue>::Element, R, C>, 

pub fn from(
    arr: [Unit<Matrix<<N as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<N as SimdValue>::Element, R, C>>::Buffer>>; 16]
) -> Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>>

Performs the conversion.

impl<N, R, C> From<[Unit<Matrix<<N as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<N as SimdValue>::Element, R, C>>::Buffer>>; 2]> for Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>> where
    C: Dim,
    N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 2]>,
    R: Dim,
    <N as SimdValue>::Element: Scalar,
    DefaultAllocator: Allocator<N, R, C>,
    DefaultAllocator: Allocator<<N as SimdValue>::Element, R, C>, 

pub fn from(
    arr: [Unit<Matrix<<N as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<N as SimdValue>::Element, R, C>>::Buffer>>; 2]
) -> Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>>

Performs the conversion.

impl<N, R, C> From<[Unit<Matrix<<N as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<N as SimdValue>::Element, R, C>>::Buffer>>; 4]> for Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>> where
    C: Dim,
    N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 4]>,
    R: Dim,
    <N as SimdValue>::Element: Scalar,
    DefaultAllocator: Allocator<N, R, C>,
    DefaultAllocator: Allocator<<N as SimdValue>::Element, R, C>, 

pub fn from(
    arr: [Unit<Matrix<<N as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<N as SimdValue>::Element, R, C>>::Buffer>>; 4]
) -> Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>>

Performs the conversion.

impl<N, R, C> From<[Unit<Matrix<<N as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<N as SimdValue>::Element, R, C>>::Buffer>>; 8]> for Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>> where
    C: Dim,
    N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 8]>,
    R: Dim,
    <N as SimdValue>::Element: Scalar,
    DefaultAllocator: Allocator<N, R, C>,
    DefaultAllocator: Allocator<<N as SimdValue>::Element, R, C>, 

pub fn from(
    arr: [Unit<Matrix<<N as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<N as SimdValue>::Element, R, C>>::Buffer>>; 8]
) -> Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>>

Performs the conversion.

impl<N> From<[Unit<Quaternion<<N as SimdValue>::Element>>; 16]> for Unit<Quaternion<N>> where
    N: Scalar + Copy + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 16]>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy, 

pub fn from(
    arr: [Unit<Quaternion<<N as SimdValue>::Element>>; 16]
) -> Unit<Quaternion<N>>

Performs the conversion.

impl<N> From<[Unit<Quaternion<<N as SimdValue>::Element>>; 2]> for Unit<Quaternion<N>> where
    N: Scalar + Copy + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 2]>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy, 

pub fn from(
    arr: [Unit<Quaternion<<N as SimdValue>::Element>>; 2]
) -> Unit<Quaternion<N>>

Performs the conversion.

impl<N> From<[Unit<Quaternion<<N as SimdValue>::Element>>; 4]> for Unit<Quaternion<N>> where
    N: Scalar + Copy + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 4]>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy, 

pub fn from(
    arr: [Unit<Quaternion<<N as SimdValue>::Element>>; 4]
) -> Unit<Quaternion<N>>

Performs the conversion.

impl<N> From<[Unit<Quaternion<<N as SimdValue>::Element>>; 8]> for Unit<Quaternion<N>> where
    N: Scalar + Copy + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 8]>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy, 

pub fn from(
    arr: [Unit<Quaternion<<N as SimdValue>::Element>>; 8]
) -> Unit<Quaternion<N>>

Performs the conversion.

impl<N> From<Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn from(q: Rotation<N, U2>) -> Unit<Complex<N>>

Performs the conversion.

impl<N> From<Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn from(q: Rotation<N, U3>) -> Unit<Quaternion<N>>

Performs the conversion.

impl<N> From<Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn from(q: Unit<Complex<N>>) -> Rotation<N, U2>

Performs the conversion.

impl<N> From<Unit<Complex<N>>> for Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn from(
    q: Unit<Complex<N>>
) -> Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer>

Performs the conversion.

impl<N> From<Unit<Complex<N>>> for Matrix<N, U2, U2, <DefaultAllocator as Allocator<N, U2, U2>>::Buffer> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn from(
    q: Unit<Complex<N>>
) -> Matrix<N, U2, U2, <DefaultAllocator as Allocator<N, U2, U2>>::Buffer>

Performs the conversion.

impl<N> From<Unit<Quaternion<N>>> for Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn from(
    q: Unit<Quaternion<N>>
) -> Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer>

Performs the conversion.

impl<N> From<Unit<Quaternion<N>>> for Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn from(q: Unit<Quaternion<N>>) -> Rotation<N, U3>

Performs the conversion.

impl<N> From<Unit<Quaternion<N>>> for Matrix<N, U4, U4, <DefaultAllocator as Allocator<N, U4, U4>>::Buffer> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn from(
    q: Unit<Quaternion<N>>
) -> Matrix<N, U4, U4, <DefaultAllocator as Allocator<N, U4, U4>>::Buffer>

Performs the conversion.

impl<T> Hash for Unit<T> where
    T: Hash, 

pub fn hash<__H>(&self, state: &mut __H) where
    __H: Hasher, 

Feeds this value into the given Hasher.

pub fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given Hasher.

