Struct nalgebra::geometry::DualQuaternion
source · #[repr(C)]pub struct DualQuaternion<T> {
pub real: Quaternion<T>,
pub dual: Quaternion<T>,
}
Expand description
A dual quaternion.
Indexing
DualQuaternions
are stored as [..real, ..dual].
Both of the quaternion components are laid out in i, j, k, w
order.
Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq = DualQuaternion::from_real_and_dual(real, dual);
assert_eq!(dq[0], 2.0);
assert_eq!(dq[1], 3.0);
assert_eq!(dq[4], 6.0);
assert_eq!(dq[7], 5.0);
NOTE: As of December 2020, dual quaternion support is a work in progress. If a feature that you need is missing, feel free to open an issue or a PR. See https://github.com/dimforge/nalgebra/issues/487
Fields§
§real: Quaternion<T>
The real component of the quaternion
dual: Quaternion<T>
The dual component of the quaternion
Implementations§
source§impl<T: SimdRealField> DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> DualQuaternion<T>where T::Element: SimdRealField,
sourcepub fn normalize(&self) -> Self
pub fn normalize(&self) -> Self
Normalizes this quaternion.
Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq = DualQuaternion::from_real_and_dual(real, dual);
let dq_normalized = dq.normalize();
relative_eq!(dq_normalized.real.norm(), 1.0);
sourcepub fn normalize_mut(&mut self) -> T
pub fn normalize_mut(&mut self) -> T
Normalizes this quaternion.
Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let mut dq = DualQuaternion::from_real_and_dual(real, dual);
dq.normalize_mut();
relative_eq!(dq.real.norm(), 1.0);
sourcepub fn conjugate(&self) -> Self
pub fn conjugate(&self) -> Self
The conjugate of this dual quaternion, containing the conjugate of the real and imaginary parts..
Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq = DualQuaternion::from_real_and_dual(real, dual);
let conj = dq.conjugate();
assert!(conj.real.i == -2.0 && conj.real.j == -3.0 && conj.real.k == -4.0);
assert!(conj.real.w == 1.0);
assert!(conj.dual.i == -6.0 && conj.dual.j == -7.0 && conj.dual.k == -8.0);
assert!(conj.dual.w == 5.0);
sourcepub fn conjugate_mut(&mut self)
pub fn conjugate_mut(&mut self)
Replaces this quaternion by its conjugate.
Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let mut dq = DualQuaternion::from_real_and_dual(real, dual);
dq.conjugate_mut();
assert!(dq.real.i == -2.0 && dq.real.j == -3.0 && dq.real.k == -4.0);
assert!(dq.real.w == 1.0);
assert!(dq.dual.i == -6.0 && dq.dual.j == -7.0 && dq.dual.k == -8.0);
assert!(dq.dual.w == 5.0);
sourcepub fn try_inverse(&self) -> Option<Self>where
T: RealField,
pub fn try_inverse(&self) -> Option<Self>where T: RealField,
Inverts this dual quaternion if it is not zero.
Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq = DualQuaternion::from_real_and_dual(real, dual);
let inverse = dq.try_inverse();
assert!(inverse.is_some());
assert_relative_eq!(inverse.unwrap() * dq, DualQuaternion::identity());
//Non-invertible case
let zero = Quaternion::new(0.0, 0.0, 0.0, 0.0);
let dq = DualQuaternion::from_real_and_dual(zero, zero);
let inverse = dq.try_inverse();
assert!(inverse.is_none());
sourcepub fn try_inverse_mut(&mut self) -> boolwhere
T: RealField,
pub fn try_inverse_mut(&mut self) -> boolwhere T: RealField,
Inverts this dual quaternion in-place if it is not zero.
Example
let real = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dual = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq = DualQuaternion::from_real_and_dual(real, dual);
let mut dq_inverse = dq;
dq_inverse.try_inverse_mut();
assert_relative_eq!(dq_inverse * dq, DualQuaternion::identity());
//Non-invertible case
let zero = Quaternion::new(0.0, 0.0, 0.0, 0.0);
let mut dq = DualQuaternion::from_real_and_dual(zero, zero);
assert!(!dq.try_inverse_mut());
sourcepub fn lerp(&self, other: &Self, t: T) -> Self
pub fn lerp(&self, other: &Self, t: T) -> Self
Linear interpolation between two dual quaternions.
