Struct Unit

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

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

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

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

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

Implementations

impl<T, D, S> Unit<Vector<T, D, S>>

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

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());

impl<T: Normed> Unit<T>

Construction with normalization

pub fn new_normalize(value: T) -> Self

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

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.

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.

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.

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.

pub fn renormalize_fast(&mut self)

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

impl<T> Unit<T>

Data extraction and construction without normalization

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

Wraps the given value, assuming it is already normalized.

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

Wraps the given reference, assuming it is already normalized.

pub fn into_inner(self) -> T

Retrieves the underlying value.

pub fn unwrap(self) -> T

👎Deprecated: use .into_inner() instead

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

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

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

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

Interpolation between two unit vectors

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

where DefaultAllocator: Allocator<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);

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

where DefaultAllocator: Allocator<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).

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

where T::Element: SimdRealField,

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);

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));

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));

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());

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);

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);

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));

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)));

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));

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.

pub fn conjugate_mut(&mut self)

Compute the conjugate of this unit quaternion in-place.

pub fn inverse_mut(&mut self)

Inverts this quaternion if it is not zero.

Example

let axisangle = Vector3::new(0.1, 0.2, 0.3);
let mut rot = UnitQuaternion::new(axisangle);
rot.inverse_mut();
assert_relative_eq!(rot * UnitQuaternion::new(axisangle), UnitQuaternion::identity());
assert_relative_eq!(UnitQuaternion::new(axisangle) * rot, UnitQuaternion::identity());

pub fn axis(&self) -> Option<Unit<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());

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);

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());

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.

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);

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);

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);

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).

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);

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);

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);

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);

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);

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);

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);

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.

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

where T::Element: SimdRealField,

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);

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);

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());

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

Creates a new unit quaternion from a quaternion.

The input quaternion will be normalized.

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);

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.

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);

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.

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.

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);

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);

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);

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);

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());

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.

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());

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());

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());

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());

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());

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());

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)

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

where T::Element: SimdRealField,

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)
));

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());

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());

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);

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);

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);

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
);

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);

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);

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.

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
);

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
);

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);

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
);

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
);

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
);

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
);

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
);

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

where T::Element: SimdRealField,

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);

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

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());

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());

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

where T::Element: SimdRealField,

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);

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);

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);

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

where T::Element: SimdRealField,

Angle extraction

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);

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());

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());

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.

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.

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);

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

where T::Element: SimdRealField,

Conjugation and inversion

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);

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);

pub fn conjugate_mut(&mut self)

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

Example

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

pub fn inverse_mut(&mut self)

Inverts in-place this unit complex number.

Example

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

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

where T::Element: SimdRealField,

Conversion to a matrix

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);

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);

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

where T::Element: SimdRealField,

Transformation of a vector or a point

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);

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);

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);

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);

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);

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

where T::Element: SimdRealField,

Interpolation

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);

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

where T::Element: SimdRealField,

Identity

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);

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

where T::Element: SimdRealField,

Construction from a 2D rotation angle

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));

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));

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));

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.

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

where T::Element: SimdRealField,

Construction from an existing 2D matrix or complex number

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));

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()));

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.

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.

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));

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.

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.

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.

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);

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);

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

where T::Element: SimdRealField,

Construction from two vectors

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);

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);

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);

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

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.

fn default_epsilon() -> Self::Epsilon

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

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.

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

The inverse of AbsDiffEq::abs_diff_eq.

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

fn as_ref(&self) -> &T

Converts this type into a shared reference of the (usually inferred) input type.

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

Formats the value using the given formatter.

impl<T> Deref for Unit<T>

type Target = T

The resulting type after dereferencing.

fn deref(&self) -> &T

Dereferences the value.