impl<'a, 'b, N> Mul<&'b Isometry<N, U2, Unit<Complex<N>>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Isometry<N, U2, Unit<Complex<N>>>
) -> <&'a Unit<Complex<N>> as Mul<&'b Isometry<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Isometry<N, U2, Unit<Complex<N>>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Isometry<N, U2, Unit<Complex<N>>>
) -> <Unit<Complex<N>> as Mul<&'b Isometry<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Isometry<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Isometry<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Mul<&'b Isometry<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Isometry<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Isometry<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Mul<&'b Isometry<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<'a, 'b, N, S> Mul<&'b Matrix<N, U2, U1, S>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    S: Storage<N, U2, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Matrix<N, U2, U1, S>
) -> <&'a Unit<Complex<N>> as Mul<&'b Matrix<N, U2, U1, S>>>::Output

Performs the * operation.

impl<'b, N, S> Mul<&'b Matrix<N, U2, U1, S>> for Unit<Complex<N>> where
    N: SimdRealField,
    S: Storage<N, U2, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Matrix<N, U2, U1, S>
) -> <Unit<Complex<N>> as Mul<&'b Matrix<N, U2, U1, S>>>::Output

Performs the * operation.

impl<'b, N, SB> Mul<&'b Matrix<N, U3, U1, SB>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    SB: Storage<N, U3, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Matrix<N, U3, U1, SB>
) -> <Unit<Quaternion<N>> as Mul<&'b Matrix<N, U3, U1, SB>>>::Output

Performs the * operation.

impl<'a, 'b, N, SB> Mul<&'b Matrix<N, U3, U1, SB>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    SB: Storage<N, U3, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Matrix<N, U3, U1, SB>
) -> <&'a Unit<Quaternion<N>> as Mul<&'b Matrix<N, U3, U1, SB>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Point<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Point<N, U2>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Point<N, U2>
) -> <Unit<Complex<N>> as Mul<&'b Point<N, U2>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Point<N, U2>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Point<N, U2>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Point<N, U2>
) -> <&'a Unit<Complex<N>> as Mul<&'b Point<N, U2>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Point<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Point<N, U3>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Point<N, U3>
) -> <Unit<Quaternion<N>> as Mul<&'b Point<N, U3>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Point<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Point<N, U3>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Point<N, U3>
) -> <&'a Unit<Quaternion<N>> as Mul<&'b Point<N, U3>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Rotation<N, U2>
) -> <Unit<Complex<N>> as Mul<&'b Rotation<N, U2>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Rotation<N, U2>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Rotation<N, U2>
) -> <&'a Unit<Complex<N>> as Mul<&'b Rotation<N, U2>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Rotation<N, U3>
) -> <Unit<Quaternion<N>> as Mul<&'b Rotation<N, U3>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Rotation<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Rotation<N, U3>
) -> <&'a Unit<Quaternion<N>> as Mul<&'b Rotation<N, U3>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Similarity<N, U2, Unit<Complex<N>>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Similarity<N, U2, Unit<Complex<N>>>
) -> <&'a Unit<Complex<N>> as Mul<&'b Similarity<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Similarity<N, U2, Unit<Complex<N>>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Similarity<N, U2, Unit<Complex<N>>>
) -> <Unit<Complex<N>> as Mul<&'b Similarity<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Similarity<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Similarity<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Mul<&'b Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Similarity<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Similarity<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Mul<&'b Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<'a, 'b, N, C> Mul<&'b Transform<N, U3, C>> for &'a Unit<Quaternion<N>> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U4>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Transform<N, U3, C>
) -> <&'a Unit<Quaternion<N>> as Mul<&'b Transform<N, U3, C>>>::Output

Performs the * operation.

impl<'b, N, C> Mul<&'b Transform<N, U3, C>> for Unit<Quaternion<N>> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U4>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Transform<N, U3, C>
) -> <Unit<Quaternion<N>> as Mul<&'b Transform<N, U3, C>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Translation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Translation<N, U2>
) -> <Unit<Complex<N>> as Mul<&'b Translation<N, U2>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Translation<N, U2>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Translation<N, U2>
) -> <&'a Unit<Complex<N>> as Mul<&'b Translation<N, U2>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Translation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Translation<N, U3>
) -> <Unit<Quaternion<N>> as Mul<&'b Translation<N, U3>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Translation<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Translation<N, U3>
) -> <&'a Unit<Quaternion<N>> as Mul<&'b Translation<N, U3>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Complex<N>>> for Similarity<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <Similarity<N, U2, Unit<Complex<N>>> as Mul<&'b Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Unit<Complex<N>>> for &'a Translation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Unit<Complex<N>>
) -> <&'a Translation<N, U2> as Mul<&'b Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Complex<N>>> for Translation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Unit<Complex<N>>
) -> <Translation<N, U2> as Mul<&'b Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Unit<Complex<N>>> for &'a Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <&'a Isometry<N, U2, Unit<Complex<N>>> as Mul<&'b Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Unit<Complex<N>>> for &'a Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <&'a Rotation<N, U2> as Mul<&'b Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <Rotation<N, U2> as Mul<&'b Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Unit<Complex<N>>> for &'a Similarity<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <&'a Similarity<N, U2, Unit<Complex<N>>> as Mul<&'b Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <Isometry<N, U2, Unit<Complex<N>>> as Mul<&'b Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Complex<N>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <Unit<Complex<N>> as Mul<&'b Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Unit<Complex<N>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <&'a Unit<Complex<N>> as Mul<&'b Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for &'a Isometry<N, D, R> where
    D: DimName,
    N: SimdRealField,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>
) -> <&'a Isometry<N, D, R> as Mul<&'b Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>>::Output

