Struct nalgebra::base::Unit

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pub struct Unit<T> { /* private fields */ }
Expand description

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:

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§

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impl<T, D, S> Unit<Vector<T, D, S>>
where T: Scalar, D: Dim, S: RawStorage<T, D, U1>,

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pub fn cast<T2: Scalar>(self) -> Unit<OVector<T2, D>>
where T: Scalar, OVector<T2, D>: SupersetOf<Vector<T, D, S>>, DefaultAllocator: Allocator<D, U1>,

Cast the components of self to another type.

§Example
let v = Vector3::<f64>::y_axis();
let v2 = v.cast::<f32>();
assert_eq!(v2, Vector3::<f32>::y_axis());
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impl<T: Normed> Unit<T>

§Construction with normalization

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pub fn new_normalize(value: T) -> Self

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

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pub fn try_new(value: T, min_norm: T::Norm) -> Option<Self>
where T::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.

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pub fn new_and_get(value: T) -> (Self, T::Norm)

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

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pub fn try_new_and_get(value: T, min_norm: T::Norm) -> Option<(Self, T::Norm)>
where T::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.

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pub fn renormalize(&mut self) -> T::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.

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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.

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impl<T> Unit<T>

§Data extraction and construction without normalization

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pub const fn new_unchecked(value: T) -> Self

Wraps the given value, assuming it is already normalized.

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pub fn from_ref_unchecked(value: &T) -> &Self

Wraps the given reference, assuming it is already normalized.

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pub fn into_inner(self) -> T

Retrieves the underlying value.

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pub fn unwrap(self) -> T

👎Deprecated: use .into_inner() instead

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

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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.

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impl<T: RealField, D: Dim, S: Storage<T, D>> Unit<Vector<T, D, S>>

§Interpolation between two unit vectors

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pub fn slerp<S2: Storage<T, D>>( &self, rhs: &Unit<Vector<T, D, S2>>, t: T ) -> Unit<OVector<T, D>>

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);
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pub fn try_slerp<S2: Storage<T, D>>( &self, rhs: &Unit<Vector<T, D, S2>>, t: T, epsilon: T ) -> Option<Unit<OVector<T, D>>>

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).

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impl<T: SimdRealField> Unit<Quaternion<T>>

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pub fn angle(&self) -> T

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);
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pub fn quaternion(&self) -> &Quaternion<T>

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));
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pub fn conjugate(&self) -> Self

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));
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pub fn inverse(&self) -> Self

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());
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pub fn angle_to(&self, other: &Self) -> T

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);
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pub fn rotation_to(&self, other: &Self) -> Self

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);
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pub fn lerp(&self, other: &Self, t: T) -> Quaternion<T>

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));
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pub fn nlerp(&self, other: &Self, t: T) -> Self

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)));
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pub fn slerp(&self, other: &Self, t: T) -> Self
where T: 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.

§Example

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));
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pub fn try_slerp(&self, other: &Self, t: T, epsilon: T) -> Option<Self>
where T: 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.
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pub fn conjugate_mut(&mut self)

Compute the conjugate of this unit quaternion in-place.

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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());
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pub fn axis(&self) -> Option<Unit<Vector3<T>>>
where T: 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());
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pub fn scaled_axis(&self) -> Vector3<T>
where T: 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);
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pub fn axis_angle(&self) -> Option<(Unit<Vector3<T>>, T)>
where T: 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());
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pub fn exp(&self) -> Quaternion<T>

Compute the exponential of a quaternion.

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

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

Compute the natural logarithm of a quaternion.

Note that this function yields a Quaternion<T> because it loses the unit property. The vector part of the return value corresponds to the axis-angle representation (divided by 2.0) of this unit quaternion.

§Example
let axisangle = Vector3::new(0.1, 0.2, 0.3);
let q = UnitQuaternion::new(axisangle);
assert_relative_eq!(q.ln().vector().into_owned(), axisangle, epsilon = 1.0e-6);
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pub fn powf(&self, n: T) -> Self
where T: 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);
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pub fn to_rotation_matrix(self) -> Rotation<T, 3>

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);
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pub fn to_euler_angles(self) -> (T, T, T)
where T: 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).

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pub fn euler_angles(&self) -> (T, T, T)
where T: 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);
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pub fn to_homogeneous(self) -> Matrix4<T>

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);
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pub fn transform_point(&self, pt: &Point3<T>) -> Point3<T>

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);
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pub fn transform_vector(&self, v: &Vector3<T>) -> Vector3<T>

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);
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pub fn inverse_transform_point(&self, pt: &Point3<T>) -> Point3<T>

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);
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pub fn inverse_transform_vector(&self, v: &Vector3<T>) -> Vector3<T>

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);
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pub fn inverse_transform_unit_vector( &self, v: &Unit<Vector3<T>> ) -> Unit<Vector3<T>>

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);
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pub fn append_axisangle_linearized(&self, axisangle: &Vector3<T>) -> Self

Appends to self a rotation given in the axis-angle form, using a linearized formulation.

This is faster, but approximate, way to compute UnitQuaternion::new(axisangle) * self.

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impl<T: SimdRealField> Unit<Quaternion<T>>

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pub fn identity() -> Self

The rotation identity.

§Example
let q = UnitQuaternion::identity();
let q2 = UnitQuaternion::new(Vector3::new(1.0, 2.0, 3.0));
let v = Vector3::new_random();
let p = Point3::from(v);

assert_eq!(q * q2, q2);
assert_eq!(q2 * q, q2);
assert_eq!(q * v, v);
assert_eq!(q * p, p);
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pub fn cast<To>(self) -> UnitQuaternion<To>
where To: SupersetOf<T> + Scalar,

Cast the components of self to another type.