Computes self * (1 - t) + other * t
.
Example
let dq1 = DualQuaternion::from_real_and_dual(
Quaternion::new(1.0, 0.0, 0.0, 4.0),
Quaternion::new(0.0, 2.0, 0.0, 0.0)
);
let dq2 = DualQuaternion::from_real_and_dual(
Quaternion::new(2.0, 0.0, 1.0, 0.0),
Quaternion::new(0.0, 2.0, 0.0, 0.0)
);
assert_eq!(dq1.lerp(&dq2, 0.25), DualQuaternion::from_real_and_dual(
Quaternion::new(1.25, 0.0, 0.25, 3.0),
Quaternion::new(0.0, 2.0, 0.0, 0.0)
));
source§impl<T: Scalar> DualQuaternion<T>
impl<T: Scalar> DualQuaternion<T>
sourcepub fn from_real_and_dual(real: Quaternion<T>, dual: Quaternion<T>) -> Self
pub fn from_real_and_dual(real: Quaternion<T>, dual: Quaternion<T>) -> Self
Creates a dual quaternion from its rotation and translation components.
Example
let rot = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let trans = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq = DualQuaternion::from_real_and_dual(rot, trans);
assert_eq!(dq.real.w, 1.0);
sourcepub fn identity() -> Selfwhere
T: SimdRealField,
pub fn identity() -> Selfwhere T: SimdRealField,
The dual quaternion multiplicative identity.
Example
let dq1 = DualQuaternion::identity();
let dq2 = DualQuaternion::from_real_and_dual(
Quaternion::new(1.,2.,3.,4.),
Quaternion::new(5.,6.,7.,8.)
);
assert_eq!(dq1 * dq2, dq2);
assert_eq!(dq2 * dq1, dq2);
sourcepub fn cast<To: Scalar>(self) -> DualQuaternion<To>where
DualQuaternion<To>: SupersetOf<Self>,
pub fn cast<To: Scalar>(self) -> DualQuaternion<To>where DualQuaternion<To>: SupersetOf<Self>,
Cast the components of self
to another type.
Example
let q = DualQuaternion::from_real(Quaternion::new(1.0f64, 2.0, 3.0, 4.0));
let q2 = q.cast::<f32>();
assert_eq!(q2, DualQuaternion::from_real(Quaternion::new(1.0f32, 2.0, 3.0, 4.0)));
source§impl<T: SimdRealField> DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> DualQuaternion<T>where T::Element: SimdRealField,
sourcepub fn from_real(real: Quaternion<T>) -> Self
pub fn from_real(real: Quaternion<T>) -> Self
Creates a dual quaternion from only its real part, with no translation component.
Example
let rot = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let dq = DualQuaternion::from_real(rot);
assert_eq!(dq.real.w, 1.0);
assert_eq!(dq.dual.w, 0.0);
Trait Implementations§
source§impl<T: RealField + AbsDiffEq<Epsilon = T>> AbsDiffEq<DualQuaternion<T>> for DualQuaternion<T>
impl<T: RealField + AbsDiffEq<Epsilon = T>> AbsDiffEq<DualQuaternion<T>> for DualQuaternion<T>
source§fn default_epsilon() -> Self::Epsilon
fn default_epsilon() -> Self::Epsilon
source§fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool
fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool
source§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: RealField + RealField> AbstractMagma<Additive> for DualQuaternion<T>
impl<T: RealField + RealField> AbstractMagma<Additive> for DualQuaternion<T>
source§impl<T: RealField + RealField> AbstractMagma<Multiplicative> for DualQuaternion<T>
impl<T: RealField + RealField> AbstractMagma<Multiplicative> for DualQuaternion<T>
source§impl<T: RealField + RealField> AbstractModule<Additive, Additive, Multiplicative> for DualQuaternion<T>
impl<T: RealField + RealField> AbstractModule<Additive, Additive, Multiplicative> for DualQuaternion<T>
§type AbstractRing = T
type AbstractRing = T
source§fn multiply_by(&self, n: T) -> Self
fn multiply_by(&self, n: T) -> Self
source§impl<'a, 'b, T: SimdRealField> Add<&'b DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Add<&'b DualQuaternion<T>> for &'a DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
+
operator.source§impl<'b, T: SimdRealField> Add<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Add<&'b DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
+
operator.source§impl<'a, T: SimdRealField> Add<DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Add<DualQuaternion<T>> for &'a DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
+