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for Isometry<N, D, R> where
    D: DimName,
    N: SimdRealField,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>
) -> <Isometry<N, D, R> as Mul<&'b Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>>::Output

Performs the * operation.

impl<'a, 'b, N, D, S> Mul<&'b Unit<Matrix<N, D, U1, S>>> for &'a Rotation<N, D> where
    D: DimName,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N>,
    S: Storage<N, D, U1>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Unit<Matrix<N, D, U1, S>>
) -> <&'a Rotation<N, D> as Mul<&'b Unit<Matrix<N, D, U1, S>>>>::Output

Performs the * operation.

impl<'b, N, D, S> Mul<&'b Unit<Matrix<N, D, U1, S>>> for Rotation<N, D> where
    D: DimName,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N>,
    S: Storage<N, D, U1>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Unit<Matrix<N, D, U1, S>>
) -> <Rotation<N, D> as Mul<&'b Unit<Matrix<N, D, U1, S>>>>::Output

Performs the * operation.

impl<'b, N, S> Mul<&'b Unit<Matrix<N, U2, U1, S>>> for Unit<Complex<N>> where
    N: SimdRealField,
    S: Storage<N, U2, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Unit<Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Matrix<N, U2, U1, S>>
) -> <Unit<Complex<N>> as Mul<&'b Unit<Matrix<N, U2, U1, S>>>>::Output

Performs the * operation.

impl<'a, 'b, N, S> Mul<&'b Unit<Matrix<N, U2, U1, S>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    S: Storage<N, U2, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Unit<Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Matrix<N, U2, U1, S>>
) -> <&'a Unit<Complex<N>> as Mul<&'b Unit<Matrix<N, U2, U1, S>>>>::Output

Performs the * operation.

impl<'a, 'b, N, SB> Mul<&'b Unit<Matrix<N, U3, U1, SB>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    SB: Storage<N, U3, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Matrix<N, U3, U1, SB>>
) -> <&'a Unit<Quaternion<N>> as Mul<&'b Unit<Matrix<N, U3, U1, SB>>>>::Output

Performs the * operation.

impl<'b, N, SB> Mul<&'b Unit<Matrix<N, U3, U1, SB>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    SB: Storage<N, U3, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Matrix<N, U3, U1, SB>>
) -> <Unit<Quaternion<N>> as Mul<&'b Unit<Matrix<N, U3, U1, SB>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Quaternion<N>>> for Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Rotation<N, U3> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Isometry<N, U3, Unit<Quaternion<N>>> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N, C> Mul<&'b Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Transform<N, U3, C> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Quaternion<N>>> for Translation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Unit<Quaternion<N>>
) -> <Translation<N, U3> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Unit<Quaternion<N>>> for &'a Translation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: &'b Unit<Quaternion<N>>
) -> <&'a Translation<N, U3> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Unit<Quaternion<N>>> for &'a Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Isometry<N, U3, Unit<Quaternion<N>>> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Unit<Quaternion<N>>> for &'a Similarity<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Similarity<N, U3, Unit<Quaternion<N>>> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Unit<Quaternion<N>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Unit<Quaternion<N>> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'b, N, C> Mul<&'b Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Transform<N, U3, C> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Rotation<N, U3> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Quaternion<N>>> for Similarity<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Similarity<N, U3, Unit<Quaternion<N>>> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Unit<Quaternion<N>> as Mul<&'b Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Isometry<N, U2, Unit<Complex<N>>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Isometry<N, U2, Unit<Complex<N>>>
) -> <&'a Unit<Complex<N>> as Mul<Isometry<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<N> Mul<Isometry<N, U2, Unit<Complex<N>>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Isometry<N, U2, Unit<Complex<N>>>
) -> <Unit<Complex<N>> as Mul<Isometry<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Isometry<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Isometry<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Mul<Isometry<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<N> Mul<Isometry<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Isometry<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Mul<Isometry<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<N, S> Mul<Matrix<N, U2, U1, S>> for Unit<Complex<N>> where
    N: SimdRealField,
    S: Storage<N, U2, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Matrix<N, U2, U1, S>
) -> <Unit<Complex<N>> as Mul<Matrix<N, U2, U1, S>>>::Output

Performs the * operation.

impl<'a, N, S> Mul<Matrix<N, U2, U1, S>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    S: Storage<N, U2, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Matrix<N, U2, U1, S>
) -> <&'a Unit<Complex<N>> as Mul<Matrix<N, U2, U1, S>>>::Output

Performs the * operation.

impl<'a, N, SB> Mul<Matrix<N, U3, U1, SB>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    SB: Storage<N, U3, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Matrix<N, U3, U1, SB>
) -> <&'a Unit<Quaternion<N>> as Mul<Matrix<N, U3, U1, SB>>>::Output

Performs the * operation.

impl<N, SB> Mul<Matrix<N, U3, U1, SB>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    SB: Storage<N, U3, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Matrix<N, U3, U1, SB>
) -> <Unit<Quaternion<N>> as Mul<Matrix<N, U3, U1, SB>>>::Output

Performs the * operation.

