Type Alias oxygengine_physics_2d::prelude::nalgebra::geometry::UnitDualQuaternion

pub type UnitDualQuaternion<T> = Unit<DualQuaternion<T>>;

A unit quaternions. May be used to represent a rotation followed by a translation.

Aliased Type

struct UnitDualQuaternion<T> { /* private fields */ }

Implementations

impl<T> Unit<T>where T: Normed,

Construction with normalization

pub fn new_normalize(value: T) -> Unit<T>

Normalize the given vector and return it wrapped on a Unit structure.

pub fn try_new(value: T, min_norm: <T as Normed>::Norm) -> Option<Unit<T>>where <T as Normed>::Norm: RealField,

Attempts to normalize the given vector and return it wrapped on a Unit structure.

Returns None if the norm was smaller or equal to min_norm.

pub fn new_and_get(value: T) -> (Unit<T>, <T as Normed>::Norm)

Normalize the given vector and return it wrapped on a Unit structure and its norm.

pub fn try_new_and_get( value: T, min_norm: <T as Normed>::Norm ) -> Option<(Unit<T>, <T as Normed>::Norm)>where <T as Normed>::Norm: RealField,

Normalize the given vector and return it wrapped on a Unit structure and its norm.

Returns None if the norm was smaller or equal to min_norm.

pub fn renormalize(&mut self) -> <T as Normed>::Norm

Normalizes this vector again. This is useful when repeated computations might cause a drift in the norm because of float inaccuracies.

Returns the norm before re-normalization. See .renormalize_fast for a faster alternative that may be slightly less accurate if self drifted significantly from having a unit length.

pub fn renormalize_fast(&mut self)

Normalizes this vector again using a first-order Taylor approximation. This is useful when repeated computations might cause a drift in the norm because of float inaccuracies.

impl<T> Unit<T>

Data extraction and construction without normalization

pub const fn new_unchecked(value: T) -> Unit<T>

Wraps the given value, assuming it is already normalized.

pub fn from_ref_unchecked(value: &T) -> &Unit<T>

Wraps the given reference, assuming it is already normalized.

pub fn into_inner(self) -> T

Retrieves the underlying value.

pub fn unwrap(self) -> T

👎Deprecated: use .into_inner() instead

Retrieves the underlying value. Deprecated: use Unit::into_inner instead.

pub fn as_mut_unchecked(&mut self) -> &mut T

Returns a mutable reference to the underlying value. This is _unchecked because modifying the underlying value in such a way that it no longer has unit length may lead to unexpected results.

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

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

The underlying dual quaternion.

Same as self.as_ref().

Example

let id = UnitDualQuaternion::identity();
assert_eq!(*id.dual_quaternion(), DualQuaternion::from_real_and_dual(
    Quaternion::new(1.0, 0.0, 0.0, 0.0),
    Quaternion::new(0.0, 0.0, 0.0, 0.0)
));

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

Compute the conjugate of this unit quaternion.

Example

let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let unit = UnitDualQuaternion::new_normalize(
    DualQuaternion::from_real_and_dual(qr, qd)
);
let conj = unit.conjugate();
assert_eq!(conj.real, unit.real.conjugate());
assert_eq!(conj.dual, unit.dual.conjugate());

pub fn conjugate_mut(&mut self)

Compute the conjugate of this unit quaternion in-place.

Example

let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let unit = UnitDualQuaternion::new_normalize(
    DualQuaternion::from_real_and_dual(qr, qd)
);
let mut conj = unit.clone();
conj.conjugate_mut();
assert_eq!(conj.as_ref().real, unit.as_ref().real.conjugate());
assert_eq!(conj.as_ref().dual, unit.as_ref().dual.conjugate());

pub fn inverse(&self) -> Unit<DualQuaternion<T>>

Inverts this dual quaternion if it is not zero.

Example

let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let unit = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qr, qd));
let inv = unit.inverse();
assert_relative_eq!(unit * inv, UnitDualQuaternion::identity(), epsilon = 1.0e-6);
assert_relative_eq!(inv * unit, UnitDualQuaternion::identity(), epsilon = 1.0e-6);

pub fn inverse_mut(&mut self)

Inverts this dual quaternion in place if it is not zero.