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

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

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

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Rotation<T, 2>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a UnitComplex<T>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Rotation<T, 2>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for UnitComplex<T>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

where T::Element: SimdRealField,

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a Isometry3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'a Unit<DualQuaternion<T>>> for &'b Translation3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'a UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

where T::Element: SimdRealField,

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for Isometry3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for Translation3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Rotation<T, 3>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T, C> Div<&'b Unit<Quaternion<T>>> for &'a Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Rotation<T, 3>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T, C> Div<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Rotation<T, 2>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a UnitComplex<T>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<Complex<T>>> for Rotation<T, 2>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

where T::Element: SimdRealField,

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a Isometry3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a Translation3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

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

where T::Element: SimdRealField,

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for Isometry3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for Translation3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Rotation<T, 3>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T, C> Div<Unit<Quaternion<T>>> for &'a Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Rotation<T, 3>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<T, C> Div<Unit<Quaternion<T>>> for Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T: SimdRealField> DivAssign<&'b Unit<Complex<T>>> for Rotation<T, 2>

where T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T, C> DivAssign<&'b Unit<Complex<T>>> for Transform<T, C, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategory,

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

Performs the /= operation.

impl<'b, T: SimdRealField> DivAssign<&'b Unit<Complex<T>>> for UnitComplex<T>

where T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T: SimdRealField> DivAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

where T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T: SimdRealField> DivAssign<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T, C> DivAssign<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategory,

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

Performs the /= operation.

impl<'b, T: SimdRealField> DivAssign<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T: SimdRealField> DivAssign<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>

where T::Element: SimdRealField,

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

Performs the /= operation.

impl<T> DivAssign<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the /= operation.

impl<T: SimdRealField> DivAssign<Unit<Complex<T>>> for Rotation<T, 2>

where T::Element: SimdRealField,

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

Performs the /= operation.

impl<T> DivAssign<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the /= operation.

impl<T, C> DivAssign<Unit<Complex<T>>> for Transform<T, C, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategory,

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

Performs the /= operation.

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

where T::Element: SimdRealField,

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

Performs the /= operation.

impl<T> DivAssign<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the /= operation.

impl<T> DivAssign<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the /= operation.

impl<T, C> DivAssign<Unit<Quaternion<T>>> for Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategory,

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

Performs the /= operation.

impl<T: SimdRealField> DivAssign<Unit<Quaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

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

Performs the /= operation.

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>>

where T: From<[<T as SimdValue>::Element; 16]> + Scalar + PrimitiveSimdValue, T::Element: Scalar, DefaultAllocator: Allocator<R, C>,

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

Converts to this type from the input type.

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>>

where T: From<[<T as SimdValue>::Element; 2]> + Scalar + PrimitiveSimdValue, T::Element: Scalar, DefaultAllocator: Allocator<R, C>,

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

Converts to this type from the input type.

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>>

where T: From<[<T as SimdValue>::Element; 4]> + Scalar + PrimitiveSimdValue, T::Element: Scalar, DefaultAllocator: Allocator<R, C>,

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

Converts to this type from the input type.

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>>

where T: From<[<T as SimdValue>::Element; 8]> + Scalar + PrimitiveSimdValue, T::Element: Scalar, DefaultAllocator: Allocator<R, C>,

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

Converts to this type from the input type.

impl<T: SimdRealField> From<Unit<Complex<T>>> for Matrix2<T>

where T::Element: SimdRealField,

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

Converts to this type from the input type.

impl<T: SimdRealField> From<Unit<Complex<T>>> for Matrix3<T>

where T::Element: SimdRealField,

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

Converts to this type from the input type.

impl<T: SimdRealField> From<Unit<Complex<T>>> for Rotation2<T>

where T::Element: SimdRealField,

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

Converts to this type from the input type.

impl From<Unit<Complex<f32>>> for Mat2

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

Converts to this type from the input type.

impl From<Unit<Complex<f64>>> for DMat2

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

Converts to this type from the input type.

impl<T: SimdRealField> From<Unit<DualQuaternion<T>>> for Isometry3<T>

where T::Element: SimdRealField,

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

Converts to this type from the input type.

impl<T: SimdRealField + RealField> From<Unit<DualQuaternion<T>>> for Matrix4<T>

where T::Element: SimdRealField,

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

Converts to this type from the input type.

impl From<Unit<Matrix<f32, Const<2>, Const<1>, ArrayStorage<f32, 2, 1>>>> for Vec2