impl<'a, N> Mul<Point<N, U2>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Point<N, U2>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Point<N, U2>
) -> <&'a Unit<Complex<N>> as Mul<Point<N, U2>>>::Output

Performs the * operation.

impl<N> Mul<Point<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Point<N, U2>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Point<N, U2>
) -> <Unit<Complex<N>> as Mul<Point<N, U2>>>::Output

Performs the * operation.

impl<N> Mul<Point<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Point<N, U3>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Point<N, U3>
) -> <Unit<Quaternion<N>> as Mul<Point<N, U3>>>::Output

Performs the * operation.

impl<'a, N> Mul<Point<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Point<N, U3>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Point<N, U3>
) -> <&'a Unit<Quaternion<N>> as Mul<Point<N, U3>>>::Output

Performs the * operation.

impl<N> Mul<Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Rotation<N, U2>
) -> <Unit<Complex<N>> as Mul<Rotation<N, U2>>>::Output

Performs the * operation.

impl<'a, N> Mul<Rotation<N, U2>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Rotation<N, U2>
) -> <&'a Unit<Complex<N>> as Mul<Rotation<N, U2>>>::Output

Performs the * operation.

impl<'a, N> Mul<Rotation<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Rotation<N, U3>
) -> <&'a Unit<Quaternion<N>> as Mul<Rotation<N, U3>>>::Output

Performs the * operation.

impl<N> Mul<Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Rotation<N, U3>
) -> <Unit<Quaternion<N>> as Mul<Rotation<N, U3>>>::Output

Performs the * operation.

impl<'a, N> Mul<Similarity<N, U2, Unit<Complex<N>>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Similarity<N, U2, Unit<Complex<N>>>
) -> <&'a Unit<Complex<N>> as Mul<Similarity<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<N> Mul<Similarity<N, U2, Unit<Complex<N>>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Similarity<N, U2, Unit<Complex<N>>>
) -> <Unit<Complex<N>> as Mul<Similarity<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<N> Mul<Similarity<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Similarity<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Mul<Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Similarity<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Similarity<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Mul<Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<N, C> Mul<Transform<N, U3, C>> for Unit<Quaternion<N>> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U4>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Transform<N, U3, C>
) -> <Unit<Quaternion<N>> as Mul<Transform<N, U3, C>>>::Output

Performs the * operation.

impl<'a, N, C> Mul<Transform<N, U3, C>> for &'a Unit<Quaternion<N>> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U4>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Transform<N, U3, C>
) -> <&'a Unit<Quaternion<N>> as Mul<Transform<N, U3, C>>>::Output

Performs the * operation.

impl<N> Mul<Translation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Translation<N, U2>
) -> <Unit<Complex<N>> as Mul<Translation<N, U2>>>::Output

Performs the * operation.

impl<'a, N> Mul<Translation<N, U2>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Translation<N, U2>
) -> <&'a Unit<Complex<N>> as Mul<Translation<N, U2>>>::Output

Performs the * operation.

impl<N> Mul<Translation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Translation<N, U3>
) -> <Unit<Quaternion<N>> as Mul<Translation<N, U3>>>::Output

Performs the * operation.

impl<'a, N> Mul<Translation<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Translation<N, U3>
) -> <&'a Unit<Quaternion<N>> as Mul<Translation<N, U3>>>::Output

Performs the * operation.

impl<'a, N> Mul<Unit<Complex<N>>> for &'a Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Complex<N>>
) -> <&'a Isometry<N, U2, Unit<Complex<N>>> as Mul<Unit<Complex<N>>>>::Output

Performs the * operation.

impl<N> Mul<Unit<Complex<N>>> for Similarity<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Complex<N>>
) -> <Similarity<N, U2, Unit<Complex<N>>> as Mul<Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Unit<Complex<N>>> for &'a Similarity<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Complex<N>>
) -> <&'a Similarity<N, U2, Unit<Complex<N>>> as Mul<Unit<Complex<N>>>>::Output

Performs the * operation.

impl<N> Mul<Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Complex<N>>
) -> <Rotation<N, U2> as Mul<Unit<Complex<N>>>>::Output

Performs the * operation.

impl<N> Mul<Unit<Complex<N>>> for Unit<Complex<N>> where
    N: SimdRealField, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(self, rhs: Unit<Complex<N>>) -> Unit<Complex<N>>

Performs the * operation.

impl<N> Mul<Unit<Complex<N>>> for Translation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Unit<Complex<N>>
) -> <Translation<N, U2> as Mul<Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Unit<Complex<N>>> for &'a Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Complex<N>>
) -> <&'a Rotation<N, U2> as Mul<Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Unit<Complex<N>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Complex<N>>
) -> <&'a Unit<Complex<N>> as Mul<Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Unit<Complex<N>>> for &'a Translation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Unit<Complex<N>>
) -> <&'a Translation<N, U2> as Mul<Unit<Complex<N>>>>::Output

Performs the * operation.

impl<N> Mul<Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Complex<N>>
) -> <Isometry<N, U2, Unit<Complex<N>>> as Mul<Unit<Complex<N>>>>::Output

Performs the * operation.

impl<'a, N, D, R> Mul<Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for &'a Isometry<N, D, R> where
    D: DimName,
    N: SimdRealField,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>
) -> <&'a Isometry<N, D, R> as Mul<Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>>::Output

Performs the * operation.

