pub struct Unit<T> { /* private fields */ }
Expand description
A wrapper that ensures the underlying algebraic entity has a unit norm.
It is likely that the only piece of documentation that you need in this page are:
- 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§
source§impl<T, D, S> Unit<Matrix<T, D, Const<1>, S>>
impl<T, D, S> Unit<Matrix<T, D, Const<1>, S>>
source§impl<T> Unit<T>where
T: Normed,
impl<T> Unit<T>where
T: Normed,
§Construction with normalization
sourcepub fn new_normalize(value: T) -> Unit<T>
pub fn new_normalize(value: T) -> Unit<T>
Normalize the given vector and return it wrapped on a Unit
structure.
sourcepub fn try_new(value: T, min_norm: <T as Normed>::Norm) -> Option<Unit<T>>
pub fn try_new(value: T, min_norm: <T as Normed>::Norm) -> Option<Unit<T>>
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
.
sourcepub fn new_and_get(value: T) -> (Unit<T>, <T as Normed>::Norm)
pub fn new_and_get(value: T) -> (Unit<T>, <T as Normed>::Norm)
Normalize the given vector and return it wrapped on a Unit
structure and its norm.
sourcepub fn try_new_and_get(
value: T,
min_norm: <T as Normed>::Norm,
) -> Option<(Unit<T>, <T as Normed>::Norm)>
pub fn try_new_and_get( value: T, min_norm: <T as Normed>::Norm, ) -> Option<(Unit<T>, <T as Normed>::Norm)>
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
.
sourcepub fn renormalize(&mut self) -> <T as Normed>::Norm
pub fn renormalize(&mut self) -> <T as Normed>::Norm
Normalizes this vector again. This is useful when repeated computations might cause a drift in the norm because of float inaccuracies.
Returns the norm before re-normalization. See .renormalize_fast
for a faster alternative
that may be slightly less accurate if self
drifted significantly from having a unit length.
sourcepub fn renormalize_fast(&mut self)
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.
source§impl<T> Unit<T>
impl<T> Unit<T>
§Data extraction and construction without normalization
sourcepub const fn new_unchecked(value: T) -> Unit<T>
pub const fn new_unchecked(value: T) -> Unit<T>
Wraps the given value, assuming it is already normalized.
sourcepub fn from_ref_unchecked(value: &T) -> &Unit<T>
pub fn from_ref_unchecked(value: &T) -> &Unit<T>
Wraps the given reference, assuming it is already normalized.
sourcepub fn into_inner(self) -> T
pub fn into_inner(self) -> T
Retrieves the underlying value.
sourcepub fn unwrap(self) -> T
👎Deprecated: use .into_inner()
instead
pub fn unwrap(self) -> T
.into_inner()
insteadRetrieves the underlying value.
Deprecated: use Unit::into_inner
instead.
sourcepub fn as_mut_unchecked(&mut self) -> &mut T
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.
source§impl<T, D, S> Unit<Matrix<T, D, Const<1>, S>>
impl<T, D, S> Unit<Matrix<T, D, Const<1>, S>>
§Interpolation between two unit vectors
sourcepub fn slerp<S2>(
&self,
rhs: &Unit<Matrix<T, D, Const<1>, S2>>,
t: T,
) -> Unit<Matrix<T, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<T>>>
pub fn slerp<S2>( &self, rhs: &Unit<Matrix<T, D, Const<1>, S2>>, t: T, ) -> Unit<Matrix<T, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<T>>>
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);
sourcepub fn try_slerp<S2>(
&self,
rhs: &Unit<Matrix<T, D, Const<1>, S2>>,
t: T,
epsilon: T,
) -> Option<Unit<Matrix<T, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<T>>>>
pub fn try_slerp<S2>( &self, rhs: &Unit<Matrix<T, D, Const<1>, S2>>, t: T, epsilon: T, ) -> Option<Unit<Matrix<T, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<T>>>>
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).
source§impl<T> Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
sourcepub fn angle(&self) -> T
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);
sourcepub fn quaternion(&self) -> &Quaternion<T>
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));
sourcepub fn conjugate(&self) -> Unit<Quaternion<T>>
pub fn conjugate(&self) -> Unit<Quaternion<T>>
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));
sourcepub fn inverse(&self) -> Unit<Quaternion<T>>
pub fn inverse(&self) -> Unit<Quaternion<T>>
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());
sourcepub fn angle_to(&self, other: &Unit<Quaternion<T>>) -> T
pub fn angle_to(&self, other: &Unit<Quaternion<T>>) -> 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);
sourcepub fn rotation_to(&self, other: &Unit<Quaternion<T>>) -> Unit<Quaternion<T>>
pub fn rotation_to(&self, other: &Unit<Quaternion<T>>) -> Unit<Quaternion<T>>
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);
sourcepub fn lerp(&self, other: &Unit<Quaternion<T>>, t: T) -> Quaternion<T>
pub fn lerp(&self, other: &Unit<Quaternion<T>>, 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));
sourcepub fn nlerp(&self, other: &Unit<Quaternion<T>>, t: T) -> Unit<Quaternion<T>>
pub fn nlerp(&self, other: &Unit<Quaternion<T>>, t: T) -> Unit<Quaternion<T>>
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)));
sourcepub fn slerp(&self, other: &Unit<Quaternion<T>>, t: T) -> Unit<Quaternion<T>>where
T: RealField,
pub fn slerp(&self, other: &Unit<Quaternion<T>>, t: T) -> Unit<Quaternion<T>>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));
sourcepub fn try_slerp(
&self,
other: &Unit<Quaternion<T>>,
t: T,
epsilon: T,
) -> Option<Unit<Quaternion<T>>>where
T: RealField,
pub fn try_slerp(
&self,
other: &Unit<Quaternion<T>>,
t: T,
epsilon: T,
) -> Option<Unit<Quaternion<T>>>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 returnNone
.
sourcepub fn conjugate_mut(&mut self)
pub fn conjugate_mut(&mut self)
Compute the conjugate of this unit quaternion in-place.
sourcepub fn inverse_mut(&mut self)
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());
sourcepub fn axis(
&self,
) -> Option<Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>>where
T: RealField,
pub fn axis(
&self,
) -> Option<Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>>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());
sourcepub fn scaled_axis(
&self,
) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>where
T: RealField,
pub fn scaled_axis(
&self,
) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>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);
sourcepub fn axis_angle(
&self,
) -> Option<(Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>, T)>where
T: RealField,
pub fn axis_angle(
&self,
) -> Option<(Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>, 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());
sourcepub fn exp(&self) -> Quaternion<T>
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.
sourcepub fn ln(&self) -> Quaternion<T>where
T: RealField,
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);
sourcepub fn powf(&self, n: T) -> Unit<Quaternion<T>>where
T: RealField,
pub fn powf(&self, n: T) -> Unit<Quaternion<T>>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);
sourcepub fn to_rotation_matrix(self) -> Rotation<T, 3>
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);
sourcepub fn to_euler_angles(self) -> (T, T, T)where
T: RealField,
👎Deprecated: This is renamed to use .euler_angles()
.
pub fn to_euler_angles(self) -> (T, T, T)where
T: RealField,
.euler_angles()
.Converts this unit quaternion into its equivalent Euler angles.
The angles are produced in the form (roll, pitch, yaw).
sourcepub fn euler_angles(&self) -> (T, T, T)where
T: RealField,
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);
sourcepub fn to_homogeneous(
self,
) -> Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>
pub fn to_homogeneous( self, ) -> Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>
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);
sourcepub fn transform_point(&self, pt: &OPoint<T, Const<3>>) -> OPoint<T, Const<3>>
pub fn transform_point(&self, pt: &OPoint<T, Const<3>>) -> OPoint<T, Const<3>>
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);
sourcepub fn transform_vector(
&self,
v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>,
) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
pub fn transform_vector( &self, v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>, ) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
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);
sourcepub fn inverse_transform_point(
&self,
pt: &OPoint<T, Const<3>>,
) -> OPoint<T, Const<3>>
pub fn inverse_transform_point( &self, pt: &OPoint<T, Const<3>>, ) -> OPoint<T, Const<3>>
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);
sourcepub fn inverse_transform_vector(
&self,
v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>,
) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
pub fn inverse_transform_vector( &self, v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>, ) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
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);
sourcepub fn inverse_transform_unit_vector(
&self,
v: &Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>,
) -> Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>
pub fn inverse_transform_unit_vector( &self, v: &Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>, ) -> Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>
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);
sourcepub fn append_axisangle_linearized(
&self,
axisangle: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>,
) -> Unit<Quaternion<T>>
pub fn append_axisangle_linearized( &self, axisangle: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>, ) -> Unit<Quaternion<T>>
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
.
source§impl<T> Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
sourcepub fn identity() -> Unit<Quaternion<T>>
pub fn identity() -> Unit<Quaternion<T>>
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);
sourcepub fn cast<To>(self) -> Unit<Quaternion<To>>where
To: Scalar + SupersetOf<T>,
pub fn cast<To>(self) -> Unit<Quaternion<To>>where
To: Scalar + SupersetOf<T>,
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);
sourcepub fn from_axis_angle<SB>(
axis: &Unit<Matrix<T, Const<3>, Const<1>, SB>>,
angle: T,
) -> Unit<Quaternion<T>>
pub fn from_axis_angle<SB>( axis: &Unit<Matrix<T, Const<3>, Const<1>, SB>>, angle: T, ) -> Unit<Quaternion<T>>
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());
sourcepub fn from_quaternion(q: Quaternion<T>) -> Unit<Quaternion<T>>
pub fn from_quaternion(q: Quaternion<T>) -> Unit<Quaternion<T>>
Creates a new unit quaternion from a quaternion.
