Struct na::DualQuaternion

#[repr(C)]
pub struct DualQuaternion<T> {
    pub real: Quaternion<T>,
    pub dual: Quaternion<T>,
}

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

impl<T> DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

pub fn normalize(&self) -> DualQuaternion<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 dq = DualQuaternion::from_real_and_dual(real, dual);

let dq_normalized = dq.normalize();

relative_eq!(dq_normalized.real.norm(), 1.0);

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);

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

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);

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);

pub fn try_inverse(&self) -> Option<DualQuaternion<T>> 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());

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());

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

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)
));

impl<T> DualQuaternion<T> where
    T: Scalar, 

pub fn from_real_and_dual(
    real: Quaternion<T>,
    dual: Quaternion<T>
) -> DualQuaternion<T>

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);

pub fn identity() -> DualQuaternion<T> where
    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);

pub fn cast<To>(self) -> DualQuaternion<To> where
    To: Scalar,
    DualQuaternion<To>: SupersetOf<DualQuaternion<T>>, 

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)));

impl<T> DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

pub fn from_real(real: Quaternion<T>) -> DualQuaternion<T>

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

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

type Epsilon = T

Used for specifying relative comparisons.

fn default_epsilon(
) -> <DualQuaternion<T> as AbsDiffEq<DualQuaternion<T>>>::Epsilon

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

fn abs_diff_eq(
    &self,
    other: &DualQuaternion<T>,
    epsilon: <DualQuaternion<T> as AbsDiffEq<DualQuaternion<T>>>::Epsilon
) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

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

The inverse of [AbsDiffEq::abs_diff_eq].

impl<'a, 'b, T> Add<&'b DualQuaternion<T>> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the + operator.

fn add(
    self,
    rhs: &'b DualQuaternion<T>
) -> <&'a DualQuaternion<T> as Add<&'b DualQuaternion<T>>>::Output

Performs the + operation.

impl<'b, T> Add<&'b DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the + operator.

fn add(
    self,
    rhs: &'b DualQuaternion<T>
) -> <DualQuaternion<T> as Add<&'b DualQuaternion<T>>>::Output

Performs the + operation.

impl<'a, T> Add<DualQuaternion<T>> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the + operator.

fn add(
    self,
    rhs: DualQuaternion<T>
) -> <&'a DualQuaternion<T> as Add<DualQuaternion<T>>>::Output

Performs the + operation.

impl<T> Add<DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the + operator.

fn add(
    self,
    rhs: DualQuaternion<T>
) -> <DualQuaternion<T> as Add<DualQuaternion<T>>>::Output

Performs the + operation.

impl<'b, T> AddAssign<&'b DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

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

Performs the += operation.

impl<T> AddAssign<DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

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

Performs the += operation.

impl<T> AsMut<[T; 8]> for DualQuaternion<T> where
    T: SimdRealField, 

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

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

impl<T> AsRef<[T; 8]> for DualQuaternion<T> where
    T: SimdRealField, 

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

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

impl<T> Clone for DualQuaternion<T> where
    T: Clone, 

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T> Debug for DualQuaternion<T> where
    T: Debug, 

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

Formats the value using the given formatter.

impl<T> Default for DualQuaternion<T> where
    T: Scalar + Zero, 

fn default() -> DualQuaternion<T>

Returns the “default value” for a type.

impl<'a, 'b, T> Div<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(
    self,
    rhs: &'b Unit<DualQuaternion<T>>
) -> <&'a DualQuaternion<T> as Div<&'b Unit<DualQuaternion<T>>>>::Output

Performs the / operation.

impl<'b, T> Div<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(
    self,
    rhs: &'b Unit<DualQuaternion<T>>
) -> <DualQuaternion<T> as Div<&'b Unit<DualQuaternion<T>>>>::Output

Performs the / operation.

impl<'a, T> Div<T> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(self, n: T) -> <&'a DualQuaternion<T> as Div<T>>::Output

Performs the / operation.

impl<T> Div<T> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(self, n: T) -> <DualQuaternion<T> as Div<T>>::Output

Performs the / operation.

impl<'a, T> Div<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(
    self,
    rhs: Unit<DualQuaternion<T>>
) -> <&'a DualQuaternion<T> as Div<Unit<DualQuaternion<T>>>>::Output