impl<N, D, R> Mul<Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for Isometry<N, D, R> where
    D: DimName,
    N: SimdRealField,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>
) -> <Isometry<N, D, R> as Mul<Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>>::Output

Performs the * operation.

impl<N, D, S> Mul<Unit<Matrix<N, D, U1, S>>> for Rotation<N, D> where
    D: DimName,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N>,
    S: Storage<N, D, U1>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Unit<Matrix<N, D, U1, S>>
) -> <Rotation<N, D> as Mul<Unit<Matrix<N, D, U1, S>>>>::Output

Performs the * operation.

impl<'a, N, D, S> Mul<Unit<Matrix<N, D, U1, S>>> for &'a Rotation<N, D> where
    D: DimName,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N>,
    S: Storage<N, D, U1>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Unit<Matrix<N, D, U1, S>>
) -> <&'a Rotation<N, D> as Mul<Unit<Matrix<N, D, U1, S>>>>::Output

Performs the * operation.

impl<N, S> Mul<Unit<Matrix<N, U2, U1, S>>> for Unit<Complex<N>> where
    N: SimdRealField,
    S: Storage<N, U2, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Unit<Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Matrix<N, U2, U1, S>>
) -> <Unit<Complex<N>> as Mul<Unit<Matrix<N, U2, U1, S>>>>::Output

Performs the * operation.

impl<'a, N, S> Mul<Unit<Matrix<N, U2, U1, S>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    S: Storage<N, U2, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Unit<Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Matrix<N, U2, U1, S>>
) -> <&'a Unit<Complex<N>> as Mul<Unit<Matrix<N, U2, U1, S>>>>::Output

Performs the * operation.

impl<'a, N, SB> Mul<Unit<Matrix<N, U3, U1, SB>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    SB: Storage<N, U3, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Matrix<N, U3, U1, SB>>
) -> <&'a Unit<Quaternion<N>> as Mul<Unit<Matrix<N, U3, U1, SB>>>>::Output

Performs the * operation.

impl<N, SB> Mul<Unit<Matrix<N, U3, U1, SB>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    SB: Storage<N, U3, U1>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Matrix<N, U3, U1, SB>>
) -> <Unit<Quaternion<N>> as Mul<Unit<Matrix<N, U3, U1, SB>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Rotation<N, U3> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<N, C> Mul<Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Transform<N, U3, C> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, N, C> Mul<Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Transform<N, U3, C> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Unit<Quaternion<N>>> for &'a Similarity<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Similarity<N, U3, Unit<Quaternion<N>>> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<N> Mul<Unit<Quaternion<N>>> for Similarity<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Similarity<N, U3, Unit<Quaternion<N>>> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<N> Mul<Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Unit<Quaternion<N>> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<N> Mul<Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Isometry<N, U3, Unit<Quaternion<N>>> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Unit<Quaternion<N>>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Unit<Quaternion<N>> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Unit<Quaternion<N>>> for &'a Translation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Unit<Quaternion<N>>
) -> <&'a Translation<N, U3> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'a, N> Mul<Unit<Quaternion<N>>> for &'a Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Isometry<N, U3, Unit<Quaternion<N>>> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<N> Mul<Unit<Quaternion<N>>> for Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Rotation<N, U3> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<N> Mul<Unit<Quaternion<N>>> for Translation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

pub fn mul(
    self,
    right: Unit<Quaternion<N>>
) -> <Translation<N, U3> as Mul<Unit<Quaternion<N>>>>::Output

Performs the * operation.

impl<'b, N> MulAssign<&'b Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn mul_assign(&mut self, rhs: &'b Rotation<N, U2>)

Performs the *= operation.

impl<'b, N> MulAssign<&'b Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn mul_assign(&mut self, rhs: &'b Rotation<N, U3>)

Performs the *= operation.

impl<'b, N> MulAssign<&'b Unit<Complex<N>>> for Similarity<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn mul_assign(&mut self, rhs: &'b Unit<Complex<N>>)

Performs the *= operation.

impl<'b, N> MulAssign<&'b Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn mul_assign(&mut self, rhs: &'b Unit<Complex<N>>)

Performs the *= operation.

impl<'b, N> MulAssign<&'b Unit<Complex<N>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn mul_assign(&mut self, rhs: &'b Unit<Complex<N>>)

Performs the *= operation.

impl<'b, N> MulAssign<&'b Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn mul_assign(&mut self, rhs: &'b Unit<Complex<N>>)

Performs the *= operation.

impl<'b, N> MulAssign<&'b Unit<Quaternion<N>>> for Similarity<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn mul_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)

Performs the *= operation.

impl<'b, N> MulAssign<&'b Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn mul_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)

Performs the *= operation.

impl<'b, N> MulAssign<&'b Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

pub fn mul_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)

Performs the *= operation.

impl<'b, N, C> MulAssign<&'b Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategory,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>, 

pub fn mul_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)

Performs the *= operation.

impl<N> MulAssign<Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn mul_assign(&mut self, rhs: Rotation<N, U2>)

Performs the *= operation.

impl<N> MulAssign<Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn mul_assign(&mut self, rhs: Rotation<N, U3>)

Performs the *= operation.

impl<N> MulAssign<Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn mul_assign(&mut self, rhs: Unit<Complex<N>>)

Performs the *= operation.