The input quaternion will be normalized.
sourcepub fn from_euler_angles(roll: T, pitch: T, yaw: T) -> Unit<Quaternion<T>>
pub fn from_euler_angles(roll: T, pitch: T, yaw: T) -> Unit<Quaternion<T>>
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);
sourcepub fn from_basis_unchecked(
basis: &[Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>; 3],
) -> Unit<Quaternion<T>>
pub fn from_basis_unchecked( basis: &[Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>; 3], ) -> Unit<Quaternion<T>>
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.
sourcepub fn from_rotation_matrix(rotmat: &Rotation<T, 3>) -> Unit<Quaternion<T>>
pub fn from_rotation_matrix(rotmat: &Rotation<T, 3>) -> Unit<Quaternion<T>>
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);
sourcepub fn from_matrix(
m: &Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>,
) -> Unit<Quaternion<T>>where
T: RealField,
pub fn from_matrix(
m: &Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>,
) -> Unit<Quaternion<T>>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.
sourcepub fn from_matrix_eps(
m: &Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>,
eps: T,
max_iter: usize,
guess: Unit<Quaternion<T>>,
) -> Unit<Quaternion<T>>where
T: RealField,
pub fn from_matrix_eps(
m: &Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>,
eps: T,
max_iter: usize,
guess: Unit<Quaternion<T>>,
) -> Unit<Quaternion<T>>where
T: RealField,
Builds an unit quaternion by extracting the rotation part of the given transformation m
.
This implements “A Robust Method to Extract the Rotational Part of Deformations” by Müller et al.
§Parameters
m
: the matrix from which the rotational part is to be extracted.eps
: the angular errors tolerated between the current rotation and the optimal one.max_iter
: the maximum number of iterations. Loops indefinitely until convergence if set to0
.guess
: an estimate of the solution. Convergence will be significantly faster if an initial solution close to the actual solution is provided. Can be set toUnitQuaternion::identity()
if no other guesses come to mind.
sourcepub fn rotation_between<SB, SC>(
a: &Matrix<T, Const<3>, Const<1>, SB>,
b: &Matrix<T, Const<3>, Const<1>, SC>,
) -> Option<Unit<Quaternion<T>>>
pub fn rotation_between<SB, SC>( a: &Matrix<T, Const<3>, Const<1>, SB>, b: &Matrix<T, Const<3>, Const<1>, SC>, ) -> Option<Unit<Quaternion<T>>>
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);
sourcepub fn scaled_rotation_between<SB, SC>(
a: &Matrix<T, Const<3>, Const<1>, SB>,
b: &Matrix<T, Const<3>, Const<1>, SC>,
s: T,
) -> Option<Unit<Quaternion<T>>>
pub fn scaled_rotation_between<SB, SC>( a: &Matrix<T, Const<3>, Const<1>, SB>, b: &Matrix<T, Const<3>, Const<1>, SC>, s: T, ) -> Option<Unit<Quaternion<T>>>
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);
sourcepub fn rotation_between_axis<SB, SC>(
a: &Unit<Matrix<T, Const<3>, Const<1>, SB>>,
b: &Unit<Matrix<T, Const<3>, Const<1>, SC>>,
) -> Option<Unit<Quaternion<T>>>
pub fn rotation_between_axis<SB, SC>( a: &Unit<Matrix<T, Const<3>, Const<1>, SB>>, b: &Unit<Matrix<T, Const<3>, Const<1>, SC>>, ) -> Option<Unit<Quaternion<T>>>
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);
sourcepub fn scaled_rotation_between_axis<SB, SC>(
na: &Unit<Matrix<T, Const<3>, Const<1>, SB>>,
nb: &Unit<Matrix<T, Const<3>, Const<1>, SC>>,
s: T,
) -> Option<Unit<Quaternion<T>>>
pub fn scaled_rotation_between_axis<SB, SC>( na: &Unit<Matrix<T, Const<3>, Const<1>, SB>>, nb: &Unit<Matrix<T, Const<3>, Const<1>, SC>>, s: T, ) -> Option<Unit<Quaternion<T>>>
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);
sourcepub fn face_towards<SB, SC>(
dir: &Matrix<T, Const<3>, Const<1>, SB>,
up: &Matrix<T, Const<3>, Const<1>, SC>,
) -> Unit<Quaternion<T>>
pub fn face_towards<SB, SC>( dir: &Matrix<T, Const<3>, Const<1>, SB>, up: &Matrix<T, Const<3>, Const<1>, SC>, ) -> Unit<Quaternion<T>>
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());
sourcepub fn new_observer_frames<SB, SC>(
dir: &Matrix<T, Const<3>, Const<1>, SB>,
up: &Matrix<T, Const<3>, Const<1>, SC>,
) -> Unit<Quaternion<T>>
👎Deprecated: renamed to face_towards
pub fn new_observer_frames<SB, SC>( dir: &Matrix<T, Const<3>, Const<1>, SB>, up: &Matrix<T, Const<3>, Const<1>, SC>, ) -> Unit<Quaternion<T>>
face_towards
Deprecated: Use UnitQuaternion::face_towards
instead.
sourcepub fn look_at_rh<SB, SC>(
dir: &Matrix<T, Const<3>, Const<1>, SB>,
up: &Matrix<T, Const<3>, Const<1>, SC>,
) -> Unit<Quaternion<T>>
pub fn look_at_rh<SB, SC>( dir: &Matrix<T, Const<3>, Const<1>, SB>, up: &Matrix<T, Const<3>, Const<1>, SC>, ) -> Unit<Quaternion<T>>
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());
sourcepub fn look_at_lh<SB, SC>(
dir: &Matrix<T, Const<3>, Const<1>, SB>,
up: &Matrix<T, Const<3>, Const<1>, SC>,
) -> Unit<Quaternion<T>>
pub fn look_at_lh<SB, SC>( dir: &Matrix<T, Const<3>, Const<1>, SB>, up: &Matrix<T, Const<3>, Const<1>, SC>, ) -> Unit<Quaternion<T>>
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());
sourcepub fn new<SB>(
axisangle: Matrix<T, Const<3>, Const<1>, SB>,
) -> Unit<Quaternion<T>>
pub fn new<SB>( axisangle: Matrix<T, Const<3>, Const<1>, SB>, ) -> Unit<Quaternion<T>>
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());
sourcepub fn new_eps<SB>(
axisangle: Matrix<T, Const<3>, Const<1>, SB>,
eps: T,
) -> Unit<Quaternion<T>>
pub fn new_eps<SB>( axisangle: Matrix<T, Const<3>, Const<1>, SB>, eps: T, ) -> Unit<Quaternion<T>>
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());
sourcepub fn from_scaled_axis<SB>(
axisangle: Matrix<T, Const<3>, Const<1>, SB>,
) -> Unit<Quaternion<T>>
pub fn from_scaled_axis<SB>( axisangle: Matrix<T, Const<3>, Const<1>, SB>, ) -> Unit<Quaternion<T>>
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());
sourcepub fn from_scaled_axis_eps<SB>(
axisangle: Matrix<T, Const<3>, Const<1>, SB>,
eps: T,
) -> Unit<Quaternion<T>>
pub fn from_scaled_axis_eps<SB>( axisangle: Matrix<T, Const<3>, Const<1>, SB>, eps: T, ) -> Unit<Quaternion<T>>
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());
sourcepub fn mean_of(
unit_quaternions: impl IntoIterator<Item = Unit<Quaternion<T>>>,
) -> Unit<Quaternion<T>>where
T: RealField,
pub fn mean_of(
unit_quaternions: impl IntoIterator<Item = Unit<Quaternion<T>>>,
) -> Unit<Quaternion<T>>where
T: RealField,
Create the mean unit quaternion from a data structure implementing IntoIterator
returning unit quaternions.
The method will panic if the iterator does not return any quaternions.
Algorithm from: Oshman, Yaakov, and Avishy Carmi. “Attitude estimation from vector observations using a genetic-algorithm-embedded quaternion particle filter.” Journal of Guidance, Control, and Dynamics 29.4 (2006): 879-891.
§Example
let q1 = UnitQuaternion::from_euler_angles(0.0, 0.0, 0.0);
let q2 = UnitQuaternion::from_euler_angles(-0.1, 0.0, 0.0);
let q3 = UnitQuaternion::from_euler_angles(0.1, 0.0, 0.0);
let quat_vec = vec![q1, q2, q3];
let q_mean = UnitQuaternion::mean_of(quat_vec);
let euler_angles_mean = q_mean.euler_angles();
assert_relative_eq!(euler_angles_mean.0, 0.0, epsilon = 1.0e-7)
source§impl<T> Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
sourcepub fn dual_quaternion(&self) -> &DualQuaternion<T>
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)
));
sourcepub fn conjugate(&self) -> Unit<DualQuaternion<T>>
pub fn conjugate(&self) -> Unit<DualQuaternion<T>>
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());
sourcepub fn conjugate_mut(&mut self)
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());
sourcepub fn inverse(&self) -> Unit<DualQuaternion<T>>
pub fn inverse(&self) -> Unit<DualQuaternion<T>>
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);
sourcepub fn inverse_mut(&mut self)
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);
sourcepub fn isometry_to(
&self,
other: &Unit<DualQuaternion<T>>,
) -> Unit<DualQuaternion<T>>
pub fn isometry_to( &self, other: &Unit<DualQuaternion<T>>, ) -> Unit<DualQuaternion<T>>
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);
sourcepub fn lerp(&self, other: &Unit<DualQuaternion<T>>, t: T) -> DualQuaternion<T>
pub fn lerp(&self, other: &Unit<DualQuaternion<T>>, 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
);
sourcepub fn nlerp(
&self,
other: &Unit<DualQuaternion<T>>,
t: T,
) -> Unit<DualQuaternion<T>>
pub fn nlerp( &self, other: &Unit<DualQuaternion<T>>, t: T, ) -> Unit<DualQuaternion<T>>
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);
sourcepub fn sclerp(
&self,
other: &Unit<DualQuaternion<T>>,
t: T,
) -> Unit<DualQuaternion<T>>where
T: RealField,
pub fn sclerp(
&self,
other: &Unit<DualQuaternion<T>>,
t: T,
) -> Unit<DualQuaternion<T>>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);
sourcepub fn try_sclerp(
&self,
other: &Unit<DualQuaternion<T>>,
t: T,
epsilon: T,
) -> Option<Unit<DualQuaternion<T>>>where
T: RealField,
pub fn try_sclerp(
&self,
other: &Unit<DualQuaternion<T>>,
t: T,
epsilon: T,
) -> Option<Unit<DualQuaternion<T>>>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 returnNone
.
