Struct nalgebra::geometry::DualQuaternion

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

A dual quaternion.

Indexing

DualQuaternions are stored as [..real, ..dual]. Both of the quaternion components are laid out in i, j, k, w order.

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<N>

The real component of the quaternion

dual: Quaternion<N>

The dual component of the quaternion

Implementations

impl<N: SimdRealField> DualQuaternion<N> where
    N::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) -> N

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
    N: 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
    N: 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: N) -> 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<N: Scalar> DualQuaternion<N>

pub fn from_real_and_dual(real: Quaternion<N>, dual: Quaternion<N>) -> 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() -> Self where
    N: 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<N: SimdRealField> DualQuaternion<N> where
    N::Element: SimdRealField, 

pub fn from_real(real: Quaternion<N>) -> 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<N: RealField + AbsDiffEq<Epsilon = N>> AbsDiffEq<DualQuaternion<N>> for DualQuaternion<N>

type Epsilon = N

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<'a, 'b, N: SimdRealField> Add<&'b DualQuaternion<N>> for &'a DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the + operator.

fn add(self, rhs: &'b DualQuaternion<N>) -> Self::Output

Performs the + operation.

impl<'b, N: SimdRealField> Add<&'b DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the + operator.

fn add(self, rhs: &'b DualQuaternion<N>) -> Self::Output

Performs the + operation.

impl<'a, N: SimdRealField> Add<DualQuaternion<N>> for &'a DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<N: SimdRealField> Add<DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'b, N: SimdRealField> AddAssign<&'b DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

fn add_assign(&mut self, rhs: &'b DualQuaternion<N>)

Performs the += operation.

impl<N: SimdRealField> AddAssign<DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

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

Performs the += operation.

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

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

Performs the conversion.

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

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

Performs the conversion.

impl<N: Clone + Scalar> Clone for DualQuaternion<N>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: Debug + Scalar> Debug for DualQuaternion<N>

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

Formats the value using the given formatter.

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

fn default() -> Self

Returns the “default value” for a type.

impl<'a, 'b, N: SimdRealField> Div<&'b Unit<DualQuaternion<N>>> for &'a DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<N>) -> Self::Output

Performs the / operation.

impl<'b, N: SimdRealField> Div<&'b Unit<DualQuaternion<N>>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitDualQuaternion<N>) -> Self::Output

Performs the / operation.

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

type Output = DualQuaternion<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N: SimdRealField> Div<N> for &'a DualQuaternion<N> where
    N::Element: SimdRealField, 

type Output = DualQuaternion<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N: SimdRealField> Div<Unit<DualQuaternion<N>>> for &'a DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N: SimdRealField> Div<Unit<DualQuaternion<N>>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N: SimdRealField> DivAssign<&'b Unit<DualQuaternion<N>>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

fn div_assign(&mut self, rhs: &'b UnitDualQuaternion<N>)

Performs the /= operation.

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

fn div_assign(&mut self, n: N)

Performs the /= operation.

impl<N: SimdRealField> DivAssign<Unit<DualQuaternion<N>>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

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

Performs the /= operation.

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

type Output = N

The returned type after indexing.

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

Performs the indexing (container[index]) operation.

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

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

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

impl<'a, 'b, N: SimdRealField> Mul<&'b DualQuaternion<N>> for &'a DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N: SimdRealField> Mul<&'b DualQuaternion<N>> for &'a UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b DualQuaternion<N>> for UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b DualQuaternion<N>) -> 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, N: SimdRealField> Mul<&'b Unit<DualQuaternion<N>>> for &'a DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<N>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b Unit<DualQuaternion<N>>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitDualQuaternion<N>) -> Self::Output

Performs the * operation.

impl<'a, N: SimdRealField> Mul<DualQuaternion<N>> for &'a DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField> Mul<DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField> Mul<DualQuaternion<N>> for &'a UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField> Mul<DualQuaternion<N>> for UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: DualQuaternion<N>) -> 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<N: SimdRealField> Mul<N> for DualQuaternion<N> where
    N::Element: SimdRealField, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField> Mul<N> for &'a DualQuaternion<N> where
    N::Element: SimdRealField, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField> Mul<Unit<DualQuaternion<N>>> for &'a DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField> Mul<Unit<DualQuaternion<N>>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N: SimdRealField> MulAssign<&'b DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

fn mul_assign(&mut self, rhs: &'b DualQuaternion<N>)

Performs the *= operation.

impl<'b, N: SimdRealField> MulAssign<&'b Unit<DualQuaternion<N>>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

fn mul_assign(&mut self, rhs: &'b UnitDualQuaternion<N>)

Performs the *= operation.

impl<N: SimdRealField> MulAssign<DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

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

Performs the *= operation.

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

fn mul_assign(&mut self, n: N)

Performs the *= operation.

impl<N: SimdRealField> MulAssign<Unit<DualQuaternion<N>>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

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

Performs the *= operation.

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

type Output = DualQuaternion<N>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<'a, N: SimdRealField> Neg for &'a DualQuaternion<N> where
    N::Element: SimdRealField, 

type Output = DualQuaternion<N>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

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

type Norm = N::SimdRealField

The type of the norm.

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

Computes the norm.

fn norm_squared(&self) -> N::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<N: SimdRealField> One for DualQuaternion<N> where
    N::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) -> bool where
    Self: PartialEq<Self>, 

Returns true if self is equal to the multiplicative identity.

impl<N: PartialEq + Scalar> PartialEq<DualQuaternion<N>> for DualQuaternion<N>

fn eq(&self, other: &DualQuaternion<N>) -> bool

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

fn ne(&self, other: &DualQuaternion<N>) -> bool

This method tests for !=.

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

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<'a, 'b, N: SimdRealField> Sub<&'b DualQuaternion<N>> for &'a DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the - operator.

fn sub(self, rhs: &'b DualQuaternion<N>) -> Self::Output

Performs the - operation.

impl<'b, N: SimdRealField> Sub<&'b DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the - operator.

fn sub(self, rhs: &'b DualQuaternion<N>) -> Self::Output

Performs the - operation.

impl<'a, N: SimdRealField> Sub<DualQuaternion<N>> for &'a DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<N: SimdRealField> Sub<DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = DualQuaternion<N>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'b, N: SimdRealField> SubAssign<&'b DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

fn sub_assign(&mut self, rhs: &'b DualQuaternion<N>)

Performs the -= operation.

impl<N: SimdRealField> SubAssign<DualQuaternion<N>> for DualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

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

Performs the -= operation.

impl<N1, N2> SubsetOf<DualQuaternion<N2>> for DualQuaternion<N1> where
    N1: SimdRealField,
    N2: SimdRealField + SupersetOf<N1>, 

fn to_superset(&self) -> DualQuaternion<N2>

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

fn is_in_subset(dq: &DualQuaternion<N2>) -> bool

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

fn from_superset_unchecked(dq: &DualQuaternion<N2>) -> 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<N: RealField + UlpsEq<Epsilon = N>> UlpsEq<DualQuaternion<N>> for DualQuaternion<N>

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<N: SimdRealField> Zero for DualQuaternion<N> where
    N::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<N: Copy + Scalar> Copy for DualQuaternion<N>

impl<N: Eq + Scalar> Eq for DualQuaternion<N>

impl<N: Scalar> StructuralEq for DualQuaternion<N>

impl<N: Scalar> StructuralPartialEq for DualQuaternion<N>