§Example
let q = UnitQuaternion::from_euler_angles(1.0f64, 2.0, 3.0);
let q2 = q.cast::<f32>();
assert_relative_eq!(q2, UnitQuaternion::from_euler_angles(1.0f32, 2.0, 3.0), epsilon = 1.0e-6);
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pub fn from_axis_angle<SB>(axis: &Unit<Vector<T, U3, SB>>, angle: T) -> Self
where SB: Storage<T, U3>,

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());
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pub fn from_quaternion(q: Quaternion<T>) -> Self

Creates a new unit quaternion from a quaternion.

The input quaternion will be normalized.

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pub fn from_euler_angles(roll: T, pitch: T, yaw: T) -> Self

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);
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pub fn from_basis_unchecked(basis: &[Vector3<T>; 3]) -> Self

Builds an unit quaternion from a basis assumed to be orthonormal.

In order to get a valid unit-quaternion, the input must be an orthonormal basis, i.e., all vectors are normalized, and the are all orthogonal to each other. These invariants are not checked by this method.

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pub fn from_rotation_matrix(rotmat: &Rotation3<T>) -> Self

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);
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pub fn from_matrix(m: &Matrix3<T>) -> Self
where T: 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.

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pub fn from_matrix_eps( m: &Matrix3<T>, eps: T, max_iter: usize, guess: Self ) -> Self
where T: RealField,

Builds an unit quaternion by extracting the rotation part of the given transformation m.

This implements “A Robust Method to Extract the Rotational Part of Deformations” by Müller et al.

§Parameters
  • m: the matrix from which the rotational part is to be extracted.
  • eps: the angular errors tolerated between the current rotation and the optimal one.
  • max_iter: the maximum number of iterations. Loops indefinitely until convergence if set 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.
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pub fn rotation_between<SB, SC>( a: &Vector<T, U3, SB>, b: &Vector<T, U3, SC> ) -> Option<Self>
where T: RealField, SB: Storage<T, U3>, SC: Storage<T, U3>,

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);
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pub fn scaled_rotation_between<SB, SC>( a: &Vector<T, U3, SB>, b: &Vector<T, U3, SC>, s: T ) -> Option<Self>
where T: RealField, SB: Storage<T, U3>, SC: Storage<T, U3>,

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);
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pub fn rotation_between_axis<SB, SC>( a: &Unit<Vector<T, U3, SB>>, b: &Unit<Vector<T, U3, SC>> ) -> Option<Self>
where T: RealField, SB: Storage<T, U3>, SC: Storage<T, U3>,

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);
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pub fn scaled_rotation_between_axis<SB, SC>( na: &Unit<Vector<T, U3, SB>>, nb: &Unit<Vector<T, U3, SC>>, s: T ) -> Option<Self>
where T: RealField, SB: Storage<T, U3>, SC: Storage<T, U3>,

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);
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pub fn face_towards<SB, SC>( dir: &Vector<T, U3, SB>, up: &Vector<T, U3, SC> ) -> Self
where SB: Storage<T, U3>, SC: Storage<T, U3>,

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());
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pub fn new_observer_frames<SB, SC>( dir: &Vector<T, U3, SB>, up: &Vector<T, U3, SC> ) -> Self
where SB: Storage<T, U3>, SC: Storage<T, U3>,

👎Deprecated: renamed to face_towards

Deprecated: Use UnitQuaternion::face_towards instead.

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pub fn look_at_rh<SB, SC>( dir: &Vector<T, U3, SB>, up: &Vector<T, U3, SC> ) -> Self
where SB: Storage<T, U3>, SC: Storage<T, U3>,

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());
source

pub fn look_at_lh<SB, SC>( dir: &Vector<T, U3, SB>, up: &Vector<T, U3, SC> ) -> Self
where SB: Storage<T, U3>, SC: Storage<T, U3>,

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());
source

pub fn new<SB>(axisangle: Vector<T, U3, SB>) -> Self
where SB: Storage<T, U3>,

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

If axisangle has a magnitude smaller than T::default_epsilon(), this returns the identity rotation.

§Example
let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);
let q = UnitQuaternion::new(axisangle);

assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// A zero vector yields an identity.
assert_eq!(UnitQuaternion::new(Vector3::<f32>::zeros()), UnitQuaternion::identity());
source

pub fn new_eps<SB>(axisangle: Vector<T, U3, SB>, eps: T) -> Self
where SB: Storage<T, U3>,

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());
source

pub fn from_scaled_axis<SB>(axisangle: Vector<T, U3, SB>) -> Self
where SB: Storage<T, U3>,

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

If axisangle has a magnitude smaller than T::default_epsilon(), this returns the identity rotation. Same as Self::new(axisangle).

§Example
let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);
let q = UnitQuaternion::from_scaled_axis(axisangle);

assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// A zero vector yields an identity.
assert_eq!(UnitQuaternion::from_scaled_axis(Vector3::<f32>::zeros()), UnitQuaternion::identity());
source

pub fn from_scaled_axis_eps<SB>(axisangle: Vector<T, U3, SB>, eps: T) -> Self
where SB: Storage<T, U3>,

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());
source

pub fn mean_of(unit_quaternions: impl IntoIterator<Item = Self>) -> Self
where T: 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)
source§

impl<T: SimdRealField> Unit<DualQuaternion<T>>

source

pub fn dual_quaternion(&self) -> &DualQuaternion<T>

The underlying dual quaternion.

Same as self.as_ref().

§Example
let id = UnitDualQuaternion::identity();
assert_eq!(*id.dual_quaternion(), DualQuaternion::from_real_and_dual(
    Quaternion::new(1.0, 0.0, 0.0, 0.0),
    Quaternion::new(0.0, 0.0, 0.0, 0.0)
));
source

pub fn conjugate(&self) -> Self

Compute the conjugate of this unit quaternion.

§Example
let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let unit = UnitDualQuaternion::new_normalize(
    DualQuaternion::from_real_and_dual(qr, qd)
);
let conj = unit.conjugate();
assert_eq!(conj.real, unit.real.conjugate());
assert_eq!(conj.dual, unit.dual.conjugate());
source

pub fn conjugate_mut(&mut self)

Compute the conjugate of this unit quaternion in-place.