sourcepub fn rotation(&self) -> Unit<Quaternion<T>>
pub fn rotation(&self) -> Unit<Quaternion<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
);
sourcepub fn translation(&self) -> Translation<T, 3>
pub fn translation(&self) -> Translation<T, 3>
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
);
sourcepub fn to_isometry(self) -> Isometry<T, Unit<Quaternion<T>>, 3>
pub fn to_isometry(self) -> Isometry<T, Unit<Quaternion<T>>, 3>
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);
sourcepub fn transform_point(&self, pt: &OPoint<T, Const<3>>) -> OPoint<T, Const<3>>
pub fn transform_point(&self, pt: &OPoint<T, Const<3>>) -> OPoint<T, Const<3>>
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
);
sourcepub fn transform_vector(
&self,
v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>,
) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
pub fn transform_vector( &self, v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>, ) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
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
);
sourcepub fn inverse_transform_point(
&self,
pt: &OPoint<T, Const<3>>,
) -> OPoint<T, Const<3>>
pub fn inverse_transform_point( &self, pt: &OPoint<T, Const<3>>, ) -> OPoint<T, Const<3>>
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
);
sourcepub fn inverse_transform_vector(
&self,
v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>,
) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
pub fn inverse_transform_vector( &self, v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>, ) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
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
);
sourcepub fn inverse_transform_unit_vector(
&self,
v: &Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>,
) -> Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>
pub fn inverse_transform_unit_vector( &self, v: &Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>, ) -> Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>
Rotate a unit vector by the inverse of this unit quaternion, ignoring the translational component. This may be cheaper than inverting the unit dual quaternion and transforming the vector.
§Example
let dq = UnitDualQuaternion::from_parts(
Vector3::new(0.0, 3.0, 0.0).into(),
UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let vector = Unit::new_unchecked(Vector3::new(0.0, 1.0, 0.0));
assert_relative_eq!(
dq.inverse_transform_unit_vector(&vector),
Unit::new_unchecked(Vector3::new(0.0, 0.0, -1.0)),
epsilon = 1.0e-6
);
source§impl<T> Unit<DualQuaternion<T>>where
T: SimdRealField + RealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<DualQuaternion<T>>where
T: SimdRealField + RealField,
<T as SimdValue>::Element: SimdRealField,
sourcepub fn to_homogeneous(
self,
) -> Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>
pub fn to_homogeneous( self, ) -> Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>
Converts this unit dual quaternion interpreted as an isometry into its equivalent homogeneous transformation matrix.
§Example
let dq = UnitDualQuaternion::from_parts(
Vector3::new(1.0, 3.0, 2.0).into(),
UnitQuaternion::from_axis_angle(&Vector3::z_axis(), std::f32::consts::FRAC_PI_6)
);
let expected = Matrix4::new(0.8660254, -0.5, 0.0, 1.0,
0.5, 0.8660254, 0.0, 3.0,
0.0, 0.0, 1.0, 2.0,
0.0, 0.0, 0.0, 1.0);
assert_relative_eq!(dq.to_homogeneous(), expected, epsilon = 1.0e-6);
source§impl<T> Unit<DualQuaternion<T>>where
T: SimdRealField,
impl<T> Unit<DualQuaternion<T>>where
T: SimdRealField,
sourcepub fn identity() -> Unit<DualQuaternion<T>>
pub fn identity() -> Unit<DualQuaternion<T>>
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());
sourcepub fn cast<To>(self) -> Unit<DualQuaternion<To>>
pub fn cast<To>(self) -> Unit<DualQuaternion<To>>
Cast the components of self
to another type.
§Example
let q = UnitDualQuaternion::<f64>::identity();
let q2 = q.cast::<f32>();
assert_eq!(q2, UnitDualQuaternion::<f32>::identity());
source§impl<T> Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
sourcepub fn from_parts(
translation: Translation<T, 3>,
rotation: Unit<Quaternion<T>>,
) -> Unit<DualQuaternion<T>>
pub fn from_parts( translation: Translation<T, 3>, rotation: Unit<Quaternion<T>>, ) -> Unit<DualQuaternion<T>>
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);
sourcepub fn from_isometry(
isometry: &Isometry<T, Unit<Quaternion<T>>, 3>,
) -> Unit<DualQuaternion<T>>
pub fn from_isometry( isometry: &Isometry<T, Unit<Quaternion<T>>, 3>, ) -> Unit<DualQuaternion<T>>
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);
sourcepub fn from_rotation(rotation: Unit<Quaternion<T>>) -> Unit<DualQuaternion<T>>
pub fn from_rotation(rotation: Unit<Quaternion<T>>) -> Unit<DualQuaternion<T>>
Creates a dual quaternion from a unit quaternion rotation.
§Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let rot = UnitQuaternion::new_normalize(q);
let dq = UnitDualQuaternion::from_rotation(rot);
assert_relative_eq!(dq.as_ref().real.norm(), 1.0, epsilon = 1.0e-6);
assert_eq!(dq.as_ref().dual.norm(), 0.0);
source§impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
§Angle extraction
sourcepub fn angle(&self) -> T
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);
sourcepub fn sin_angle(&self) -> T
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());
sourcepub fn cos_angle(&self) -> T
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());
sourcepub fn scaled_axis(
&self,
) -> Matrix<T, Const<1>, Const<1>, ArrayStorage<T, 1, 1>>
pub fn scaled_axis( &self, ) -> Matrix<T, Const<1>, Const<1>, ArrayStorage<T, 1, 1>>
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.
sourcepub fn axis_angle(
&self,
) -> Option<(Unit<Matrix<T, Const<1>, Const<1>, ArrayStorage<T, 1, 1>>>, T)>where
T: RealField,
pub fn axis_angle(
&self,
) -> Option<(Unit<Matrix<T, Const<1>, Const<1>, ArrayStorage<T, 1, 1>>>, T)>where
T: RealField,
The rotation axis and angle in (0, pi] of this complex number.
This is generally used in the context of generic programming. Using
the .angle()
method instead is more common.
Returns None
if the angle is zero.
source§impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
§Conjugation and inversion
sourcepub fn conjugate(&self) -> Unit<Complex<T>>
pub fn conjugate(&self) -> Unit<Complex<T>>
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);
sourcepub fn inverse(&self) -> Unit<Complex<T>>
pub fn inverse(&self) -> Unit<Complex<T>>
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);
sourcepub fn conjugate_mut(&mut self)
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);
sourcepub fn inverse_mut(&mut self)
pub fn inverse_mut(&mut self)
Inverts in-place this unit complex number.
§Example
let angle = 1.7;
let mut rot = UnitComplex::new(angle);
rot.inverse_mut();
assert_relative_eq!(rot * UnitComplex::new(angle), UnitComplex::identity());
assert_relative_eq!(UnitComplex::new(angle) * rot, UnitComplex::identity());
source§impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
§Conversion to a matrix
sourcepub fn to_rotation_matrix(self) -> Rotation<T, 2>
pub fn to_rotation_matrix(self) -> Rotation<T, 2>
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);
sourcepub fn to_homogeneous(
self,
) -> Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>
pub fn to_homogeneous( self, ) -> Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>
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);
source§impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
§Transformation of a vector or a point
sourcepub fn transform_point(&self, pt: &OPoint<T, Const<2>>) -> OPoint<T, Const<2>>
pub fn transform_point(&self, pt: &OPoint<T, Const<2>>) -> OPoint<T, Const<2>>
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);
sourcepub fn transform_vector(
&self,
v: &Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>,
) -> Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>
pub fn transform_vector( &self, v: &Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>, ) -> Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>
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);
sourcepub fn inverse_transform_point(
&self,
pt: &OPoint<T, Const<2>>,
) -> OPoint<T, Const<2>>
pub fn inverse_transform_point( &self, pt: &OPoint<T, Const<2>>, ) -> OPoint<T, Const<2>>
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);
sourcepub fn inverse_transform_vector(
&self,
v: &Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>,
) -> Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>
pub fn inverse_transform_vector( &self, v: &Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>, ) -> Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>
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);
sourcepub fn inverse_transform_unit_vector(
&self,
v: &Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>,
) -> Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>
pub fn inverse_transform_unit_vector( &self, v: &Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>, ) -> Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>
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);
source§impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
§Interpolation
sourcepub fn slerp(&self, other: &Unit<Complex<T>>, t: T) -> Unit<Complex<T>>
pub fn slerp(&self, other: &Unit<Complex<T>>, t: T) -> Unit<Complex<T>>
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);
source§impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
§Identity
source§impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
§Construction from a 2D rotation angle
sourcepub fn new(angle: T) -> Unit<Complex<T>>
pub fn new(angle: T) -> Unit<Complex<T>>
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));
sourcepub fn from_angle(angle: T) -> Unit<Complex<T>>
pub fn from_angle(angle: T) -> Unit<Complex<T>>
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));
sourcepub fn from_cos_sin_unchecked(cos: T, sin: T) -> Unit<Complex<T>>
pub fn from_cos_sin_unchecked(cos: T, sin: T) -> Unit<Complex<T>>
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));
sourcepub fn from_scaled_axis<SB>(
axisangle: Matrix<T, Const<1>, Const<1>, SB>,
) -> Unit<Complex<T>>
pub fn from_scaled_axis<SB>( axisangle: Matrix<T, Const<1>, Const<1>, SB>, ) -> Unit<Complex<T>>
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.
source§impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
§Construction from an existing 2D matrix or complex number
sourcepub fn cast<To>(self) -> Unit<Complex<To>>
pub fn cast<To>(self) -> Unit<Complex<To>>
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));
sourcepub fn complex(&self) -> &Complex<T>
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()));
sourcepub fn from_complex(q: Complex<T>) -> Unit<Complex<T>>
pub fn from_complex(q: Complex<T>) -> Unit<Complex<T>>
Creates a new unit complex number from a complex number.