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

Converts to this type from the input type.

impl From<Unit<Matrix<f32, Const<3>, Const<1>, ArrayStorage<f32, 3, 1>>>> for Vec3

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

Converts to this type from the input type.

impl From<Unit<Matrix<f32, Const<3>, Const<1>, ArrayStorage<f32, 3, 1>>>> for Vec3A

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

Converts to this type from the input type.

impl From<Unit<Matrix<f32, Const<4>, Const<1>, ArrayStorage<f32, 4, 1>>>> for Vec4

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

Converts to this type from the input type.

impl From<Unit<Matrix<f64, Const<2>, Const<1>, ArrayStorage<f64, 2, 1>>>> for DVec2

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

Converts to this type from the input type.

impl From<Unit<Matrix<f64, Const<3>, Const<1>, ArrayStorage<f64, 3, 1>>>> for DVec3

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

Converts to this type from the input type.

impl From<Unit<Matrix<f64, Const<4>, Const<1>, ArrayStorage<f64, 4, 1>>>> for DVec4

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

Converts to this type from the input type.

impl<T: SimdRealField> From<Unit<Quaternion<T>>> for Matrix3<T>

where T::Element: SimdRealField,

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

Converts to this type from the input type.

impl<T: SimdRealField> From<Unit<Quaternion<T>>> for Matrix4<T>

where T::Element: SimdRealField,

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

Converts to this type from the input type.

impl<T: SimdRealField> From<Unit<Quaternion<T>>> for Rotation3<T>

where T::Element: SimdRealField,

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

Converts to this type from the input type.

impl From<Unit<Quaternion<f32>>> for Quat

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

Converts to this type from the input type.

impl From<Unit<Quaternion<f64>>> for DQuat

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

Converts to this type from the input type.

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

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

Feeds this value into the given Hasher.

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

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Rotation<T, 2>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, C> Mul<&'b Unit<Complex<T>>> for &'a Transform<T, C, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Translation<T, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a UnitComplex<T>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Rotation<T, 2>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'b, T, C> Mul<&'b Unit<Complex<T>>> for Transform<T, C, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Translation<T, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for UnitComplex<T>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

where T::Element: SimdRealField,

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a Isometry3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'a Unit<DualQuaternion<T>>> for &'b Translation3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

where T::Element: SimdRealField,

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for Isometry3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for Translation3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for &'a UnitComplex<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for UnitComplex<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, SB: Storage<T, U3>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, SB: Storage<T, U3>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitQuaternion<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation.

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>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Unit<SVector<T, D>>) -> Self::Output

Performs the * operation.

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>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Unit<SVector<T, D>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, S, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, S>>> for &'a Rotation<T, D>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, S: Storage<T, Const<D>>, ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the * operation.

impl<'b, T, S, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, S>>> for Rotation<T, D>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, S: Storage<T, Const<D>>, ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Rotation<T, 3>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, C> Mul<&'b Unit<Quaternion<T>>> for &'a Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Translation<T, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Rotation<T, 3>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T, C> Mul<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Translation<T, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Rotation<T, 2>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, T, C> Mul<Unit<Complex<T>>> for &'a Transform<T, C, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Translation<T, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a UnitComplex<T>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Rotation<T, 2>

where T::Element: SimdRealField,

type Output = Unit<Complex<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<T, C> Mul<Unit<Complex<T>>> for Transform<T, C, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Translation<T, 2>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>

where T::Element: SimdRealField,

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a Isometry3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a Translation3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

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

where T::Element: SimdRealField,

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for Isometry3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for Translation3<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, S: Storage<T, Const<2>>> Mul<Unit<Matrix<T, Const<2>, Const<1>, S>>> for &'a UnitComplex<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, S: Storage<T, Const<2>>> Mul<Unit<Matrix<T, Const<2>, Const<1>, S>>> for UnitComplex<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, SB: Storage<T, U3>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, SB: Storage<T, U3>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitQuaternion<T>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the * operation.