Example

let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let unit = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qr, qd));
let mut inv = unit.clone();
inv.inverse_mut();
assert_relative_eq!(unit * inv, UnitDualQuaternion::identity(), epsilon = 1.0e-6);
assert_relative_eq!(inv * unit, UnitDualQuaternion::identity(), epsilon = 1.0e-6);

pub fn isometry_to( &self, other: &Unit<DualQuaternion<T>> ) -> Unit<DualQuaternion<T>>

The unit dual quaternion needed to make self and other coincide.

The result is such that: self.isometry_to(other) * self == other.

Example

let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
let dq1 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qr, qd));
let dq2 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qd, qr));
let dq_to = dq1.isometry_to(&dq2);
assert_relative_eq!(dq_to * dq1, dq2, epsilon = 1.0e-6);

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

Linear interpolation between two unit dual quaternions.

The result is not normalized.

Example

let dq1 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
    Quaternion::new(0.5, 0.0, 0.5, 0.0),
    Quaternion::new(0.0, 0.5, 0.0, 0.5)
));
let dq2 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
    Quaternion::new(0.5, 0.0, 0.0, 0.5),
    Quaternion::new(0.5, 0.0, 0.5, 0.0)
));
assert_relative_eq!(
    UnitDualQuaternion::new_normalize(dq1.lerp(&dq2, 0.5)),
    UnitDualQuaternion::new_normalize(
        DualQuaternion::from_real_and_dual(
            Quaternion::new(0.5, 0.0, 0.25, 0.25),
            Quaternion::new(0.25, 0.25, 0.25, 0.25)
        )
    ),
    epsilon = 1.0e-6
);

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

Normalized linear interpolation between two unit quaternions.

This is the same as self.lerp except that the result is normalized.

Example

let dq1 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
    Quaternion::new(0.5, 0.0, 0.5, 0.0),
    Quaternion::new(0.0, 0.5, 0.0, 0.5)
));
let dq2 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
    Quaternion::new(0.5, 0.0, 0.0, 0.5),
    Quaternion::new(0.5, 0.0, 0.5, 0.0)
));
assert_relative_eq!(dq1.nlerp(&dq2, 0.2), UnitDualQuaternion::new_normalize(
    DualQuaternion::from_real_and_dual(
        Quaternion::new(0.5, 0.0, 0.4, 0.1),
        Quaternion::new(0.1, 0.4, 0.1, 0.4)
    )
), epsilon = 1.0e-6);

pub fn sclerp( &self, other: &Unit<DualQuaternion<T>>, t: T ) -> Unit<DualQuaternion<T>>where T: RealField,

Screw linear interpolation between two unit quaternions. This creates a smooth arc from one dual-quaternion to another.

Panics if the angle between both quaternion is 180 degrees (in which case the interpolation is not well-defined). Use .try_sclerp instead to avoid the panic.

Example

let dq1 = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0),
);

let dq2 = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 0.0, 3.0).into(),
    UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0),
);

let dq = dq1.sclerp(&dq2, 1.0 / 3.0);

assert_relative_eq!(
    dq.rotation().euler_angles().0, std::f32::consts::FRAC_PI_2, epsilon = 1.0e-6
);
assert_relative_eq!(dq.translation().vector.y, 3.0, epsilon = 1.0e-6);

pub fn try_sclerp( &self, other: &Unit<DualQuaternion<T>>, t: T, epsilon: T ) -> Option<Unit<DualQuaternion<T>>>where T: RealField,

Computes the screw-linear interpolation between two unit quaternions or returns None if both quaternions are approximately 180 degrees apart (in which case the interpolation is not well-defined).