The input complex number will be normalized.
sourcepub fn from_complex_and_get(q: Complex<T>) -> (Unit<Complex<T>>, T)
pub fn from_complex_and_get(q: Complex<T>) -> (Unit<Complex<T>>, 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.
sourcepub fn from_rotation_matrix(rotmat: &Rotation<T, 2>) -> Unit<Complex<T>>
pub fn from_rotation_matrix(rotmat: &Rotation<T, 2>) -> Unit<Complex<T>>
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));
sourcepub fn from_basis_unchecked(
basis: &[Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>; 2],
) -> Unit<Complex<T>>
pub fn from_basis_unchecked( basis: &[Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>; 2], ) -> Unit<Complex<T>>
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.
sourcepub fn from_matrix(
m: &Matrix<T, Const<2>, Const<2>, ArrayStorage<T, 2, 2>>,
) -> Unit<Complex<T>>where
T: RealField,
pub fn from_matrix(
m: &Matrix<T, Const<2>, Const<2>, ArrayStorage<T, 2, 2>>,
) -> Unit<Complex<T>>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.
sourcepub fn from_matrix_eps(
m: &Matrix<T, Const<2>, Const<2>, ArrayStorage<T, 2, 2>>,
eps: T,
max_iter: usize,
guess: Unit<Complex<T>>,
) -> Unit<Complex<T>>where
T: RealField,
pub fn from_matrix_eps(
m: &Matrix<T, Const<2>, Const<2>, ArrayStorage<T, 2, 2>>,
eps: T,
max_iter: usize,
guess: Unit<Complex<T>>,
) -> Unit<Complex<T>>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 to0
.guess
: an estimate of the solution. Convergence will be significantly faster if an initial solution close to the actual solution is provided. Can be set toUnitQuaternion::identity()
if no other guesses come to mind.
sourcepub fn rotation_to(&self, other: &Unit<Complex<T>>) -> Unit<Complex<T>>
pub fn rotation_to(&self, other: &Unit<Complex<T>>) -> Unit<Complex<T>>
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);
sourcepub fn powf(&self, n: T) -> Unit<Complex<T>>
pub fn powf(&self, n: T) -> Unit<Complex<T>>
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);
source§impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
§Construction from two vectors
sourcepub fn rotation_between<SB, SC>(
a: &Matrix<T, Const<2>, Const<1>, SB>,
b: &Matrix<T, Const<2>, Const<1>, SC>,
) -> Unit<Complex<T>>
pub fn rotation_between<SB, SC>( a: &Matrix<T, Const<2>, Const<1>, SB>, b: &Matrix<T, Const<2>, Const<1>, SC>, ) -> Unit<Complex<T>>
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);
sourcepub fn scaled_rotation_between<SB, SC>(
a: &Matrix<T, Const<2>, Const<1>, SB>,
b: &Matrix<T, Const<2>, Const<1>, SC>,
s: T,
) -> Unit<Complex<T>>
pub fn scaled_rotation_between<SB, SC>( a: &Matrix<T, Const<2>, Const<1>, SB>, b: &Matrix<T, Const<2>, Const<1>, SC>, s: T, ) -> Unit<Complex<T>>
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);
sourcepub fn rotation_between_axis<SB, SC>(
a: &Unit<Matrix<T, Const<2>, Const<1>, SB>>,
b: &Unit<Matrix<T, Const<2>, Const<1>, SC>>,
) -> Unit<Complex<T>>
pub fn rotation_between_axis<SB, SC>( a: &Unit<Matrix<T, Const<2>, Const<1>, SB>>, b: &Unit<Matrix<T, Const<2>, Const<1>, SC>>, ) -> Unit<Complex<T>>
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);
sourcepub fn scaled_rotation_between_axis<SB, SC>(
na: &Unit<Matrix<T, Const<2>, Const<1>, SB>>,
nb: &Unit<Matrix<T, Const<2>, Const<1>, SC>>,
s: T,
) -> Unit<Complex<T>>
pub fn scaled_rotation_between_axis<SB, SC>( na: &Unit<Matrix<T, Const<2>, Const<1>, SB>>, nb: &Unit<Matrix<T, Const<2>, Const<1>, SC>>, s: T, ) -> Unit<Complex<T>>
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§
source§impl<T> AbsDiffEq for Unit<Complex<T>>where
T: RealField,
impl<T> AbsDiffEq for Unit<Complex<T>>where
T: RealField,
source§fn default_epsilon() -> <Unit<Complex<T>> as AbsDiffEq>::Epsilon
fn default_epsilon() -> <Unit<Complex<T>> as AbsDiffEq>::Epsilon
source§fn abs_diff_eq(
&self,
other: &Unit<Complex<T>>,
epsilon: <Unit<Complex<T>> as AbsDiffEq>::Epsilon,
) -> bool
fn abs_diff_eq( &self, other: &Unit<Complex<T>>, epsilon: <Unit<Complex<T>> as AbsDiffEq>::Epsilon, ) -> bool
§fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
AbsDiffEq::abs_diff_eq
].source§impl<T> AbsDiffEq for Unit<DualQuaternion<T>>where
T: RealField<Epsilon = T> + AbsDiffEq,
impl<T> AbsDiffEq for Unit<DualQuaternion<T>>where
T: RealField<Epsilon = T> + AbsDiffEq,
source§fn default_epsilon() -> <Unit<DualQuaternion<T>> as AbsDiffEq>::Epsilon
fn default_epsilon() -> <Unit<DualQuaternion<T>> as AbsDiffEq>::Epsilon
source§fn abs_diff_eq(
&self,
other: &Unit<DualQuaternion<T>>,
epsilon: <Unit<DualQuaternion<T>> as AbsDiffEq>::Epsilon,
) -> bool
fn abs_diff_eq( &self, other: &Unit<DualQuaternion<T>>, epsilon: <Unit<DualQuaternion<T>> as AbsDiffEq>::Epsilon, ) -> bool
§fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
AbsDiffEq::abs_diff_eq
].source§impl<T, R, C, S> AbsDiffEq for Unit<Matrix<T, R, C, S>>where
R: Dim,
C: Dim,
T: Scalar + AbsDiffEq,
S: RawStorage<T, R, C>,
<T as AbsDiffEq>::Epsilon: Clone,
impl<T, R, C, S> AbsDiffEq for Unit<Matrix<T, R, C, S>>where
R: Dim,
C: Dim,
T: Scalar + AbsDiffEq,
S: RawStorage<T, R, C>,
<T as AbsDiffEq>::Epsilon: Clone,
source§fn default_epsilon() -> <Unit<Matrix<T, R, C, S>> as AbsDiffEq>::Epsilon
fn default_epsilon() -> <Unit<Matrix<T, R, C, S>> as AbsDiffEq>::Epsilon
source§fn abs_diff_eq(
&self,
other: &Unit<Matrix<T, R, C, S>>,
epsilon: <Unit<Matrix<T, R, C, S>> as AbsDiffEq>::Epsilon,
) -> bool
fn abs_diff_eq( &self, other: &Unit<Matrix<T, R, C, S>>, epsilon: <Unit<Matrix<T, R, C, S>> as AbsDiffEq>::Epsilon, ) -> bool
§fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
AbsDiffEq::abs_diff_eq
].source§impl<T> AbsDiffEq for Unit<Quaternion<T>>where
T: RealField<Epsilon = T> + AbsDiffEq,
impl<T> AbsDiffEq for Unit<Quaternion<T>>where
T: RealField<Epsilon = T> + AbsDiffEq,
source§fn default_epsilon() -> <Unit<Quaternion<T>> as AbsDiffEq>::Epsilon
fn default_epsilon() -> <Unit<Quaternion<T>> as AbsDiffEq>::Epsilon
source§fn abs_diff_eq(
&self,
other: &Unit<Quaternion<T>>,
epsilon: <Unit<Quaternion<T>> as AbsDiffEq>::Epsilon,
) -> bool
fn abs_diff_eq( &self, other: &Unit<Quaternion<T>>, epsilon: <Unit<Quaternion<T>> as AbsDiffEq>::Epsilon, ) -> bool
§fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
AbsDiffEq::abs_diff_eq
].source§impl<T> AbstractRotation<T, 2> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> AbstractRotation<T, 2> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn inverse_mut(&mut self)
fn inverse_mut(&mut self)
self
to its inverse.source§fn transform_vector(
&self,
v: &Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>,
) -> Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>
fn transform_vector( &self, v: &Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>, ) -> Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>
source§fn transform_point(&self, p: &OPoint<T, Const<2>>) -> OPoint<T, Const<2>>
fn transform_point(&self, p: &OPoint<T, Const<2>>) -> OPoint<T, Const<2>>
source§fn inverse_transform_vector(
&self,
v: &Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>,
) -> Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>
fn inverse_transform_vector( &self, v: &Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>, ) -> Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>
source§fn inverse_transform_point(
&self,
p: &OPoint<T, Const<2>>,
) -> OPoint<T, Const<2>>
fn inverse_transform_point( &self, p: &OPoint<T, Const<2>>, ) -> OPoint<T, Const<2>>
source§fn inverse_transform_unit_vector(
&self,
v: &Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>,
) -> Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>
fn inverse_transform_unit_vector( &self, v: &Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>, ) -> Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>
source§impl<T> AbstractRotation<T, 3> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> AbstractRotation<T, 3> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn identity() -> Unit<Quaternion<T>>
fn identity() -> Unit<Quaternion<T>>
source§fn inverse(&self) -> Unit<Quaternion<T>>
fn inverse(&self) -> Unit<Quaternion<T>>
source§fn inverse_mut(&mut self)
fn inverse_mut(&mut self)
self
to its inverse.source§fn transform_vector(
&self,
v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>,
) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
fn transform_vector( &self, v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>, ) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
source§fn transform_point(&self, p: &OPoint<T, Const<3>>) -> OPoint<T, Const<3>>
fn transform_point(&self, p: &OPoint<T, Const<3>>) -> OPoint<T, Const<3>>
source§fn inverse_transform_vector(
&self,
v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>,
) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
fn inverse_transform_vector( &self, v: &Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>, ) -> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>
source§fn inverse_transform_point(
&self,
p: &OPoint<T, Const<3>>,
) -> OPoint<T, Const<3>>
fn inverse_transform_point( &self, p: &OPoint<T, Const<3>>, ) -> OPoint<T, Const<3>>
source§fn inverse_transform_unit_vector(
&self,
v: &Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>,
) -> Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>
fn inverse_transform_unit_vector( &self, v: &Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>, ) -> Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>
source§impl<T> Default for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Default for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Default for Unit<DualQuaternion<T>>where
T: RealField,
impl<T> Default for Unit<DualQuaternion<T>>where
T: RealField,
source§impl<T> Default for Unit<Quaternion<T>>where
T: RealField,
impl<T> Default for Unit<Quaternion<T>>where
T: RealField,
source§impl<'de, T> Deserialize<'de> for Unit<T>where
T: Deserialize<'de>,
impl<'de, T> Deserialize<'de> for Unit<T>where
T: Deserialize<'de>,
source§fn deserialize<D>(
deserializer: D,
) -> Result<Unit<T>, <D as Deserializer<'de>>::Error>where
D: Deserializer<'de>,
fn deserialize<D>(
deserializer: D,
) -> Result<Unit<T>, <D as Deserializer<'de>>::Error>where
D: Deserializer<'de>,
source§impl<'a, 'b, T> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<DualQuaternion<T>> as Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<DualQuaternion<T>> as Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<'a, 'b, T> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Isometry<T, Unit<Quaternion<T>>, 3>
type Output = Isometry<T, Unit<Quaternion<T>>, 3>
/
operator.source§fn div(
self,