operator.source§impl<T: SimdRealField> Add<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Add<DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
+
operator.source§impl<'b, T: SimdRealField> AddAssign<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> AddAssign<&'b DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn add_assign(&mut self, rhs: &'b DualQuaternion<T>)
fn add_assign(&mut self, rhs: &'b DualQuaternion<T>)
+=
operation. Read moresource§impl<T: SimdRealField> AddAssign<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> AddAssign<DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn add_assign(&mut self, rhs: DualQuaternion<T>)
fn add_assign(&mut self, rhs: DualQuaternion<T>)
+=
operation. Read moresource§impl<T> Arbitrary for DualQuaternion<T>where
T: SimdRealField + Arbitrary + Send,
T::Element: SimdRealField,
impl<T> Arbitrary for DualQuaternion<T>where T: SimdRealField + Arbitrary + Send, T::Element: SimdRealField,
source§impl<T> Archive for DualQuaternion<T>where
T: Archive,
Quaternion<T>: Archive<Archived = Quaternion<T::Archived>> + Archive,
impl<T> Archive for DualQuaternion<T>where T: Archive, Quaternion<T>: Archive<Archived = Quaternion<T::Archived>> + Archive,
§type Archived = DualQuaternion<<T as Archive>::Archived>
type Archived = DualQuaternion<<T as Archive>::Archived>
§type Resolver = DualQuaternionResolver<T>
type Resolver = DualQuaternionResolver<T>
source§impl<T: SimdRealField> AsMut<[T; 8]> for DualQuaternion<T>
impl<T: SimdRealField> AsMut<[T; 8]> for DualQuaternion<T>
source§impl<T: SimdRealField> AsRef<[T; 8]> for DualQuaternion<T>
impl<T: SimdRealField> AsRef<[T; 8]> for DualQuaternion<T>
source§impl<__C: ?Sized, T> CheckBytes<__C> for DualQuaternion<T>where
Quaternion<T>: CheckBytes<__C>,
impl<__C: ?Sized, T> CheckBytes<__C> for DualQuaternion<T>where Quaternion<T>: CheckBytes<__C>,
source§unsafe fn check_bytes<'__bytecheck>(
value: *const Self,
context: &mut __C
) -> Result<&'__bytecheck Self, StructCheckError>
unsafe fn check_bytes<'__bytecheck>( value: *const Self, context: &mut __C ) -> Result<&'__bytecheck Self, StructCheckError>
source§impl<T: Clone> Clone for DualQuaternion<T>
impl<T: Clone> Clone for DualQuaternion<T>
source§fn clone(&self) -> DualQuaternion<T>
fn clone(&self) -> DualQuaternion<T>
1.0.0 · source§fn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
source
. Read moresource§impl<T: Debug> Debug for DualQuaternion<T>
impl<T: Debug> Debug for DualQuaternion<T>
source§impl<'a, T> Deserialize<'a> for DualQuaternion<T>where
T: Deserialize<'a> + SimdRealField,
impl<'a, T> Deserialize<'a> for DualQuaternion<T>where T: Deserialize<'a> + SimdRealField,
source§fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>where
Des: Deserializer<'a>,
fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>where Des: Deserializer<'a>,
source§impl<__D: Fallible + ?Sized, T> Deserialize<DualQuaternion<T>, __D> for Archived<DualQuaternion<T>>where
T: Archive,
Quaternion<T>: Archive<Archived = Quaternion<T::Archived>> + Archive,
Archived<Quaternion<T>>: Deserialize<Quaternion<T>, __D>,
impl<__D: Fallible + ?Sized, T> Deserialize<DualQuaternion<T>, __D> for Archived<DualQuaternion<T>>where T: Archive, Quaternion<T>: Archive<Archived = Quaternion<T::Archived>> + Archive, Archived<Quaternion<T>>: Deserialize<Quaternion<T>, __D>,
source§fn deserialize(
&self,
deserializer: &mut __D
) -> Result<DualQuaternion<T>, __D::Error>
fn deserialize( &self, deserializer: &mut __D ) -> Result<DualQuaternion<T>, __D::Error>
source§impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
/
operator.source§impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
/
operator.source§impl<'a, T: SimdRealField> Div<T> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<T> for &'a DualQuaternion<T>where T::Element: SimdRealField,
source§impl<T: SimdRealField> Div<T> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<T> for DualQuaternion<T>where T::Element: SimdRealField,