§Example
let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let unit = UnitDualQuaternion::new_normalize(
    DualQuaternion::from_real_and_dual(qr, qd)
);
let mut conj = unit.clone();
conj.conjugate_mut();
assert_eq!(conj.as_ref().real, unit.as_ref().real.conjugate());
assert_eq!(conj.as_ref().dual, unit.as_ref().dual.conjugate());
source

pub fn inverse(&self) -> Self

Inverts this dual quaternion if it is not zero.

§Example
let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let unit = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qr, qd));
let inv = unit.inverse();
assert_relative_eq!(unit * inv, UnitDualQuaternion::identity(), epsilon = 1.0e-6);
assert_relative_eq!(inv * unit, UnitDualQuaternion::identity(), epsilon = 1.0e-6);
source

pub fn inverse_mut(&mut self)

Inverts this dual quaternion in place if it is not zero.

§Example
let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let unit = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qr, qd));
let mut inv = unit.clone();
inv.inverse_mut();
assert_relative_eq!(unit * inv, UnitDualQuaternion::identity(), epsilon = 1.0e-6);
assert_relative_eq!(inv * unit, UnitDualQuaternion::identity(), epsilon = 1.0e-6);
source

pub fn isometry_to(&self, other: &Self) -> Self

The unit dual quaternion needed to make self and other coincide.

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

§Example
let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq1 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qr, qd));
let dq2 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qd, qr));
let dq_to = dq1.isometry_to(&dq2);
assert_relative_eq!(dq_to * dq1, dq2, epsilon = 1.0e-6);
source

pub fn lerp(&self, other: &Self, t: T) -> DualQuaternion<T>

Linear interpolation between two unit dual quaternions.

The result is not normalized.

§Example
let dq1 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
    Quaternion::new(0.5, 0.0, 0.5, 0.0),
    Quaternion::new(0.0, 0.5, 0.0, 0.5)
));
let dq2 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
    Quaternion::new(0.5, 0.0, 0.0, 0.5),
    Quaternion::new(0.5, 0.0, 0.5, 0.0)
));
assert_relative_eq!(
    UnitDualQuaternion::new_normalize(dq1.lerp(&dq2, 0.5)),
    UnitDualQuaternion::new_normalize(
        DualQuaternion::from_real_and_dual(
            Quaternion::new(0.5, 0.0, 0.25, 0.25),
            Quaternion::new(0.25, 0.25, 0.25, 0.25)
        )
    ),
    epsilon = 1.0e-6
);
source

pub fn nlerp(&self, other: &Self, t: T) -> Self

Normalized linear interpolation between two unit quaternions.

This is the same as self.lerp except that the result is normalized.

§Example
let dq1 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
    Quaternion::new(0.5, 0.0, 0.5, 0.0),
    Quaternion::new(0.0, 0.5, 0.0, 0.5)
));
let dq2 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
    Quaternion::new(0.5, 0.0, 0.0, 0.5),
    Quaternion::new(0.5, 0.0, 0.5, 0.0)
));
assert_relative_eq!(dq1.nlerp(&dq2, 0.2), UnitDualQuaternion::new_normalize(
    DualQuaternion::from_real_and_dual(
        Quaternion::new(0.5, 0.0, 0.4, 0.1),
        Quaternion::new(0.1, 0.4, 0.1, 0.4)
    )
), epsilon = 1.0e-6);
source

pub fn sclerp(&self, other: &Self, t: T) -> Self
where T: RealField,

Screw linear interpolation between two unit quaternions. This creates a smooth arc from one dual-quaternion to another.

Panics if the angle between both quaternion is 180 degrees (in which case the interpolation is not well-defined). Use .try_sclerp instead to avoid the panic.

§Example

let dq1 = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0),
);

let dq2 = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 0.0, 3.0).into(),
    UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0),
);

let dq = dq1.sclerp(&dq2, 1.0 / 3.0);

assert_relative_eq!(
    dq.rotation().euler_angles().0, std::f32::consts::FRAC_PI_2, epsilon = 1.0e-6
);
assert_relative_eq!(dq.translation().vector.y, 3.0, epsilon = 1.0e-6);
source

pub fn try_sclerp(&self, other: &Self, t: T, epsilon: T) -> Option<Self>
where T: RealField,

Computes the screw-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.
source

pub fn rotation(&self) -> UnitQuaternion<T>

Return the rotation part of this unit dual quaternion.

§Example
let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0)
);

assert_relative_eq!(
    dq.rotation().angle(), std::f32::consts::FRAC_PI_4, epsilon = 1.0e-6
);
source

pub fn translation(&self) -> Translation3<T>

Return the translation part of this unit dual quaternion.

§Example
let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0)
);

assert_relative_eq!(
    dq.translation().vector, Vector3::new(0.0, 3.0, 0.0), epsilon = 1.0e-6
);
source

pub fn to_isometry(self) -> Isometry3<T>

Builds an isometry from this unit dual quaternion.

§Example
let rotation = UnitQuaternion::from_euler_angles(std::f32::consts::PI, 0.0, 0.0);
let translation = Vector3::new(1.0, 3.0, 2.5);
let dq = UnitDualQuaternion::from_parts(
    translation.into(),
    rotation
);
let iso = dq.to_isometry();

assert_relative_eq!(iso.rotation.angle(), std::f32::consts::PI, epsilon = 1.0e-6);
assert_relative_eq!(iso.translation.vector, translation, epsilon = 1.0e-6);
source

pub fn transform_point(&self, pt: &Point3<T>) -> Point3<T>

Rotate and translate a point by this unit dual quaternion interpreted as an isometry.

This is the same as the multiplication self * pt.

§Example
let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let point = Point3::new(1.0, 2.0, 3.0);

assert_relative_eq!(
    dq.transform_point(&point), Point3::new(1.0, 0.0, 2.0), epsilon = 1.0e-6
);
source

pub fn transform_vector(&self, v: &Vector3<T>) -> Vector3<T>

Rotate a vector by this unit dual quaternion, ignoring the translational component.