right: &'b Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<Quaternion<T>> as Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, right: &'b Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<Quaternion<T>> as Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<'b, T> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<DualQuaternion<T>> as Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<DualQuaternion<T>> as Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<'b, T> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Isometry<T, Unit<Quaternion<T>>, 3>
type Output = Isometry<T, Unit<Quaternion<T>>, 3>
/
operator.source§fn div(
self,
right: &'b Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<Quaternion<T>> as Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, right: &'b Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<Quaternion<T>> as Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<'a, 'b, T> Div<&'b Rotation<T, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Rotation<T, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Div<&'b Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Div<&'b Rotation<T, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Rotation<T, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Div<&'b Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Similarity<T, Unit<Quaternion<T>>, 3>
type Output = Similarity<T, Unit<Quaternion<T>>, 3>
/
operator.source§fn div(
self,
right: &'b Similarity<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<Quaternion<T>> as Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, right: &'b Similarity<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<Quaternion<T>> as Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<'b, T> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Similarity<T, Unit<Quaternion<T>>, 3>
type Output = Similarity<T, Unit<Quaternion<T>>, 3>
/
operator.source§fn div(
self,
right: &'b Similarity<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<Quaternion<T>> as Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, right: &'b Similarity<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<Quaternion<T>> as Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<'a, 'b, T, C> Div<&'b Transform<T, C, 3>> for &'a Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
impl<'a, 'b, T, C> Div<&'b Transform<T, C, 3>> for &'a Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
source§impl<'b, T, C> Div<&'b Transform<T, C, 3>> for Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
impl<'b, T, C> Div<&'b Transform<T, C, 3>> for Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
source§impl<'a, 'b, T> Div<&'b Translation<T, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Translation<T, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Translation<T, 3>,
) -> <&'a Unit<DualQuaternion<T>> as Div<&'b Translation<T, 3>>>::Output
fn div( self, rhs: &'b Translation<T, 3>, ) -> <&'a Unit<DualQuaternion<T>> as Div<&'b Translation<T, 3>>>::Output
/
operation. Read moresource§impl<'b, T> Div<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Translation<T, 3>,
) -> <Unit<DualQuaternion<T>> as Div<&'b Translation<T, 3>>>::Output
fn div( self, rhs: &'b Translation<T, 3>, ) -> <Unit<DualQuaternion<T>> as Div<&'b Translation<T, 3>>>::Output
/
operation. Read moresource§impl<'a, 'b, T> Div<&'b Unit<Complex<T>>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Unit<Complex<T>>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Div<&'b Unit<Complex<T>>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Unit<Complex<T>>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Div<&'b Unit<DualQuaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Unit<DualQuaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Unit<DualQuaternion<T>>,
) -> <&'a Unit<DualQuaternion<T>> as Div<&'b Unit<DualQuaternion<T>>>>::Output
fn div( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <&'a Unit<DualQuaternion<T>> as Div<&'b Unit<DualQuaternion<T>>>>::Output
/
operation. Read moresource§impl<'a, 'b, T> Div<&'b Unit<DualQuaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Unit<DualQuaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Unit<DualQuaternion<T>>,
) -> <&'a Unit<Quaternion<T>> as Div<&'b Unit<DualQuaternion<T>>>>::Output
fn div( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <&'a Unit<Quaternion<T>> as Div<&'b Unit<DualQuaternion<T>>>>::Output
/
operation. Read moresource§impl<'b, T> Div<&'b Unit<DualQuaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Unit<DualQuaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Unit<DualQuaternion<T>>,
) -> <Unit<DualQuaternion<T>> as Div<&'b Unit<DualQuaternion<T>>>>::Output
fn div( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <Unit<DualQuaternion<T>> as Div<&'b Unit<DualQuaternion<T>>>>::Output
/
operation. Read moresource§impl<'b, T> Div<&'b Unit<DualQuaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Unit<DualQuaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Unit<DualQuaternion<T>>,
) -> <Unit<Quaternion<T>> as Div<&'b Unit<DualQuaternion<T>>>>::Output
fn div( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <Unit<Quaternion<T>> as Div<&'b Unit<DualQuaternion<T>>>>::Output
/
operation. Read moresource§impl<'a, 'b, T> Div<&'b Unit<Quaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Unit<Quaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Unit<Quaternion<T>>,
) -> <&'a Unit<DualQuaternion<T>> as Div<&'b Unit<Quaternion<T>>>>::Output
fn div( self, rhs: &'b Unit<Quaternion<T>>, ) -> <&'a Unit<DualQuaternion<T>> as Div<&'b Unit<Quaternion<T>>>>::Output
/
operation. Read moresource§impl<'a, 'b, T> Div<&'b Unit<Quaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Div<&'b Unit<Quaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<Quaternion<T>>
type Output = Unit<Quaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Unit<Quaternion<T>>,
) -> <&'a Unit<Quaternion<T>> as Div<&'b Unit<Quaternion<T>>>>::Output
fn div( self, rhs: &'b Unit<Quaternion<T>>, ) -> <&'a Unit<Quaternion<T>> as Div<&'b Unit<Quaternion<T>>>>::Output
/
operation. Read moresource§impl<'b, T> Div<&'b Unit<Quaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Unit<Quaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Unit<Quaternion<T>>,
) -> <Unit<DualQuaternion<T>> as Div<&'b Unit<Quaternion<T>>>>::Output
fn div( self, rhs: &'b Unit<Quaternion<T>>, ) -> <Unit<DualQuaternion<T>> as Div<&'b Unit<Quaternion<T>>>>::Output
/
operation. Read moresource§impl<'b, T> Div<&'b Unit<Quaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Div<&'b Unit<Quaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<Quaternion<T>>
type Output = Unit<Quaternion<T>>
/
operator.source§fn div(
self,
rhs: &'b Unit<Quaternion<T>>,
) -> <Unit<Quaternion<T>> as Div<&'b Unit<Quaternion<T>>>>::Output
fn div( self, rhs: &'b Unit<Quaternion<T>>, ) -> <Unit<Quaternion<T>> as Div<&'b Unit<Quaternion<T>>>>::Output
/
operation. Read moresource§impl<'a, T> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<DualQuaternion<T>> as Div<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, rhs: Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<DualQuaternion<T>> as Div<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<'a, T> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Isometry<T, Unit<Quaternion<T>>, 3>
type Output = Isometry<T, Unit<Quaternion<T>>, 3>
/
operator.source§fn div(
self,
right: Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<Quaternion<T>> as Div<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, right: Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<Quaternion<T>> as Div<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<T> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<DualQuaternion<T>> as Div<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, rhs: Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<DualQuaternion<T>> as Div<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<T> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Isometry<T, Unit<Quaternion<T>>, 3>
type Output = Isometry<T, Unit<Quaternion<T>>, 3>
/
operator.source§fn div(
self,
right: Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<Quaternion<T>> as Div<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, right: Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<Quaternion<T>> as Div<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<'a, T> Div<Rotation<T, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Rotation<T, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Div<Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div<Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, T> Div<Rotation<T, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Rotation<T, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Div<Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div<Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, T> Div<Similarity<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Similarity<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Similarity<T, Unit<Quaternion<T>>, 3>
type Output = Similarity<T, Unit<Quaternion<T>>, 3>
/
operator.source§fn div(
self,
right: Similarity<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<Quaternion<T>> as Div<Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, right: Similarity<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<Quaternion<T>> as Div<Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<T> Div<Similarity<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div<Similarity<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Similarity<T, Unit<Quaternion<T>>, 3>
type Output = Similarity<T, Unit<Quaternion<T>>, 3>
/
operator.source§fn div(
self,
right: Similarity<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<Quaternion<T>> as Div<Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
fn div( self, right: Similarity<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<Quaternion<T>> as Div<Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
/
operation. Read moresource§impl<'a, T, C> Div<Transform<T, C, 3>> for &'a Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
impl<'a, T, C> Div<Transform<T, C, 3>> for &'a Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
source§impl<T, C> Div<Transform<T, C, 3>> for Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
impl<T, C> Div<Transform<T, C, 3>> for Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
source§impl<'a, T> Div<Translation<T, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Translation<T, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: Translation<T, 3>,
) -> <&'a Unit<DualQuaternion<T>> as Div<Translation<T, 3>>>::Output