source§impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
/
operator.source§impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
/
operator.source§impl<'b, T: SimdRealField> DivAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> DivAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)
fn div_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)
/=
operation. Read moresource§impl<T: SimdRealField> DivAssign<T> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> DivAssign<T> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn div_assign(&mut self, n: T)
fn div_assign(&mut self, n: T)
/=
operation. Read moresource§impl<T: SimdRealField> DivAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> DivAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn div_assign(&mut self, rhs: UnitDualQuaternion<T>)
fn div_assign(&mut self, rhs: UnitDualQuaternion<T>)
/=
operation. Read moresource§impl<T: RealField + RealField> FiniteDimVectorSpace for DualQuaternion<T>
impl<T: RealField + RealField> FiniteDimVectorSpace for DualQuaternion<T>
source§fn canonical_basis_element(i: usize) -> Self
fn canonical_basis_element(i: usize) -> Self
source§unsafe fn component_unchecked(&self, i: usize) -> &T
unsafe fn component_unchecked(&self, i: usize) -> &T
&self[i]
but without bound-checking.source§unsafe fn component_unchecked_mut(&mut self, i: usize) -> &mut T
unsafe fn component_unchecked_mut(&mut self, i: usize) -> &mut T
&mut self[i]
but without bound-checking.source§impl<T: RealField + RealField> Identity<Multiplicative> for DualQuaternion<T>
impl<T: RealField + RealField> Identity<Multiplicative> for DualQuaternion<T>
source§impl<T: SimdRealField> Index<usize> for DualQuaternion<T>
impl<T: SimdRealField> Index<usize> for DualQuaternion<T>
source§impl<T: SimdRealField> IndexMut<usize> for DualQuaternion<T>
impl<T: SimdRealField> IndexMut<usize> for DualQuaternion<T>
source§impl<'a, 'b, T: SimdRealField> Mul<&'b DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b DualQuaternion<T>> for &'a DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<'a, 'b, T: SimdRealField> Mul<&'b DualQuaternion<T>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b DualQuaternion<T>> for &'a UnitDualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<'b, T: SimdRealField> Mul<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<'b, T: SimdRealField> Mul<&'b DualQuaternion<T>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b DualQuaternion<T>> for UnitDualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<'a, T: SimdRealField> Mul<DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<DualQuaternion<T>> for &'a DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<'a, T: SimdRealField> Mul<DualQuaternion<T>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<DualQuaternion<T>> for &'a UnitDualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<T: SimdRealField> Mul<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<T: SimdRealField> Mul<DualQuaternion<T>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<DualQuaternion<T>> for UnitDualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<'a, T: SimdRealField> Mul<T> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<T> for &'a DualQuaternion<T>where T::Element: SimdRealField,
source§impl<T: SimdRealField> Mul<T> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<T> for DualQuaternion<T>where T::Element: SimdRealField,
source§impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
*
operator.source§impl<'b, T: SimdRealField> MulAssign<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> MulAssign<&'b DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn mul_assign(&mut self, rhs: &'b DualQuaternion<T>)
fn mul_assign(&mut self, rhs: &'b DualQuaternion<T>)
*=
operation. Read moresource§impl<'b, T: SimdRealField> MulAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> MulAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn mul_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)