This is the same as the multiplication self * v.

§Example
let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let vector = Vector3::new(1.0, 2.0, 3.0);

assert_relative_eq!(
    dq.transform_vector(&vector), Vector3::new(1.0, -3.0, 2.0), epsilon = 1.0e-6
);
source

pub fn inverse_transform_point(&self, pt: &Point3<T>) -> Point3<T>

Rotate and translate a point by the inverse of this unit quaternion.

This may be cheaper than inverting the unit dual quaternion and transforming the point.

§Example
let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let point = Point3::new(1.0, 2.0, 3.0);

assert_relative_eq!(
    dq.inverse_transform_point(&point), Point3::new(1.0, 3.0, 1.0), epsilon = 1.0e-6
);
source

pub fn inverse_transform_vector(&self, v: &Vector3<T>) -> Vector3<T>

Rotate a vector by the inverse of this unit quaternion, ignoring the translational component.

This may be cheaper than inverting the unit dual quaternion and transforming the vector.

§Example
let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let vector = Vector3::new(1.0, 2.0, 3.0);

assert_relative_eq!(
    dq.inverse_transform_vector(&vector), Vector3::new(1.0, 3.0, -2.0), epsilon = 1.0e-6
);
source

pub fn inverse_transform_unit_vector( &self, v: &Unit<Vector3<T>> ) -> Unit<Vector3<T>>

Rotate a unit vector by the inverse of this unit quaternion, ignoring the translational component. This may be cheaper than inverting the unit dual quaternion and transforming the vector.

§Example
let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let vector = Unit::new_unchecked(Vector3::new(0.0, 1.0, 0.0));

assert_relative_eq!(
    dq.inverse_transform_unit_vector(&vector),
    Unit::new_unchecked(Vector3::new(0.0, 0.0, -1.0)),
    epsilon = 1.0e-6
);
source§

impl<T: SimdRealField + RealField> Unit<DualQuaternion<T>>

source

pub fn to_homogeneous(self) -> Matrix4<T>

Converts this unit dual quaternion interpreted as an isometry into its equivalent homogeneous transformation matrix.

§Example
let dq = UnitDualQuaternion::from_parts(
    Vector3::new(1.0, 3.0, 2.0).into(),
    UnitQuaternion::from_axis_angle(&Vector3::z_axis(), std::f32::consts::FRAC_PI_6)
);
let expected = Matrix4::new(0.8660254, -0.5,      0.0, 1.0,
                            0.5,       0.8660254, 0.0, 3.0,
                            0.0,       0.0,       1.0, 2.0,
                            0.0,       0.0,       0.0, 1.0);

assert_relative_eq!(dq.to_homogeneous(), expected, epsilon = 1.0e-6);
source§

impl<T: SimdRealField> Unit<DualQuaternion<T>>

source

pub fn identity() -> Self

The unit dual quaternion multiplicative identity, which also represents the identity transformation as an isometry.

§Example
let ident = UnitDualQuaternion::identity();
let point = Point3::new(1.0, -4.3, 3.33);

assert_eq!(ident * point, point);
assert_eq!(ident, ident.inverse());
source

pub fn cast<To: Scalar>(self) -> UnitDualQuaternion<To>
where UnitDualQuaternion<To>: SupersetOf<Self>,

Cast the components of self to another type.

§Example
let q = UnitDualQuaternion::<f64>::identity();
let q2 = q.cast::<f32>();
assert_eq!(q2, UnitDualQuaternion::<f32>::identity());
source§

impl<T: SimdRealField> Unit<DualQuaternion<T>>

source

pub fn from_parts( translation: Translation3<T>, rotation: UnitQuaternion<T> ) -> Self

Return a dual quaternion representing the translation and orientation given by the provided rotation quaternion and translation vector.

§Example
let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let point = Point3::new(1.0, 2.0, 3.0);

assert_relative_eq!(dq * point, Point3::new(1.0, 0.0, 2.0), epsilon = 1.0e-6);
source

pub fn from_isometry(isometry: &Isometry3<T>) -> Self

Return a unit dual quaternion representing the translation and orientation given by the provided isometry.

§Example
let iso = Isometry3::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let dq = UnitDualQuaternion::from_isometry(&iso);
let point = Point3::new(1.0, 2.0, 3.0);

assert_relative_eq!(dq * point, iso * point, epsilon = 1.0e-6);
source

pub fn from_rotation(rotation: UnitQuaternion<T>) -> Self

Creates a dual quaternion from a unit quaternion rotation.

§Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let rot = UnitQuaternion::new_normalize(q);

let dq = UnitDualQuaternion::from_rotation(rot);
assert_relative_eq!(dq.as_ref().real.norm(), 1.0, epsilon = 1.0e-6);
assert_eq!(dq.as_ref().dual.norm(), 0.0);
source§

impl<T: SimdRealField> Unit<Complex<T>>

§Angle extraction

source

pub fn angle(&self) -> T

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

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

pub fn sin_angle(&self) -> T

The sine of the rotation angle.

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

pub fn cos_angle(&self) -> T

The cosine of the rotation angle.