fn div( self, rhs: Translation<T, 3>, ) -> <&'a Unit<DualQuaternion<T>> as Div<Translation<T, 3>>>::Output
/
operation. Read moresource§impl<T> Div<Translation<T, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div<Translation<T, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: Translation<T, 3>,
) -> <Unit<DualQuaternion<T>> as Div<Translation<T, 3>>>::Output
fn div( self, rhs: Translation<T, 3>, ) -> <Unit<DualQuaternion<T>> as Div<Translation<T, 3>>>::Output
/
operation. Read moresource§impl<'a, T> Div<Unit<Complex<T>>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Unit<Complex<T>>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, T> Div<Unit<DualQuaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Unit<DualQuaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: Unit<DualQuaternion<T>>,
) -> <&'a Unit<DualQuaternion<T>> as Div<Unit<DualQuaternion<T>>>>::Output
fn div( self, rhs: Unit<DualQuaternion<T>>, ) -> <&'a Unit<DualQuaternion<T>> as Div<Unit<DualQuaternion<T>>>>::Output
/
operation. Read moresource§impl<'a, T> Div<Unit<DualQuaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Unit<DualQuaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: Unit<DualQuaternion<T>>,
) -> <&'a Unit<Quaternion<T>> as Div<Unit<DualQuaternion<T>>>>::Output
fn div( self, rhs: Unit<DualQuaternion<T>>, ) -> <&'a Unit<Quaternion<T>> as Div<Unit<DualQuaternion<T>>>>::Output
/
operation. Read moresource§impl<T> Div<Unit<DualQuaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div<Unit<DualQuaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: Unit<DualQuaternion<T>>,
) -> <Unit<Quaternion<T>> as Div<Unit<DualQuaternion<T>>>>::Output
fn div( self, rhs: Unit<DualQuaternion<T>>, ) -> <Unit<Quaternion<T>> as Div<Unit<DualQuaternion<T>>>>::Output
/
operation. Read moresource§impl<'a, T> Div<Unit<Quaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Unit<Quaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: Unit<Quaternion<T>>,
) -> <&'a Unit<DualQuaternion<T>> as Div<Unit<Quaternion<T>>>>::Output
fn div( self, rhs: Unit<Quaternion<T>>, ) -> <&'a Unit<DualQuaternion<T>> as Div<Unit<Quaternion<T>>>>::Output
/
operation. Read moresource§impl<'a, T> Div<Unit<Quaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Div<Unit<Quaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<Quaternion<T>>
type Output = Unit<Quaternion<T>>
/
operator.source§fn div(
self,
rhs: Unit<Quaternion<T>>,
) -> <&'a Unit<Quaternion<T>> as Div<Unit<Quaternion<T>>>>::Output
fn div( self, rhs: Unit<Quaternion<T>>, ) -> <&'a Unit<Quaternion<T>> as Div<Unit<Quaternion<T>>>>::Output
/
operation. Read moresource§impl<T> Div<Unit<Quaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div<Unit<Quaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: Unit<Quaternion<T>>,
) -> <Unit<DualQuaternion<T>> as Div<Unit<Quaternion<T>>>>::Output
fn div( self, rhs: Unit<Quaternion<T>>, ) -> <Unit<DualQuaternion<T>> as Div<Unit<Quaternion<T>>>>::Output
/
operation. Read moresource§impl<T> Div for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Div for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
/
operator.source§fn div(
self,
rhs: Unit<DualQuaternion<T>>,
) -> <Unit<DualQuaternion<T>> as Div>::Output
fn div( self, rhs: Unit<DualQuaternion<T>>, ) -> <Unit<DualQuaternion<T>> as Div>::Output
/
operation. Read moresource§impl<T> Div for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Div for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<Quaternion<T>>
type Output = Unit<Quaternion<T>>
/
operator.source§fn div(self, rhs: Unit<Quaternion<T>>) -> <Unit<Quaternion<T>> as Div>::Output
fn div(self, rhs: Unit<Quaternion<T>>) -> <Unit<Quaternion<T>> as Div>::Output
/
operation. Read moresource§impl<'b, T> DivAssign<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> DivAssign<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>)
fn div_assign(&mut self, rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>)
/=
operation. Read moresource§impl<'b, T> DivAssign<&'b Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> DivAssign<&'b Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: &'b Rotation<T, 2>)
fn div_assign(&mut self, rhs: &'b Rotation<T, 2>)
/=
operation. Read moresource§impl<'b, T> DivAssign<&'b Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> DivAssign<&'b Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: &'b Rotation<T, 3>)
fn div_assign(&mut self, rhs: &'b Rotation<T, 3>)
/=
operation. Read moresource§impl<'b, T> DivAssign<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> DivAssign<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: &'b Translation<T, 3>)
fn div_assign(&mut self, rhs: &'b Translation<T, 3>)
/=
operation. Read moresource§impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> DivAssign<&'b Unit<DualQuaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> DivAssign<&'b Unit<DualQuaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: &'b Unit<DualQuaternion<T>>)
fn div_assign(&mut self, rhs: &'b Unit<DualQuaternion<T>>)
/=
operation. Read moresource§impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: &'b Unit<Quaternion<T>>)
fn div_assign(&mut self, rhs: &'b Unit<Quaternion<T>>)
/=
operation. Read moresource§impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: &'b Unit<Quaternion<T>>)
fn div_assign(&mut self, rhs: &'b Unit<Quaternion<T>>)
/=
operation. Read moresource§impl<T> DivAssign<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> DivAssign<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: Isometry<T, Unit<Quaternion<T>>, 3>)
fn div_assign(&mut self, rhs: Isometry<T, Unit<Quaternion<T>>, 3>)
/=
operation. Read moresource§impl<T> DivAssign<Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> DivAssign<Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: Rotation<T, 2>)
fn div_assign(&mut self, rhs: Rotation<T, 2>)
/=
operation. Read moresource§impl<T> DivAssign<Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> DivAssign<Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: Rotation<T, 3>)
fn div_assign(&mut self, rhs: Rotation<T, 3>)
/=
operation. Read moresource§impl<T> DivAssign<Translation<T, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> DivAssign<Translation<T, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: Translation<T, 3>)
fn div_assign(&mut self, rhs: Translation<T, 3>)
/=
operation. Read moresource§impl<T> DivAssign<Unit<Quaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> DivAssign<Unit<Quaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: Unit<Quaternion<T>>)
fn div_assign(&mut self, rhs: Unit<Quaternion<T>>)
/=
operation. Read moresource§impl<T> DivAssign for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> DivAssign for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> DivAssign for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> DivAssign for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: Unit<DualQuaternion<T>>)
fn div_assign(&mut self, rhs: Unit<DualQuaternion<T>>)
/=
operation. Read moresource§impl<T> DivAssign for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> DivAssign for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: Unit<Quaternion<T>>)
fn div_assign(&mut self, rhs: Unit<Quaternion<T>>)
/=
operation. Read moresource§impl<T, R, C> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 16]> for Unit<Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>>
impl<T, R, C> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 16]> for Unit<Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>>
source§impl<T, R, C> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 2]> for Unit<Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>>
impl<T, R, C> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 2]> for Unit<Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>>
source§impl<T, R, C> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 4]> for Unit<Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>>
impl<T, R, C> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 4]> for Unit<Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>>
source§impl<T, R, C> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 8]> for Unit<Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>>
impl<T, R, C> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<<T as SimdValue>::Element>>>; 8]> for Unit<Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>>
source§impl<T> From<[Unit<Quaternion<<T as SimdValue>::Element>>; 16]> for Unit<Quaternion<T>>
impl<T> From<[Unit<Quaternion<<T as SimdValue>::Element>>; 16]> for Unit<Quaternion<T>>
source§fn from(
arr: [Unit<Quaternion<<T as SimdValue>::Element>>; 16],
) -> Unit<Quaternion<T>>
fn from( arr: [Unit<Quaternion<<T as SimdValue>::Element>>; 16], ) -> Unit<Quaternion<T>>
source§impl<T> From<[Unit<Quaternion<<T as SimdValue>::Element>>; 2]> for Unit<Quaternion<T>>
impl<T> From<[Unit<Quaternion<<T as SimdValue>::Element>>; 2]> for Unit<Quaternion<T>>
source§fn from(
arr: [Unit<Quaternion<<T as SimdValue>::Element>>; 2],
) -> Unit<Quaternion<T>>
fn from( arr: [Unit<Quaternion<<T as SimdValue>::Element>>; 2], ) -> Unit<Quaternion<T>>
source§impl<T> From<[Unit<Quaternion<<T as SimdValue>::Element>>; 4]> for Unit<Quaternion<T>>
impl<T> From<[Unit<Quaternion<<T as SimdValue>::Element>>; 4]> for Unit<Quaternion<T>>
source§fn from(
arr: [Unit<Quaternion<<T as SimdValue>::Element>>; 4],
) -> Unit<Quaternion<T>>
fn from( arr: [Unit<Quaternion<<T as SimdValue>::Element>>; 4], ) -> Unit<Quaternion<T>>
source§impl<T> From<[Unit<Quaternion<<T as SimdValue>::Element>>; 8]> for Unit<Quaternion<T>>
impl<T> From<[Unit<Quaternion<<T as SimdValue>::Element>>; 8]> for Unit<Quaternion<T>>
source§fn from(
arr: [Unit<Quaternion<<T as SimdValue>::Element>>; 8],
) -> Unit<Quaternion<T>>
fn from( arr: [Unit<Quaternion<<T as SimdValue>::Element>>; 8], ) -> Unit<Quaternion<T>>
source§impl<T> From<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> From<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn from(iso: Isometry<T, Unit<Quaternion<T>>, 3>) -> Unit<DualQuaternion<T>>
fn from(iso: Isometry<T, Unit<Quaternion<T>>, 3>) -> Unit<DualQuaternion<T>>
source§impl<T> From<Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> From<Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> From<Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> From<Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> From<Unit<Complex<T>>> for Matrix<T, Const<2>, Const<2>, ArrayStorage<T, 2, 2>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> From<Unit<Complex<T>>> for Matrix<T, Const<2>, Const<2>, ArrayStorage<T, 2, 2>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> From<Unit<Complex<T>>> for Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> From<Unit<Complex<T>>> for Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> From<Unit<DualQuaternion<T>>> for Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>where
