DualQuaternion in nalgebra::geometry - Rust
Description: A dual quaternion.
Keywords: rust, rustlang, rust-lang, DualQuaternion

# Struct nalgebra::geometry::DualQuaternion

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    #[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§

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### impl<T: SimdRealField> DualQuaternion<T>where
T::Element: SimdRealField,

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#### 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);

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#### 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);

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#### 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);

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#### 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);

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#### 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());

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#### pub fn try_inverse_mut(&mut self) -> bool where
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());

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#### 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)
    ));

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### impl<T: Scalar> DualQuaternion<T>

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#### 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);

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#### 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);

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#### 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)));

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### impl<T: SimdRealField> DualQuaternion<T>where
T::Element: SimdRealField,

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#### 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§

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### impl<T: RealField + AbsDiffEq<Epsilon = T>> AbsDiffEq<DualQuaternion<T>> for DualQuaternion<T>

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#### type Epsilon = T

Used for specifying relative comparisons.
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#### fn default_epsilon() -> Self::Epsilon

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

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

The inverse of `AbsDiffEq::abs_diff_eq`.
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### impl<'a, 'b, T: SimdRealField> Add<&'b DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `+` operator.
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#### fn add(self, rhs: &'b DualQuaternion<T>) -> Self::Output

Performs the `+` operation. Read more
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### impl<'b, T: SimdRealField> Add<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `+` operator.
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#### fn add(self, rhs: &'b DualQuaternion<T>) -> Self::Output

Performs the `+` operation. Read more
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### impl<'a, T: SimdRealField> Add<DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `+` operator.
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#### fn add(self, rhs: DualQuaternion<T>) -> Self::Output

Performs the `+` operation. Read more
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### impl<T: SimdRealField> Add<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `+` operator.
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#### fn add(self, rhs: DualQuaternion<T>) -> Self::Output

Performs the `+` operation. Read more
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### impl<'b, T: SimdRealField> AddAssign<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### fn add_assign(&mut self, rhs: &'b DualQuaternion<T>)

Performs the `+=` operation. Read more
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### impl<T: SimdRealField> AddAssign<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### fn add_assign(&mut self, rhs: DualQuaternion<T>)

Performs the `+=` operation. Read more
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### impl<T: SimdRealField> AsMut<[T; 8]> for DualQuaternion<T>

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#### fn as_mut(&mut self) -> &mut [T; 8]

Converts this type into a mutable reference of the (usually inferred) input type.
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### impl<T: SimdRealField> AsRef<[T; 8]> for DualQuaternion<T>

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#### fn as_ref(&self) -> &[T; 8]

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

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#### fn clone(&self) -> DualQuaternion<T>

Returns a copy of the value. Read more
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#### fn clone_from(&mut self, source: &Self)

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

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

Formats the value using the given formatter. Read more
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### impl<T: Scalar + Zero> Default for DualQuaternion<T>

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#### fn default() -> Self

Returns the “default value” for a type. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

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

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

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#### type Output = DualQuaternion<T>

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

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

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#### type Output = DualQuaternion<T>

The resulting type after applying the `/` operator.
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#### fn div(self, n: T) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField> Div<T> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `/` operator.
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#### fn div(self, n: T) -> Self::Output

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

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#### type Output = DualQuaternion<T>

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

Performs the `/` operation. Read more
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### impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

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

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

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

Performs the `/=` operation. Read more
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### impl<T: SimdRealField> DivAssign<T> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### fn div_assign(&mut self, n: T)

Performs the `/=` operation. Read more
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### impl<T: SimdRealField> DivAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

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

Performs the `/=` operation. Read more
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### impl<T: SimdRealField> Index<usize> for DualQuaternion<T>

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#### type Output = T

The returned type after indexing.
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#### fn index(&self, i: usize) -> &Self::Output

Performs the indexing (`container[index]`) operation. Read more
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### impl<T: SimdRealField> IndexMut<usize> for DualQuaternion<T>

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#### fn index_mut(&mut self, i: usize) -> &mut T

Performs the mutable indexing (`container[index]`) operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

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

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

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#### type Output = DualQuaternion<T>

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

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

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#### type Output = DualQuaternion<T>

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

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

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#### type Output = DualQuaternion<T>

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

Performs the `*` operation. Read more
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### impl<'b> Mul<&'b DualQuaternion<f32>> for f32

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#### type Output = DualQuaternion<f32>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b DualQuaternion<f32>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b> Mul<&'b DualQuaternion<f64>> for f64

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#### type Output = DualQuaternion<f64>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b DualQuaternion<f64>) -> Self::Output

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

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#### type Output = DualQuaternion<T>

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

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

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#### type Output = DualQuaternion<T>

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

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

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#### type Output = DualQuaternion<T>

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

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

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#### type Output = DualQuaternion<T>

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

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

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

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<DualQuaternion<T>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

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

Performs the `*` operation. Read more
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### impl Mul<DualQuaternion<f32>> for f32

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#### type Output = DualQuaternion<f32>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: DualQuaternion<f32>) -> Self::Output

Performs the `*` operation. Read more
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### impl Mul<DualQuaternion<f64>> for f64

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#### type Output = DualQuaternion<f64>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: DualQuaternion<f64>) -> Self::Output

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

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#### type Output = DualQuaternion<T>

The resulting type after applying the `*` operator.
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#### fn mul(self, n: T) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<T> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `*` operator.
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#### fn mul(self, n: T) -> Self::Output

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

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#### type Output = DualQuaternion<T>

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

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

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

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> MulAssign<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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

