# Struct euclid::rotation::Rotation3D

``````#[repr(C)]pub struct Rotation3D<T, Src, Dst> {
pub i: T,
pub j: T,
pub k: T,
pub r: T,
/* private fields */
}``````
Expand description

A transform that can represent rotations in 3d, represented as a quaternion.

Most methods expect the quaternion to be normalized. When in doubt, use `unit_quaternion` instead of `quaternion` to create a rotation as the former will ensure that its result is normalized.

Some people use the `x, y, z, w` (or `w, x, y, z`) notations. The equivalence is as follows: `x -> i`, `y -> j`, `z -> k`, `w -> r`. The memory layout of this type corresponds to the `x, y, z, w` notation

## Fields§

§`i: T`

Component multiplied by the imaginary number `i`.

§`j: T`

Component multiplied by the imaginary number `j`.

§`k: T`

Component multiplied by the imaginary number `k`.

§`r: T`

The real part.

## Implementations§

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### impl<T, Src, Dst> Rotation3D<T, Src, Dst>

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#### pub fn quaternion(a: T, b: T, c: T, r: T) -> Self

Creates a rotation around from a quaternion representation.

The parameters are a, b, c and r compose the quaternion `a*i + b*j + c*k + r` where `a`, `b` and `c` describe the vector part and the last parameter `r` is the real part.

The resulting quaternion is not necessarily normalized. See `unit_quaternion`.

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#### pub fn identity() -> Selfwhere    T: Zero + One,

Creates the identity rotation.

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### impl<T, Src, Dst> Rotation3D<T, Src, Dst>where    T: Copy,

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#### pub fn vector_part(&self) -> Vector3D<T, UnknownUnit>

Returns the vector part (i, j, k) of this quaternion.

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#### pub fn cast_unit<Src2, Dst2>(&self) -> Rotation3D<T, Src2, Dst2>

Cast the unit, preserving the numeric value.

##### Example
``````enum Local {}
enum World {}

enum Local2 {}
enum World2 {}

let to_world: Rotation3D<_, Local, World> = Rotation3D::quaternion(1, 2, 3, 4);

assert_eq!(to_world.i, to_world.cast_unit::<Local2, World2>().i);
assert_eq!(to_world.j, to_world.cast_unit::<Local2, World2>().j);
assert_eq!(to_world.k, to_world.cast_unit::<Local2, World2>().k);
assert_eq!(to_world.r, to_world.cast_unit::<Local2, World2>().r);``````
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#### pub fn to_untyped(&self) -> Rotation3D<T, UnknownUnit, UnknownUnit>

Drop the units, preserving only the numeric value.

##### Example
``````enum Local {}
enum World {}

let to_world: Rotation3D<_, Local, World> = Rotation3D::quaternion(1, 2, 3, 4);

assert_eq!(to_world.i, to_world.to_untyped().i);
assert_eq!(to_world.j, to_world.to_untyped().j);
assert_eq!(to_world.k, to_world.to_untyped().k);
assert_eq!(to_world.r, to_world.to_untyped().r);``````
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#### pub fn from_untyped(r: &Rotation3D<T, UnknownUnit, UnknownUnit>) -> Self

Tag a unitless value with units.

##### Example
``````use euclid::UnknownUnit;
enum Local {}
enum World {}

let rot: Rotation3D<_, UnknownUnit, UnknownUnit> = Rotation3D::quaternion(1, 2, 3, 4);

assert_eq!(rot.i, Rotation3D::<_, Local, World>::from_untyped(&rot).i);
assert_eq!(rot.j, Rotation3D::<_, Local, World>::from_untyped(&rot).j);
assert_eq!(rot.k, Rotation3D::<_, Local, World>::from_untyped(&rot).k);
assert_eq!(rot.r, Rotation3D::<_, Local, World>::from_untyped(&rot).r);``````
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### impl<T, Src, Dst> Rotation3D<T, Src, Dst>where    T: Float,

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#### pub fn unit_quaternion(i: T, j: T, k: T, r: T) -> Self

Creates a rotation around from a quaternion representation and normalizes it.

The parameters are a, b, c and r compose the quaternion `a*i + b*j + c*k + r` before normalization, where `a`, `b` and `c` describe the vector part and the last parameter `r` is the real part.

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#### pub fn around_axis(axis: Vector3D<T, Src>, angle: Angle<T>) -> Self

Creates a rotation around a given axis.

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#### pub fn around_x(angle: Angle<T>) -> Self

Creates a rotation around the x axis.

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#### pub fn around_y(angle: Angle<T>) -> Self

Creates a rotation around the y axis.

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#### pub fn around_z(angle: Angle<T>) -> Self

Creates a rotation around the z axis.

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#### pub fn euler(roll: Angle<T>, pitch: Angle<T>, yaw: Angle<T>) -> Self

Creates a rotation from Euler angles.

The rotations are applied in roll then pitch then yaw order.

• Roll (also called bank) is a rotation around the x axis.
• Pitch (also called bearing) is a rotation around the y axis.
• Yaw (also called heading) is a rotation around the z axis.
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#### pub fn inverse(&self) -> Rotation3D<T, Dst, Src>

Returns the inverse of this rotation.

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#### pub fn norm(&self) -> T

Computes the norm of this quaternion.

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#### pub fn square_norm(&self) -> T

Computes the squared norm of this quaternion.