T: SimdRealField + RealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> From<Unit<DualQuaternion<T>>> for Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>where
T: SimdRealField + RealField,
<T as SimdValue>::Element: SimdRealField,
source§fn from(
dq: Unit<DualQuaternion<T>>,
) -> Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>
fn from( dq: Unit<DualQuaternion<T>>, ) -> Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>
source§impl<T> From<Unit<Quaternion<T>>> for Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> From<Unit<Quaternion<T>>> for Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn from(
q: Unit<Quaternion<T>>,
) -> Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>
fn from( q: Unit<Quaternion<T>>, ) -> Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>
source§impl<T> From<Unit<Quaternion<T>>> for Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> From<Unit<Quaternion<T>>> for Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§fn from(
q: Unit<Quaternion<T>>,
) -> Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>
fn from( q: Unit<Quaternion<T>>, ) -> Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>
source§impl<'a, 'b, T> Mul<&'b DualQuaternion<T>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b DualQuaternion<T>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§fn mul(
self,
rhs: &'b DualQuaternion<T>,
) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b DualQuaternion<T>>>::Output
fn mul( self, rhs: &'b DualQuaternion<T>, ) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b DualQuaternion<T>>>::Output
*
operation. Read moresource§impl<'b, T> Mul<&'b DualQuaternion<T>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b DualQuaternion<T>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§fn mul(
self,
rhs: &'b DualQuaternion<T>,
) -> <Unit<DualQuaternion<T>> as Mul<&'b DualQuaternion<T>>>::Output
fn mul( self, rhs: &'b DualQuaternion<T>, ) -> <Unit<DualQuaternion<T>> as Mul<&'b DualQuaternion<T>>>::Output
*
operation. Read moresource§impl<'a, 'b, T> Mul<&'b Isometry<T, Unit<Complex<T>>, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Isometry<T, Unit<Complex<T>>, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Mul<&'b Isometry<T, Unit<Complex<T>>, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Isometry<T, Unit<Complex<T>>, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<'a, 'b, T> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Isometry<T, Unit<Quaternion<T>>, 3>
type Output = Isometry<T, Unit<Quaternion<T>>, 3>
*
operator.source§fn mul(
self,
right: &'b Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<Quaternion<T>> as Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, right: &'b Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<Quaternion<T>> as Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<'b, T> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<DualQuaternion<T>> as Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<DualQuaternion<T>> as Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<'b, T> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Isometry<T, Unit<Quaternion<T>>, 3>
type Output = Isometry<T, Unit<Quaternion<T>>, 3>
*
operator.source§fn mul(
self,
right: &'b Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<Quaternion<T>> as Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, right: &'b Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<Quaternion<T>> as Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<'a, 'b, T, S> Mul<&'b Matrix<T, Const<2>, Const<1>, S>> for &'a Unit<Complex<T>>
impl<'a, 'b, T, S> Mul<&'b Matrix<T, Const<2>, Const<1>, S>> for &'a Unit<Complex<T>>
source§impl<'a, 'b, T, SB> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for &'a Unit<DualQuaternion<T>>
impl<'a, 'b, T, SB> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for &'a Unit<DualQuaternion<T>>
source§impl<'a, 'b, T, SB> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for &'a Unit<Quaternion<T>>
impl<'a, 'b, T, SB> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for &'a Unit<Quaternion<T>>
source§impl<'b, T, SB> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for Unit<DualQuaternion<T>>
impl<'b, T, SB> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for Unit<DualQuaternion<T>>
source§impl<'b, T, SB> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for Unit<Quaternion<T>>
impl<'b, T, SB> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for Unit<Quaternion<T>>
source§impl<'a, 'b, T> Mul<&'b OPoint<T, Const<2>>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b OPoint<T, Const<2>>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Mul<&'b OPoint<T, Const<2>>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b OPoint<T, Const<2>>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Mul<&'b OPoint<T, Const<3>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b OPoint<T, Const<3>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Mul<&'b OPoint<T, Const<3>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b OPoint<T, Const<3>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Mul<&'b OPoint<T, Const<3>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b OPoint<T, Const<3>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Mul<&'b OPoint<T, Const<3>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b OPoint<T, Const<3>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Mul<&'b Rotation<T, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Rotation<T, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Mul<&'b Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Mul<&'b Rotation<T, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Rotation<T, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Mul<&'b Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Mul<&'b Similarity<T, Unit<Complex<T>>, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Similarity<T, Unit<Complex<T>>, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Mul<&'b Similarity<T, Unit<Complex<T>>, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Similarity<T, Unit<Complex<T>>, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Similarity<T, Unit<Quaternion<T>>, 3>
type Output = Similarity<T, Unit<Quaternion<T>>, 3>
*
operator.source§fn mul(
self,
right: &'b Similarity<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<Quaternion<T>> as Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, right: &'b Similarity<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<Quaternion<T>> as Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<'b, T> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Similarity<T, Unit<Quaternion<T>>, 3>
type Output = Similarity<T, Unit<Quaternion<T>>, 3>
*
operator.source§fn mul(
self,
right: &'b Similarity<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<Quaternion<T>> as Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, right: &'b Similarity<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<Quaternion<T>> as Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<'a, 'b, T, C> Mul<&'b Transform<T, C, 2>> for &'a Unit<Complex<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
impl<'a, 'b, T, C> Mul<&'b Transform<T, C, 2>> for &'a Unit<Complex<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
source§impl<'b, T, C> Mul<&'b Transform<T, C, 2>> for Unit<Complex<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
impl<'b, T, C> Mul<&'b Transform<T, C, 2>> for Unit<Complex<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
source§impl<'a, 'b, T, C> Mul<&'b Transform<T, C, 3>> for &'a Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
impl<'a, 'b, T, C> Mul<&'b Transform<T, C, 3>> for &'a Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
source§impl<'b, T, C> Mul<&'b Transform<T, C, 3>> for Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
impl<'b, T, C> Mul<&'b Transform<T, C, 3>> for Unit<Quaternion<T>>where
T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField,
C: TCategoryMul<TAffine>,
source§impl<'a, 'b, T> Mul<&'b Translation<T, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Translation<T, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Mul<&'b Translation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Translation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Mul<&'b Translation<T, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Translation<T, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Translation<T, 3>,
) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b Translation<T, 3>>>::Output
fn mul( self, rhs: &'b Translation<T, 3>, ) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b Translation<T, 3>>>::Output
*
operation. Read moresource§impl<'a, 'b, T> Mul<&'b Translation<T, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Translation<T, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Isometry<T, Unit<Quaternion<T>>, 3>
type Output = Isometry<T, Unit<Quaternion<T>>, 3>
*
operator.source§fn mul(
self,
right: &'b Translation<T, 3>,
) -> <&'a Unit<Quaternion<T>> as Mul<&'b Translation<T, 3>>>::Output
fn mul( self, right: &'b Translation<T, 3>, ) -> <&'a Unit<Quaternion<T>> as Mul<&'b Translation<T, 3>>>::Output
*
operation. Read moresource§impl<'b, T> Mul<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Translation<T, 3>,
) -> <Unit<DualQuaternion<T>> as Mul<&'b Translation<T, 3>>>::Output
fn mul( self, rhs: &'b Translation<T, 3>, ) -> <Unit<DualQuaternion<T>> as Mul<&'b Translation<T, 3>>>::Output
*
operation. Read moresource§impl<'b, T> Mul<&'b Translation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Translation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Isometry<T, Unit<Quaternion<T>>, 3>
type Output = Isometry<T, Unit<Quaternion<T>>, 3>
*
operator.source§fn mul(
self,
right: &'b Translation<T, 3>,
) -> <Unit<Quaternion<T>> as Mul<&'b Translation<T, 3>>>::Output
fn mul( self, right: &'b Translation<T, 3>, ) -> <Unit<Quaternion<T>> as Mul<&'b Translation<T, 3>>>::Output
*
operation. Read moresource§impl<'a, 'b, T> Mul<&'b Unit<Complex<T>>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Unit<Complex<T>>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'b, T> Mul<&'b Unit<Complex<T>>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Unit<Complex<T>>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, 'b, T> Mul<&'b Unit<DualQuaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Unit<DualQuaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Unit<DualQuaternion<T>>,
) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b Unit<DualQuaternion<T>>>>::Output
fn mul( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b Unit<DualQuaternion<T>>>>::Output
*
operation. Read moresource§impl<'a, 'b, T> Mul<&'b Unit<DualQuaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Unit<DualQuaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Unit<DualQuaternion<T>>,
) -> <&'a Unit<Quaternion<T>> as Mul<&'b Unit<DualQuaternion<T>>>>::Output
fn mul( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <&'a Unit<Quaternion<T>> as Mul<&'b Unit<DualQuaternion<T>>>>::Output
*
operation. Read moresource§impl<'b, T> Mul<&'b Unit<DualQuaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Unit<DualQuaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Unit<DualQuaternion<T>>,
) -> <Unit<DualQuaternion<T>> as Mul<&'b Unit<DualQuaternion<T>>>>::Output
fn mul( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <Unit<DualQuaternion<T>> as Mul<&'b Unit<DualQuaternion<T>>>>::Output
*
operation. Read moresource§impl<'b, T> Mul<&'b Unit<DualQuaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Unit<DualQuaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Unit<DualQuaternion<T>>,
) -> <Unit<Quaternion<T>> as Mul<&'b Unit<DualQuaternion<T>>>>::Output
fn mul( self, rhs: &'b Unit<DualQuaternion<T>>, ) -> <Unit<Quaternion<T>> as Mul<&'b Unit<DualQuaternion<T>>>>::Output
*
operation. Read moresource§impl<'a, 'b, T, S> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for &'a Unit<Complex<T>>
impl<'a, 'b, T, S> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for &'a Unit<Complex<T>>
source§impl<'b, T, S> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for Unit<Complex<T>>
impl<'b, T, S> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for Unit<Complex<T>>
source§impl<'a, 'b, T, SB> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a Unit<DualQuaternion<T>>
impl<'a, 'b, T, SB> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a Unit<DualQuaternion<T>>
source§impl<'a, 'b, T, SB> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a Unit<Quaternion<T>>
impl<'a, 'b, T, SB> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a Unit<Quaternion<T>>
source§impl<'b, T, SB> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for Unit<DualQuaternion<T>>
impl<'b, T, SB> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for Unit<DualQuaternion<T>>
source§impl<'b, T, SB> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for Unit<Quaternion<T>>
impl<'b, T, SB> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for Unit<Quaternion<T>>
source§impl<'a, 'b, T> Mul<&'b Unit<Quaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Unit<Quaternion<T>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Unit<Quaternion<T>>,
) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b Unit<Quaternion<T>>>>::Output
fn mul( self, rhs: &'b Unit<Quaternion<T>>, ) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b Unit<Quaternion<T>>>>::Output
*
operation. Read moresource§impl<'a, 'b, T> Mul<&'b Unit<Quaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, 'b, T> Mul<&'b Unit<Quaternion<T>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<Quaternion<T>>
type Output = Unit<Quaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Unit<Quaternion<T>>,
) -> <&'a Unit<Quaternion<T>> as Mul<&'b Unit<Quaternion<T>>>>::Output
fn mul( self, rhs: &'b Unit<Quaternion<T>>, ) -> <&'a Unit<Quaternion<T>> as Mul<&'b Unit<Quaternion<T>>>>::Output
*
operation. Read moresource§impl<'b, T> Mul<&'b Unit<Quaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Unit<Quaternion<T>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Unit<Quaternion<T>>,
) -> <Unit<DualQuaternion<T>> as Mul<&'b Unit<Quaternion<T>>>>::Output
fn mul( self, rhs: &'b Unit<Quaternion<T>>, ) -> <Unit<DualQuaternion<T>> as Mul<&'b Unit<Quaternion<T>>>>::Output
*
operation. Read moresource§impl<'b, T> Mul<&'b Unit<Quaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'b, T> Mul<&'b Unit<Quaternion<T>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<Quaternion<T>>
type Output = Unit<Quaternion<T>>
*
operator.source§fn mul(
self,
rhs: &'b Unit<Quaternion<T>>,
) -> <Unit<Quaternion<T>> as Mul<&'b Unit<Quaternion<T>>>>::Output
fn mul( self, rhs: &'b Unit<Quaternion<T>>, ) -> <Unit<Quaternion<T>> as Mul<&'b Unit<Quaternion<T>>>>::Output
*
operation. Read moresource§impl<'a, T> Mul<DualQuaternion<T>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<DualQuaternion<T>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§fn mul(
self,
rhs: DualQuaternion<T>,
) -> <&'a Unit<DualQuaternion<T>> as Mul<DualQuaternion<T>>>::Output
fn mul( self, rhs: DualQuaternion<T>, ) -> <&'a Unit<DualQuaternion<T>> as Mul<DualQuaternion<T>>>::Output
*
operation. Read moresource§impl<T> Mul<DualQuaternion<T>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<DualQuaternion<T>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§fn mul(
self,
rhs: DualQuaternion<T>,
) -> <Unit<DualQuaternion<T>> as Mul<DualQuaternion<T>>>::Output
fn mul( self, rhs: DualQuaternion<T>, ) -> <Unit<DualQuaternion<T>> as Mul<DualQuaternion<T>>>::Output
*
operation. Read moresource§impl<'a, T> Mul<Isometry<T, Unit<Complex<T>>, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<Isometry<T, Unit<Complex<T>>, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Mul<Isometry<T, Unit<Complex<T>>, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<Isometry<T, Unit<Complex<T>>, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, T> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<DualQuaternion<T>> as Mul<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, rhs: Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<DualQuaternion<T>> as Mul<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<'a, T> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Isometry<T, Unit<Quaternion<T>>, 3>
type Output = Isometry<T, Unit<Quaternion<T>>, 3>
*
operator.source§fn mul(
self,
right: Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<Quaternion<T>> as Mul<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, right: Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<Quaternion<T>> as Mul<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<T> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Unit<DualQuaternion<T>>
type Output = Unit<DualQuaternion<T>>
*
operator.source§fn mul(
self,
rhs: Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<DualQuaternion<T>> as Mul<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, rhs: Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<DualQuaternion<T>> as Mul<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<T> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Isometry<T, Unit<Quaternion<T>>, 3>
type Output = Isometry<T, Unit<Quaternion<T>>, 3>
*
operator.source§fn mul(
self,
right: Isometry<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<Quaternion<T>> as Mul<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, right: Isometry<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<Quaternion<T>> as Mul<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<'a, T, SB> Mul<Matrix<T, Const<3>, Const<1>, SB>> for &'a Unit<DualQuaternion<T>>
impl<'a, T, SB> Mul<Matrix<T, Const<3>, Const<1>, SB>> for &'a Unit<DualQuaternion<T>>
source§impl<'a, T> Mul<OPoint<T, Const<2>>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<OPoint<T, Const<2>>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Mul<OPoint<T, Const<2>>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<OPoint<T, Const<2>>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, T> Mul<OPoint<T, Const<3>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<OPoint<T, Const<3>>> for &'a Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, T> Mul<OPoint<T, Const<3>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<OPoint<T, Const<3>>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Mul<OPoint<T, Const<3>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<OPoint<T, Const<3>>> for Unit<DualQuaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Mul<OPoint<T, Const<3>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<OPoint<T, Const<3>>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, T> Mul<Rotation<T, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<Rotation<T, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Mul<Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<Rotation<T, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, T> Mul<Rotation<T, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<Rotation<T, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Mul<Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<Rotation<T, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, T> Mul<Similarity<T, Unit<Complex<T>>, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<Similarity<T, Unit<Complex<T>>, 2>> for &'a Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<T> Mul<Similarity<T, Unit<Complex<T>>, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<Similarity<T, Unit<Complex<T>>, 2>> for Unit<Complex<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§impl<'a, T> Mul<Similarity<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<'a, T> Mul<Similarity<T, Unit<Quaternion<T>>, 3>> for &'a Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Similarity<T, Unit<Quaternion<T>>, 3>
type Output = Similarity<T, Unit<Quaternion<T>>, 3>
*
operator.source§fn mul(
self,
right: Similarity<T, Unit<Quaternion<T>>, 3>,
) -> <&'a Unit<Quaternion<T>> as Mul<Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, right: Similarity<T, Unit<Quaternion<T>>, 3>, ) -> <&'a Unit<Quaternion<T>> as Mul<Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read moresource§impl<T> Mul<Similarity<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
impl<T> Mul<Similarity<T, Unit<Quaternion<T>>, 3>> for Unit<Quaternion<T>>where
T: SimdRealField,
<T as SimdValue>::Element: SimdRealField,
source§type Output = Similarity<T, Unit<Quaternion<T>>, 3>
type Output = Similarity<T, Unit<Quaternion<T>>, 3>
*
operator.source§fn mul(
self,
right: Similarity<T, Unit<Quaternion<T>>, 3>,
) -> <Unit<Quaternion<T>> as Mul<Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
fn mul( self, right: Similarity<T, Unit<Quaternion<T>>, 3>, ) -> <Unit<Quaternion<T>> as Mul<Similarity<T, Unit<Quaternion<T>>, 3>>>::Output
*
operation. Read more