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>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: Unit<SVector<T, D>>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for Isometry<T, R, D>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: Unit<SVector<T, D>>) -> Self::Output

Performs the * operation.

impl<'a, T, S, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, S>>> for &'a Rotation<T, D>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, S: Storage<T, Const<D>>, ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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

The resulting type after applying the * operator.

fn mul(self, right: Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the * operation.

impl<T, S, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, S>>> for Rotation<T, D>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, S: Storage<T, Const<D>>, ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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

The resulting type after applying the * operator.

fn mul(self, right: Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Rotation<T, 3>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T, C> Mul<Unit<Quaternion<T>>> for &'a Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Translation<T, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Rotation<T, 3>

where T::Element: SimdRealField,

type Output = Unit<Quaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<T, C> Mul<Unit<Quaternion<T>>> for Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategoryMul<TAffine>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Translation<T, 3>

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T> MulAssign<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T: SimdRealField> MulAssign<&'b Unit<Complex<T>>> for Rotation<T, 2>

where T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T> MulAssign<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T, C> MulAssign<&'b Unit<Complex<T>>> for Transform<T, C, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategory,

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

Performs the *= operation.

impl<'b, T: SimdRealField> MulAssign<&'b Unit<Complex<T>>> for UnitComplex<T>

where T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T: SimdRealField> MulAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>

where T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T: SimdRealField> MulAssign<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T> MulAssign<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T> MulAssign<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T, C> MulAssign<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategory,

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

Performs the *= operation.

impl<'b, T: SimdRealField> MulAssign<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T: SimdRealField> MulAssign<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>

where T::Element: SimdRealField,

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

Performs the *= operation.

impl<T> MulAssign<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the *= operation.

impl<T: SimdRealField> MulAssign<Unit<Complex<T>>> for Rotation<T, 2>

where T::Element: SimdRealField,

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

Performs the *= operation.

impl<T> MulAssign<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the *= operation.

impl<T, C> MulAssign<Unit<Complex<T>>> for Transform<T, C, 2>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategory,

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

Performs the *= operation.

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

where T::Element: SimdRealField,

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

Performs the *= operation.

impl<T> MulAssign<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the *= operation.

impl<T> MulAssign<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + SimdRealField, T::Element: SimdRealField,

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

Performs the *= operation.

impl<T, C> MulAssign<Unit<Quaternion<T>>> for Transform<T, C, 3>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, C: TCategory,

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

Performs the *= operation.

impl<T: SimdRealField> MulAssign<Unit<Quaternion<T>>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

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

Performs the *= operation.

impl<T: Scalar + ClosedNeg, R: Dim, C: Dim> Neg for Unit<OMatrix<T, R, C>>

where DefaultAllocator: Allocator<R, C>,

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

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

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>,

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

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

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,

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

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.

fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

The inverse of RelativeEq::relative_eq.

impl<T: Serialize> Serialize for Unit<T>

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

impl<T1, T2> SubsetOf<Unit<Complex<T2>>> for Rotation2<T1>

where T1: RealField, T2: RealField + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(q: &UnitComplex<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(q: &UnitComplex<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2> SubsetOf<Unit<Complex<T2>>> for UnitComplex<T1>

where T1: RealField, T2: RealField + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(uq: &UnitComplex<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(uq: &UnitComplex<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for Isometry3<T1>

where T1: RealField, T2: RealField + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for Rotation3<T1>

where T1: RealField, T2: RealField + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for Translation3<T1>

where T1: RealField, T2: RealField + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for UnitDualQuaternion<T1>

where T1: SimdRealField, T2: SimdRealField + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for UnitQuaternion<T1>

where T1: RealField, T2: RealField + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2> SubsetOf<Unit<Quaternion<T2>>> for Rotation3<T1>

where T1: RealField, T2: RealField + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(q: &UnitQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(q: &UnitQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2> SubsetOf<Unit<Quaternion<T2>>> for UnitQuaternion<T1>

where T1: Scalar, T2: Scalar + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(uq: &UnitQuaternion<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(uq: &UnitQuaternion<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

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,

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

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.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.

impl<T: Copy> Copy for Unit<T>

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>,