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#### pub fn normalize(&self) -> Self

Returns a unit quaternion from this one.

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#### pub fn is_normalized(&self) -> boolwhere    T: ApproxEq<T>,

Returns `true` if norm of this quaternion is (approximately) one.

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#### pub fn slerp(&self, other: &Self, t: T) -> Selfwhere    T: ApproxEq<T>,

Spherical linear interpolation between this rotation and another rotation.

`t` is expected to be between zero and one.

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#### pub fn lerp(&self, other: &Self, t: T) -> Self

Basic Linear interpolation between this rotation and another rotation.

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#### pub fn transform_point3d(&self, point: Point3D<T, Src>) -> Point3D<T, Dst>where    T: ApproxEq<T>,

Returns the given 3d point transformed by this rotation.

The input point must be use the unit Src, and the returned point has the unit Dst.

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#### pub fn transform_point2d(&self, point: Point2D<T, Src>) -> Point2D<T, Dst>where    T: ApproxEq<T>,

Returns the given 2d point transformed by this rotation then projected on the xy plane.

The input point must be use the unit Src, and the returned point has the unit Dst.

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#### pub fn transform_vector3d(&self, vector: Vector3D<T, Src>) -> Vector3D<T, Dst>where    T: ApproxEq<T>,

Returns the given 3d vector transformed by this rotation.

The input vector must be use the unit Src, and the returned point has the unit Dst.

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#### pub fn transform_vector2d(&self, vector: Vector2D<T, Src>) -> Vector2D<T, Dst>where    T: ApproxEq<T>,

Returns the given 2d vector transformed by this rotation then projected on the xy plane.

The input vector must be use the unit Src, and the returned point has the unit Dst.

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#### pub fn to_transform(&self) -> Transform3D<T, Src, Dst>where    T: ApproxEq<T>,

Returns the matrix representation of this rotation.

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#### pub fn pre_rotate<NewSrc>(    &self,    other: &Rotation3D<T, NewSrc, Src>) -> Rotation3D<T, NewSrc, Dst>where    T: ApproxEq<T>,

Returns a rotation representing the other rotation followed by this rotation.

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#### pub fn post_rotate<NewDst>(    &self,    other: &Rotation3D<T, Dst, NewDst>) -> Rotation3D<T, Src, NewDst>where    T: ApproxEq<T>,

Returns a rotation representing this rotation followed by the other rotation.

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## Trait Implementations§

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### impl<T, Src, Dst> ApproxEq<T> for Rotation3D<T, Src, Dst>where    T: Copy + Neg<Output = T> + ApproxEq<T>,

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#### fn approx_epsilon() -> T

Default epsilon value
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#### fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool

Returns `true` is this object is approximately equal to the other one, using a provided epsilon value.
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#### fn approx_eq(&self, other: &Self) -> bool

Returns `true` is this object is approximately equal to the other one, using the `approx_epsilon()` epsilon value.
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### impl<T: Clone, Src, Dst> Clone for Rotation3D<T, Src, Dst>

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#### fn clone(&self) -> Self

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

Performs copy-assignment from `source`. Read more
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### impl<T: Debug, Src, Dst> Debug for Rotation3D<T, Src, Dst>

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

Formats the value using the given formatter. Read more
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### impl<'de, T, Src, Dst> Deserialize<'de> for Rotation3D<T, Src, Dst>where    T: Deserialize<'de>,

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#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>where    __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer. Read more
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### impl<T: Display, Src, Dst> Display for Rotation3D<T, Src, Dst>

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

Formats the value using the given formatter. Read more
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### impl<T: Float + ApproxEq<T>, Src, Dst> From<Rotation3D<T, Src, Dst>> for RigidTransform3D<T, Src, Dst>

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#### fn from(rot: Rotation3D<T, Src, Dst>) -> Self

Converts to this type from the input type.
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### impl<T, Src, Dst> Hash for Rotation3D<T, Src, Dst>where    T: Hash,

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#### fn hash<H: Hasher>(&self, h: &mut H)

Feeds this value into the given `Hasher`. Read more
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#### fn hash_slice<H>(data: &[Self], state: &mut H)where    H: Hasher,    Self: Sized,

Feeds a slice of this type into the given `Hasher`. Read more
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### impl<T, Src, Dst> PartialEq<Rotation3D<T, Src, Dst>> for Rotation3D<T, Src, Dst>where    T: PartialEq,

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

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

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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### impl<T, Src, Dst> Serialize for Rotation3D<T, Src, Dst>where    T: Serialize,

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#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>where    __S: Serializer,

Serialize this value into the given Serde serializer. Read more
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## Blanket Implementations§

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

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

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

const: unstable · source§

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

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

const: unstable · source§

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

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

const: unstable · source§

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

Returns the argument unchanged.

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

const: unstable · source§

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

Calls `U::from(self)`.

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

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### impl<T> ToOwned for Twhere    T: Clone,

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#### type Owned = T

The resulting type after obtaining ownership.
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#### fn to_owned(&self) -> T

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

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T> ToString for Twhere    T: Display + ?Sized,

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#### default fn to_string(&self) -> String

Converts the given value to a `String`. Read more
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### impl<T, U> TryFrom<U> for Twhere    U: Into<T>,

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#### type Error = Infallible

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

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

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

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

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

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

Performs the conversion.
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