Performs the / operation.

impl<T> Div<Unit<DualQuaternion<T>>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(
    self,
    rhs: Unit<DualQuaternion<T>>
) -> <DualQuaternion<T> as Div<Unit<DualQuaternion<T>>>>::Output

Performs the / operation.

impl<'b, T> DivAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

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

Performs the /= operation.

impl<T> DivAssign<T> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

fn div_assign(&mut self, n: T)

Performs the /= operation.

impl<T> DivAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

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

Performs the /= operation.

impl<T> Index<usize> for DualQuaternion<T> where
    T: SimdRealField, 

type Output = T

The returned type after indexing.

fn index(&self, i: usize) -> &<DualQuaternion<T> as Index<usize>>::Output

Performs the indexing (container[index]) operation.

impl<T> IndexMut<usize> for DualQuaternion<T> where
    T: SimdRealField, 

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

Performs the mutable indexing (container[index]) operation.

impl<'a, 'b, T> Mul<&'b DualQuaternion<T>> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b DualQuaternion<T>
) -> <&'a DualQuaternion<T> as Mul<&'b DualQuaternion<T>>>::Output

Performs the * operation.

impl<'b, T> Mul<&'b DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b DualQuaternion<T>
) -> <DualQuaternion<T> as Mul<&'b DualQuaternion<T>>>::Output

Performs the * operation.

impl<'a, 'b, T> Mul<&'b DualQuaternion<T>> for &'a Unit<DualQuaternion<T>> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b DualQuaternion<T>
) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b DualQuaternion<T>>>::Output

Performs the * operation.

impl<'b, T> Mul<&'b DualQuaternion<T>> for Unit<DualQuaternion<T>> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b DualQuaternion<T>
) -> <Unit<DualQuaternion<T>> as Mul<&'b DualQuaternion<T>>>::Output

Performs the * operation.

impl<'b, T> Mul<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b Unit<DualQuaternion<T>>
) -> <DualQuaternion<T> as Mul<&'b Unit<DualQuaternion<T>>>>::Output

Performs the * operation.

impl<'a, 'b, T> Mul<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b Unit<DualQuaternion<T>>
) -> <&'a DualQuaternion<T> as Mul<&'b Unit<DualQuaternion<T>>>>::Output

Performs the * operation.

impl<'a, T> Mul<DualQuaternion<T>> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: DualQuaternion<T>
) -> <&'a DualQuaternion<T> as Mul<DualQuaternion<T>>>::Output

Performs the * operation.

impl<T> Mul<DualQuaternion<T>> for Unit<DualQuaternion<T>> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: DualQuaternion<T>
) -> <Unit<DualQuaternion<T>> as Mul<DualQuaternion<T>>>::Output

Performs the * operation.

impl<'a, T> Mul<DualQuaternion<T>> for &'a Unit<DualQuaternion<T>> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: DualQuaternion<T>
) -> <&'a Unit<DualQuaternion<T>> as Mul<DualQuaternion<T>>>::Output

Performs the * operation.

impl<T> Mul<DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: DualQuaternion<T>
) -> <DualQuaternion<T> as Mul<DualQuaternion<T>>>::Output

Performs the * operation.

impl<T> Mul<T> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(self, n: T) -> <DualQuaternion<T> as Mul<T>>::Output

Performs the * operation.

impl<'a, T> Mul<T> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(self, n: T) -> <&'a DualQuaternion<T> as Mul<T>>::Output

Performs the * operation.

impl<'a, T> Mul<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Unit<DualQuaternion<T>>
) -> <&'a DualQuaternion<T> as Mul<Unit<DualQuaternion<T>>>>::Output

Performs the * operation.

impl<T> Mul<Unit<DualQuaternion<T>>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Unit<DualQuaternion<T>>
) -> <DualQuaternion<T> as Mul<Unit<DualQuaternion<T>>>>::Output

Performs the * operation.

impl<'b, T> MulAssign<&'b DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

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

Performs the *= operation.

impl<'b, T> MulAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

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

Performs the *= operation.

impl<T> MulAssign<DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

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

Performs the *= operation.

impl<T> MulAssign<T> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

fn mul_assign(&mut self, n: T)