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

pub fn scaled_axis(&self) -> Vector1<T>

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.

source

pub fn axis_angle(&self) -> Option<(Unit<Vector1<T>>, T)>
where T: 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.

source

pub fn angle_to(&self, other: &Self) -> T

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);
source§

impl<T: SimdRealField> Unit<Complex<T>>

§Conjugation and inversion

source

pub fn conjugate(&self) -> Self

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);
source

pub fn inverse(&self) -> Self

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);
source

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);
source

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());
source§

impl<T: SimdRealField> Unit<Complex<T>>

§Conversion to a matrix

source

pub fn to_rotation_matrix(self) -> Rotation2<T>

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);
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pub fn to_homogeneous(self) -> Matrix3<T>

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);
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impl<T: SimdRealField> Unit<Complex<T>>

§Transformation of a vector or a point

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pub fn transform_point(&self, pt: &Point2<T>) -> Point2<T>

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);
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pub fn transform_vector(&self, v: &Vector2<T>) -> Vector2<T>

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);
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pub fn inverse_transform_point(&self, pt: &Point2<T>) -> Point2<T>

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);
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pub fn inverse_transform_vector(&self, v: &Vector2<T>) -> Vector2<T>

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);
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pub fn inverse_transform_unit_vector( &self, v: &Unit<Vector2<T>> ) -> Unit<Vector2<T>>

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);
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impl<T: SimdRealField> Unit<Complex<T>>

§Interpolation

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pub fn slerp(&self, other: &Self, t: T) -> Self

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);
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impl<T: SimdRealField> Unit<Complex<T>>

§Identity

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pub fn identity() -> Self

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);
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impl<T: SimdRealField> Unit<Complex<T>>

§Construction from a 2D rotation angle

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pub fn new(angle: T) -> Self

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));
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pub fn from_angle(angle: T) -> Self

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));
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pub fn from_cos_sin_unchecked(cos: T, sin: T) -> Self

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));
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pub fn from_scaled_axis<SB: Storage<T, U1>>( axisangle: Vector<T, U1, SB> ) -> Self

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.

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impl<T: SimdRealField> Unit<Complex<T>>

§Construction from an existing 2D matrix or complex number

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pub fn cast<To: Scalar>(self) -> UnitComplex<To>
where UnitComplex<To>: SupersetOf<Self>,

Cast the components of self to another type.

§Example
#[macro_use] extern crate approx;
let c = UnitComplex::new(1.0f64);
let c2 = c.cast::<f32>();
assert_relative_eq!(c2, UnitComplex::new(1.0f32));
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pub fn complex(&self) -> &Complex<T>

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()));
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pub fn from_complex(q: Complex<T>) -> Self

Creates a new unit complex number from a complex number.

The input complex number will be normalized.

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pub fn from_complex_and_get(q: Complex<T>) -> (Self, T)

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.

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pub fn from_rotation_matrix(rotmat: &Rotation2<T>) -> Self

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));
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pub fn from_basis_unchecked(basis: &[Vector2<T>; 2]) -> Self

Builds a rotation from a basis assumed to be orthonormal.

In order to get a valid unit-quaternion, the input must be an orthonormal basis, i.e., all vectors are normalized, and the are all orthogonal to each other. These invariants are not checked by this method.

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pub fn from_matrix(m: &Matrix2<T>) -> Self
where T: 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.

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pub fn from_matrix_eps( m: &Matrix2<T>, eps: T, max_iter: usize, guess: Self ) -> Self
where T: 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.
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pub fn rotation_to(&self, other: &Self) -> Self

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);
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pub fn powf(&self, n: T) -> Self

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);
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impl<T: SimdRealField> Unit<Complex<T>>

§Construction from two vectors

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pub fn rotation_between<SB, SC>( a: &Vector<T, U2, SB>, b: &Vector<T, U2, SC> ) -> Self
where T: RealField, SB: Storage<T, U2>, SC: Storage<T, U2>,

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);
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pub fn scaled_rotation_between<SB, SC>( a: &Vector<T, U2, SB>, b: &Vector<T, U2, SC>, s: T ) -> Self
where T: RealField, SB: Storage<T, U2>, SC: Storage<T, U2>,

The smallest rotation needed to make a and b collinear and point toward the same direction, raised to the power s.

§Example
let a = Vector2::new(1.0, 2.0);
let b = Vector2::new(2.0, 1.0);
let rot2 = 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);
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pub fn rotation_between_axis<SB, SC>( a: &Unit<Vector<T, U2, SB>>, b: &Unit<Vector<T, U2, SC>> ) -> Self
where SB: Storage<T, U2>, SC: Storage<T, U2>,

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);
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pub fn scaled_rotation_between_axis<SB, SC>( na: &Unit<Vector<T, U2, SB>>, nb: &Unit<Vector<T, U2, SC>>, s: T ) -> Self
where SB: Storage<T, U2>, SC: Storage<T, U2>,

The smallest rotation needed to make a and b collinear and point toward the same direction, raised to the power s.

§Example
let a = 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§

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impl<T, R: Dim, C: Dim, S> AbsDiffEq for Unit<Matrix<T, R, C, S>>
where T: Scalar + AbsDiffEq, S: RawStorage<T, R, C>, T::Epsilon: Clone,

§

type Epsilon = <T as AbsDiffEq>::Epsilon

Used for specifying relative comparisons.
source§

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together. Read more
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fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.
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fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.
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impl<T> AsRef<T> for Unit<T>

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fn as_ref(&self) -> &T

Converts this type into a shared reference of the (usually inferred) input type.
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impl<T: Clone> Clone for Unit<T>

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

Returns a copy of the value. Read more
1.0.0 · source§

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

Performs copy-assignment from source. Read more
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impl<T: Debug> Debug for Unit<T>

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

Formats the value using the given formatter. Read more
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impl<T> Deref for Unit<T>

§

type Target = T

The resulting type after dereferencing.
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fn deref(&self) -> &T

Dereferences the value.
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Rotation<T, 2>

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type Output = Unit<Complex<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

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type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a UnitComplex<T>

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type Output = Unit<Complex<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Rotation<T, 2>

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type Output = Unit<Complex<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for UnitComplex<T>

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type Output = Unit<Complex<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a Isometry3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'a Unit<DualQuaternion<T>>> for &'b Translation3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'a UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for Isometry3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for Translation3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for UnitQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Rotation<T, 3>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

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type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T, C> Div<&'b Unit<Quaternion<T>>> for &'a Transform<T, C, 3>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a UnitQuaternion<T>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Rotation<T, 3>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T, C> Div<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Rotation<T, 2>

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type Output = Unit<Complex<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

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type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a UnitComplex<T>