Arguments

• self: the first quaternion to interpolate from.
• other: the second quaternion to interpolate toward.
• t: the interpolation parameter. Should be between 0 and 1.
• epsilon: the value below which the sinus of the angle separating both quaternion must be to return None.

pub fn rotation(&self) -> Unit<Quaternion<T>>

Return the rotation part of this unit dual quaternion.

let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0)
);

assert_relative_eq!(
    dq.rotation().angle(), std::f32::consts::FRAC_PI_4, epsilon = 1.0e-6
);

pub fn translation(&self) -> Translation<T, 3>

Return the translation part of this unit dual quaternion.

let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0)
);

assert_relative_eq!(
    dq.translation().vector, Vector3::new(0.0, 3.0, 0.0), epsilon = 1.0e-6
);

pub fn to_isometry(self) -> Isometry<T, Unit<Quaternion<T>>, 3>

Builds an isometry from this unit dual quaternion.

let rotation = UnitQuaternion::from_euler_angles(std::f32::consts::PI, 0.0, 0.0);
let translation = Vector3::new(1.0, 3.0, 2.5);
let dq = UnitDualQuaternion::from_parts(
    translation.into(),
    rotation
);
let iso = dq.to_isometry();

assert_relative_eq!(iso.rotation.angle(), std::f32::consts::PI, epsilon = 1.0e-6);
assert_relative_eq!(iso.translation.vector, translation, epsilon = 1.0e-6);

pub fn transform_point(&self, pt: &OPoint<T, Const<3>>) -> OPoint<T, Const<3>>

Rotate and translate a point by this unit dual quaternion interpreted as an isometry.

This is the same as the multiplication self * pt.

let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let point = Point3::new(1.0, 2.0, 3.0);

assert_relative_eq!(
    dq.transform_point(&point), Point3::new(1.0, 0.0, 2.0), epsilon = 1.0e-6
);

pub fn transform_vector( &self, v: &Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, ArrayStorage<T, 3, 1>> ) -> Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, ArrayStorage<T, 3, 1>>

Rotate a vector by this unit dual quaternion, ignoring the translational component.

This is the same as the multiplication self * v.

let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let vector = Vector3::new(1.0, 2.0, 3.0);

assert_relative_eq!(
    dq.transform_vector(&vector), Vector3::new(1.0, -3.0, 2.0), epsilon = 1.0e-6
);

pub fn inverse_transform_point( &self, pt: &OPoint<T, Const<3>> ) -> OPoint<T, Const<3>>

Rotate and translate a point by the inverse of this unit quaternion.

This may be cheaper than inverting the unit dual quaternion and transforming the point.

let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let point = Point3::new(1.0, 2.0, 3.0);

assert_relative_eq!(
    dq.inverse_transform_point(&point), Point3::new(1.0, 3.0, 1.0), epsilon = 1.0e-6
);

pub fn inverse_transform_vector( &self, v: &Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, ArrayStorage<T, 3, 1>> ) -> Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, ArrayStorage<T, 3, 1>>

Rotate a vector by the inverse of this unit quaternion, ignoring the translational component.

This may be cheaper than inverting the unit dual quaternion and transforming the vector.

let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let vector = Vector3::new(1.0, 2.0, 3.0);

assert_relative_eq!(
    dq.inverse_transform_vector(&vector), Vector3::new(1.0, 3.0, -2.0), epsilon = 1.0e-6
);

pub fn inverse_transform_unit_vector( &self, v: &Unit<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, ArrayStorage<T, 3, 1>>> ) -> Unit<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, ArrayStorage<T, 3, 1>>>

Rotate a unit vector by the inverse of this unit quaternion, ignoring the translational component. This may be cheaper than inverting the unit dual quaternion and transforming the vector.

let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let vector = Unit::new_unchecked(Vector3::new(0.0, 1.0, 0.0));

assert_relative_eq!(
    dq.inverse_transform_unit_vector(&vector),
    Unit::new_unchecked(Vector3::new(0.0, 0.0, -1.0)),
    epsilon = 1.0e-6
);

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

pub fn to_homogeneous( self ) -> Matrix<T, Const<nalgebra::::base::dimension::U4::{constant#0}>, Const<nalgebra::::base::dimension::U4::{constant#0}>, ArrayStorage<T, 4, 4>>

Converts this unit dual quaternion interpreted as an isometry into its equivalent homogeneous transformation matrix.

let dq = UnitDualQuaternion::from_parts(
    Vector3::new(1.0, 3.0, 2.0).into(),
    UnitQuaternion::from_axis_angle(&Vector3::z_axis(), std::f32::consts::FRAC_PI_6)
);
let expected = Matrix4::new(0.8660254, -0.5,      0.0, 1.0,
                            0.5,       0.8660254, 0.0, 3.0,
                            0.0,       0.0,       1.0, 2.0,
                            0.0,       0.0,       0.0, 1.0);

assert_relative_eq!(dq.to_homogeneous(), expected, epsilon = 1.0e-6);