impl<N> MulAssign<Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn mul_assign(&mut self, rhs: Unit<Complex<N>>)

Performs the *= operation.

impl<N> MulAssign<Unit<Complex<N>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn mul_assign(&mut self, rhs: Unit<Complex<N>>)

Performs the *= operation.

impl<N> MulAssign<Unit<Complex<N>>> for Similarity<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn mul_assign(&mut self, rhs: Unit<Complex<N>>)

Performs the *= operation.

impl<N> MulAssign<Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn mul_assign(&mut self, rhs: Unit<Quaternion<N>>)

Performs the *= operation.

impl<N> MulAssign<Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

pub fn mul_assign(&mut self, rhs: Unit<Quaternion<N>>)

Performs the *= operation.

impl<N> MulAssign<Unit<Quaternion<N>>> for Similarity<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn mul_assign(&mut self, rhs: Unit<Quaternion<N>>)

Performs the *= operation.

impl<N, C> MulAssign<Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategory,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>, 

pub fn mul_assign(&mut self, rhs: Unit<Quaternion<N>>)

Performs the *= operation.

impl<N, R, C> Neg for Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>> where
    C: Dim,
    N: Scalar + ClosedNeg,
    R: Dim,
    DefaultAllocator: Allocator<N, R, C>, 

type Output = Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>>

The resulting type after applying the - operator.

pub fn neg(
    self
) -> <Unit<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>> as Neg>::Output

Performs the unary - operation.

impl<N> One for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn one() -> Unit<Quaternion<N>>

Returns the multiplicative identity element of Self, 1.

pub fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

pub fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 

Returns true if self is equal to the multiplicative identity.

impl<N> One for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

pub fn one() -> Unit<Complex<N>>

Returns the multiplicative identity element of Self, 1.

pub fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

pub fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 

Returns true if self is equal to the multiplicative identity.

impl<N> PartialEq<Unit<Complex<N>>> for Unit<Complex<N>> where
    N: Scalar + PartialEq<N>, 

pub fn eq(&self, rhs: &Unit<Complex<N>>) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

pub fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<N, R, C, S> PartialEq<Unit<Matrix<N, R, C, S>>> for Unit<Matrix<N, R, C, S>> where
    C: Dim,
    N: Scalar + PartialEq<N>,
    S: Storage<N, R, C>,
    R: Dim, 

pub fn eq(&self, rhs: &Unit<Matrix<N, R, C, S>>) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

pub fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<N> PartialEq<Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: Scalar + ClosedNeg + PartialEq<N>, 

pub fn eq(&self, rhs: &Unit<Quaternion<N>>) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

pub fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<N> RelativeEq<Unit<Complex<N>>> for Unit<Complex<N>> where
    N: RealField, 

pub fn default_max_relative(
) -> <Unit<Complex<N>> as AbsDiffEq<Unit<Complex<N>>>>::Epsilon

The default relative tolerance for testing values that are far-apart.

pub fn relative_eq(
    &self,
    other: &Unit<Complex<N>>,
    epsilon: <Unit<Complex<N>> as AbsDiffEq<Unit<Complex<N>>>>::Epsilon,
    max_relative: <Unit<Complex<N>> as AbsDiffEq<Unit<Complex<N>>>>::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.

pub fn relative_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of RelativeEq::relative_eq.

impl<N, R, C, S> RelativeEq<Unit<Matrix<N, R, C, S>>> for Unit<Matrix<N, R, C, S>> where
    C: Dim,
    N: Scalar + RelativeEq<N>,
    S: Storage<N, R, C>,
    R: Dim,
    <N as AbsDiffEq<N>>::Epsilon: Copy, 

pub fn default_max_relative(
) -> <Unit<Matrix<N, R, C, S>> as AbsDiffEq<Unit<Matrix<N, R, C, S>>>>::Epsilon

The default relative tolerance for testing values that are far-apart.

pub fn relative_eq(
    &self,
    other: &Unit<Matrix<N, R, C, S>>,
    epsilon: <Unit<Matrix<N, R, C, S>> as AbsDiffEq<Unit<Matrix<N, R, C, S>>>>::Epsilon,
    max_relative: <Unit<Matrix<N, R, C, S>> as AbsDiffEq<Unit<Matrix<N, R, C, S>>>>::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.

pub fn relative_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of RelativeEq::relative_eq.

impl<N> RelativeEq<Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: RealField<Epsilon = N> + RelativeEq<N>, 

pub fn default_max_relative(
) -> <Unit<Quaternion<N>> as AbsDiffEq<Unit<Quaternion<N>>>>::Epsilon

The default relative tolerance for testing values that are far-apart.

pub fn relative_eq(
    &self,
    other: &Unit<Quaternion<N>>,
    epsilon: <Unit<Quaternion<N>> as AbsDiffEq<Unit<Quaternion<N>>>>::Epsilon,
    max_relative: <Unit<Quaternion<N>> as AbsDiffEq<Unit<Quaternion<N>>>>::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.

pub fn relative_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of RelativeEq::relative_eq.

impl<T> Serialize for Unit<T> where
    T: Serialize, 

pub fn serialize<S>(
    &self,
    serializer: S
) -> Result<<S as Serializer>::Ok, <S as Serializer>::Error> where
    S: Serializer, 

Serialize this value into the given Serde serializer.