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type Output = Unit<Complex<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<Complex<T>>> for Rotation<T, 2>

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type Output = Unit<Complex<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a Isometry3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a Translation3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for Isometry3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for Translation3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for UnitQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Rotation<T, 3>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

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type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T, C> Div<Unit<Quaternion<T>>> for &'a Transform<T, C, 3>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a UnitQuaternion<T>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Rotation<T, 3>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T, C> Div<Unit<Quaternion<T>>> for Transform<T, C, 3>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

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fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the /= operation. Read more
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impl<'b, T: SimdRealField> DivAssign<&'b Unit<Complex<T>>> for Rotation<T, 2>

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fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the /= operation. Read more
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impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the /= operation. Read more
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impl<'b, T, C> DivAssign<&'b Unit<Complex<T>>> for Transform<T, C, 2>

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fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the /= operation. Read more
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impl<'b, T: SimdRealField> DivAssign<&'b Unit<Complex<T>>> for UnitComplex<T>

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fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the /= operation. Read more
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impl<'b, T: SimdRealField> DivAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

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fn div_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)

Performs the /= operation. Read more
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impl<'b, T: SimdRealField> DivAssign<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

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fn div_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)

Performs the /= operation. Read more
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impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

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fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the /= operation. Read more
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impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the /= operation. Read more
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impl<'b, T, C> DivAssign<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>

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fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the /= operation. Read more
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impl<'b, T: SimdRealField> DivAssign<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>

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fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the /= operation. Read more
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impl<'b, T: SimdRealField> DivAssign<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>

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fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the /= operation. Read more
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impl<T> DivAssign<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

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fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the /= operation. Read more
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impl<T: SimdRealField> DivAssign<Unit<Complex<T>>> for Rotation<T, 2>

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fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the /= operation. Read more
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impl<T> DivAssign<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the /= operation. Read more
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impl<T, C> DivAssign<Unit<Complex<T>>> for Transform<T, C, 2>

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fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the /= operation. Read more
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impl<T: SimdRealField> DivAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>

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fn div_assign(&mut self, rhs: UnitDualQuaternion<T>)

Performs the /= operation. Read more
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impl<T> DivAssign<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

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fn div_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the /= operation. Read more
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impl<T> DivAssign<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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fn div_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the /= operation. Read more
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impl<T, C> DivAssign<Unit<Quaternion<T>>> for Transform<T, C, 3>

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fn div_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the /= operation. Read more
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impl<T: SimdRealField> DivAssign<Unit<Quaternion<T>>> for UnitDualQuaternion<T>

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fn div_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the /= operation. Read more
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impl<T, R: Dim, C: Dim> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 16]> for Unit<OMatrix<T, R, C>>

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fn from(arr: [Unit<OMatrix<T::Element, R, C>>; 16]) -> Self

Converts to this type from the input type.
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impl<T, R: Dim, C: Dim> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 2]> for Unit<OMatrix<T, R, C>>

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fn from(arr: [Unit<OMatrix<T::Element, R, C>>; 2]) -> Self

Converts to this type from the input type.
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impl<T, R: Dim, C: Dim> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 4]> for Unit<OMatrix<T, R, C>>

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fn from(arr: [Unit<OMatrix<T::Element, R, C>>; 4]) -> Self

Converts to this type from the input type.
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impl<T, R: Dim, C: Dim> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 8]> for Unit<OMatrix<T, R, C>>

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fn from(arr: [Unit<OMatrix<T::Element, R, C>>; 8]) -> Self

Converts to this type from the input type.
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impl<T: SimdRealField> From<Unit<Complex<T>>> for Matrix2<T>

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fn from(q: UnitComplex<T>) -> Self

Converts to this type from the input type.
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impl<T: SimdRealField> From<Unit<Complex<T>>> for Matrix3<T>

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fn from(q: UnitComplex<T>) -> Matrix3<T>

Converts to this type from the input type.
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impl<T: SimdRealField> From<Unit<Complex<T>>> for Rotation2<T>

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fn from(q: UnitComplex<T>) -> Self

Converts to this type from the input type.
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impl From<Unit<Complex<f32>>> for Mat2

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fn from(e: UnitComplex<f32>) -> Mat2

Converts to this type from the input type.
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impl From<Unit<Complex<f64>>> for DMat2

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fn from(e: UnitComplex<f64>) -> DMat2

Converts to this type from the input type.
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impl<T: SimdRealField> From<Unit<DualQuaternion<T>>> for Isometry3<T>

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fn from(dq: UnitDualQuaternion<T>) -> Self

Converts to this type from the input type.
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impl<T: SimdRealField + RealField> From<Unit<DualQuaternion<T>>> for Matrix4<T>

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fn from(dq: UnitDualQuaternion<T>) -> Self

Converts to this type from the input type.
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impl From<Unit<Matrix<f32, Const<2>, Const<1>, ArrayStorage<f32, 2, 1>>>> for Vec2

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fn from(e: UnitVector2<f32>) -> Vec2

Converts to this type from the input type.
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impl From<Unit<Matrix<f32, Const<3>, Const<1>, ArrayStorage<f32, 3, 1>>>> for Vec3

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fn from(e: UnitVector3<f32>) -> Vec3

Converts to this type from the input type.
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impl From<Unit<Matrix<f32, Const<3>, Const<1>, ArrayStorage<f32, 3, 1>>>> for Vec3A

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fn from(e: UnitVector3<f32>) -> Vec3A

Converts to this type from the input type.
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impl From<Unit<Matrix<f32, Const<4>, Const<1>, ArrayStorage<f32, 4, 1>>>> for Vec4

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fn from(e: UnitVector4<f32>) -> Vec4

Converts to this type from the input type.
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impl From<Unit<Matrix<f64, Const<2>, Const<1>, ArrayStorage<f64, 2, 1>>>> for DVec2

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fn from(e: UnitVector2<f64>) -> DVec2