fn mul_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)
*=
operation. Read moresource§impl<T: SimdRealField> MulAssign<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> MulAssign<DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn mul_assign(&mut self, rhs: DualQuaternion<T>)
fn mul_assign(&mut self, rhs: DualQuaternion<T>)
*=
operation. Read moresource§impl<T: SimdRealField> MulAssign<T> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> MulAssign<T> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn mul_assign(&mut self, n: T)
fn mul_assign(&mut self, n: T)
*=
operation. Read moresource§impl<T: SimdRealField> MulAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> MulAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn mul_assign(&mut self, rhs: UnitDualQuaternion<T>)
fn mul_assign(&mut self, rhs: UnitDualQuaternion<T>)
*=
operation. Read moresource§impl<'a, T: SimdRealField> Neg for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Neg for &'a DualQuaternion<T>where T::Element: SimdRealField,
source§impl<T: SimdRealField> Neg for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Neg for DualQuaternion<T>where T::Element: SimdRealField,
source§impl<T: SimdRealField> Normed for DualQuaternion<T>
impl<T: SimdRealField> Normed for DualQuaternion<T>
§type Norm = <T as SimdComplexField>::SimdRealField
type Norm = <T as SimdComplexField>::SimdRealField
source§fn norm(&self) -> T::SimdRealField
fn norm(&self) -> T::SimdRealField
source§fn norm_squared(&self) -> T::SimdRealField
fn norm_squared(&self) -> T::SimdRealField
source§fn unscale_mut(&mut self, n: Self::Norm)
fn unscale_mut(&mut self, n: Self::Norm)
self
by n.source§impl<T: RealField + RealField> NormedSpace for DualQuaternion<T>
impl<T: RealField + RealField> NormedSpace for DualQuaternion<T>
§type RealField = T
type RealField = T
§type ComplexField = T
type ComplexField = T
source§fn norm_squared(&self) -> T
fn norm_squared(&self) -> T
source§fn normalize_mut(&mut self) -> T
fn normalize_mut(&mut self) -> T
source§fn try_normalize(&self, min_norm: T) -> Option<Self>
fn try_normalize(&self, min_norm: T) -> Option<Self>
eps
.source§fn try_normalize_mut(&mut self, min_norm: T) -> Option<T>
fn try_normalize_mut(&mut self, min_norm: T) -> Option<T>
eps
. Read moresource§impl<T: SimdRealField> One for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> One for DualQuaternion<T>where T::Element: SimdRealField,
source§impl<T: Scalar> PartialEq<DualQuaternion<T>> for DualQuaternion<T>
impl<T: Scalar> PartialEq<DualQuaternion<T>> for DualQuaternion<T>
source§impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq<DualQuaternion<T>> for DualQuaternion<T>
impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq<DualQuaternion<T>> for DualQuaternion<T>
source§fn default_max_relative() -> Self::Epsilon
fn default_max_relative() -> Self::Epsilon
source§fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
fn relative_eq( &self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon ) -> bool
source§fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon ) -> bool
RelativeEq::relative_eq
.source§impl<__S: Fallible + ?Sized, T> Serialize<__S> for DualQuaternion<T>where
T: Archive,
Quaternion<T>: Archive<Archived = Quaternion<T::Archived>> + Serialize<__S>,
impl<__S: Fallible + ?Sized, T> Serialize<__S> for DualQuaternion<T>where T: Archive, Quaternion<T>: Archive<Archived = Quaternion<T::Archived>> + Serialize<__S>,
source§impl<T> Serialize for DualQuaternion<T>where
T: Serialize + SimdRealField,
impl<T> Serialize for DualQuaternion<T>where T: Serialize + SimdRealField,
source§fn serialize<S>(
&self,
serializer: S
) -> Result<<S as Serializer>::Ok, <S as Serializer>::Error>where
S: Serializer,
fn serialize<S>( &self, serializer: S ) -> Result<<S as Serializer>::Ok, <S as Serializer>::Error>where S: Serializer,
