Struct nalgebra::geometry::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: SimdRealField> DualQuaternion<T>where
    T::Element: SimdRealField,

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);

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) -> 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);

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<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());

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());

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)
));

impl<T: Scalar> DualQuaternion<T>

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);

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);

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)));

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

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

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

type Epsilon = T

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

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

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

The inverse of AbsDiffEq::abs_diff_eq.

impl<T: RealField + RealField> AbstractMagma<Additive> for DualQuaternion<T>

fn operate(&self, rhs: &Self) -> Self

Performs an operation.

fn op(&self, O, lhs: &Self) -> Self

Performs specific operation.

impl<T: RealField + RealField> AbstractMagma<Multiplicative> for DualQuaternion<T>

fn operate(&self, rhs: &Self) -> Self

Performs an operation.

fn op(&self, O, lhs: &Self) -> Self

Performs specific operation.

impl<T: RealField + RealField> AbstractModule<Additive, Additive, Multiplicative> for DualQuaternion<T>

type AbstractRing = T

The underlying scalar field.

fn multiply_by(&self, n: T) -> Self

Multiplies an element of the ring with an element of the module.

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

type Output = DualQuaternion<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

impl<T> Arbitrary for DualQuaternion<T>where
    T: SimdRealField + Arbitrary + Send,
    T::Element: SimdRealField,

fn arbitrary(rng: &mut Gen) -> Self

Return an arbitrary value.

fn shrink(&self) -> Box<dyn Iterator<Item = Self> + 'static, Global>

Return an iterator of values that are smaller than itself.

impl<T> Archive for DualQuaternion<T>where
    Quaternion<T>: Archive,
    Quaternion<T>: Archive,

type Archived = ArchivedDualQuaternion<T>

The archived representation of this type.

type Resolver = DualQuaternionResolver<T>

The resolver for this type. It must contain all the additional information from serializing needed to make the archived type from the normal type.

unsafe fn resolve(
    &self,
    pos: usize,
    resolver: Self::Resolver,
    out: *mut Self::Archived
)

Creates the archived version of this value at the given position and writes it to the given output.

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

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

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

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

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

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

impl<__C: ?Sized, T> CheckBytes<__C> for DualQuaternion<T>where
    Quaternion<T>: CheckBytes<__C>,
    Quaternion<T>: CheckBytes<__C>,

type Error = StructCheckError

The error that may result from checking the type.

unsafe fn check_bytes<'__bytecheck>(
    value: *const Self,
    context: &mut __C
) -> Result<&'__bytecheck Self, StructCheckError>

Checks whether the given pointer points to a valid value within the given context.

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

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> Debug for DualQuaternion<T>

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

Formats the value using the given formatter.

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

fn default() -> Self

Returns the “default value” for a type.

impl<'a, T: SimdRealField> Deserialize<'a> for DualQuaternion<T>where
    T: Deserialize<'a>,

fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>where
    Des: Deserializer<'a>,

Deserialize this value from the given Serde deserializer.

impl<__D: Fallible + ?Sized, T> Deserialize<DualQuaternion<T>, __D> for Archived<DualQuaternion<T>>where
    Quaternion<T>: Archive,
    Archived<Quaternion<T>>: Deserialize<Quaternion<T>, __D>,
    Quaternion<T>: Archive,
    Archived<Quaternion<T>>: Deserialize<Quaternion<T>, __D>,

fn deserialize(
    &self,
    deserializer: &mut __D
) -> Result<DualQuaternion<T>, __D::Error>

Deserializes using the given deserializer

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

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(self, n: T) -> Self::Output

Performs the / operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

fn div(self, n: T) -> Self::Output

Performs the / operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

Performs the /= operation.

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

fn div_assign(&mut self, n: T)

Performs the /= operation.

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

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

Performs the /= operation.

impl<T: RealField + RealField> FiniteDimVectorSpace for DualQuaternion<T>

fn dimension() -> usize

The vector space dimension.

fn canonical_basis_element(i: usize) -> Self

The i-the canonical basis element.

fn dot(&self, other: &Self) -> T

The dot product between two vectors.

unsafe fn component_unchecked(&self, i: usize) -> &T

Same as &self[i] but without bound-checking.