Converts to this type from the input type.
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impl From<Unit<Matrix<f64, Const<3>, Const<1>, ArrayStorage<f64, 3, 1>>>> for DVec3

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fn from(e: UnitVector3<f64>) -> DVec3

Converts to this type from the input type.
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impl From<Unit<Matrix<f64, Const<4>, Const<1>, ArrayStorage<f64, 4, 1>>>> for DVec4

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fn from(e: UnitVector4<f64>) -> DVec4

Converts to this type from the input type.
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impl<T: SimdRealField> From<Unit<Quaternion<T>>> for Matrix3<T>

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fn from(q: UnitQuaternion<T>) -> Self

Converts to this type from the input type.
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impl<T: SimdRealField> From<Unit<Quaternion<T>>> for Matrix4<T>

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fn from(q: UnitQuaternion<T>) -> Self

Converts to this type from the input type.
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impl<T: SimdRealField> From<Unit<Quaternion<T>>> for Rotation3<T>

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fn from(q: UnitQuaternion<T>) -> Self

Converts to this type from the input type.
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impl From<Unit<Quaternion<f32>>> for Quat

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fn from(e: UnitQuaternion<f32>) -> Quat

Converts to this type from the input type.
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impl From<Unit<Quaternion<f64>>> for DQuat

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fn from(e: UnitQuaternion<f64>) -> DQuat

Converts to this type from the input type.
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impl<T: Hash> Hash for Unit<T>

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

Feeds this value into the given Hasher. Read more
1.3.0 · source§

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

Feeds a slice of this type into the given Hasher. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Rotation<T, 2>

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type Output = Unit<Complex<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

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type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T, C> Mul<&'b Unit<Complex<T>>> for &'a Transform<T, C, 2>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Translation<T, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, right: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a UnitComplex<T>

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type Output = Unit<Complex<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Rotation<T, 2>

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type Output = Unit<Complex<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T, C> Mul<&'b Unit<Complex<T>>> for Transform<T, C, 2>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Translation<T, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, right: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for UnitComplex<T>

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type Output = Unit<Complex<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a Isometry3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'a Unit<DualQuaternion<T>>> for &'b Translation3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'a UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for Isometry3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for Translation3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for UnitQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for &'a UnitComplex<T>

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type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for UnitComplex<T>

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type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, SB: Storage<T, U3>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitDualQuaternion<T>

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type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitQuaternion<T>

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type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, SB: Storage<T, U3>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitDualQuaternion<T>

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type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitQuaternion<T>

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type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for &'a Isometry<T, R, D>

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type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the * operator.
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fn mul(self, right: &'b Unit<SVector<T, D>>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for Isometry<T, R, D>

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type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the * operator.
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fn mul(self, right: &'b Unit<SVector<T, D>>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T, S, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, S>>> for &'a Rotation<T, D>

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type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the * operator.
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fn mul(self, right: &'b Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T, S, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, S>>> for Rotation<T, D>

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type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the * operator.
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fn mul(self, right: &'b Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Rotation<T, 3>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

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type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T, C> Mul<&'b Unit<Quaternion<T>>> for &'a Transform<T, C, 3>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Translation<T, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, right: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a UnitQuaternion<T>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Rotation<T, 3>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T, C> Mul<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Translation<T, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, right: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Rotation<T, 2>

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type Output = Unit<Complex<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

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type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T, C> Mul<Unit<Complex<T>>> for &'a Transform<T, C, 2>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Translation<T, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, right: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a UnitComplex<T>

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type Output = Unit<Complex<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Rotation<T, 2>

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type Output = Unit<Complex<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<T, C> Mul<Unit<Complex<T>>> for Transform<T, C, 2>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Translation<T, 2>

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type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.
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fn mul(self, right: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a Isometry3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a Translation3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for DualQuaternion<T>

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type Output = DualQuaternion<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for Isometry3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for Translation3<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for UnitQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, S: Storage<T, Const<2>>> Mul<Unit<Matrix<T, Const<2>, Const<1>, S>>> for &'a UnitComplex<T>

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type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, S: Storage<T, Const<2>>> Mul<Unit<Matrix<T, Const<2>, Const<1>, S>>> for UnitComplex<T>

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type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, SB: Storage<T, U3>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitDualQuaternion<T>

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type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitQuaternion<T>

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type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, SB: Storage<T, U3>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitDualQuaternion<T>

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type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitQuaternion<T>

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type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, R, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for &'a Isometry<T, R, D>

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type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the * operator.
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fn mul(self, right: Unit<SVector<T, D>>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, R, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for Isometry<T, R, D>

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type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the * operator.
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fn mul(self, right: Unit<SVector<T, D>>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T, S, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, S>>> for &'a Rotation<T, D>

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type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the * operator.
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fn mul(self, right: Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the * operation. Read more
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impl<T, S, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, S>>> for Rotation<T, D>

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type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the * operator.
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fn mul(self, right: Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Rotation<T, 3>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

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type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T, C> Mul<Unit<Quaternion<T>>> for &'a Transform<T, C, 3>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Translation<T, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, right: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a UnitQuaternion<T>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Rotation<T, 3>

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type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T, C> Mul<Unit<Quaternion<T>>> for Transform<T, C, 3>

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type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Translation<T, 3>

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type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.
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fn mul(self, right: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for UnitDualQuaternion<T>

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type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T> MulAssign<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

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fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the *= operation. Read more
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impl<'b, T: SimdRealField> MulAssign<&'b Unit<Complex<T>>> for Rotation<T, 2>

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fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the *= operation. Read more
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impl<'b, T> MulAssign<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the *= operation. Read more
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impl<'b, T, C> MulAssign<&'b Unit<Complex<T>>> for Transform<T, C, 2>

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fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the *= operation. Read more
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impl<'b, T: SimdRealField> MulAssign<&'b Unit<Complex<T>>> for UnitComplex<T>

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fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the *= operation. Read more
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impl<'b, T: SimdRealField> MulAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

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fn mul_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)