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

pub fn identity() -> Unit<DualQuaternion<T>>

The unit dual quaternion multiplicative identity, which also represents the identity transformation as an isometry.

let ident = UnitDualQuaternion::identity();
let point = Point3::new(1.0, -4.3, 3.33);

assert_eq!(ident * point, point);
assert_eq!(ident, ident.inverse());

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

Cast the components of self to another type.

Example

let q = UnitDualQuaternion::<f64>::identity();
let q2 = q.cast::<f32>();
assert_eq!(q2, UnitDualQuaternion::<f32>::identity());

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

pub fn from_parts( translation: Translation<T, 3>, rotation: Unit<Quaternion<T>> ) -> Unit<DualQuaternion<T>>

Return a dual quaternion representing the translation and orientation given by the provided rotation quaternion and translation vector.

let dq = UnitDualQuaternion::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let point = Point3::new(1.0, 2.0, 3.0);

assert_relative_eq!(dq * point, Point3::new(1.0, 0.0, 2.0), epsilon = 1.0e-6);

pub fn from_isometry( isometry: &Isometry<T, Unit<Quaternion<T>>, 3> ) -> Unit<DualQuaternion<T>>

Return a unit dual quaternion representing the translation and orientation given by the provided isometry.

let iso = Isometry3::from_parts(
    Vector3::new(0.0, 3.0, 0.0).into(),
    UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
);
let dq = UnitDualQuaternion::from_isometry(&iso);
let point = Point3::new(1.0, 2.0, 3.0);

assert_relative_eq!(dq * point, iso * point, epsilon = 1.0e-6);

pub fn from_rotation(rotation: Unit<Quaternion<T>>) -> Unit<DualQuaternion<T>>

Creates a dual quaternion from a unit quaternion rotation.

Example

let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let rot = UnitQuaternion::new_normalize(q);

let dq = UnitDualQuaternion::from_rotation(rot);
assert_relative_eq!(dq.as_ref().real.norm(), 1.0, epsilon = 1.0e-6);
assert_eq!(dq.as_ref().dual.norm(), 0.0);

Trait Implementations

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

type Epsilon = T

Used for specifying relative comparisons.

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

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

fn abs_diff_eq( &self, other: &Unit<DualQuaternion<T>>, epsilon: <Unit<DualQuaternion<T>> as AbsDiffEq<Unit<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<T> AsRef<T> for Unit<T>

fn as_ref(&self) -> &T

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

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

Formats the value using the given formatter.

impl<T> Default for Unit<DualQuaternion<T>>where T: RealField,

fn default() -> Unit<DualQuaternion<T>>

Returns the “default value” for a type.

impl<T> Deref for Unit<T>

type Target = T

The resulting type after dereferencing.

fn deref(&self) -> &T

Dereferences the value.

impl<'de, T> Deserialize<'de> for Unit<T>where T: Deserialize<'de>,

fn deserialize<D>( deserializer: D ) -> Result<Unit<T>, <D as Deserializer<'de>>::Error>where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T> Display for Unit<DualQuaternion<T>>where T: RealField + Display,

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

Formats the value using the given formatter.

impl<'b, T> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3> ) -> <Unit<DualQuaternion<T>> as Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output

Performs the / operation.

impl<'b, T> Div<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: &'b Translation<T, 3> ) -> <Unit<DualQuaternion<T>> as Div<&'b Translation<T, 3>>>::Output

Performs the / operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: Isometry<T, Unit<Quaternion<T>>, 3> ) -> <Unit<DualQuaternion<T>> as Div<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output

Performs the / operation.

impl<T> Div<Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: Translation<T, 3> ) -> <Unit<DualQuaternion<T>> as Div<Translation<T, 3>>>::Output

Performs the / operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, T> DivAssign<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn div_assign(&mut self, rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>)

Performs the /= operation.

impl<'b, T> DivAssign<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn div_assign(&mut self, rhs: &'b Translation<T, 3>)