source§impl<'a, 'b, T: SimdRealField> Sub<&'b DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, 'b, T: SimdRealField> Sub<&'b DualQuaternion<T>> for &'a DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
-
operator.source§impl<'b, T: SimdRealField> Sub<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> Sub<&'b DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
-
operator.source§impl<'a, T: SimdRealField> Sub<DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,
impl<'a, T: SimdRealField> Sub<DualQuaternion<T>> for &'a DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
-
operator.source§impl<T: SimdRealField> Sub<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Sub<DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
§type Output = DualQuaternion<T>
type Output = DualQuaternion<T>
-
operator.source§impl<'b, T: SimdRealField> SubAssign<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<'b, T: SimdRealField> SubAssign<&'b DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn sub_assign(&mut self, rhs: &'b DualQuaternion<T>)
fn sub_assign(&mut self, rhs: &'b DualQuaternion<T>)
-=
operation. Read moresource§impl<T: SimdRealField> SubAssign<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> SubAssign<DualQuaternion<T>> for DualQuaternion<T>where T::Element: SimdRealField,
source§fn sub_assign(&mut self, rhs: DualQuaternion<T>)
fn sub_assign(&mut self, rhs: DualQuaternion<T>)
-=
operation. Read moresource§impl<T1, T2> SubsetOf<DualQuaternion<T2>> for DualQuaternion<T1>where
T1: SimdRealField,
T2: SimdRealField + SupersetOf<T1>,
impl<T1, T2> SubsetOf<DualQuaternion<T2>> for DualQuaternion<T1>where T1: SimdRealField, T2: SimdRealField + SupersetOf<T1>,
source§fn to_superset(&self) -> DualQuaternion<T2>
fn to_superset(&self) -> DualQuaternion<T2>
self
to the equivalent element of its superset.source§fn is_in_subset(dq: &DualQuaternion<T2>) -> bool
fn is_in_subset(dq: &DualQuaternion<T2>) -> bool
element
is actually part of the subset Self
(and can be converted to it).source§fn from_superset_unchecked(dq: &DualQuaternion<T2>) -> Self
fn from_superset_unchecked(dq: &DualQuaternion<T2>) -> Self
self.to_superset
but without any property checks. Always succeeds.source§impl<T: RealField + RealField> TwoSidedInverse<Additive> for DualQuaternion<T>
impl<T: RealField + RealField> TwoSidedInverse<Additive> for DualQuaternion<T>
source§fn two_sided_inverse(&self) -> Self
fn two_sided_inverse(&self) -> Self
source§fn two_sided_inverse_mut(&mut self)
fn two_sided_inverse_mut(&mut self)
source§impl<T: RealField + UlpsEq<Epsilon = T>> UlpsEq<DualQuaternion<T>> for DualQuaternion<T>
impl<T: RealField + UlpsEq<Epsilon = T>> UlpsEq<DualQuaternion<T>> for DualQuaternion<T>
source§impl<T: RealField + RealField> VectorSpace for DualQuaternion<T>
impl<T: RealField + RealField> VectorSpace for DualQuaternion<T>
source§impl<T: SimdRealField> Zero for DualQuaternion<T>where
T::Element: SimdRealField,
impl<T: SimdRealField> Zero for DualQuaternion<T>where T::Element: SimdRealField,
source§impl<T> Zeroable for DualQuaternion<T>where
T: Scalar + Zeroable,
Quaternion<T>: Zeroable,
impl<T> Zeroable for DualQuaternion<T>where T: Scalar + Zeroable, Quaternion<T>: Zeroable,
impl<T: RealField + RealField> AbstractGroup<Additive> for DualQuaternion<T>
impl<T: RealField + RealField> AbstractGroupAbelian<Additive> for DualQuaternion<T>
impl<T: RealField + RealField> AbstractLoop<Additive> for DualQuaternion<T>
impl<T: RealField + RealField> AbstractMonoid<Additive> for DualQuaternion<T>
impl<T: RealField + RealField> AbstractMonoid<Multiplicative> for DualQuaternion<T>
impl<T: RealField + RealField> AbstractQuasigroup<Additive> for DualQuaternion<T>
impl<T: RealField + RealField> AbstractSemigroup<Additive> for DualQuaternion<T>
impl<T: RealField + RealField> AbstractSemigroup<Multiplicative> for DualQuaternion<T>
impl<T: Copy> Copy for DualQuaternion<T>
impl<T: DeviceCopy> DeviceCopy for DualQuaternion<T>