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

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

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<T> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, n: T)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

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

Performs the `*=` operation. Read more
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### impl<'a, T: SimdRealField> Neg for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

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

Performs the unary `-` operation. Read more
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### impl<T: SimdRealField> Neg for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

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

Performs the unary `-` operation. Read more
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### impl<T: SimdRealField> Normed for DualQuaternion<T>

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#### type Norm = <T as SimdComplexField>::SimdRealField

The type of the norm.
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#### fn norm(&self) -> T::SimdRealField

Computes the norm.
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#### fn norm_squared(&self) -> T::SimdRealField

Computes the squared norm.
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#### fn scale_mut(&mut self, n: Self::Norm)

Multiply `self` by n.
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#### fn unscale_mut(&mut self, n: Self::Norm)

Divides `self` by n.
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### impl<T: SimdRealField> One for DualQuaternion<T>where
T::Element: SimdRealField,

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#### fn one() -> Self

Returns the multiplicative identity element of `Self`, `1`. Read more
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#### fn set_one(&mut self)

Sets `self` to the multiplicative identity element of `Self`, `1`.
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#### fn is_one(&self) -> bool where
Self: PartialEq<Self>,

Returns `true` if `self` is equal to the multiplicative identity. Read more
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### impl<T: Scalar> PartialEq<DualQuaternion<T>> for DualQuaternion<T>

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

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

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
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### impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq<DualQuaternion<T>> for DualQuaternion<T>

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#### fn default_max_relative() -> Self::Epsilon

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

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

The inverse of `RelativeEq::relative_eq`.
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### impl<'a, 'b, T: SimdRealField> Sub<&'b DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `-` operator.
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#### fn sub(self, rhs: &'b DualQuaternion<T>) -> Self::Output

Performs the `-` operation. Read more
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### impl<'b, T: SimdRealField> Sub<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `-` operator.
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#### fn sub(self, rhs: &'b DualQuaternion<T>) -> Self::Output

Performs the `-` operation. Read more
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### impl<'a, T: SimdRealField> Sub<DualQuaternion<T>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `-` operator.
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#### fn sub(self, rhs: DualQuaternion<T>) -> Self::Output

Performs the `-` operation. Read more
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### impl<T: SimdRealField> Sub<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `-` operator.
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#### fn sub(self, rhs: DualQuaternion<T>) -> Self::Output

Performs the `-` operation. Read more
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### impl<'b, T: SimdRealField> SubAssign<&'b DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### fn sub_assign(&mut self, rhs: &'b DualQuaternion<T>)

Performs the `-=` operation. Read more
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### impl<T: SimdRealField> SubAssign<DualQuaternion<T>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### fn sub_assign(&mut self, rhs: DualQuaternion<T>)

Performs the `-=` operation. Read more
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### impl<T1, T2> SubsetOf<DualQuaternion<T2>> for DualQuaternion<T1>where
T1: SimdRealField,
T2: SimdRealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> DualQuaternion<T2>

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

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

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T: RealField + UlpsEq<Epsilon = T>> UlpsEq<DualQuaternion<T>> for DualQuaternion<T>

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#### fn default_max_ulps() -> u32

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

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

The inverse of `UlpsEq::ulps_eq`.
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### impl<T: SimdRealField> Zero for DualQuaternion<T>where
T::Element: SimdRealField,

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#### fn zero() -> Self

Returns the additive identity element of `Self`, `0`. Read more
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#### fn is_zero(&self) -> bool

Returns `true` if `self` is equal to the additive identity.
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#### fn set_zero(&mut self)

Sets `self` to the additive identity element of `Self`, `0`.
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### impl<T: Copy> Copy for DualQuaternion<T>

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### impl<T: Scalar + Eq> Eq for DualQuaternion<T>

## Auto Trait Implementations§

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### impl<T> RefUnwindSafe for DualQuaternion<T>where
T: RefUnwindSafe,

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### impl<T> Send for DualQuaternion<T>where
T: Send,

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### impl<T> Sync for DualQuaternion<T>where
T: Sync,

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### impl<T> Unpin for DualQuaternion<T>where
T: Unpin,

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### impl<T> UnwindSafe for DualQuaternion<T>where
T: UnwindSafe,

## Blanket Implementations§

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

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#### fn type_id(&self) -> TypeId

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

const: unstable · source§

#### fn borrow(&self) -> &T

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

const: unstable · source§

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

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

const: unstable · source§

#### fn from(t: T) -> T

Returns the argument unchanged.

source§

### impl<T, U> Into<U> for Twhere
U: From<T>,

const: unstable · source§

#### fn into(self) -> U

Calls `U::from(self)`.

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

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### impl<T> Same<T> for T

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#### type Output = T

Should always be `Self`
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### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

#### fn is_in_subset(&self) -> bool

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

Use with care! Same as `self.to_subset` but without any property checks. Always succeeds.
source§

#### fn from_subset(element: &SS) -> SP

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

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#### type Owned = T

The resulting type after obtaining ownership.
source§

#### fn to_owned(&self) -> T

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

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T, U> TryFrom<U> for Twhere
U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

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

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

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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### impl<T, Right> ClosedAdd<Right> for Twhere
T: Add<Right, Output = T> + AddAssign<Right>,

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### impl<T, Right> ClosedDiv<Right> for Twhere
T: Div<Right, Output = T> + DivAssign<Right>,

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

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### impl<T> ClosedNeg for Twhere
T: Neg<Output = T>,

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### impl<T, Right> ClosedSub<Right> for Twhere
T: Sub<Right, Output = T> + SubAssign<Right>,