Performs the *= operation.

impl<T> MulAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

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

Performs the *= operation.

impl<'a, T> Neg for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

fn neg(self) -> <&'a DualQuaternion<T> as Neg>::Output

Performs the unary - operation.

impl<T> Neg for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

fn neg(self) -> <DualQuaternion<T> as Neg>::Output

Performs the unary - operation.

impl<T> Normed for DualQuaternion<T> where
    T: SimdRealField, 

type Norm = <T as SimdComplexField>::SimdRealField

The type of the norm.

fn norm(&self) -> <T as SimdComplexField>::SimdRealField

Computes the norm.

fn norm_squared(&self) -> <T as SimdComplexField>::SimdRealField

Computes the squared norm.

fn scale_mut(&mut self, n: <DualQuaternion<T> as Normed>::Norm)

Multiply self by n.

fn unscale_mut(&mut self, n: <DualQuaternion<T> as Normed>::Norm)

Divides self by n.

impl<T> One for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

fn one() -> DualQuaternion<T>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 

Returns true if self is equal to the multiplicative identity.

impl<T> PartialEq<DualQuaternion<T>> for DualQuaternion<T> where
    T: Scalar, 

fn eq(&self, right: &DualQuaternion<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=.

impl<T> RelativeEq<DualQuaternion<T>> for DualQuaternion<T> where
    T: RealField<Epsilon = T> + RelativeEq<T>, 

fn default_max_relative(
) -> <DualQuaternion<T> as AbsDiffEq<DualQuaternion<T>>>::Epsilon

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

fn relative_eq(
    &self,
    other: &DualQuaternion<T>,
    epsilon: <DualQuaternion<T> as AbsDiffEq<DualQuaternion<T>>>::Epsilon,
    max_relative: <DualQuaternion<T> as AbsDiffEq<DualQuaternion<T>>>::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.

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

The inverse of [RelativeEq::relative_eq].

impl<'b, T> Sub<&'b DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

fn sub(
    self,
    rhs: &'b DualQuaternion<T>
) -> <DualQuaternion<T> as Sub<&'b DualQuaternion<T>>>::Output

Performs the - operation.

impl<'a, 'b, T> Sub<&'b DualQuaternion<T>> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

fn sub(
    self,
    rhs: &'b DualQuaternion<T>
) -> <&'a DualQuaternion<T> as Sub<&'b DualQuaternion<T>>>::Output

Performs the - operation.

impl<'a, T> Sub<DualQuaternion<T>> for &'a DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

fn sub(
    self,
    rhs: DualQuaternion<T>
) -> <&'a DualQuaternion<T> as Sub<DualQuaternion<T>>>::Output

Performs the - operation.

impl<T> Sub<DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

fn sub(
    self,
    rhs: DualQuaternion<T>
) -> <DualQuaternion<T> as Sub<DualQuaternion<T>>>::Output

Performs the - operation.

impl<'b, T> SubAssign<&'b DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

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

Performs the -= operation.

impl<T> SubAssign<DualQuaternion<T>> for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

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

Performs the -= operation.

impl<T1, T2> SubsetOf<DualQuaternion<T2>> for DualQuaternion<T1> where
    T1: SimdRealField,
    T2: SimdRealField + SupersetOf<T1>, 

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

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

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

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

fn from_superset_unchecked(dq: &DualQuaternion<T2>) -> DualQuaternion<T1>

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

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

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

impl<T> UlpsEq<DualQuaternion<T>> for DualQuaternion<T> where
    T: RealField<Epsilon = T> + UlpsEq<T>, 

fn default_max_ulps() -> u32

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

fn ulps_eq(
    &self,
    other: &DualQuaternion<T>,
    epsilon: <DualQuaternion<T> as AbsDiffEq<DualQuaternion<T>>>::Epsilon,
    max_ulps: u32
) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

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

The inverse of [UlpsEq::ulps_eq].

impl<T> Zero for DualQuaternion<T> where
    T: SimdRealField,
    <T as SimdValue>::Element: SimdRealField, 

fn zero() -> DualQuaternion<T>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<T> Copy for DualQuaternion<T> where
    T: Copy, 

impl<T> Eq for DualQuaternion<T> where
    T: Scalar + Eq,