impl<T: Scalar + Eq> Eq for DualQuaternion<T>
impl<T> Pod for DualQuaternion<T>where T: Scalar + Pod, Quaternion<T>: Pod,
Auto Trait Implementations§
impl<T> RefUnwindSafe for DualQuaternion<T>where T: RefUnwindSafe,
impl<T> Send for DualQuaternion<T>where T: Send,
impl<T> Sync for DualQuaternion<T>where T: Sync,
impl<T> Unpin for DualQuaternion<T>where T: Unpin,
impl<T> UnwindSafe for DualQuaternion<T>where T: UnwindSafe,
Blanket Implementations§
source§impl<T> ArchivePointee for T
impl<T> ArchivePointee for T
§type ArchivedMetadata = ()
type ArchivedMetadata = ()
source§fn pointer_metadata(
_: &<T as ArchivePointee>::ArchivedMetadata
) -> <T as Pointee>::Metadata
fn pointer_metadata( _: &<T as ArchivePointee>::ArchivedMetadata ) -> <T as Pointee>::Metadata
source§impl<T> ArchiveUnsized for Twhere
T: Archive,
impl<T> ArchiveUnsized for Twhere T: Archive,
§type Archived = <T as Archive>::Archived
type Archived = <T as Archive>::Archived
Archive
, it may be unsized. Read more§type MetadataResolver = ()
type MetadataResolver = ()
source§unsafe fn resolve_metadata(
&self,
_: usize,
_: <T as ArchiveUnsized>::MetadataResolver,
_: *mut <<T as ArchiveUnsized>::Archived as ArchivePointee>::ArchivedMetadata
)
unsafe fn resolve_metadata( &self, _: usize, _: <T as ArchiveUnsized>::MetadataResolver, _: *mut <<T as ArchiveUnsized>::Archived as ArchivePointee>::ArchivedMetadata )
source§impl<T> BorrowMut<T> for Twhere
T: ?Sized,
impl<T> BorrowMut<T> for Twhere T: ?Sized,
source§fn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
source§impl<T> CheckedBitPattern for Twhere
T: AnyBitPattern,
impl<T> CheckedBitPattern for Twhere T: AnyBitPattern,
§type Bits = T
type Bits = T
Self
must have the same layout as the specified Bits
except for
the possible invalid bit patterns being checked during
is_valid_bit_pattern
.source§fn is_valid_bit_pattern(_bits: &T) -> bool
fn is_valid_bit_pattern(_bits: &T) -> bool
bits
as &Self
.source§impl<F, W, T, D> Deserialize<With<T, W>, D> for Fwhere
W: DeserializeWith<F, T, D>,
D: Fallible + ?Sized,
F: ?Sized,
impl<F, W, T, D> Deserialize<With<T, W>, D> for Fwhere W: DeserializeWith<F, T, D>, D: Fallible + ?Sized, F: ?Sized,
source§impl<T> LayoutRaw for T
impl<T> LayoutRaw for T
source§fn layout_raw(_: <T as Pointee>::Metadata) -> Result<Layout, LayoutError>
fn layout_raw(_: <T as Pointee>::Metadata) -> Result<Layout, LayoutError>
§impl<T> Pointable for T
impl<T> Pointable for T
source§impl<T, S> SerializeUnsized<S> for Twhere
T: Serialize<S>,
S: Serializer + ?Sized,
impl<T, S> SerializeUnsized<S> for Twhere T: Serialize<S>, S: Serializer + ?Sized,
source§impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,
impl<SS, SP> SupersetOf<SS> for SPwhere SS: SubsetOf<SP>,
source§fn to_subset(&self) -> Option<SS>
fn to_subset(&self) -> Option<SS>
self
from the equivalent element of its
superset. Read moresource§fn is_in_subset(&self) -> bool
fn is_in_subset(&self) -> bool
self
is actually part of its subset T
(and can be converted to it).source§fn to_subset_unchecked(&self) -> SS
fn to_subset_unchecked(&self) -> SS
self.to_subset
but without any property checks. Always succeeds.source§fn from_subset(element: &SS) -> SP
fn from_subset(element: &SS) -> SP
self
to the equivalent element of its superset.source§impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,
impl<SS, SP> SupersetOf<SS> for SPwhere SS: SubsetOf<SP>,
source§fn to_subset(&self) -> Option<SS>
fn to_subset(&self) -> Option<SS>
self
from the equivalent element of its
superset. Read moresource§fn is_in_subset(&self) -> bool
fn is_in_subset(&self) -> bool
self
is actually part of its subset T
(and can be converted to it).source§unsafe fn to_subset_unchecked(&self) -> SS
unsafe fn to_subset_unchecked(&self) -> SS
self.to_subset
but without any property checks. Always succeeds.source§fn from_subset(element: &SS) -> SP
fn from_subset(element: &SS) -> SP
self
to the equivalent element of its superset.