impl<N> SimdValue for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

type Element = Unit<Complex<<N as SimdValue>::Element>>

The type of the elements of each lane of this SIMD value.

type SimdBool = <N as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like self.

pub fn lanes() -> usize

The number of lanes of this SIMD value.

pub fn splat(val: <Unit<Complex<N>> as SimdValue>::Element) -> Unit<Complex<N>>

Initializes an SIMD value with each lanes set to val.

pub fn extract(&self, i: usize) -> <Unit<Complex<N>> as SimdValue>::Element

Extracts the i-th lane of self.

pub unsafe fn extract_unchecked(
    &self,
    i: usize
) -> <Unit<Complex<N>> as SimdValue>::Element

Extracts the i-th lane of self without bound-checking.

pub fn replace(
    &mut self,
    i: usize,
    val: <Unit<Complex<N>> as SimdValue>::Element
)

Replaces the i-th lane of self by val.

pub unsafe fn replace_unchecked(
    &mut self,
    i: usize,
    val: <Unit<Complex<N>> as SimdValue>::Element
)

Replaces the i-th lane of self by val without bound-checking.

pub fn select(
    self,
    cond: <Unit<Complex<N>> as SimdValue>::SimdBool,
    other: Unit<Complex<N>>
) -> Unit<Complex<N>>

Merges self and other depending on the lanes of cond.

pub fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Self where
    Self: Clone, 

Applies a function to each lane of self.

pub fn zip_map_lanes(
    self,
    b: Self,
    f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Self where
    Self: Clone, 

Applies a function to each lane of self paired with the corresponding lane of b.

impl<N> SimdValue for Unit<Quaternion<N>> where
    N: Scalar + SimdValue,
    <N as SimdValue>::Element: Scalar, 

type Element = Unit<Quaternion<<N as SimdValue>::Element>>

The type of the elements of each lane of this SIMD value.

type SimdBool = <N as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like self.

pub fn lanes() -> usize

The number of lanes of this SIMD value.

pub fn splat(
    val: <Unit<Quaternion<N>> as SimdValue>::Element
) -> Unit<Quaternion<N>>

Initializes an SIMD value with each lanes set to val.

pub fn extract(&self, i: usize) -> <Unit<Quaternion<N>> as SimdValue>::Element

Extracts the i-th lane of self.

pub unsafe fn extract_unchecked(
    &self,
    i: usize
) -> <Unit<Quaternion<N>> as SimdValue>::Element

Extracts the i-th lane of self without bound-checking.

pub fn replace(
    &mut self,
    i: usize,
    val: <Unit<Quaternion<N>> as SimdValue>::Element
)

Replaces the i-th lane of self by val.

pub unsafe fn replace_unchecked(
    &mut self,
    i: usize,
    val: <Unit<Quaternion<N>> as SimdValue>::Element
)

Replaces the i-th lane of self by val without bound-checking.

pub fn select(
    self,
    cond: <Unit<Quaternion<N>> as SimdValue>::SimdBool,
    other: Unit<Quaternion<N>>
) -> Unit<Quaternion<N>>

Merges self and other depending on the lanes of cond.

pub fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Self where
    Self: Clone, 

Applies a function to each lane of self.

pub fn zip_map_lanes(
    self,
    b: Self,
    f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Self where
    Self: Clone, 

Applies a function to each lane of self paired with the corresponding lane of b.