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

Same as &mut self[i] but without bound-checking.

fn canonical_basis<F>(f: F)where
    F: FnMut(&Self) -> bool,

Applies the given closule to each element of this vector space’s canonical basis. Stops if f returns false.

impl<T: RealField + RealField> Identity<Additive> for DualQuaternion<T>

fn identity() -> Self

The identity element.

fn id(O) -> Self

Specific identity.

impl<T: RealField + RealField> Identity<Multiplicative> for DualQuaternion<T>

fn identity() -> Self

The identity element.

fn id(O) -> Self

Specific identity.

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

type Output = T

The returned type after indexing.

fn index(&self, i: usize) -> &Self::Output

Performs the indexing (container[index]) operation.

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

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

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

impl<T: RealField + RealField> Module for DualQuaternion<T>

type Ring = T

The underlying scalar field.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b> Mul<&'b DualQuaternion<f32>> for f32

type Output = DualQuaternion<f32>

The resulting type after applying the * operator.

fn mul(self, right: &'b DualQuaternion<f32>) -> Self::Output

Performs the * operation.

impl<'b> Mul<&'b DualQuaternion<f64>> for f64

type Output = DualQuaternion<f64>

The resulting type after applying the * operator.

fn mul(self, right: &'b DualQuaternion<f64>) -> Self::Output

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<DualQuaternion<f32>> for f32

type Output = DualQuaternion<f32>

The resulting type after applying the * operator.

fn mul(self, right: DualQuaternion<f32>) -> Self::Output

Performs the * operation.

impl Mul<DualQuaternion<f64>> for f64

type Output = DualQuaternion<f64>

The resulting type after applying the * operator.

fn mul(self, right: DualQuaternion<f64>) -> Self::Output

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(self, n: T) -> Self::Output

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

fn mul(self, n: T) -> Self::Output

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

fn mul_assign(&mut self, n: T)

Performs the *= operation.

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

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

Performs the *= operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

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

type Norm = <T as SimdComplexField>::SimdRealField

The type of the norm.

fn norm(&self) -> T::SimdRealField

Computes the norm.

fn norm_squared(&self) -> T::SimdRealField

Computes the squared norm.

fn scale_mut(&mut self, n: Self::Norm)

Multiply self by n.

fn unscale_mut(&mut self, n: Self::Norm)

Divides self by n.

impl<T: RealField + RealField> NormedSpace for DualQuaternion<T>

type RealField = T

The result of the norm (not necessarily the same same as the field used by this vector space).

type ComplexField = T

The field of this space must be this complex number.

fn norm_squared(&self) -> T

The squared norm of this vector.

fn norm(&self) -> T

The norm of this vector.

fn normalize(&self) -> Self

Returns a normalized version of this vector.

fn normalize_mut(&mut self) -> T

Normalizes this vector in-place and returns its norm.

fn try_normalize(&self, min_norm: T) -> Option<Self>

Returns a normalized version of this vector unless its norm as smaller or equal to eps.

fn try_normalize_mut(&mut self, min_norm: T) -> Option<T>

Normalizes this vector in-place or does nothing if its norm is smaller or equal to eps.

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

fn one() -> Self

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) -> boolwhere
    Self: PartialEq<Self>,

Returns true if self is equal to the multiplicative identity.

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

fn eq(&self, right: &Self) -> 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 !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

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

fn default_max_relative() -> Self::Epsilon

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

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

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

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

The inverse of RelativeEq::relative_eq.

impl<__S: Fallible + ?Sized, T> Serialize<__S> for DualQuaternion<T>where
    Quaternion<T>: Serialize<__S>,
    Quaternion<T>: Serialize<__S>,

fn serialize(&self, serializer: &mut __S) -> Result<Self::Resolver, __S::Error>

Writes the dependencies for the object and returns a resolver that can create the archived type.

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

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

Serialize this value into the given Serde serializer.

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

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = DualQuaternion<T>

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

impl<T: SimdRealField> SubAssign<DualQuaternion<T>> for DualQuaternion<T>where
    T::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>) -> Self

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

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

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

impl<T: RealField + RealField> TwoSidedInverse<Additive> for DualQuaternion<T>

fn two_sided_inverse(&self) -> Self

Returns the two_sided_inverse of self, relative to the operator O.

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O.

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

fn default_max_ulps() -> u32

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

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

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

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

The inverse of UlpsEq::ulps_eq.

impl<T: RealField + RealField> VectorSpace for DualQuaternion<T>

type Field = T

The underlying scalar field.

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

fn zero() -> Self

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> Zeroable for DualQuaternion<T>where
    T: Scalar + Zeroable,
    Quaternion<T>: Zeroable,

fn zeroed() -> Self

Calls zeroed.

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,