Performs the *= operation. Read more
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impl<'b, T: SimdRealField> MulAssign<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

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fn mul_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)

Performs the *= operation. Read more
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impl<'b, T> MulAssign<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

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fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the *= operation. Read more
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impl<'b, T> MulAssign<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the *= operation. Read more
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impl<'b, T, C> MulAssign<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>

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fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the *= operation. Read more
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impl<'b, T: SimdRealField> MulAssign<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>

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fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the *= operation. Read more
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impl<'b, T: SimdRealField> MulAssign<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>

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fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the *= operation. Read more
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impl<T> MulAssign<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

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fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the *= operation. Read more
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impl<T: SimdRealField> MulAssign<Unit<Complex<T>>> for Rotation<T, 2>

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fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the *= operation. Read more
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impl<T> MulAssign<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the *= operation. Read more
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impl<T, C> MulAssign<Unit<Complex<T>>> for Transform<T, C, 2>

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fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the *= operation. Read more
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impl<T: SimdRealField> MulAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>

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fn mul_assign(&mut self, rhs: UnitDualQuaternion<T>)

Performs the *= operation. Read more
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impl<T> MulAssign<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

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fn mul_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the *= operation. Read more
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impl<T> MulAssign<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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fn mul_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the *= operation. Read more
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impl<T, C> MulAssign<Unit<Quaternion<T>>> for Transform<T, C, 3>

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fn mul_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the *= operation. Read more
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impl<T: SimdRealField> MulAssign<Unit<Quaternion<T>>> for UnitDualQuaternion<T>

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fn mul_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the *= operation. Read more
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impl<T: Scalar + ClosedNeg, R: Dim, C: Dim> Neg for Unit<OMatrix<T, R, C>>

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type Output = Unit<Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>>

The resulting type after applying the - operator.
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fn neg(self) -> Self::Output

Performs the unary - operation. Read more
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impl<T, R, C, S> PartialEq for Unit<Matrix<T, R, C, S>>
where T: Scalar + PartialEq, R: Dim, C: Dim, S: RawStorage<T, R, C>,

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fn eq(&self, rhs: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<T, R: Dim, C: Dim, S> RelativeEq for Unit<Matrix<T, R, C, S>>
where T: Scalar + RelativeEq, S: Storage<T, R, C>, T::Epsilon: Clone,

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fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
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fn relative_eq( &self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon ) -> bool

A test for equality that uses a relative comparison if the values are far apart.
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fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon ) -> bool

The inverse of RelativeEq::relative_eq.
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impl<T1, T2> SubsetOf<Unit<Complex<T2>>> for Rotation2<T1>
where T1: RealField, T2: RealField + SupersetOf<T1>,

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fn to_superset(&self) -> UnitComplex<T2>

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(q: &UnitComplex<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(q: &UnitComplex<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T1, T2> SubsetOf<Unit<Complex<T2>>> for UnitComplex<T1>
where T1: RealField, T2: RealField + SupersetOf<T1>,

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fn to_superset(&self) -> UnitComplex<T2>

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(uq: &UnitComplex<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(uq: &UnitComplex<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for Isometry3<T1>
where T1: RealField, T2: RealField + SupersetOf<T1>,

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fn to_superset(&self) -> UnitDualQuaternion<T2>

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for Rotation3<T1>
where T1: RealField, T2: RealField + SupersetOf<T1>,

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fn to_superset(&self) -> UnitDualQuaternion<T2>

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for Translation3<T1>
where T1: RealField, T2: RealField + SupersetOf<T1>,

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fn to_superset(&self) -> UnitDualQuaternion<T2>

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for UnitDualQuaternion<T1>
where T1: SimdRealField, T2: SimdRealField + SupersetOf<T1>,

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fn to_superset(&self) -> UnitDualQuaternion<T2>

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for UnitQuaternion<T1>
where T1: RealField, T2: RealField + SupersetOf<T1>,

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fn to_superset(&self) -> UnitDualQuaternion<T2>

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T1, T2> SubsetOf<Unit<Quaternion<T2>>> for Rotation3<T1>
where T1: RealField, T2: RealField + SupersetOf<T1>,

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fn to_superset(&self) -> UnitQuaternion<T2>

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(q: &UnitQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(q: &UnitQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T1, T2> SubsetOf<Unit<Quaternion<T2>>> for UnitQuaternion<T1>
where T1: Scalar, T2: Scalar + SupersetOf<T1>,

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fn to_superset(&self) -> UnitQuaternion<T2>

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(uq: &UnitQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(uq: &UnitQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T, R: Dim, C: Dim, S> UlpsEq for Unit<Matrix<T, R, C, S>>
where T: Scalar + UlpsEq, S: RawStorage<T, R, C>, T::Epsilon: Clone,

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fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
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fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.
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fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.
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impl<T: Copy> Copy for Unit<T>

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impl<T, R, C, S> Eq for Unit<Matrix<T, R, C, S>>
where T: Scalar + Eq, R: Dim, C: Dim, S: RawStorage<T, R, C>,

Auto Trait Implementations§

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

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

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

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

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

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

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

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

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impl<T> Same for T

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type Output = T

Should always be Self
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impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

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fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).
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fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.
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fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> ToString for T
where T: Display + ?Sized,

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default fn to_string(&self) -> String

Converts the given value to a String. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<T, Right> ClosedDiv<Right> for T
where T: Div<Right, Output = T> + DivAssign<Right>,

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impl<T, Right> ClosedDivAssign<Right> for T
where T: ClosedDiv<Right> + DivAssign<Right>,

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impl<T, Right> ClosedMul<Right> for T
where T: Mul<Right, Output = T> + MulAssign<Right>,

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impl<T, Right> ClosedMulAssign<Right> for T
where T: ClosedMul<Right> + MulAssign<Right>,

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impl<T> ClosedNeg for T
where T: Neg<Output = T>,

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impl<T> Scalar for T
where T: 'static + Clone + PartialEq + Debug,