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

impl<T> DivAssign<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn div_assign(&mut self, rhs: Isometry<T, Unit<Quaternion<T>>, 3>)

Performs the /= operation.

impl<T> DivAssign<Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn div_assign(&mut self, rhs: Translation<T, 3>)

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

impl<T> From<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn from(iso: Isometry<T, Unit<Quaternion<T>>, 3>) -> Unit<DualQuaternion<T>>

Converts to this type from the input type.

impl<T> Hash for Unit<T>where T: Hash,

fn hash<__H>(&self, state: &mut __H)where __H: Hasher,

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

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 Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3> ) -> <Unit<DualQuaternion<T>> as Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>>>::Output

Performs the * operation.

impl<'b, T, SB> Mul<&'b Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB>> for Unit<DualQuaternion<T>>where T: SimdRealField, SB: Storage<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>>, <T as SimdValue>::Element: SimdRealField,

type Output = Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, ArrayStorage<T, 3, 1>>

The resulting type after applying the * operator.

fn mul( self, rhs: &'b Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB> ) -> <Unit<DualQuaternion<T>> as Mul<&'b Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB>>>::Output

Performs the * operation.

impl<'b, T> Mul<&'b OPoint<T, Const<3>>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = OPoint<T, Const<3>>

The resulting type after applying the * operator.

fn mul( self, rhs: &'b OPoint<T, Const<3>> ) -> <Unit<DualQuaternion<T>> as Mul<&'b OPoint<T, Const<3>>>>::Output

Performs the * operation.

impl<'b, T> Mul<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: &'b Translation<T, 3> ) -> <Unit<DualQuaternion<T>> as Mul<&'b Translation<T, 3>>>::Output

Performs the * operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, T, SB> Mul<&'b Unit<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB>>> for Unit<DualQuaternion<T>>where T: SimdRealField, SB: Storage<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>>, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the * operator.

fn mul( self, rhs: &'b Unit<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB>> ) -> <Unit<DualQuaternion<T>> as Mul<&'b Unit<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB>>>>::Output

Performs the * operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: &'b Unit<Quaternion<T>> ) -> <Unit<DualQuaternion<T>> as Mul<&'b Unit<Quaternion<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<T> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: Isometry<T, Unit<Quaternion<T>>, 3> ) -> <Unit<DualQuaternion<T>> as Mul<Isometry<T, Unit<Quaternion<T>>, 3>>>::Output

Performs the * operation.

impl<T, SB> Mul<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB>> for Unit<DualQuaternion<T>>where T: SimdRealField, SB: Storage<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>>, <T as SimdValue>::Element: SimdRealField,

type Output = Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, ArrayStorage<T, 3, 1>>

The resulting type after applying the * operator.

fn mul( self, rhs: Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB> ) -> <Unit<DualQuaternion<T>> as Mul<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB>>>::Output

Performs the * operation.

impl<T> Mul<OPoint<T, Const<3>>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = OPoint<T, Const<3>>

The resulting type after applying the * operator.

fn mul( self, rhs: OPoint<T, Const<3>> ) -> <Unit<DualQuaternion<T>> as Mul<OPoint<T, Const<3>>>>::Output

Performs the * operation.

impl<T> Mul<Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: Translation<T, 3> ) -> <Unit<DualQuaternion<T>> as Mul<Translation<T, 3>>>::Output

Performs the * operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, SB> Mul<Unit<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB>>> for Unit<DualQuaternion<T>>where T: SimdRealField, SB: Storage<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>>, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the * operator.

fn mul( self, rhs: Unit<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB>> ) -> <Unit<DualQuaternion<T>> as Mul<Unit<Matrix<T, Const<nalgebra::::base::dimension::U3::{constant#0}>, Const<1>, SB>>>>::Output

Performs the * operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, T> MulAssign<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn mul_assign(&mut self, rhs: &'b Isometry<T, Unit<Quaternion<T>>, 3>)

Performs the *= operation.

impl<'b, T> MulAssign<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn mul_assign(&mut self, rhs: &'b Translation<T, 3>)

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<T> MulAssign<Isometry<T, Unit<Quaternion<T>>, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn mul_assign(&mut self, rhs: Isometry<T, Unit<Quaternion<T>>, 3>)

Performs the *= operation.

impl<T> MulAssign<Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn mul_assign(&mut self, rhs: Translation<T, 3>)

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the - operator.