impl<N1, N2, R> SubsetOf<Isometry<N2, U2, R>> for Unit<Complex<N1>> where
    R: AbstractRotation<N2, U2> + SupersetOf<Unit<Complex<N1>>>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Isometry<N2, U2, R>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(iso: &Isometry<N2, U2, R>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(iso: &Isometry<N2, U2, R>) -> Unit<Complex<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, R> SubsetOf<Isometry<N2, U3, R>> for Unit<Quaternion<N1>> where
    R: AbstractRotation<N2, U3> + SupersetOf<Unit<Quaternion<N1>>>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Isometry<N2, U3, R>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(iso: &Isometry<N2, U3, R>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(
    iso: &Isometry<N2, U3, R>
) -> Unit<Quaternion<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2> SubsetOf<Matrix<N2, U3, U3, <DefaultAllocator as Allocator<N2, U3, U3>>::Buffer>> for Unit<Complex<N1>> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(
    &self
) -> Matrix<N2, U3, U3, <DefaultAllocator as Allocator<N2, U3, U3>>::Buffer>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(
    m: &Matrix<N2, U3, U3, <DefaultAllocator as Allocator<N2, U3, U3>>::Buffer>
) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(
    m: &Matrix<N2, U3, U3, <DefaultAllocator as Allocator<N2, U3, U3>>::Buffer>
) -> Unit<Complex<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2> SubsetOf<Matrix<N2, U4, U4, <DefaultAllocator as Allocator<N2, U4, U4>>::Buffer>> for Unit<Quaternion<N1>> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(
    &self
) -> Matrix<N2, U4, U4, <DefaultAllocator as Allocator<N2, U4, U4>>::Buffer>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(
    m: &Matrix<N2, U4, U4, <DefaultAllocator as Allocator<N2, U4, U4>>::Buffer>
) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(
    m: &Matrix<N2, U4, U4, <DefaultAllocator as Allocator<N2, U4, U4>>::Buffer>
) -> Unit<Quaternion<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2> SubsetOf<Rotation<N2, U2>> for Unit<Complex<N1>> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Rotation<N2, U2>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(rot: &Rotation<N2, U2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(rot: &Rotation<N2, U2>) -> Unit<Complex<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2> SubsetOf<Rotation<N2, U3>> for Unit<Quaternion<N1>> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Rotation<N2, U3>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(rot: &Rotation<N2, U3>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(rot: &Rotation<N2, U3>) -> Unit<Quaternion<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, R> SubsetOf<Similarity<N2, U2, R>> for Unit<Complex<N1>> where
    R: AbstractRotation<N2, U2> + SupersetOf<Unit<Complex<N1>>>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Similarity<N2, U2, R>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(sim: &Similarity<N2, U2, R>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(sim: &Similarity<N2, U2, R>) -> Unit<Complex<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, R> SubsetOf<Similarity<N2, U3, R>> for Unit<Quaternion<N1>> where
    R: AbstractRotation<N2, U3> + SupersetOf<Unit<Quaternion<N1>>>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Similarity<N2, U3, R>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(sim: &Similarity<N2, U3, R>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(
    sim: &Similarity<N2, U3, R>
) -> Unit<Quaternion<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, C> SubsetOf<Transform<N2, U2, C>> for Unit<Complex<N1>> where
    C: SuperTCategoryOf<TAffine>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Transform<N2, U2, C>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(t: &Transform<N2, U2, C>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(t: &Transform<N2, U2, C>) -> Unit<Complex<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, C> SubsetOf<Transform<N2, U3, C>> for Unit<Quaternion<N1>> where
    C: SuperTCategoryOf<TAffine>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Transform<N2, U3, C>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(t: &Transform<N2, U3, C>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(t: &Transform<N2, U3, C>) -> Unit<Quaternion<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2> SubsetOf<Unit<Complex<N2>>> for Rotation<N1, U2> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Unit<Complex<N2>>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(q: &Unit<Complex<N2>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(q: &Unit<Complex<N2>>) -> Rotation<N1, U2>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2> SubsetOf<Unit<Complex<N2>>> for Unit<Complex<N1>> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Unit<Complex<N2>>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(uq: &Unit<Complex<N2>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(uq: &Unit<Complex<N2>>) -> Unit<Complex<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2> SubsetOf<Unit<Quaternion<N2>>> for Rotation<N1, U3> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Unit<Quaternion<N2>>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(q: &Unit<Quaternion<N2>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(q: &Unit<Quaternion<N2>>) -> Rotation<N1, U3>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2> SubsetOf<Unit<Quaternion<N2>>> for Unit<Quaternion<N1>> where
    N1: SimdRealField,
    N2: SimdRealField + SupersetOf<N1>, 

pub fn to_superset(&self) -> Unit<Quaternion<N2>>

The inclusion map: converts self to the equivalent element of its superset.

pub fn is_in_subset(uq: &Unit<Quaternion<N2>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

pub fn from_superset_unchecked(
    uq: &Unit<Quaternion<N2>>
) -> Unit<Quaternion<N1>>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N> UlpsEq<Unit<Complex<N>>> for Unit<Complex<N>> where
    N: RealField, 

pub fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

pub fn ulps_eq(
    &self,
    other: &Unit<Complex<N>>,
    epsilon: <Unit<Complex<N>> as AbsDiffEq<Unit<Complex<N>>>>::Epsilon,
    max_ulps: u32
) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

pub fn ulps_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_ulps: u32
) -> bool

The inverse of UlpsEq::ulps_eq.

impl<N, R, C, S> UlpsEq<Unit<Matrix<N, R, C, S>>> for Unit<Matrix<N, R, C, S>> where
    C: Dim,
    N: Scalar + UlpsEq<N>,
    S: Storage<N, R, C>,
    R: Dim,
    <N as AbsDiffEq<N>>::Epsilon: Copy, 

pub fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

pub fn ulps_eq(
    &self,
    other: &Unit<Matrix<N, R, C, S>>,
    epsilon: <Unit<Matrix<N, R, C, S>> as AbsDiffEq<Unit<Matrix<N, R, C, S>>>>::Epsilon,
    max_ulps: u32
) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

pub fn ulps_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_ulps: u32
) -> bool

The inverse of UlpsEq::ulps_eq.

impl<N> UlpsEq<Unit<Quaternion<N>>> for Unit<Quaternion<N>> where
    N: RealField<Epsilon = N> + UlpsEq<N>, 

pub fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

pub fn ulps_eq(
    &self,
    other: &Unit<Quaternion<N>>,
    epsilon: <Unit<Quaternion<N>> as AbsDiffEq<Unit<Quaternion<N>>>>::Epsilon,
    max_ulps: u32
) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

pub fn ulps_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_ulps: u32
) -> bool

The inverse of UlpsEq::ulps_eq.

impl<T> Copy for Unit<T> where
    T: Copy, 

impl<N, R, C, S> Eq for Unit<Matrix<N, R, C, S>> where
    C: Dim,
    N: Scalar + Eq,
    S: Storage<N, R, C>,
    R: Dim, 

impl<N> Eq for Unit<Quaternion<N>> where
    N: Scalar + ClosedNeg + Eq, 

impl<N> Eq for Unit<Complex<N>> where
    N: Scalar + Eq,