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

Performs the unary - operation.

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

fn one() -> Unit<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) -> boolwhere Self: PartialEq<Self>,

Returns true if self is equal to the multiplicative identity.

impl<T> PartialEq<Unit<DualQuaternion<T>>> for Unit<DualQuaternion<T>>where T: Scalar + ClosedNeg + PartialEq<T> + SimdRealField,

fn eq(&self, rhs: &Unit<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 !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

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

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

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

fn relative_eq( &self, other: &Unit<DualQuaternion<T>>, epsilon: <Unit<DualQuaternion<T>> as AbsDiffEq<Unit<DualQuaternion<T>>>>::Epsilon, max_relative: <Unit<DualQuaternion<T>> as AbsDiffEq<Unit<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<T> Serialize for Unit<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<T1, T2> SubsetOf<Isometry<T2, Unit<Quaternion<T2>>, 3>> for Unit<DualQuaternion<T1>>where T1: RealField, T2: RealField + SupersetOf<T1>,

fn to_superset(&self) -> Isometry<T2, Unit<Quaternion<T2>>, 3>

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

fn is_in_subset(iso: &Isometry<T2, Unit<Quaternion<T2>>, 3>) -> bool

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

fn from_superset_unchecked( iso: &Isometry<T2, Unit<Quaternion<T2>>, 3> ) -> Unit<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<T1, T2> SubsetOf<Matrix<T2, Const<nalgebra::::base::dimension::U4::{constant#0}>, Const<nalgebra::::base::dimension::U4::{constant#0}>, ArrayStorage<T2, 4, 4>>> for Unit<DualQuaternion<T1>>where T1: RealField, T2: RealField + SupersetOf<T1>,

fn to_superset( &self ) -> Matrix<T2, Const<nalgebra::::base::dimension::U4::{constant#0}>, Const<nalgebra::::base::dimension::U4::{constant#0}>, ArrayStorage<T2, 4, 4>>

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

fn is_in_subset( m: &Matrix<T2, Const<nalgebra::::base::dimension::U4::{constant#0}>, Const<nalgebra::::base::dimension::U4::{constant#0}>, ArrayStorage<T2, 4, 4>> ) -> bool

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

fn from_superset_unchecked( m: &Matrix<T2, Const<nalgebra::::base::dimension::U4::{constant#0}>, Const<nalgebra::::base::dimension::U4::{constant#0}>, ArrayStorage<T2, 4, 4>> ) -> Unit<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<T1, T2> SubsetOf<Similarity<T2, Unit<Quaternion<T2>>, 3>> for Unit<DualQuaternion<T1>>where T1: RealField, T2: RealField + SupersetOf<T1>,

fn to_superset(&self) -> Similarity<T2, Unit<Quaternion<T2>>, 3>

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

fn is_in_subset(sim: &Similarity<T2, Unit<Quaternion<T2>>, 3>) -> bool

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

fn from_superset_unchecked( sim: &Similarity<T2, Unit<Quaternion<T2>>, 3> ) -> Unit<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<T1, T2, C> SubsetOf<Transform<T2, C, 3>> for Unit<DualQuaternion<T1>>where T1: RealField, T2: RealField + SupersetOf<T1>, C: SuperTCategoryOf<TAffine>,

fn to_superset(&self) -> Transform<T2, C, 3>

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

fn is_in_subset(t: &Transform<T2, C, 3>) -> bool

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

fn from_superset_unchecked(t: &Transform<T2, C, 3>) -> Unit<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<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for Unit<DualQuaternion<T1>>where T1: SimdRealField, T2: SimdRealField + SupersetOf<T1>,

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

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

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

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

fn from_superset_unchecked( dq: &Unit<DualQuaternion<T2>> ) -> Unit<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<Unit<DualQuaternion<T>>> for Unit<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: &Unit<DualQuaternion<T>>, epsilon: <Unit<DualQuaternion<T>> as AbsDiffEq<Unit<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> Copy for Unit<T>where T: Copy,

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